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RECENT ADVANCES IN GAS SEPARATION BY MICROPOROUS CERAMIC MEMBRANES

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Membrane Science and Technology Series, 6

RECENT ADVANCES IN GAS SEPARATION BY MICROPOROUS CERAMIC MEMBtlANES

Edited

by

N.K. Kanellopoulos NCSR "Demokritos", Membranes for Environmental Separations Laboratory, 15310 Aghia Paraskevi Attikis, Greece

2000 ELSEVIER Amsterdam

- Lausanne - New York - Oxford - Shannon

- Singapore - Tokyo

ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 EO. Box 211, 1000 AE Amsterdam, The Netherlands

9 2000 Elsevier Science B.V. All rights reserved.

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First edition 2000 Library o f Congress Cataloging-in-Publication Data

Recent advances in gas separation by microporous ceramic membranes / edited by N.K. Kanellopoulos.-- Ist ed. p. em. -- (Membrane science and technology series ; 6) Includes bibliographical references and index. ISBN 0-444-50272-6 (alk. paper) 1. Gas separation membranes. 2. Ceramic materials. 3. Gases--Separation. I. KaneUopoulos, N. K. (Nick K.) II. Series. TP159.M4 R43 2000 660'.2842--dc21 00-056192

ISBN: 0-444-50272-6 ISSN: 0927-5193

(~The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands.

CONTENTS

List of Contributors

VII

Preface

Xl

1. Fundamentals and Sorption in Micropores 1.1

Membrane characterisation by combination of static and dynamic techniques Th. A. Steriotis, K. L. Stefanopoulos, A. Ch. Mitropoulos and N. K. Kanellopoulos

1.2 In situ X-ray diffraction studies on micropore filling T. liyama, T. Ohkubo and K. Kaneko

35

1.3 Neutron and ion beam scattering techniques J. D. F. Ramsay

67

1.4 Application of pulsed field gradient NMR to characterize the transport properties of microporous membranes W. Heink, J. Karger and S. Vasenkov 1.5 Diffusion studies using quasi-elastic neutron scatttering H. Jobic

97 109

1.6 Frequency Response methods for the characterisation of microporous solids L. V. C. Rees and L. Song

139

1.7 Measurement of diffusion in porous solids by Zero Length Column (ZLC) methods D. M. Ruth'ven and S. Brandani

187

1.8 Characterisation of microporous materials by adsorption microcalorimetry P. Llewellyn

213

2.

Modeling of Sorption and Diffusion in Microporous Membranes

2.1 Simulation of adsorption in micropores D. Nicholson and T. Stubos

231 257

2.2

Molecular simulation of transport in a single micropore D. Nicholson and K. Travis

2.3

Simulation of gas transport in a "network of micropores". The effect of pore structure on transport properties E. S. Kikkinides, M. E. Kainourgiakis and N. K. Kanellopoulos

3.

Recent Advances in Microporous Membrane Preparation

3.1

Microporous carbon membranes S. Morooka, K. Kusakabe, Y. Kusuki and N. Tanihara

323

3.2

Microporous silica membranes N. Benes, A. Nijmeijer and H. Verweij

335

297

3.3 Zeolite membranes J. D. F. Ramsay and S. Kallus

373

3.4

Chemical vapor deposition membranes M. Tsapatsis, G. R. Gavalas and G. Xomeritakis

397

3.5

Composite ceramic membranes from Langmuir-Blodgett and Self-Assembly precursors K. Beltsios, E. Soterakou and N. K. Kanellopoulos

417

3.6

Nanophase ceramic ion transport membranes for oxygen separation and gas stream enrichment C. G. Guizard and A. C. Julbe

435

4.

Gas Separation Applications

4.1

Nanoporous carbon membranes for gas separation S. Sircar and M. B. Rao

4.2

Microporous inorganic and polymeric membranes as catalytic reactors and membrane contactors E. Driofi and A. Criscuofi

473

497

vii

List of Contributors K. Beltsios MESL, Institute of Physical Chemistry, NCSR "Demokritos", 15310 Aghia Paraskevi Attikis, Greece N. Benes Laboratory of Inorganic Materials Science, Department of Chemical Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands S. Brandani Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, UK A. Criscuoli Department of Chemical Engineering and Materials, University of Calabria, Via Pietro Bucci, Cubo 17/C, Arcavacata di Rende (CS), 87030 Italy E, Drioli Research Institute on Membranes and Modelling of Chemical Reactors, and Department of Chemical Engineering and Materials, University of Calabria, Via Pietro Bucci, Cubo 17/C, Arcavacata di Rende (CS), 87030 Italy G. R, Gavalas Division of Chemistry and Chemical Engineering, 210-41, California Institute of Technology, Pasadena, CA 91125, USA C, G, Guizard Laboratoire des Mat6riaux et Proc6d6s Membranaires, UMR CNRS 5635, Ecole Nationale Sup6rieure de Chimie, 8, rue de I'Ecole Normale, 34296 Montpellier Cedex 5, France W. Heink Fakult~t f0r Physik und Geowissenschaften, Universit~t Leipzig, Linn6stral3e 5, D-04103 Leipzig, Germany T. liyama Physical Chemistry, Material Science, Graduate School of Natural Science and Technology, Chiba University, Yayoi, Inage, Chiba, 263-8522 Japan H. Jobic Institut de Recherches sur la Catalyse, CNRS, 2 Avenue Albert Einstein, 69626 Villeurbanne, France A. C. Julbe Laboratoire des Mat6riaux et Proc~d6s Membranaires, UMR CNRS 5635, Ecole Nationale Sup6rieure de Chimie, 8, rue de I'Ecole Normale, 34296 Montpellier Cedex 5, France M. Kainourgiakis MESL, Institute of Physical Chemistry, NCSR "Demokritos", 15310 Aghia Paraskevi Attikis, Greece S. Kallus Laboratoire des Mat6riaux et des Proc6d~s Membranaires, UMR CNRS 5635, Universit6 Montpellier II, 2 pl Eugene Bataillon, 34095 Montpellier, France

viii

K. Kaneko Physical Chemistry, Material Science, Graduate School of Natural Science and Technology, Chiba University, Yayoi, Inage, Chiba, 263-8522 Japan N. K. Kanellopoulos MESL, Institute of Physical Chemistry, NCSR "Demokritos", 15310 Aghia Paraskevi Attikis, Greece J. K~irger Fakult~t for Physik und Geowissenschaften, Universit~t Leipzig, Linn6stral~e 5, D-04103 Leipzig, Germany E, S. Kikkinides Chemical Process Engineering Research Institute, P.O. Box 361, ThermiThessaloniki 57001, Greece K, Kusakabe Department of Materials Physics and Chemistry, Graduate School of Engineering, Kyushu University, Fukuoka 812-8581, Japan Y. Kusuki Polymer Laboratory, Corporate Research and Development, Ube Industries, Ichihara 290-0045, Japan P. Llewellyn Centre of Thermodynamics and Microcalorimetry - CNRS, 26 rue du 141~rne RIA, 13331 Marseille cedex 3, France A. Ch. Mitropoulos Cavala's Institute of Technology, Department of Petroleum Technology, 65404 St. Lucas, Cavala, Greece S, Morooka Department of Materials Physics and Chemistry, Graduate School of Engineering, Kyushu University, Fukuoka 812-8581, Japan D. Nicholson Department of Chemistry, Imperial College of Science, Technology and Medicine, London SW7 2AY, UK A, Nijmeijer Laboratory of Inorganic Materials Science, Department of Chemical Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands T. Ohkubo Physical Chemistry, Material Science, Graduate School of Natural Science and Technology, Chiba University, Yayoi, Inage, Chiba, 263-8522 Japan J, D. F. Ramsay Laboratoire des Materiaux et des Proc~des Membranaires, UMR CNRS 5635, Universite Montpellier II, 2 pl Eug6ne Bataillon, 34095 Montpellier, France M. B. Rao Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, PA 18195-1501, USA

L. V. C. Rees

Department of Chemistry, The University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, UK

D. M. Ruthven

Department of Chemical Engineering, University of Maine, Jenness Hall, Orono, ME 04469-5737, USA S. Sircar Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, PA 18195-1501, USA L. Song

Department of Chemistry, The University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, UK

E. Soterakou MESL, Institute of Physical Chemistry, NCSR "Demokritos", 15310 Aghia Paraskevi Attikis, Greece K, L, Stefanopoulos

MESL, Institute of Physical Chemistry, NCSR "Demokritos", 15310 Aghia Paraskevi Attikis, Greece

Th. A. Steriotis


T. Stubos


N. Tanihara Polymer Laboratory, Corporate Research and Development, Ube Industries, Ichihara 290-0045, Japan K. Travis Department of Chemistry, Imperial College of Science, Technology and Medicine, London SW7 2AY, UK M. Tsapatsis

Department of Chemical Engineering, 159 Goessmann Laboratory, University of Massachusetts, Amherst, MA 01003-3110, USA

S. Vasenkov

Fakult~t for Physik und Geowissenschaften, Universit~t Leipzig, Linn6stral~e 5, D-04103 Leipzig, Germany

H. Verweij

Laboratory of Inorganic Materials Science, Department of Chemical Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

G. Xomeritakis

Department of Chemical Engineering, 159 Goessmann Laboratory, University of Massachusetts, Amherst, MA 01003-3110, USA


PREFACE

This book is dedicated to the rapidly grown field of microporous ceramic membranes with separating layers of pore diameter less than 2 nm. In spite of the recent rapid growth of the research effort directed towards the development of microporous ceramic membranes the field is still considered to be at its infancy and exhibits a significant future growth potential. The driving force for these efforts is of course the very promising opportunities for cost-effective large scale gas separation applications, which can be classified into two major categories: the "high temperature molecular sieving" and the "low-temperature reverse molecular sieving" modes of separation techniques. For high temperature applications, molecular sieving, based on the size exclusion of large molecules, is very often identified as the major mode of separation by microporous membranes. For low temperatures, the "reverse molecular sieving" is considered as a very efficient mode of separation in which preferential sorption of heavy gas mixture components results in the exclusion of the light components of the gas mixtures and the permeation of the heavy components through the membrane. The idea of the reverse sieving was initially introduced during the early sixties by professor R.M. Barrer and coworkers and even though it has been demonstrated that the method can combine high permeances with high selectivities, no major application has been developed as yet. One of the reasons, of course, is that the production of large surface areas of microporous separating layers with a minimum number of defects and a minimum thickness is an extremely challenging task. Over the recent years, significant progress has been made with respect to the development of novel microporous asymmetric membranes, mainly involving modification by means of deposition of additional material within the pores of the substrates. Most state-of-the-art technologies aiming in the development of microporous ceramic membrane are presented in chapters 3.1, 3.2 and 3.3. These include several material deposition methods and techniques on macroporous or mesoporous supports and substrates from the liquid or vapour phase, namely those involving sol-gel, zeolite and chemical vapour deposition techniques. In addition to the above-mentioned methods, the classical technique of carbonizing polymeric deposits along with one of the novel techniques of plasma-treating, organically deposited Langmuir-Blodgett films, are also presented. Finally, chapter 3.6 is dedicated to nanophase mixed ionic-electron membranes for enhanced oxygen transport, which pose a strong candidacy for a number of significant commercial applications. Another significant factor that seriously hinders further development of the microporous ceramic technology is the lack of comprehensive understanding of the equilibrium and transport properties of molecules confined within nanopores. The development of a satisfactory sorption and transport equation for the microporous membrane performance requires the development of efficient characterization techniques for the elucidation of the structural characteristics of the separating layer. Combining

xii sorption techniques, scattering and differential permeability techniques, the characterization of the complex pore structure of the microporous layer, interpenetrated by a network of larger pores can be obtained. These are analytically presented in chapter 1.1. The study of the physical state of sorbed phase confined in micropores can be determined by nondestructive scattering techniques. The recent advances of in situ X-Ray Diffraction (XRD) are presented in chaptem 1.2, whereas the principles of Small Angle Scattering techniques are outlined in chapter 1.3 along with recent developments employing the contrast matching technique. Several chapters of the first section are dedicated to the study of the diffusion processes in the micropores. "Microscopic" methods allow for the direct determination of the self-diffusion coefficient under equilibrium conditions by using two complementary methods, the pulse field gradient neutron magnetic resonance (PFGNMR) and quasi-elastic neutron scattering (QENS) techniques. "Macroscopic" or non-equilibrium methods, which allow the determination of transport diffusivities measured under the application of a concentration gradient, are also explicitly presented. The recently developed QENS technique allows the simultaneous determination of both transport and self-diffusion coefficients. In combination with the methods of differential permeability, frequency response and zero-length column chromatography, presented in chapters 1.4, 1.5 and 1.6 respectively, understanding of the effect of micropore confinement on the self- and transport diffusion coefficients may be obtained. The second section is devoted to the modeling of the sorption and transport through the complex porous structure of the microporous separating layer. Chapters 2.1 and 2.2 provide an overview of the recent advances in the simulation of sorption and transport processes at the single pore level. In chapter 2.3 the theory of networks of single pores is presented. Although the network theory is fully developed, insufficient description of the transport process in a single micropore precludes explicit assessment of the effect of the pore structm'al characteristics (pore size distribution, degree of connectivity etc.) to the overall transport and selectivity performance of the membrane. Since a micropore network model is currently under development, the analysis in chapter 2.3 is limited to networks comprised of mesopores, which are necessary for the description of transport through the larger pore network interpenetrating the network of micropores in the separating layer. In chapter 4.1 some of the most promising applications for the "low temperature reverse molecular sieving" mode of separation are presented, namely the recovery of paraffins and olefins from fluid catalytic cracking off gas along with the carbon dioxide removal from natural gas. These are two major processes that merit further consideration for full commercial exploitation. In addition to the above, some applications based on the "high temperature molecular sieving" technique are presented in chapter 4.2. It should be noted that the chapters of this book bring forward a wide range of issues, namely fundamentals of complex sorption and transport processes in micropore structures, highly innovative methods of preparation of microporous membranes and examples of their possible commercial applications. It is hoped that the reader will find useful and will take advantage of the insights presented by the distinguished investigators, who have contributed significantly to the advance of research efforts in the diverse topics presented in this book.

xiii

Acknowledgments I would like to thank the staff of Elsevier Science and especially Drs. Huub MantenWerker and the members of our lab Drs. G. Papadopoulos, F. Katsaros, G. Romanos, V. Kouvelos, G. Pilatos and N. Kakizis. The contribution of our secretary Ms. S. Botta is gratefully acknowledged. Special thanks go to European Commission for the financial assistance and to all our partners in several microporous membrane research projects funded by the European Commission and especially to Steve Tennison from Mast International Ltd.

Nick Kanellopoulos


RecentAdvancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) 2000 ElsevierScienceB.V. All rightsreserved.

MEMBRANE CHARACTERISATION BY COMBINATION OF STATIC AND DYNAMIC TECHNIQUES

Th. A. Steriotis l, K. L. Stefanopoulos 1, A. Ch. Mitropoulos 2, and N. K. Kanellopoulos 1

1Membranes for Environmental Separations Laboratory, Institute of Physical Chemistry, NCSR "DEMOKRITOS", 15310 Aghia Paraskevi Attikis, Greece 2Cavala's Institute of Technology, Department of Petroleum Technology, 65404, St. Lucas, Cavala, Greece *(current address)

The combination of static and dynamic techniques is a powerful tool which can provide detailed information for the characterisation of membranes. We here present the type of information obtainable by the adsorption, permeability, and small angle scattering (SAS) techniques and important combinations of them. Additionally, examples of recent applications of the methods and their selected combinations on a series of characteristic membrane materials are presented. Important conclusions are drawn regarding the pore and internal surface morphology of various types of membranes.

1. INTRODUCTION Membrane technology is of great industrial interest, as in many cases it can replace successfully traditional, pollution-prone and energy consuming separation processes. The thorough assessment of structural features of the pore network and surface physicochemical properties is probably the most important part of the characterisation of a membrane system and a number of equilibrium and dynamic experimental techniques can be used for that purpose. It is generally accepted that detailed description of a membrane system can only be possible when different techniques are combined.

In the following, we briefly survey three independent methods of membrane characterisation (adsorption, permeability, small-angle scattering (SAS) of x-rays and neutrons) and two significant combinations of them, permeability in conjunction with adsorption and adsorption in conjunction with SAS, with special emphasis on the type of information obtainable in each case. Additionally, we demonstrate examples of the application of the methods to the following materials: i. y-Al203 mesoporous pellets, prepared by symmetrical compaction of Degussa aluminium oxide of type-C (particle radius ~ 100 A) in eleven sections. During compaction, special care was taken to avoid non-homogeneity effects by applying an appropriate level of compression to each section. ii. A Vycor 7930 type porous silica. According to the manufacturer (Coming) the sample has a porosity of ~ 28% and pores of ~ 40 A diameter. iii. Asymmetric gas-separating carbon membranes obtained through carbonisation of a polymer resin precursor and subsequent activation (1). These membranes have a microporous carbon skin on top of a macroporous carbon substrate. The pore diameter of the microporous material appears to be in the 12-15 A range, while microporosity is about 38%. iv. Silicalite-1 membranes prepared by in situ hydrothermal synthesis and crystallisation of the zeolite inside the pores of ct-A1203 macroporous disk-shaped supports. Syntheses were performed by dissolving pyrogenic silica (Aerosil 380, Degussa) in aqueous solutions of tetrapropylammonium hydroxide (templating agent). After ageing the mixtures were heated with the support in Teflon lined stainless steel autoclaves. Finally, the organic template was removed by calcination (2).

2. DYNAMIC AND EQUILIBRIUM METHODS

2.1. Adsorption The adsorption isotherm, i.e. the quantity of gas (vapour) adsorbed on a solid at different pressures, at constant temperature, is a function of the surface area and the pore structure of the solid and thus can provide useful information about these two factors. To this

end adsorption isotherms (especially N 2 at 77 K) is a widely used technique for the characterisation of porous materials. The presence of certain types of pores (micropores, i.e. pore width, w, less than 20 A, mesopores with 20 A < w < 500 i~ and macropores with w > 500 A) produce different shapes of isotherms. The majority of these isotherms can be grouped into in five classes (six with the stepped isotherm) after Brunauer, Deming, Deming and Teller (3) according to the pore size of the solid and, the adsorbent-adsorbate interaction. The analysis of adsorption data can in principle produce values for the surface area and total (or micro) pore volume of the solid under investigation, by means of well-established methods such as BET, Langrnuir or DR (4). The pore size distribution (psd) of mesoporous solids can be derived through isotherm analysis methods, based on the Kelvin equation (5). Clearly the above analysis can be only applied to pores accessible to the penetrating gas (open pores), while inaccessible (closed) pores can only be detected with the aid of other methods such as SAS. Furthermore, Kelvin equation is not applicable to micropores, due to their small size (few molecular diameters) and the overlapping potential fields of neighbouring walls. In this case the processing of adsorption data using the potential theory (6) is possible and can lead to psd estimates of semi-quantitative validity. Typical examples of N2 adsorption isotherms (77 K) for mesoporous alumina and Vycor and microporous carbon membranes are shown in Figure 1, while the corresponding pore size distributions are presented in Figure 2. While a number of more or less established characterization methods exist for mesopores and macropores, the assessment of microporosity is much less advanced, due to experimental difficulties and the lack of an appropriate model for the interpretation of adsorption data. N2 adsorption at 77 K is probably the most studied technique, however obtaining accurate experimental isotherms is hampered by the long equilibration times required at the low liquid nitrogen temperature. In order to overcome this limitation the micropore structure evaluation can be based on isotherms of carbon dioxide or other vapours obtained at higher temperatures, provided that suitable equilibrium models for the sorption of non-spherical molecules are available.

200

J

180

160 140

._._ Car~n

n 120 Ior) 100 E 0 v 80

_._v,

_,,iA~

cor

....

- o - Alumina

:" /

j/

60 40 20 0

i

r

i

,

0.2

0.4

0.6

0.8

1

piP0

Figure 1. N2 adsorption isotherms of Vycor, AI203 and microporous carbon membranes, at 77K. 70

"~

60

4 - Carbon

50

- . - Vycor

II

- o - Alumin

or)

% ~

>* -~

30 20 10

10

100

r (A)

Figure 2. Pore size distributions based on the Kelvin equation (Vycor, alumina) and DubininAstakov method (carbon).

The Grand Canonical Monte Carlo (GCMC) method is ideally suited to adsorption problems because the chemical potential of each adsorbed species is specified in advance (7,8). At equilibrium, this chemical potential can be related to the external pressure by making use of an equation of state. Consequently, the independent variables in the GCMC simulations are the temperature, the pressure and the micropore volume, i.e. a convenient set, since temperature and pressure are the adsorption isotherm independent variables. Therefore, the adsorption isotherm for a given pore can be obtained directly from the simulation by evaluating the ensemble average of the number of adsorbate molecules whose chemical potential equals that of the bulk gas at a given temperature and pressure. To this end, a method for the determination of the micropore size distribution based on Monte Carlo simulation has been developed (9). In this work the mean CO2 density inside a single slit shaped graphitic pore of given width, is found on the basis of G.C.M.C. simulations for a pre-defined temperature and different relative pressures. Starting from an initial PSD guess, it is then possible to produce a computed CO 2 sorption isotherm and compare it to the measured one. After a few iterations, the procedure results in a PSD which, if desired, can be further refined at the cost of additional computational effort.

2.2 Permeability The fluid flow properties of porous media, are extremely sensitive functions of the pore size distribution (psd) and additional pore structural characteristics (shape, connectivity). To this end permeability is a dynamic technique, which can provide useful data concerning the structure of membranes and evaluate their overall quality simultaneously. We may note that open pores can be either conductive or blind (dead-end). Both open pore types contribute to adsorption, while permeation occurs through conducting pores only. The measurement of the permeability, P, of a weakly adsorbed gas (e.g. helium) through a membrane can be used for the calculation of gas diffusion coefficient, Dg (in this case P=Dg.e where e is the porosity). As the pressure gradient across the membrane increases, the flow regime changes from Knudsen to viscous (Poisseuille). Additional surface or condensate flow occurs when the gas (vapour) is adsorbed or condensed in the pores of the membrane. On Knudsen flow, which occurs when the pore radius, r, is sufficiently smaller

than the mean free path, ~., of the flowing molecules (r 25 ~tm), with a high resolution.

1. INTRODUCTION Over the past decade there has been considerable progress in the development of microporous membranes (1,2). These membranes have been synthesised from several different materials which include microporous carbon (3), glass (4) and different oxides, such as silica (5-7) for example. Compared to organic polymers, such inorganic materials have superior properties (e.g. chemical, thermal stability) which makes them attractive for novel membrane applications (e.g. gas separation and catalytic membrane reactors (8)). The porous microstructure, or texture of these membranes may however be complex, and will depend on the type and conditions of the synthesis process employed, as has been discussed (9,10). Furthermore the diffusion and transport processes of gases in such microporous membranes will be controlled by the microstructure. A detailed understanding of membrane microstructure (e.g. pore geometry, size, shape, connectivity and surface properties) is thus required in order to optimise separation performance. A wide range of techniques has been used for the characterisation of porous solids; the basis and recommendations on the suitability of these techniques has recently been given by IUPAC (11). Thus the choice of a

68 particular technique is dictated by the sample characteristics, such as the nature of the material, whether it is supported of not, its size, shape, isotropy and mechanical resistance, as well as the range of pore size. The destructive nature of the technique may also require attention. Thus the sample may require pretreatment (drying, outgassing) to eliminate adsorbed species, such as water, especially in the case of microporous materials. The characteristics of membranes is more demanding than most other porous materials. Firstly, the membrane separation layer is generally thin and supported, which requires a sensitive technique capable of analysing a sample in such a form. The membrane material in powdered form may indeed have a different texture. Secondly, the structure is frequently anisotropic and may moreover be microporous. Assessment of microporosity is much less advanced compared to meso- and macroporosity, despite the widespread emphasis given to this topic recently. The two traditional techniques of mercury intrusion and gas adsorption have important limitations. Both of these are destructive methods, which require outgassing of the sample. Furthermore in the case of mercury intrusion, the sample is subjected to very high pressures to access micropores, which frequently leads to destruction of the microstructure. The application of gas adsorption isotherm measurements to analyse microporosity has recently advanced considerably, although there are reservations which still exist concerning the general application of theories to describe adsorption in such small pores in ill defined structures (12). This situation has lead to a growing interest in other complementary and specialised techniques which are suitable for the characterisation of microporosity. These include methods involving NMR and radiation scattering with X-rays and neutrons for example. In the present chapter the techniques of small angle neutron scattering (SANS) and resonant ion backscattering will be described. Although the SANS technique is not new, there have recently been important technical advances, and developments in the characterisation of porous materials. Two of these developments will be described in detail. The first concerns the analysis of anisotropic pore structures, e.g. in microporous carbon fibres and anodic alumina membranes. In the second, contrast matching methods have been applied, to investigate, in situ, the mechanisms of gas adsorption in porous materials. Other related information, on the physical state of condensed gas phases confined in microporous media, obtained from neutron diffraction measurements, will also be illustrated. Finally, the techniques of resonant back scattering, with protons and a-particles, will be described. Using such microfocussed ion beam methods, unique information on the structure of thin porous layers can be obtained, as will be illustrated with microporous oxide rims, prepared by sol gel processes.

2. CHARACTERISATION OF POROUS MATERIALS BY NEUTRON SCATTERING

2.1 General aspects of neutron scattering techniques The energy of neutrons used in scattering studies normally falls within the range - 300 to 0.4 meV, and corresponds to a wavelength, ~, between-~ 0.5 to -~ 15 A. Traditional sources of neutrons have been nuclear reactors, some of which have been designed to produce a flux within this energy range, typical of these is the high flux reactor (HFR) at ILL, Grenoble (13). These reactors have more recently been complemented by pulsed sources which employ particle accelerators to generate neutrons by the bombardment of a target, as for example in

69 the Spallation Source, ISIS, at the Rutherford Appleton Laboratory in Oxfordshire (14). Neutron scattering by matter arises either through an interaction with the atomic nucleus or magnetically, if atoms have unpaired electron spins. Since detailed treatments of these different scattering processes have been given in numerous reviews and books (15-17) the following outline will only indicate the basic principles and information which can be derived from the technique when applied in the present context. In particular we will confine our attention to the more important phenomenon of nuclear scattering. We can describe the scattering from a single rigidly fixed atom in terms of its cross section, or, where cr = 4rc b 2

(1)

here b is defined as the scattering length of the bound atom. However, when scattering occurs from matter which is composed of an assembly of non-rigidly bound atoms, there will be two distinct contributions to the total cross section, which arise from coherent and incoherent effects. The first of these, Or results in interference between the neutron waves scattered by the nuclei, and is associated with a coherent cross section given by

O'~oh = 4zCb:o h

(2)

The second, (Yinc, is due to interactions between the spin states of the neutron and the nucleus, and gives rise to isotropic scattering ; it does not exist for nuclei having zero spin, e.g. 12C and 160. Values of bcoh, O'ine, and the neutron absorption cross section Oa, for different nuclei are given in Table 1. Table 1 9Coherent scattering length, bcoh, and incoherent and adsorption cross sections, ~inc, and Oa for different elements. 1012beoh/Cm2 1024ainc/cm2 ..... 10240Jcm2 H -0.374 79.7 0.33 D 0.667 2.0 0.0005 C 0.665 0.0 0.0035 N 0.94 0.3 1.9 O 0.58 0.0 0.00019 A1 0.35 0.0 0.23 Si 0.42 0.0 0.17 Ti -0.34 3.0 6.1 Fe 0.95 0.4 2.6 Zr 0.72 0.3 0.18 Ce 0.48 0.0 0.63 Th 0.98 0.00 7.4 U 0.842 0.00 7.5 Data are for natural isotopic mixture and neutron wavelength of 1 A (as compiled by S.W. Lovesey ref. 16).

70 This shows that beohvaries erratically from element to element, and even for different isotopes - a feature which can be exploited in contrast variation studies (18), as will be described. Another important feature is the large value of 6i,r for the proton, which dominates that of other nuclei ; this makes incoherent scattering measurements particularly suitable for the study of hydrogenous materials (e.g. water, hydrocarbons, polymers etc.), in situations where other spectroscopic techniques (infrared and Raman spectroscopy, NMR) are unsuited because of absorption problems. This feature which has been exploited extensively in investigations of the diffusion and dynamics of water and hydrocarbons sorbed in oxide gels and zeolites for example, will be discussed in detail by Jobic in Chapter 1.4 of this volume. Neutron coherent scattering has its counterpart in small angle X-ray scattering (SAXS) and diffraction, for which the theory is very similar (19), although the possibilities afforded by contrast variation are unique to neutron scattering (18). Small angle scattering, SAS, arises from variations of scattering length density (see below) which occur over a distances dsAs (where dsAs ~ 2/20 corresponding to scattering angle 2 0 for radiation with a wavelength ~,) exceeding the normal interatomic spacings in solids and liquids. Such an effect thus occurs with : (i) assemblies of small particles in air or vacuum comprising a porous material (20-22) ; (ii) solid materials containing voids or pores (23) ; (iii) solid solutions such as alloys (23) ; and colloidal dispersions of particles and polymers in liquids (24-26). With many of these systems there are frequently inherent practical advantages in using neutron radiation became of its lower absorption in most materials compared to that of Xrays ; the latter usually require very thin specimens and considerable restrictions of sample environment. In the subsequent section the application of small angle neutron scattering in studies of porous materials will be described in more detail. 2.2 Small Angle Neutron Scattering (SANS)

2.2.1 Theory of SANS Small angle neutron scattering measurements of both X-rays and neutrons can provide structural details of porous materials on a scale covering a range from 1 nm to > 100 nm. SANS arises from variations of scattering length density, Pb, which occur over distances exceeding the normal interatomic spacings and occurs when solids contain pores. Details of the porosity and surface area can be obtained from measurements of the angular distribution of the scattered intensity (see Figure 1). The appropriate range (20) where this information is contained is defined by the momentum transfer, Q, and the size of the pore, d, where 4re sin O

Q =----T--

(3)

An analysis of the scattering in the range 0. I < Qd < 1 provides details of the size and form of scattering object (pores); information of the surface properties may be obtained at larger angles (Qd > > 1) as depicted schematically in Figure 2.

71

Since the theory of SAS for both X-rays and neutrons has been covered extensively in several comprehensive reviews and books (19, 27), the following outline will only indicate the basic principles briefly. The scattering associated with the coherent cross section of nuclei in a material has a spatial distribution, which is a function of the distribution of these nuclei. This scattering can be expressed as a partial coherent cross section (4)

do"cob _ I s ( O ) dO

IoN

Where Is is the scattered intensity (neutronsl,s l ) in solid angle .(2, I(Q) is the incident flux (usually expressed as neutrons,sl,cm 2) and N the number of scattering nuclei exposed to the beam. The coherent scattering cross-section per atom at small angles 2 0 is given in the static approximation as

d O = -N

R exp(iQR)

1

(5)

where bR is the coherent scattering length of the chemical species occupying a site with the position vector R in the material. By replacing ba by a locally averaged scattering length density pb(x), where r is a variable position vector, we can write

do" _

f(pb(r)exp(iQr)d3r )

d.O-

v

12

(6)

where the integration extends over the sample volume, K Debye and Bueche (28) showed that Eq. (6) can be simplified for small vectors r to give the final expression do" _ 1 _ 2 ~ , sin(Qr) d.Q - -N ~7 V .11 ( r ) 4 zcr2dr o

Qr

(7)

m2

where ~1 is the mean fluctuation in scattering density, viz 2

= (p~(r)

_

~

)2

(8)

and y ( r ) is a correlation function in scattering density defined as

(r/,r r(r) =

m2

7?

(9)

72

2O

NEUTRON BEAM

!

I

|--

I I J

- -

I

I

l

SAMPLE

I

2 D-DETECTOR

Figure 1. Schematic diagram of small angle neutron scattering system.

Guini er R a n g e

i

10-1 -

@

10-2 -

I-'-4

Pofod

10-3 -

P.ange

10-4 -

I

10 -1

i

1

I

10

Qd

Figure 2. Schematic illustration of SANS curve for objects, such as pores, with a dimension of d. In the Guinier range the scattering depends on the size and form of the object. In the Porod range information on the surface are obtained.

73 The function 7'(r ) is complex and contains all information from the effects of the form, (size, shape) of the inhomogeneities (e.g. pores) and their mutual arrangement. Although separation of this information is difficult, precise interpretation can be obtained from y(r_), in particular for two phase systems composed of discrete particles as considered here. Porod (29) considered a particular case of an arbitrary two phase system with sharp boundaries in which the scattering density of one phase, pl, was constant and that of the other zero. We can then write --2

rl = p~qk,(1-~k, )

(10)

where ~bl is the volume fraction of phase 1. This theory leads to the general expression for do~dO in the limit of high Q do')

2nS (11)

where S is the total surface between the phases. This equation predicts that in the high angle tail of the scattering curve the intensity decreases asymptotically as Q-4. Furthermore the absolute intensity of scattering in this region is dependent on only two parameters of the system : the difference in scattering length density between the two phases, and S, the total area of the interface between the two phases. Where the interfacial boundary is not sharp, deviations from Porod behaviour may occur (3032). More recently this has been demonstrated for a number of porous systems (e.g. microporous carbons and silicas) which have a surface roughness on a scale in the range of the inverse of Q covered in the SAS measurements. Such materials, which can be described as having surface fractal properties, show a decay of

I(Q).-. SQ -(6-~

(12)

where D is the fractal dimension. For smooth surfaces, D = 2, however in extreme cases where the surface is irregular, or has a curvature on a scale smaller than reciprocal Q space, D may become greater than 2. This can lead to the power law exponents which are smaller than -4. Typically D falls in a range between 2 and 3 for such systems. Two other linear parameters can also be derived from scattering measurements. The first, defined as the 'range of homogeneity' by Porod, is given by

l-~ - 4Vqk, S

(13)

and represents an average diameter of the heterogeneities comprising the phase having volume fraction ~1 (see Figure 3). Thus for a collection of spheres radius R, li = (4/3)R. The length, l/, like S/V, is a differential property of ~ r_) evaluated at r = 0 and consequently is unaffected by any effects of interference due to long range correlation between heterogeneities.

74 The integral breadth of the correlation function, gives another linear parameter, the 'distance of heterogeneity', lc oo

lc = 2 i),(r)dr

(14)

0

The scattering for many porous systems can be expressed more simply than the generalised expression (Eq. (7)) by using the classical theory developed to describe the scattering from assemblies of particles. The scattering cross section for such systems can be expressed as 2 I(Q) = V2 np(pp - Ps ) 2 P(Q)S(Q)

(lS)

where Vp is the volume of pores np their number density, pp and/as are respectively the scattering length densities of the pores and continuous solid phase and P(Q) is the single pore form factor. S(Q) is the structure factor, which is determined by the spatial ordering of the pores, and describes the effects of interference in the scattering from pores which are in close separation. In the limit of high Q, S(Q) tends to unity. The form factor, P(Q), has been evaluated for a variety of particle (or pore) shapes which include spheres (33), ellipsoids (34), rods (35) and flat discs (viz. slits) (36) for example. A general relationship for P(Q), which is valid for all shapes, and describes the decay of P(Q) in the region of low Q (see Figure 2) is given by Guinier.

Figure 3. Geometrical interpretation of the distance parameter ll, or 'range of homogeneity' as defmed by Porod. Here, ll, is represented by the alternate succession of chords passing through phase 1 in a two phase random medium.

75

/ 22)

P(Q) ~ exp

- Q Rg

3

(16)

where Rg is the radius of gyration of the particle or pore. The relationship is valid when QRg < 1. It will be noted that for anisotropic particles (or pores), P(Q) will depend on the particle orientation with respect to the incident and scattering vectors. The scattering from randomly distributed pores will thus differ from that where there is a preferred orientation, a feature which will be illustrated subsequently. The static structure factor,

S(Q), is given by

S(Q)=l+4nnP~I(g(r)-l)resinQrlo Qr

(17)

where g(r_) is the particle pair distribution function which describes the spatial distribution of the particles (pores) as a function of the mean separation distance. 2.2.2 Applications of SANS Two recent applications of SANS will now be described where some of the special features of the technique have been exploited. These include first the scattering from anisotropic porous structures and secondly the use of contrast variation for in situ sudies. Both of these areas are currently under development, and have importance in the context of the structure of micro and meso porous membranes and the mechanisms of gas adsorption in such structures. (a) Anisotropic pore structures The pore structure of materials may frequently be anisotropic. Some examples of such materials are given in Table 2. Information on the microstructure of these oriented pore systems is often important in the applications envisaged. Thus the mechanical strength can be influenced by pore anisotropy and orientation in substances such as carbon and ceramic fibres, thin ceramic films and construction materials. The pore orientation may also control the microscopic flow and diffusion of fluids in materials as diverse as membranes and geologic media. Table 2. Materials containing anisotropic pore structures Carbon fibres Ceramic fibres Ceramic membranes Sol-gel films Clay and zeolite minerals Templated mesoporous materials e.g. MCM-41 Crystalline solids (after topotactic decomposition) Bio-inorganic skeletal structures

76

For these materials unique microstructural information can be derived from SAS with both neutrons and X-rays. These details are not obtainable from bulk measurements, such as adsorption isotherms. This application of SANS has recently been demonstrated with ceramic alumina fibres (37), microporous carbon (38), sol-gel films (39) and alumina membranes produced by anodic oxidation (40). SAXS investigations of pore-orientation periodicity in porous polymer and carbon materials have also been recently reported by Olivier et al. (41) We will illustrate the information obtainable firstly by describing in outline the results obtained by SANS on activated carbon fibres (ACF) (38). In ACF the micropores are slitshaped and are formed by the parallel alignment of microcrystals of graphite along the axes of the carbon fibres (42). This has been established by SANS with ACF samples oriented in two different directions to the incident neutron beam (see Figure 4). Results showing SANS along the two-dimensional detector for ACF samples oriented horizontally indicate that the scattering is anisotropic (see Figure 5.a). In (i) the scattering arises from the surface of the microcrystals (> 103 m~g"1) which have 'smooth' surfaces; this gives a power law decrease in scattering of Q4. In (ii) the scattering arises from the edges of the microcrystals, which are 'rough' and have a surface fractal dimension of = 2.5. This gives rise to a Q-3.5 power law as shown. When the fibres are oriented with their axes parallel to the incident beam (see Figure 5.b), the scattering is isotropic, as can be inferred from theoretical analysis of scattering from oriented particles (43). In this situation the scattering contribution comes from both the surfaces and edges of the microcrystals, with the former dominating. The power law component is consequently close to Q-4.

(a) ACF NEt;fROM

BEAM

Detector (b)

ACF NEUTRON BEAM

Figure 4. SANS of oriented carbon fibres. Orientation of ACF (a) horizontal and (b) parallel to the incident neutron beam with respect to the two-dimensional detector. After (38).

77

(a)

10

6

(b) 9

_

104

0 0

_

O O

10 z

I ~(~4

0

0

0

o

l

~0 l 9

0 v

0

9

10

/

9

o ".

10 2

o IQ ( i i )~ ~(i) o ",

+ok"% ]

10-3 I

10 -3

I

10-2_1

I

I

10 -2

I

10 -1

Q//~-I

10 -1

Q/A Figure 5. SANS of oriented carbon fibres. (a) Fibers are oriented horizontaly with their axes perpendicular to the incident beam. (i) SANS along the vertical axis. (ii) SANS along the horizontal axis of the detector. (b) Fibers are oriented with their axes parallel to the incident beam. Scattering is isotropic and I(Q) is radially averaged data.

Another illustration where SANS measurements have been made on oriented samples having an anisotropic pore structure concems alumina membranes (40) which have been prepared by anodic oxidation of alumina in a suitable electrolyte. Such a process can result in the formation of a porous surface film which consists of a close-packed hexagonal array of cells, each containing a cylindrical pore (44). Hoare and Mort and later workers (45-47) have shown that the pore morphology of these films is remarkably regular and can be controlled by the electrolysis conditions. Subsequent developments have lead to techniques for detaching these films from the aluminium metal thus resulting in thin alumina membranes with a very uniform pore structure. Such membranes have more recently been commercialised (48) and are available with controlled narrow pore size distributions in the mesopore range. These membranes have applications in the ultrafiltration of biological samples and in gas separation by Knudsen diffusion, although at the present these are limited to a laboratory scale (8).

78 The highly uniform and oriented structure of a typical membrane (pore diameter - 200 nm) is illustrated by the field emission scanning electron microscopy results in Figure 6.a) and b). The schematic arrangement for the SANS measurements made with such a membrane (47 mm OD) sample is illustrated in Figures 7.(a) and 7.(b). Here the membrane has two different orientations to the incident collimated neutron beam: In (a) the membrane disc is perpendicular to the beam; in (b) the disc is almost parallel. (In practice, to obtain a sufficient sample area in the beam, the disc was oriented slightly ( - 3 ~ away from the parallel axis.) The corresponding orientation of the columnar pores to the neutron beam for these two sample configurations is illustrated in Figures 8.(a) and 8.(b). The SANS intensity distributions measured on a 2D detector for these two sample configurations are very different, as depicted schematically in Figures 7.(a) and 7.(b). For (a) the scattering was isotropic, and for (b) markedly anisotropic. On the detector this feature is depicted schematically (of. Figures 7.(a) and 7.(b)) by the closed lines of iso-intensity, viz.; circular and highly elliptical, respectively. A more quantitative representation of the anisotropy is shown in Figures 9.(a) and 9.(b). Here the intensity of scattering along the vertical axis, I(QO, and horizontal axis, l(Qn), on the detector, for the two different sample configurations, is displayed. Thus in Figure 9.(a), with the membrane in the perpendicular configuration the scattering is very similar along both axes, in accord with the isotropic pattern observed. In contrast the scattering in the parallel configuration (Figure 9.(b)) is highly anisotropic. Here I(Qv) is very weak compared to I(Q~ ( by a factor o f - 103).

79

(a)

neutron beam

~

.| ............................................

QH '\ (b) ~v

\ neutron beam

\

QH ann

Figure 7. Schematic arrangement for SANS measurements on oriented membranes. (a) perpendicular orientation, (b) parallel orientation to the incident neutron beam. (a)

(b)

perpendicular position

parallel position

n e utron.............

beam

n e na~ '

~

~

~

beam

Figure 8. Corresponding orientations of columnar pores in membranes having two different configurations shown in Figure 6. The stronger scattering behaviour observed for both axes in Figure 9.(a) and I(Qn) in 9.(b), has an intensity which decays with a power law close to that observed in the Porod scattering region, viz. I(Q) "-' Q-4

(18)

Such behaviour indicates that the inverse size of the scattering objects (viz. pores) is much smaller than that of the corresponding range of Q covered in the present measurements (1).

80 This implies that the pore size is >> 102 A, and is in accord with the SEM results shown in Figure 6. Further analysis of these preliminary SANS results is complex and can only be outlined here. The treatment takes as its basis, a model composed of an array of parallel cylindrical objects, length, l and cross-sectional radius, a (43). When such a system is oriented, where y corresponds to the angle between Q and the cylindrical axis, two specific cases can be defined for the scattering behaviour. For the first, where the vector Q is parallel to the cylindrical axis (y = 0) the scattering will be only a function of the axial length. Thus for a single isolated cylinder

sin(Ql/2))2 I(Q, y = O)~ K poV Ql/2

(19)

Where ,oo is the scattering-length function and V is the cylindrical volume. This situation corresponds to the SANS in Figure 9.(b) corresponding to I(Qv). Secondly, if the Q vector is perpendicular to the cylindrical axis, the scattering will be a function only of the radius. In this case I(Q,y = m ' 2 ) - K ( 2 p o V

J'(Qa)) 2Qa

(20)

Jl(X) is the first order Bessel function of the first kind. This situation corresponds to the SANS in Figure 9.(a) for both I(QH) and l(Qv) and also in Figure 9.(b) for I(QH). The origin of the anisotropy in the SANS behaviour observed is thus evident. It has also been possible to obtain an insight into the ordering or spacing of the pores in the present membrane, from measurements at much smaller scattering vectors (Q/A1 = 100 A 2 and "c, therefore for the same diffusion coefficient.

4.2. Jump diffusion While Fickian diffusion is obtained at small Q values (Figure 1), jump diffusion implies a deviation from the straight line at shorter distances. The interpretation of the QENS spectra at larger Q values requires a model which contains as parameters the characteristic lengths and times of the elementary steps. 4.2.1. Existing models : Chudley-Elliott, Singwi-SjSlander, Hall-Ross The first model by Chudley and Elliott (CE) was developed for diffusion in liquids, where a lattice-like structure is assumed to exist locally [10]. In fact, this model has found many applications in solid state diffusion. The CE model is based on the following hypotheses: an atom vibrates on a given site during a time .c. After this time, it jumps to another site situated at a distance d (the time taken for the jump is much shorter than the residence time), an atom having n jump possibilities. CE have shown that with these hypotheses, the incoherent scattering function is still a Lorentzian function

116

S(Q,co) =

l

Aco(Q)

(18)

/1:(0 2 + (A(o(Q)) 2

but the HWHM has a different value compared with Eq. (15)

Aa)(Q) = __1~[1- exp(iQ.d)]

(19)

nz" d

Here, all the sites are supposed to be equivalent. However, the model can be generalised to deal with crystallographically or energetically different sites [11]. The diffusion of hydrogen in metals can be well described by this model. Single crystal experiments allow to orient the vector Q along selected crystallographic directions. 4 3

v

=1A-1

-

>.,

~9 2 -

E

c-

1

-

i !

!

.

=2A-1

o

.

,|

i

i

i

4

=3A-1 o

o

!

-1 .o

-.5

0.0

,,

i

.

i

.5

1.0 Energy

Fig. 2. Simulated spectra (without convolution with instrumental resolution) for jumps between octahedral sites in a fcc lattice (the jump distance is of 3 A). The continuous line is obtained after powder averaging, the dotted line corresponds to a Lorentzian fitted on the exact profile.

117

If only polycrystalline samples are available, Eq. (18) must be averaged to take into account all possible orientations of the crystallites with respect to the scattering vector. Accurate numerical methods exist, based on the generation of optimally chosen points in the three dimensional space [12,13]. For each Q value, one obtains a sum of Lorentzians with different widths so that the total profile can be different from a Lorentzian. At small Q values, however, the calculated profile is well described by a Lorentzian function, as shown in Figure 2. This example corresponds to jumps between octahedral sites in a fcc lattice (a jump distance of 3 A has been arbitrarily selected). At larger Q values, the profile deviates from a Lorentzian function, however the exact value of the HWHM is not much different from the one obtained assuming a Lorentzian profile. For a random motion, the mean-square displacement is proportional to the square of the jump distance =Nd 2 (20)

where N is the number of jumps. In QENS, one can measure broadenings for Q values of about 0.1 A~, which corresponds to distances in real space of 2rdQ = 60 A. For jump lengths of 3 A, this means that one is able to follow the motion of a particle after 400 jumps. On this space scale, the vector d can take any direction, the isotropic approximation is justified, and the term IQ.dl 2 can be replaced by Q2d2 /3. The limit of Eq. (19), for small Q values is then Aco(Q)_ -O2d2 -_002 (21) 6"r Therefore using Einstein's relation, Eq. (16), one recovers the broadening characteristic of a macroscopic system. Chudley and Elliott have also shown that if the jumps of a fixed length d may occur in any direction, like in a liquid, the sum in Eq. (19) is replaced by an integral

Aco(Q) =

1 - -~ o~dO sinO exp(iQdcosO) 1(sin(Qd)) 1- Q-- 7 -

(22)

This function is plotted in Figure 1 for a jump length of 10 A. It has a maximum for Q = 3rd2d (Q2 = 0.2 A 2) and oscillates for larger Q values around ,(1, the jump rate. At small Q values, an expansion of the sinus function up to the third order yields again the DQ 2 law. This can be checked in Figure 1 where the lines corresponding to Fickian diffusion and to the CE model are indistinguishable below Q2 = 0.03 A 2 (Q = 0.17 A-l). The CE model was found to describe the diffusion of molecules in zeolites where specific interactions occur. For example, in the case of n-pentane in NaX [14], broadenings derived from individual fits of the spectra show a maximum at Q2 = 0.4 A 2 (Figure 3). This maximum is characteristic of a jump diffusion process with jumps of a fixed length occurring in random directions. The jump length, 7 A, is shorter than the distance between the centres of two adjacent supercages, = 11 A, which means

118

.04 (b)

.03 -

-l-

> v

E

.02 -

"1"1-

.01 0.00

0.0

!

!

!

!

.2

.4

.6

.8

Q2(A-2)

1.0

Fig. 3. Broadenings due to diffusion of n-pentane in NaX at" (a) 300 K, (b) 380 K. The points were obtained by fitting each spectrum individually, the curves correspond to simultaneous fits with all spectra using the CE model. that the long-range diffusion does not correspond to jumps from one cage to another. This picture is in agreement with recent MD simulations [15]. Another notable result obtained by Chudley and Elliott is that if the jumps have a distribution p(r), the broadening takes the form

Aro(Q)= ~1 ( 1- sin(Qr))Q...p(..7r) dr / ~p( r) dr

(23)

Since we will use only normalised distributions, Eq. (23) reduces to

Aro(Q)=~II l-~ sin(Qr) Qr p(r)dr 1

(24)

For the normal CE model, this distribution is of the form &(r-d). The other models which were proposed afterwards can be recovered starting from Eq. (24). It seems that Egelstaff [16] was the first to demonstrate that if a distribution of the form p(r)-rexp(-r/to) was used, a simplified version of the Singwi-Sj6lander model [17] could be obtained, neglecting the time taken for the jump. In order to compare the different models, we will use for the SS model a normalised distribution

0 ss (r)=

rro2 exp/r/ro

This distribution is plotted in Figure 4 as a dotted line. The mean-square jump length corresponding to this distribution is

119

=~r2p(r)dr=

1---~r3exp r2o

o

(26)

dr=6ro2

From Eq. (24), one obtains for the HWHM A(_OSs(Q)= l I 1-

=

I

1 oo Isin(Qr)exp ("~o) - r dr ] Qdo

1 ) l

1-

Q2

=

(27)

Q2ro2 22

1+ r2 1+0 ro Using Eq. (26), the broadening can also be written

AcoSS (Q) = 1

Q2 < r 2 > 6Vl+Q 2 /6

(28)

In the low Q limit, the broadening tends to < r 2 > Q2 / 6v, that is DQ 2, using a slightly different version of Einstein's relation D(29) 6~:

.12 .10 v

Q_

..."

.08 -

.1/

9

/

9

/

9

.06 -

9

J

0

/

",

/ /

9 9

\

~

/

9

.02 -

'\

/

9

.04 -

\

/

9

0.00

r\

/

/ /

/

\

\

\

\

\

\

\ 9~

N

~ ~

,

~~'.: ~ ~

!

5

I

10

15

I

20

~ ~

~

............. I

25

30

r(A) Fig. 4. Jump length distributions corresponding to the models of Chudley-Elliott (8 function at 10 A), Singwi-Sj61ander (dotted line), and Hall-Ross (dashed line). The two curves are calculated for the same value of < r 2 > = 100 A 2", this implies to= 4.082 A for SS and ro = 5.773 A for HR.

120

where the mean-square jump length replaces the square of the jump distance (cf. Eq. 16). This model was found to apply in the case of ammonia in silicalite [18]. The broadenings plotted in Figure 5 for the individual fits do not show a maximum, but converge progressively to an asymptotic value. All the spectra could be fitted simultaneously with the SS model, yielding a mean jump length of 5 A.

.06 .05 -

~"

.04 -

E

+

.03 -

d

.02

r

.01 0.00 0.0

I

!

I

I

I

!

.2

.4

.6

.8

1.0

1.2

Q2

1.4

(A-2)

Fig. 5. Broadenings measured for ammonia in silicalite (4.3 molecules per u.c., T = 360 K). (+) individual fits of the spectra, the solid line corresponds to a simultaneous fit with all spectra using the SS model, the dashed line to Fickian diffusion. The third model, proposed by Hall distribution of the form [19]

and

Ross

(HR), is based on a jump length

p H R ( r ) - r3(2~:)1/2 exp -

(30)

This distribution, which is normalised, is plotted in Figure 4 as a dashed line. Compared with the SS distribution, the maximum is situated at a larger r value, so that the width reaches its asymptotic value more rapidly (Figure 1). The mean-square jump length corresponding to the HR distribution is < r2 > = I r2p(r) dr = 2 I r4 exp 0 r03(2/~) 1/2 0

For this model, the HWHM is given by

dr = 3 r2

(31)

121

A(o HR (Q) - 4~

_l

[

~ rsin(Qr) exp Qr3(21c) 1/2 0

l - exp -

02 r2 ]

(32)

6

It is worth noting that Hall and Ross obtain the same result using a different derivation [19]. In fact, since all the models are based on the same postulates: Markovian random walk with one mean jump rate, one can always obtain the width through Eq. (24), only the jump distribution varies. The HWHMs for the different jump models, represented in Figure 1, correspond to the jump length distributions plotted in Figure 4. All the widths were calculated for the same values of < r 2 > and ~:, hence for the same diffusion coefficient D. This is manifested in Figure 1 by the fact that all the curves share the same linear variation at low Q, in the Fickian regime. It can also be noted that only the Chudley-Elliott model has an oscillatory behaviour, the two other models converge more or less rapidly towards 1/'c at large Q. 4.2.2. New Model In metals, the adsorption sites for the hydrogen atoms are well defined. In zeolites without cations, the spatial distribution of adsorbed molecules at finite temperatures can fill a channel segment or a cavity. For example, Monte Carlo simulations have shown that the centre of mass of linear alkanes is elongated in the channel segments of silicalite [20]. If one defines the distance between two sites by d o and if the delocalisation of the molecule on its site is taken into account by an additional parameter ro (physically one should have ro < d o), one can propose a new jump length distribution p(r) =

r / (r-do)2 / exp d O r0 (2~) 1/2 2 r2

(33)

This distribution is normalised, it is represented in Figure 6(a) for different values of r0 and d o. The mean-square jump length corresponding to this new model is given by ~'

< r2 > = I r 2 p ( r ) dr -

0

~ ((r-do) 2) 2 ~ r 3 exp dr = d 2 + 3 r2 d o r0 (2to) 1/2 0 2r2

(34)

The distributions plotted in Figure 6(a) were calculated for several values of ro, the value of d o being derived from Eq. (34). For this model, the following analytical expression is obtained for the HWHM of the Lorentzian l ll ~sin(Qr)expA(_o(Q) = "c Q d 0 r0 (2/01/2 0

[ sin0o, / 02ro)l

=l

l - ~ e x p -

T

Qd o

2

, dr 2r2 (35)

122

.3

/~ / \

Q.2-

,1

/

\

(a)

"

o.o

-~,.~ 0

5

f

,

" -,~-'----,--

10

I'~-

15

~

.

.

.

20

r(A)

.

:~ 3

"T" -r

25

(b)

2

0.0

!

!

i

.2

.4

.6

!

.8 Q2

(A-2)

1.0

Fig. 6. Results obtained for the new jump diffusion model" (a) jump length distributions calculated for the same value of < r 2 >= 100 A 2" the dotted line corresponds to ro = 0.1 A (d o = 9.998 A), the dashed-dotted line to to= 2.2 A (d o = 9.246 A), and the dashed line to to= 4.5 A (do= 6.265 A), (b) broadenings calculated with the same values of the parameters as in (a). y

It appears from Figure 6 that the new model is able to reproduce the variations of the CE and HR models, as well as intermediate cases. For a small delocalisation of the molecule (to= 0.1 A), the broadening is equivalent to the one obtained with Eq. (22). For a large delocalisation (r o= 4.5 A), the jump length distribution and the width are similar with the ones computed with HR model (see Figure 1). This new model is able to describe the small hump in the broadenings found for small nalkanes in the MFI structure, both experimentally [21] and theoretically [21,22]. Eq. (35) has the expected asymptotic behaviours at low and high Q. For large Q values, the width tends to 1/'~. For small Q, an expansion of the sinus and exponential functions yields

123

, E,_/,_

Aco(Q)- ~

~

6

2

(36)

Neglecting the term in Q4 and using Eqs. (34) and (29) one has

Q2 (do2+ 3r~ A(_o(Q) - --~--

= DQ 2

(37)

In conclusion, whatever the model, the broadening at low Q is always of the form DQ 2, characteristic of Fickian behaviour. The data obtained at larger Q values, i.e. short distances, can be analysed with a jump diffusion model to probe the diffusion mechanism on the atomic scale. It would be interesting to compare this information obtained by QENS with molecular simulations methods. 5. ANISOTROPIC DIFFUSION

Several models have been developed to describe diffusion in restricted geometries: between two walls [23], in a sphere [24], and in a cylinder [25]. The case of unbounded anisotropic diffusion has been treated for liquid crystals [26]. Some materials like zeolites or aluminophosphates can be true one-dimensional (1D) systems. Unidirectional diffusion effects could eventually be observed with the new mesoporous molecular sieves (e.g. MCM-41) or with carbon nanotubes. In these materials the channels, whose diameter varies from 4 to 40 A, are parallel and unconnected. Each molecule remains and diffuses in the same channel. Two extreme cases can be found:if the molecules in a given channel can cross each other, it corresponds to normal 1D diffusion, Figure 7(a). However, if the radius of the channel is smaller than the molecule diameter, the molecules cannot pass each other and this special case is called single-file, Figure 7(b). The implications of this model were envisaged a long time ago for biological membranes [27], but it is only recently that microscopic measurements have been realised by PFG NMR [28] and QENS [29]. The two extreme cases of unidirectional diffusion will now be examined separately, examples will be given in section 6.2.

C)

-Q

Normal 1D diffusion f

Fig. 7. Q

Q

~

Single-file diffusion

124

5.1. Normal one-dimensional diffusion Let us consider a molecule diffusing along a 1D channel, with a diffusion coefficient D. Motion perpendicular to the channel axis is neglected, which is reasonable when the molecules can just pass each other. However, such a motion tends to average the scattering function if the diameter of the channel is much larger than the molecule diameter (e.g. methane in MCM-41). If the channel makes an angle 0 with the direction of Q, the incoherent scattering function for this particular channel will be [30] 1 D Q2 cos2 0 S1o(Q,(_o) = ~ (.02 + ( D Q 2 cos2 0) 2 (38) The shape of this energy spectrum is a Lorentzian function, but the width depends on the angle 0. If big oriented samples were available, it would be possible to obtain the largest broadening by orienting Q along the channel axes, and no broadening at all (i.e. the instrumental resolution) by orienting Q perpendicular to the channel axes. In fact, it is almost impossible to get a few grams of oriented molecular sieves samples. The largest AIPO4-5 crystals have dimensions 400x100x100 pm 3, and it would be necessary to align hundreds of thousands of such crystals to get sufficient signal from the adsorbates. Therefore, one has to use powders so that an orientational average of Eq. (38) has to be performed 1 ~ D Q2 cos 2 0 sin 0 S1D(Q'(0) = 2-~'~J0d0 ~ 2 + ( D Q 2 cos2 0) 2

(39)

Integration leads to the following expression

1 {

S1D ( Q' r176 ) = 4 ~.4r2 eo y In l + y 2 +,J-2 y + 2 arc tan(l + ~

with

y

2

-

y ) - 2 arc t a n ( l - ~

DQ 2

y)

(40)

co

It is worth noting that the same expression is obtained when considering a sample of isotropically distributed 1D channels [31]. In such a system, the selfcorrelation function for a given channel is still a Gaussian

/

G l ( r ' t ) = ~[2~ exp - 2 < o"2 >

where < ~ 2 > diffusion

/

(41)

is the mean-square displacement for the molecule performing 1D < 0 .2 > - 2D t

(42)

In order to obtain the three-dimensional self-correlation function, one has to take into account that the probability to find a given channel on the surface of a sphere of radius r is l/27c r2 (there is a factor 2 compared to the surface of a sphere because a channel found on the surface at r is also found at - r ) . ,

,

G3(r't) = 2~:r 2 G l ( r ' t ) = (2~:) 3/2 ( 2 D t ) l l 2 r 2 exp - 4 D ~

(43)

125

While the self-correlation function for isotropic diffusion is a Gaussian, Eq. (12), G3(r,t) is not a Gaussian any more. There is a factor r 2 in the denominator which introduces a discontinuity at r = 0 , so that the self-correlation function for 1D diffusion is a cusp-shaped function. One obtains for the scattering function 1 SID(Q,oJ)=-~dt ~dr exp(-icot)exp(iQ.r)G3(r,t) (44)

After integration, one recovers Eq. (40) [31]. Therefore, whatever the sequence of integration, S1D becomes infinite at co=0 due to the discontinuity in G3(r,t). Experimentally, there is no discontinuity in the spectra because of the finite energy resolution. The simplest way to consider this influence is to convolute Eq. (38) with the instrumental resolution and to perform the powder average numerically. The resulting curve is not Lorentzian any more so that the analysis cannot be based on the width of the function. This effect appears more clearly when the 50

(a)

40-

>..,

,,... U)

3020-

c"

- ] 10 0 -,2

-.1

0.0

.1

.2

(b) ~. 2 v

>.., t-

,-. 9 1 t-

................ i

-.2

-.1

f

9"

-...

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

i

i

0.0

.1

.2 E (meV)

Fig. 8. Spectra simulated for (a) normal 1D diffusion (D = 10 .8 m2/s, Q = 0.3 A ~) ; (b) single-file diffusion (F = 10 ~ m2/s~/2, Q = 0.3 A~). The dotted line corresponds to an isotropic diffusion (triangular resolution function of HWHM = 9 peV).

126

instrumental resolution is high enough [29]. The spectrum shown in Figure 8(a) as a solid line was calculated with an intermediate resolution, for typical values of the parameters D and Q. The dotted line is a Lorentzian function, convoluted with the instrumental resolution and fitted on the solid line. It appears that the difference between the two profiles is small so that good statistics are needed to differentiate 1D from 3D diffusion. Of course, the difference would be larger with a better resolution.

,5.2. Single-file diffusion

As for normal 1D diffusion, the scattering function for single-file diffusion can be derived in two different ways either 9 by calculating the scattering function for a single channel and performing the powder average or by considering an isotropic distribution of channels and calculating the scattering function from the threedimensional self-correlation function [31]. The first derivation will be given here. The self-correlation function for a given channel is similar to Eq. (41), but the meansquare displacement for a molecule performing single-file diffusion is [32] < G 2 > =

2F t 112

(45)

where F is the single-file mobility factor (its unit is in m2s1/2). The essential difference with normal 1D diffusion is that the mean-square displacement is now proportional to the square root of the observation time. The long-range mobility should thus be reduced because of increased correlations between the molecules. For the same reason, a strong loading dependence is expected for the mobility factor. Considering a particular channel parallel with the direction of Q, one obtains for the intermediate scattering function (46) l ( Q , t ) = ~ dr r r) G 1(r,t) = r 112 ) The time Fourier transform yields the scattering function

SsF(Q,(_o) =--1 Tdt cos(cot) exp(-FQ2t 1/2 ) ~0

Z[cos z

, z ll

F2Q 4 2~(o C(v) and S(v) represent the Fresnel integrals. Powder averaging leads to

with

2

z -

Ssr(Q,co)=~(2oo)3/2 [dOsinOcos20 cos(~z ) -2-C(z) +sin(-~-z ) ~-S(z)

(47)

(48)

0

For a numerical calculation of this scattering function, it is useful to introduce the auxiliary function [33]

g(z)= cos(~z 2) -~-C(z) +sin(~z 2) -~-S(z)

(49)

When co is not too close to zero, one can use for g(z) a rational approximation [33]

127

g(z)

=

1

+e(z)

2 + 4.142z + 3.492z 2 + 6.670z 3

with

I~(z)l_, 300

Ooo 1 l~176 1 0

~ ~""

-~- ~ - ' - "

-10

fl "-~"--~- ~

-5

.

.

.

.

.

0

.

.

5

E (peV)

10

Fig. 11. Comparison of experimental and simulated spectra obtained for a branched and linear alkane in ZSM-5 9(a) isobutane at 570 K, (b) n-octane at 400 K. The dotted line represents the resolution function (Q = 0.87 AI). 6.2. Unidimensional systems

The influence of 1D diffusion on the QENS spectra measured for benzene in Namordenite was recognised [30], but the calculated profiles were almost indistinguishable from those expected for 3D diffusion, after convolution with the instrumental resolution. This was due to the resolution of the spectrometer, which was not high enough, or alternatively to the slow mobility of benzene. Another attempt was made in the mordenite structure by measuring methane diffusion [43]. However, a large proportion of methane was found to be trapped in the side pockets, in agreement with molecular simulations [44,45]. The first clear measurements of 1D diffusion with QENS were obtained for methane in AIPO4-5 [29,46]. A priori, it was not easy to guess if the diffusion would follow the normal 1D or single-file models, because the value of the free diameter which is quoted in the literature for this aluminophosphate is 7.3 A. Since the kinetic

131

diameter of methane is 3.8 A, the molecules could just pass each other in the channels. In fact, two series of experiments performed with PFG NMR are contradictory: one group interpreted the results in terms of normal 1D diffusion [47] while the other group found that methane was undergoing single-file diffusion [28]. A possible explanation of this discrepancy is that different crystals were used. It was found by measuring adsorption isotherms that some samples could adsorb up to 4 molecules/uc, but others up to 6 molecules/uc [48,49]. Two simulations were later realised on this system, using different potentials [50,51]. The simulations were able to explain how it is possible to accommodate 4 or 6 methane molecules in the unit cell of AIPO,-5. Therefore, it appears that the free diameter is much larger than the nominal value, it was estimated as 8.2 ,~, in the presence of methane molecules [49]. The QENS spectra obtained at various methane concentrations in AIPO,-5 could be fitted with the normal 1D diffusion model, Eq. (38) convoluted with the instrumental resolution and averaged over 0 [29]. The diffusion coefficient obtained at 155 K, 1.6 • 10-9 m2/s for a loading of 0.7 molecule/uc [29] is in keeping with the value obtained by PFG NMR at 300 K, for the same concentration, 2.9 x 10.9 m2/s [47]. For higher methane Ioadings, the diffusion coefficients derived from two QENS studies are in good agreement: 1.0 • 10.9 m2/s at 97 K for 1.2 molecule/uc, and 1.2 • 10.9 m2/s at 155 K for 1 molecule/uc. MD simulations performed on this system are also in favour of normal 1D diffusion [52]. However, it is found in these simulations [52] that ethane molecules cannot pass each other easily and exhibit a mobility in between single-file and normal 1D diffusion. Experimentally, the same group has found by PFG NMR that ethane molecules follow single-file diffusion [53] while QENS measurements suggest normal 1D diffusion, like for methane [29]. Again, the most probable explanation for this discrepancy is the different origin of the samples. It is known that this aluminophosphate is less stable than a zeolite, and that the crystallinity deteriorates with time and water moisture. The calcination procedure is a crucial step since defects or a partial collapse of the structure may happen during the temperature rise. For a slightly larger molecule, cyclopropane, a much larger concentration effect in AIPO4-5 was observed by QENS [29]. At low loading, a significant broadening was measured and it could be fitted with the normal 1D diffusion model. However, at higher concentration, an elastic response was obtained which could only be assigned to single-file diffusion. The crossover between the two regimes was attributed to the variation of the mean free distance between molecules with respect to the space scale of the QENS measurements. The mobility factor of cyclopropane in AIPO,-5 was too small to be determined. Single-file motion was more clearly observed for methane in ZSM-48 [29]. This zeolite has 1D channels of smaller dimension compared with AIPO,-5 : 5.3 x 5.6 A. QENS spectra obtained at two different concentrations at 155 K are shown in Figure 12. For a relatively small pore occupancy, 0 = 0.11, a large broadening is observed at small Q values, Figure 12(a). At this Q value, only 5% of the signal intensity comes from the rotation so that one can be confident that the broadening is due to diffusion. For this loading, the best refinement (lower weighted profile R factor) was obtained with the normal 1D diffusion model, the diffusion coefficient being 2.5 x 10.9 m2/s. For a higher loading, e = 0.48, the spectrum obtained at the same Q value is completely different, Figure 12(b). This large loading dependence of the diffusivity of methane,

132

which was not observed in AIPO4-5, indicates that single-file diffusion is observed for this molecule in ZSM-48. The evidence is provided by the quasi-elastic foot in Figure 12(b), which cannot be fitted adequately by an isotropic or normal 1D diffusion. The mobility factor, obtained by fitting spectra with Eq. (48), is 2 • 10 12 m2/s1/2. Again, the crossover between the two regimes is due to the time and space scale of the experiment. At low loading, the molecules can be considered as isolated, and they perform 1D diffusion unaffected by the other molecules. At higher loading, mutual encounters between adjacent diffusants become relevant, ensuring the necessary condition for single-file behaviour.

2.5 2 0 1

o~ c"

(a)

5

1 0 s

c

0 0

-.2

--7-. =

8

oO

4

r-

-.1

0.0

.1

-

.2

(b)

t--

O

~--

-.2

--

I

-.1

!

0.0

I

.1

.

.2

E(meV) Fig. 12. Comparison of experimental (m) and calculated (--) spectra obtained at 155 K for methane adsorbed in ZSM-48 9(a) 8 = 0.11, the solid line corresponds to normal 1D diffusion, (b) e = 0.48, the solid line corresponds to single-file diffusion (Q = 0.35 AI).

133

6.3 Simultaneous measurement of self- and transport diffusivities The diffusivities which are measured under the influence of concentration gradients, i.e. under non-equilibrium conditions, are usually called transport diffusivities, D t (other expressions can be found such as collective or chemical diffusivities). For comparison with the self- (or tracer) diffusivities, D s , the transport diffusivities are often represented in terms of the so-called corrected diffusivity, D 0, which is defined by the 'Darken' relation

Dt(c)= DO(C) d In where c denotes the adsorbate concentration in equilibrium with the pressure p.The term (dlnpldlnc) is the thermodynamic factor. Since adsorption isotherms in zeolites can generally be fitted with the Langmuir model, the thermodynamic factor is equal to or larger than 1. If one assumes that D o = D s , i.e. neglecting intermolecular interactions, the transport diffusivity should be larger than the self-diffusivity, which was not found in many experimental studies. As mentioned in section 2.2, collective motions can be probed if the scattering is coherent. The corrected diffusivity can be expressed in terms of time-dependent pair correlations [54], and the intensity at small Q values is related to the thermodynamic factor [55,56]. The transport diffusivity can be derived from the QENS experiments, because there natural density fluctuations at equilibrium. If a scatterer with both incoherent and coherent contributions is selected, it is then possible to measure D s and D t simultaneously. Such an experiment has been performed for different concentrations of D2 adsorbed at 100 K in NaX zeolite [8]. The self-diffusivities were derived from the broadenings measured at the same Ioadings for H2, after correcting from the mass difference between the two isotopes. The values of D s are plotted in Figure 13, the increase of the self-diffusivity which is observed for larger concentrations indicates an interaction with the sodium cations. The width of the coherent scattering showed a minimum corresponding to the maximum of the structure factor. This line narrowing is characteristic of quasi-elastic coherent scattering and it was first predicted by de Gennes, through sum rules [57]. The values of D t , obtained at the various Ioadings, are reported in Figure 13. It appears that at low 02 concentration, the self- and transport diffusivities are similar, but for higher Ioadings the transport diffusivity increases rapidly and exceeds the self-diffusivity. Such an increase of the transport diffusivity has been calculated from nonequilibrium MD simulations [54,58], and D2 in NaX represents the first system for which an experimental observation of this effect by means of a microscopic method could be performed. Only close to the saturation of the zeolite does the transport diffusivity start to decrease, indicating that collective motions become affected by the packing density. The corrected diffusivity, D 0, was obtained from D t and from the thermodynamic factor calculated by fitting a Langmuir isotherm to the adsorbed quantities. It is clear from Figure 13 that for D2 in NaX the corrected diffusivity is not constant, this assumption being often made in the interpretation of macroscopic measurements.

134

35 30-

t

25E 20O

Do

o 15a 10.

0

i

0

1

i

i

i

i

i

i

2

3

4

5

6

7

8

Molecules/supercage Fig. 13. Different diffusion coefficients obtained for D2 in NaX zeolite, as a function of loading (T = 100 K). D s, D o, and D t are, respectively, the self-, corrected, and transport diffusion coefficients.

6.4. Diffusivities of benzene and cyclohexane in a microporous silica With amorphous silica films deposited on a meso-/macroporous support, it is possible to vary the pore size of a membrane in a wider range than with zeolites. State-of-the-art silica membranes with pore sizes in the range 4 - 10 A can be prepared by sol-gel processes. Present understanding of gas separation by microporous SiO2 membranes is insufficient. It suffers from the lack of experimental data on microscopic parameters, such as diffusivities. For sensitivity reasons, mobility measurements with microscopic methods on a real supported membrane are not possible. One has to use non-supported films prepared in the same conditions as the supported membrane. After drying and calcination, it has been found that the pore structure of the unsupported and supported materials was similar [59-61]. The diffusivity of benzene and of cyclohexane in a microporous silica powder was studied by QENS and PFG NMR [60,61]. Good agreement was observed between the two techniques, despite the fact that the diffusion paths followed are of different magnitude : a few nm in QENS and several pm in PFG NMR. This means that there are no transport resistances with spacings above the nm scale. Such transport resistances would lead to a reduction of the NMR diffusivities, while the QENS values would remain essentially unaffected by them. Two different regimes of diffusion for benzene at 300 K are shown in Figure 14 [60]. Knudsen diffusion, which is appropriate in mesopores, is clearly different from diffusion in zeolites. For the zeolites, the values obtained at low loading in ZSM-5 and in NaX were considered (pore dimensions 5.5 and 7.5 A, respectively). It

135

appears that the diffusion of benzene in the silica powder, D = 101~ m2s1, approaches the diffusion regime in zeolites, due to the presence of small pores between larger cavities. This particular silica powder had therefore an effective (limiting) pore diameter of the order of 10 A. Further, an activation energy for diffusion of 11 kJ/mol was obtained, which shows that the mobility of benzene in this material is similar to the activated diffusion in zeolites.

10.5 10"6

-

1 0 -7 -

108 r

/

-

Knudsen

f

/

0-9

/

vE 10I~ E3 10-11_ 10-12-

membrane

zeolites

10-13-

10-14-

I

I

I Illll

1

10

100

Pore diameter (nm) Fig. 14. Diffusion coefficients of benzene, at 300 K, as a function of pore diameter. Very close diffusivities and activation energies were obtained for cyclohexane in the same silica powder [61]. This indicates that there are no specific interactions with the silica. Since the dimensions of the pores of the silica particles (the bottle-necks) are larger than the molecular diameters of benzene or cyclohexane, the diffusivities are not dramatically reduced in comparison with the neat liquids. Smaller diffusivities were measured at high Ioadings, due to the mutual hindrance of the molecules. 7. CONCLUSION

A detailed characterisation of molecular migration is essential to model the transport properties of microporous materials, for example in zeolite or silica membranes. Quasi-elastic neutron scattering is a powerful technique, even if the number of spectrometers is limited. Continuous progress is being made in experimental and theoretical aspects of QENS. The space and time scales of this technique are unique, and increased comparisons with the results obtained from molecular simulations can be foreseen.

136

REFERENCES

!. A. N. Fitch and H. Jobic, 'Molecular Sieves', H. G. Karge and J. Weitkamp (eds.), Springer-Verlag, Berlin Heidelberg, Vol.2 (1999) p. 31. 2. J. D. F. Ramsay (next contribution). 3. H. Jobic, Physica B (in press). 4. R. Hempelmann, J. Less-Common Met., 101 (1984) 69. .5. T Springer, Quasielastic Neutron Scattering for the Investigation of Diffusive Motions in Solids and Liquids, Springer Tracts in Modern Physics, SpringerVerlag, Berlin Heidelberg, 1972. 6. M. B~e, Quasielastic Neutron Scattering, Adam Hilger, Bristol, 1988. 7. J. C. Cook, D. Richter, O. Sch&rpf, M. J. Benham, D. K. Ross, R. Hempelmann, i. S. Anderson and S. K. Sinha, J. Phys. : Condens. Matter, 2 (1990) 79. 8. H. Jobic, J. K&rger and M. B~e, Phys. Rev. Lett., 82 (1999) 4260. 9. A. Einstein, Ann. Phys., 17 (1905) 349. 10. C. T. Chudley and R. J. Elliott, Proc. Phys. Soc. London, 77 (1961) 353. 1]. J. M. Rowe, K. Sk61d, H. E. Flotow and J. J. Rush, J. Phys. Chem. Solids, 32 (1971)41. 12. H. Conroy, J. Chem. Phys., 47 (1967) 5307. 13. H. H. Suzukawa, Jr. and M. Wolfsberg, J. Chem. Phys., 59 (1973) 3992. 14. H. Jobic, Phys. Chem. Chem. Phys., 1 (1999)525. 1.5. L. A. Clark, G. T. Ye, A. Gupta, L. L. Hall and R. Q. Snurr, J. Chem. Phys., 111 (1999) 1209. 16. P. A. Egelstaff, An Introduction to the Liquid State, Academic, London, 1967. ]7. K. S. Singwi and A. Sj61ander, Phys. Rev., 119 (1960) 863. 18. H. Jobic, H. Ernst, W. Heink, J. K&rger, A. Tuel and M. B~e, Microporous and Mesoporous Materials, 26 (1998) 67. ]9. P. L. Hall and D. K. Ross, Mol. Phys., 42 (1981) 673. 20. R. L. June, A. T. Bell and D. N. Theodorou, J. Phys. Chem., 94 (1990) 1508. 2.1. L. Gergidis, H. Jobic and D. N. Theodorou (in preparation). 22. M. Gaub, S. Fritzsche, R. Haberlandt and D. N. Theodorou, J. Phys. Chem. B, 103 (1999) 4721. 23. P. L. Hall and D. K. Ross, Mol. Phys., 36 (1978) 1549. 24. F. Volino and A. J. Dianoux, Mol. Phys., 41 (1980) 271. 2.5. A. J. Dianoux, M. Pin~ri and F. Volino, Mol. Phys., 46 (1982) 129. 26. A. J. Dianoux, F. Volino and H. Hervet, Mol. Phys., 30 (1975) 1181. 27. A. L. Hodkin and R. D. Keynes, J. Physiol. (London), 128 (1955) 61. 28. K. Hahn, J. K&rger and V. Kukla, Phys. Rev. Lett., 76 (1996) 2762. 29. H. Jobic, K. Hahn, J. K&rger, M. B~e, A. Tuel, M. Noack, I. Girnus and G. J. Kearley, J. Phys. Chem. B, 101 (1997) 5834. 30. H. Jobic, M. B~e and A. Renouprez, Surf. Sci., 140 (1984) 307. 3 ]. K. Hahn, H. Jobic and J. K&rger, Phys. Rev. E, 59 (1999) 6662. 32. K. Hahn and J. K&rger, J. Phys. A, 28 (1995) 3061. 33. M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, NewYork, 1968. 34. H. Jobic, J. Physique (in press). 35. H. Jobic, J. Mol. Catalysis (in press).

137

36. A. G. Stepanov, A. A. Shubin, M. V. Luzgin, H. Jobic and A. Tuel, J. Phys. Chem. B, 102 (1998) 10860. 37. R. C. Runnebaum and E. J. Maginn, J. Phys. Chem. B, 101 (1997) 6394. 38. E. J. Maginn, A. T. Bell and D. N. Theodorou, J. Phys. Chem., 100 (1996) 7155. 39. O. Talu, M. S. Sun and D. B. Shah, AIChE Journal, 44 (1998) 681. 40. M. Eic and D. M. Ruthven, Studies in Surf. Sci. Catal., 49 B (1989) 897. 41. E. J. Maginn (private communication). 42. B. Millot, A. M6thivier, H. Jobic, H. Moueddeb and M. B6e, J. Phys. Chem. B, 103 (1999) 1096. 43. H. Jobic and M. B6e, Z. Phys. Chem., 189 (1995) 179. 44. B. Smit and C. J. J. den Ouden, J. Phys. Chem., 92 (1988) 7169. 45. A. R. George, C. R. A. Catlow and J. M. Thomas, Microporous Materials, 11 (1997) 97. 46. C. Martin, J. P. Coulomb, Y. Grillet and R. Kahn, in 'Fundamentals of Adsorption', M. D. Le Van, Ed., Kluwer Academic Publishers, Boston, 1996, p. 587. 47. S. S. Nivarthi, A. V. Mc. Cormik and H. T. Davies, Chem. Phys. Lett., 229 (1994) 297. 48. J. P. Coulomb, C. Martin, Y. Grillet and N. Tosi-Pellenq, Studies in Surface Science and Catalysis, Elsevier, Amsterdam, Vol. 84 (1994), p.445. 49. C. Martin, N. Tosi-Pellenq, J. Patarin and J. P. Coulomb, Langmuir, 14 (1998) 1774. 50. V. Lachet, A. Boutin, R. J. Pellenq, D. Nicholson and A. Fuchs, J. Phys. Chem., 100 (1996) 9006. .51. T. Maris, T. J. H. Vlugt and B. Smit, J. Phys. Chem. B, 102 (1998) 7183. .52. D. Keffer, A. V. Mc. Cormik and H. T. Davies, Mol. Phys., 87 (1996) 367. .53. V. Gupta, S. S. Nivarthi, A. V. Mc. Cormik and H. T. Davies, Chem. Phys. Lett., 247 (1995) 596. .54. E. J. Maginn, A. T. Bell and D. N. Theodorou, J. Phys. Chem., 97 (1993) 4173. 5.5. H. Conrad, G. Bauer, G. Alefeld, T. Springer and W. Schmatz, Z. Physik, 266 (1974) 239. 56. S. K. Sinha and D. K. Ross, Physica B, 149 (1988) 51. 57. P. G. de Gennes, Physica, 25 (1959) 825. 58. D. Nicholson (private communication). 59. R. S. A. de Lange, K. Keiser and A. J. Burggraf, J. Porous Mat., 1 (1995) 139. 60. H. Jobic, M. B6e, J. K&rger, C. Balzer and A. Julbe, Adsorption, 1 (1995) 197. 61. H. Jobic, M. B6e, J. K&rger, R. S. Vartapetian, C. Balzer and A. Julbe, J. Membrane Sci., 108 (1995) 71.


RecentAdvancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) 2000 ElsevierScienceB.V.All rightsreserved.

139

Frequency Response Method for the Characterisation of Microporous Solids Lovat V. C. Rees and Lijuan Song Department of Chemistry, The University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, U. K. 1. INTRODUCTION The Frequency Response (FR) technique is a quasi-steady state relaxation technique in which a parameter influencing the equilibrium state of the system is perturbed periodically at a particular frequency. The response of a parameter characteristic of the state of the system depends upon the time scale of the dynamic processes affecting the parameter relative to the period of perturbation, the type of perturbation and physical characteristics of the system. The response of the system to the frequency spectrum thus allows the determination of the dynamic parameters. This technique was firstly used by Yasuda to measure diffusion coefficients in gas-zeolite systems [1-3] by applying a sinusoidal-wave perturbation to the equilibrium gas phase volume of the system [3,4]. Rees et al. have improved this technique by the use of"pure" square-wave perturbations, by reduction of the response time of the pressure transducer, by automation of the apparatus, and finally, by an expansion of the frequency-range [5-9]. The FR technique has proved to be a very effective and a very powerful method for determining inter- and intracrystalline diffusivities of sorbate molecules in zeolites. An outstanding advantage of the FR method is its ability to distinguish multi-kinetic processes in an FR spectrum, i.e. various 'independent' rate processes which occur simultaneously can be investigated by this technique [2]. More recently, this method has been extended to characterise the acid sites present in zeolite catalysts using ammonia as the probe molecule at catalytic temperatures and metal aggregates in bifunctional zeolite catalysts using oxygen and hydrogen as the probe molecules. Frequency techniques have been used to study many physical and chemical phenomena in flow and batch systems. In this chapter the discussion will be focused on the theory and experimental principle of a gaseous batch system subject to square wave volume perturbations and the application of the method to the characterisation of mieroporous solid materials. Two FR methods have been developed by Rees et al, (a) the flail and (b) the single-step method. The salient features of the FR methods can be summarised as follows. The sorbate/zeolite system is brought into sorption equilibrium and then a small _+1% square-wave volume modulation of this equilibrium situation is applied. The uptake/release of the sorbate following this disturbance takes place at a virtual constant composition of the sorbed phase and the diffusion coefficient controlling the uptake/release can be taken to be the differential diffusion coefficient that applies for the equilibrium concentration of sorbate in the zeolite. The equilibrium concentration can be varied, so the differential diffusion coefficient can be ascertained as a function of sorbate concentration. Both FR methods follow the rates of

140 sorption and desorption during each half square-wave disturbance respectively, so differences in these two rates can be detected. The single-step method can follow very rapid uptake/desorption rates in a millisecond time scale and many data points can be accumulated over quite short periods. Both FR methods can cope with fast diffusion processes and can determine, therefore, very large diffusion coefficients, especially if it is possible to select the size of zeolite crystals to be used in the measurements. Finally, as will be shown in the results section, the full FR method can separate two simultaneous diffusion processes if they are controlled by diffusion coefficients that differ by a factor of 3 or greater and the full FR method could also be used to study the simultaneous intra- and inter-diffusion processes which occur in pelleted zeolite sorbents and catalysts [10]. 2. EXPERIMENTAL 2.1. The FR Apparatus The principal features of the FR apparatus developed by Rees et al. are shown in Figure 1. An accurately known amount of sorbent sample is scattered in a plug of glass wool and outgassed at a pressure of ]

(59)

154

The parameter Bi is the Biot number, which is a measure of the resistance through the external fluid film surrounding the particle. Small Biot numbers are characteristic of a large film resistance, as shown in Figure 9. Model 3. Macropore diffusion and adsorption

This model describes the situation when micropore d ~ i o n rate is much faster than both macropore diffusion rate (y>> 1) and the rate of adsorption at the pore mouth of the micropore (B

(s)

(s)

0.5 1.22 1.31

2.0

0.19 1.00

28.0

0.18 33.1(32.0)* 1.03 0.31

1.34

0.23

2.6

1.1

0.15

3.24

1.0 1.10 1.10

1.7

0.22 1.76

15.9

0.35 34333.7) 0.75

1.13

0.34

2.4

0.55

0.15

6.55

2.0 0.91 1.06

2.0

0.16 2.30

12.2

0.50 32.0(29.7) 0.55 0.44 0.99

0.44

3.1

0.60

0.11

5.38

3.0 0.76 0.77

1.1

0.27 2.70

10.4

0.63 32.1(31.9) 0.39 0.37 0.76

0.49

2.1

0.24

0.14 12.53

4.0 0.64 0.63

1.1

0.25 2.77

10.1

0.74 32.7(33.1) 0.31

0.35 0.66

0.53

2.2

0.20

0.10 14.20

6.0 0.48 0.45

1.0

0.25 2.79

10.0

0.83 32.7(33.8) 0.18 0.24 0.42

0.57

2.3

0.16

0.11

14.87

0.5 0.45 0.59

5.0

0.08 0.25

110.6

0.12 48.9(42.9) 0.49 0.09

0.58

0.16

5.6

5.6

0.07

0.70

1.0 0.44 0.50

4.5

0.09 0.50

56.0

0.14 37.8(35.6) 0.41

0.09 0.50

0.18

5.1

2.8

0.08

1.37

2.0 0.42 0.46

3.5

0.09 0.65

43.1

0.21 33.6(32.1) 0.33 0.11 0.44

0.25

4.6

1.9

0.08

1.99

3.0 0.40 0.28

2.2

0.16 0.76

36.8

0.26 31.3(37.4) 0.20 0.09 0.29

0.31

3.1

1.5

0.12

2.55

4.0 0.38 0.28

2.3

0.16 0.85

32.9

0.33 31.3(36.5) 0.19 0.09 0.28

0.32

3.2

1.2

0.11

3.12

6.0 0.35 0.25

2.0

0.17 1.03

27.2

0.42 30.2(35.6) 0.15 0.10 0.25

0.40

3.1

0.86

0.11

3.85

8.0 0.32 0.22

2.1

0.16 1.13

24.8

0.48 29.2(35.1) 0.13 0.09 0.22

0.41

3.3

0.74

0.10

4.42

* The values in brackets

are calculated from FR K values, the others from K,,

0.38

161

that for the smaller sorbates in silicalite-1, i.e. ethane, propane and benzene, the phase angle shifts and the in- and out-of-phase characteristic curves for each sorbate could be fitted with the single diffusion process model whereas for n-butane, 2-butyne and p-xylene two diffusion coefficients were required to fit these characteristic curves. In the case of the smaller sorbate molecules the single diffusion coefficient represents the average diffusivity of the sorbate in both the straight and sinusoidal channels of silicalite-1. The two diffusion coefficients found for the larger sorbates have been ascribed to the independent diffusion fluxes in the respective channel networks. Recently the FR diffusion of propane [32] has been studied in silicalite-1 over a "wide" range of equilibrium pressures and temperatures. Figure 13 shows the experimental frequency response curves of this system, fitted by (a) the non-isothermal diffusion, (b) the two independent diffusion processes and (c) the single-diffusion models, respectively, using the kinetic parameters listed in Tables 1 and 2. Other parameters involved were the gas-phase volume, Ve=80cm3, density of the crystals, p~=1760kg/m3, volumetric heat capacity of the crystals, G=1400kJ rn3K"~. It can be seen that the bimodal behaviour of the FR spectra of a system with small sorbate molecules such as propane can be observed at high loadings, i.e. lower temperatures and higher pressures, while at lower loadings the bimodal form of the response curves disappeared to give only simple, single diffusion coefficient response curves. A close agreements between the theoretical models and the experimental data can be seen in all eases and K values obtained from the experimental data fits are in good agreement with those obtained from the isotherms (see Table 1). Such agreements clearly indicate the difficulty in interpreting the FR spectra correctly. One can, however, test the validity of theoretical models by analysing the physical parameters derived from the fits. Table 2 FR parameters calculated from the single-diffusion model

r)I '

_

i

|,l

i

P' / Yorr 1.0 2.0 3.0 4.0 4.0 6.0

"

,

348

,,m

.

363 iii

.

.

i

.

.

u

,

.

.

.

.

.

i

K ......

9

,

.

,

9

,

0.20 0.19 0.16 0.16 0.12 0.11 i

,,

i

i

.

,

Ill

Ill,

ii

i

i

,,,,,,

_

iiiii

I| I I

Dox

.

0.07 0.09 0.11 0.09 0.06 0.06

i

| i

i

ta / s

..=,.,

.

iii

.

,

.

iii

.

,.,.

.

,

,,

I

II

I

109 / m2s~ 6.0 4.7 3.6 4.3 7.0 7.0 ,,,

,,

--

Figure 14 shows that with decreasing pressure or increasing temperature an increase of the heat transfer coefficients is observed. An estimation of the heat transfer coefficient can be obtained from h=

k Ot [ A t On n=0

(75)

where h is heat transfer coefficient, k is the thermal conductivity of the sorbate, At the 3t temperature difference between gas and solid phases, and -~-I ,=0 is the temperature gradient

162

120

100

80 r !

60

40

20

0

2

4

6

Pressure

8

10

/ Torr

Fig. 14. Pressure dependence of the heat transfer coefficient calculated from non-isothermal diffusion model for propane diffusion in silicalite- 1 at 303K (11) and 323K (o). of the boundary layer between the external surface of crystals and the bulk gas phase. For FR measurements the heat transfer between the zeolite and its surroundings takes place primarily by conduction. Thermal conductivity of gases is generally proportional to the temperature, which results in an increase of the heat transfer coefficient with increasing temperature according to Equation (75). An increase of the thermal conductivity also increases the temperature gradient, so that the heat transfer coefficient increases still further. At a constant temperature, thermal conductivity of gases is generally independent of pressure. Increasing pressure reduces the mean free path of the molecules, 2, (see Table 3), causing a increase of the temperature gradient (molecular diffusion domains in the chamber). Meanwhile increasing pressure may also induce an increase in the temperature difference (see Table 3) between the Table 3 Estimated values of some parameters associated with the kinetic processes for propane in silicalite-1 system i

r (K) 303

323

P (Torr) 0.5 1.0 4.0 0.5 1.0 4.0

i

i

i

Aq (mmol ~;-1) 0.001 0.002 0.004 0.0004 0.0007 0.003 i i

i

Aq (mo!ecules uc ~) 0.0057 0.0114 0.0228 0.00228 0.00399 0.0171 i

i

i i

i

i

AQ (J) 0.001 0.0021 0.0042 0.00042 0.00073 0.0031 ii

i

1

AT (fK), 0.05 0.1 0.2 0.02 0.035 0.15

i

2xlO 6

, (In) 59 29 7.3 63 31 7.8 i

i

163

1 0 r"

08

06

04

02

00

i

0

~

i

il

2

,

I

4

......

i

I

i

6

I

8

l0

Pressure / Torr Fig. 15. Pressure dependence of the non-isothermalicity parameter, y, derived from non-isothermal diffusion model for propane diffusion in silicalite-1 at 303 K ( t ) and 323 K (O). sorbate and zeolite. The pressure dependence of the heat transfer coefficient is, thus, a balance between the temperature difference and the temperature gradient. The pressure and temperature dependence of the heat transfer coefficient, derived from the fits of the experimental data by the non-isothermal diffusion model as shown in Figure 14 is in agreement with the above physical concepts. The pressure and temperature dependence of the time constants for heat exchange calculated from fits by the non-isothermal diffusion model to the low frequency peak can be seen in Table 1. The values increase with rising pressure but for increasing temperature the opposite trend was observed. Such variations are reasonable since (i) the heat absorbed or released increases with increase in pressure or reduction in temperature (see Table 3), and (ii) as illustrated in Figure 14, the heat transfer coefficient in the system decreases with increasing pressure or decreasing temperature, so prolonging the time of the heat transfer. Moreover, the ? constant is a parameter describing the non-isothermalicity of the system. The larger the 7 values are, the more significant is the heat effect on mass transfer. Figure 15 and Table 1 show that the ? value, derived from the experimental data using the non-isothermal diffusion model, increases with decreasing temperature or with increasing pressure, which is in accordance with the fact that the higher the pressure or the lower the temperature, the more significant is the heat effect. Furthermore, Figure 16 and Table 1 present the values of the adsorption heat of propane obtained from the fits. These adsorption heats are in good agreement with the isosteric heat of adsorption of 40kJ/mol, which increases only slightly with increasing coverage as reported in the literature [43] as shown in Figure 16. Finally, since the channel intersections have a free diameter of ~0.54 nm it seems reasonable to expect that a flexible propane molecule of 0.652 nm length should be able to rotate at the channel intersections and it is, thus, unlikely that two independent diffusion

164 60 50 t ~ o

,.~

40

30

~ ~

20 100

i

2

9

i

4

Pressure

9

i

6

i

/

s

10

/ Torr

Fig. 16. Concentration dependence of the heat of adsorption for propane in silicalite-1 fitted by non-isothermal diffusion model with K constants estimated from fitting at 303 K (x) and 323 K (O), and K values from isotherms at 303 K (+) and 323 K (*). processes would be observed. One can conclude, therefore, that the FR bimodal behaviour of propane in silicalite-1 results from the effect of heat of adsorption on mass transfer of propane. Figure 13 c (1-4) also shows that for the FR spectra of propane in silicalite-1 at lower pressures and higher temperatures, at which the heat effect becomes insignificant, the bimodal response behaviour disappears and only single-peak response data can be observed. The agreement between the single-diffusion model and experimental spectra worsens with increasing pressure or lowering temperature, which reflects the small influence of the heat of adsorption on the diffusion and indicates that the heat effect can be virtually eliminated by choosing appropriate experimental conditions. Pure diffusion kinetic parameters of propane in silicalite-1 can, therefore, be measured by the frequency response technique. The intracrystalline self-diffusivities of propane in silicalite-1 have been measured by different methods, and a comparison of these diffusivities with those obtained in the present study can be made from Figure 17. In agreement with the PFG NMR results, the intracrystalline self-diffusion coefficient (corrected via Equation 74) has also been found to decrease with increasing concentration as explained previously [31,44]. The diffusivities are also in excellent agreement with those obtained from PFG NMR. Further study [34] shows that the FR bimodal behaviour can also be observed for the diffusion of methane and ethane in silicalite-1 at higher loadings, i.e. lower temperatures and higher pressures. The non-isothermal model was used to fit the bimodal data, while at lower loadings the single diifusion process was sufficient. Good agreement between experimental data and these theoretical models can be observed in all cases. The equilibrium constants K and the heats of adsorption obtained from the fits of the FR curves for methane, ethane and propane in silicalite-1 are listed in Tables 4 and 5, respectively. They are in excellent agreement with those reported in the literature or derived from the isotherms, indicating that the FR

165

I

bimodal behaviour of these systems results from the effect of heat of adsorption on the 10 8 L~48K mass transfer of the sorbate molecules. f]~.,"363K The two independent diffusion processes model was first proposed by Yasuda and Yamamoto [30] and was used to describe the r~ frequency response data they got for propane/Linde 5A zeolite system. They attributed the bimodal out-of-phase curves to * 0-9 ~ 1 two diffusion processes associated with tightly and loosely bound species within the zeolite framework. Shen and Rees [25,37-39] reported similar features for n-butane, 2-butyne and p-xylene in silicalite-1 as shown in Figures 18 and 19. 10-10 .... , . , ......... The FR bimodal behaviour was ascribed to 0 2 4 6 8 10 12 14 the two independent diffusion processes in the straight and the sinusoidal channels of nm / molecules UC"1 silicalite-1. The data suggested that the dit~sivities in the straight channels are about Fig. 17. Comparison of the concentration one order of magnitude faster than those in dependence of the self-diffiasion the sinusoidal channels. coefficients of propane in silicalite-1 These two independent diffusion processes determined by the FR technique (O, *, indicate the inability of the larger sorbate x), the single-step frequency response molecules to change directions at the channel method[31] at 333 K (A), and the intersections. Molecular dynamics simulations Pulsed-Field-Gradient NMR [44] (V) at have confirmed such a suggestion [47,48]. 333 K. Although this assumption has been questioned in the literature it seems to be quite reasonable to accept, for example, that p-xylene which is -~1.0 nm in length cannot rotate at a chalmel intersection which has a free diameter of 0.4-0.6 nm. The assumption was confirmed by a study [37] of the diffusion of p-xylene in silicalite-2 which has only intersecting straight channels. Although p-xylene molecules still cannot rotate at the intersections in silicalite-2 because of space limitations and thus two independent fluxes still exist. These fluxes are controlled by a single diffusion coefficient (see Figure 20) which has been found to be equal to the higher diffusion coefficient measured in silicalite-1. Thus this higher diffusion coefficient can reasonably be ascribed to the di~sion in the straight channels in silicalite-1 while the lower one represents the diffusion of p-xylene in the sinusoidal channels. NMR line shape analysis of deuterated p-xylene molecules have, also, shown that p-xylene molecules are sited in the channel intersections with their methyl groups in adjacent straight channel segments of silicalite-1 at loadings below 4 molecules/u.c.. These molecules show no rotational freedom about the axis perpendicular to the benzene ring [49,50]. The argument that the lower frequency peak of p-xylene results from the dissipation of the heat of adsorption [18] can be excluded because i) calorimetric measurements show that the heat of adsorption increases with increasing loading [51 ], while for the FR spectra, the second

166 Table 4 Comparison of K values derived from the FR data and those obtained from the isotherms, K,so, for methane to propane i

' Sorbate

"

273

303

Propane

I

i

303

323

I

_

III

9

1.0 1.5 2.0 4.0 1.0 2.0 3.0 5.0 1.0 3.0 5.0 1.0 2.0 4.0 1.0 2.0 4.0 I

.

0.39 0.58 0.76 1.45 0.42 0.80 1.19 1.96 0.13 0.33 0.54 1.15 2.09 3.53 0.41 0.80 1.52

,

I

I

r,=o

(m/u.c.)

fforr),

195

.

'Ethane

iii

. ,

Methane

i

T

.

.

.

i i

I

.

0.34 0.33 0.32 0.29 0.41 0.41 0.41 0.41 0.11 0.11 0.11 1.10 0.91 0.64 0.44 0.42 0.38

.

I

Ir

-

6.35" 0.32 0.27 0.25 0.42 0.40 0.38 0.35 0.13 0.12 0.12 1.10 1.06 0.63 0.50 0.46 0.28 .

I

Table 5 Heat of adsorption calculated from the FR method using the non-isothermal diffusion model, Q,~, compared with those reported in literature Sorbates Q~t(FR) Literature (,kJ/mp, (kJ/mol).. Methane 17.4-18.9 18.4145] Ethane 29.0-33.3 30.5146] . . 37-8[46] , Pr9pane ,,, 32:1-42-9, it

,,

.

ii

.

ii

.

i

. . . . .

.

peak tends to disappear with increasing loading [38,40]; ii) the rate of heat dissipation depends on the rate of adsorption or the diffusivities of sorbate molecules. In the case of p-xylene, the latter is much slower than that for the n-alkanes/silicalite-1 systems, implying that the time constant associated with the dissipation of the heat of p-xylene adsorption could be too high to be detected in the range of frequencies scanned. The FR technique has been applied to the diffusivities of cyclic hydrocarbons in MFI zeolites[36-40]. Figure 21 and 22 presents some typical FR spectra of these systems. The mass transfer of benzene, cyclohexane, ethylbenzene and cis-l,4-dimethycyclohexane molecules in MFI zeolites is mainly controlled by a simple, single micropore diffusion process. But at low temperature, the diffusivities of the latter two molecules in the sorbents may be influenced by the rotation of the methyl groups in these molecules. The transport properties of toluene and

167

(c,l) 0.2 0.3

; ' |

2)

0.1 0.2 0.0

'" -'

......

-'

. . . .

i r --I

.

.

. | ....

i

,

.

.

(b,1)

0

0.1

MI

0.3

0.0

9

9

.

-

i

. . t L

.

.

.

.

.

.

.

.

I

0.1

.

p .

-

0.I 0.0

.

(a,2)

0.2

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

(a,l)

!,"

9

o.sm

0.2

o+ . . . .

,

0.1

1

0.1 00' "0.01 . . . . . . 0:1 . . . . . . . . i

" "

Frequency / Hz Fig. 18. Out-of-phase characteristic function vs. Frequency curves (symbols) of n-butane (1) and 2-butyne (2) diffusion in silicalite-1 at 1.5Torr and 298 (a), 323 (b) and 348K (c) fitted by Equations (18) and (22) (lines). I and II indicate the contribution of the first and second terms, respectively [25]. p-xylene inside the pores of MFI are dependent on loading. At loadings < ca. 1 rn/u.c, and > ca. 4 m/u.c., only a single diffusion process can be detected by the FR measurements, while at intermediate loadings, a bimodal FR behaviour is found. The diffusivities of the four aromatics decrease in the order of p-xylene > toluene > benzene > ethylbenzene, and the diffusion coefficients of the two cyclic alkanes are at least one order of magnitude smaller than the values for benzene. Some diffusion coefficients measured using the FR method for these systems are listed in Table 6. At high loadings, experimental results show deviations of the sorption kinetics from Fickian behaviour for some sorbate molecules such as n-hexane in zeolites [33,52]. Attempts have been made to explain this non-Fickian behaviour based on the concept of heterogeneous channel topology which causes complex diffusion and immobilisation phenomena. Micke etal. [53] and Do et al. [54] have obtained uptake rates for such a system. A

168

o.~

(c) i

0,2

x .~ . ~

(~,1) P=l.0Torr ' ~ T=323K I N

(a,2) 12o P=-l.0Torr] " T=348K l 1-5

.

(,) --~ P=l.0Torr - ~

, ]1.2 P=l.0Torrt

:~\

a

q--'~uc t _ \

q-~-'~u~l~0

/

0,1

d

o.e ~

:

(b)

\

.

T~,~

'~ .........

.El

: ~ 7

1"$IX

,

O. . 0,I

I

IO

Fig. 19. FR spectra of p-xylene diffusion in 30mg silicalite-1 at 1.3 m/u.c, and temperatures of 375 (a), 395 (b) and 415K (c). Symbols denote experimental data and the lines are fitted by Equations (19)-(22). I and II represent the two different diffusion processes [39]. 1.4 1.2 1.0 "O

0.8 0.6

~

0.4 0.2 0.0 0.0i

-~, \

oo

~

~

: OAO

~ " ~

......... 1.00

10.(10

I-Iz Fig.20. FR spectra of p-xylene diffusion in 30rag of silicalite-2 at 1.3 m/u.c, and 395K. Symbols denote experimental data and lines are fitted by single diffusion model with parallelepiped shape. Frequency /

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

_ ...... -~7--~00

P=I 0Tort ~

P=l.0Torr 0.3

T~4,~

, T~4~,~

.~

_ . ~ =0.4m/u-d 0"2

(d,l) P'~.71Torr[~

(d,2) P=l.8Torr 0 2

~--~4~

T-,4~

I

N

"

0.2 i';

Frequency / Hz

K109

_....~ q=3.6m/u.c.

" I,. "

0.01

N

q=4.1m/u.c."::-: ...... ..~ q=3.3m/u.ctO.6

" ....

....

Frequency / Hz Fig. 21. FR spectra of benzene (a), toluene (b), ethylbenzene (c) and p-xylene (d) in silicalite-1. Lines are the fits of theoretical models and the symbols (F'I,O) present experimental in-phase and out-of-phase characteristic function data, respectively. diffusion-rearrangement model (see 3.1.4) has been proposed [18,21] to described the FR data for such a system. The FR measurements for n-butane, n-pentane and n-hexane in silicalite-1 at high loadings proved the assumption [33,34]. Some typical FR spectra of n-C4 to n-C6/silicalite-1 systems are presented in Figure 23. It is clear that the FR spectra for these systems tend to be more complicated than those with smaller hydrocarbons. At higher temperatures, a simple, single diffusion process applied,

169

Table 6 Diffusion coefficients of the cyclic hydrocarbons in silicalite-1 i

IIIII

I

II

I

T

Sorbate .

I

P

(K) .

.

.

I

II

q

(Torr) .

.

.

I

I

I ]

aDolX1013 bDoex1013

(m/u.e.)

2 .i

.

2 -i (ms,)

~ene

323 1.0 3.2 0.15 348 1.0 2.1 0.64 373 1.0 1.1 2.6 toluene . . . . . . . 323 1.0 4.1 0.35 348 1.0 3.3 3.0 0.54 373 1.0 2.0 9.6 1.3 395 1.0 0.95 7.7 415 1.0 0.5 13.4 ethylbenzene 323 0.6 4.0 0.051 348 1.0 3.6 0.28 373 1.17 2.9 1.0 395 1.0 1.3 4.2 415 1.0 0.81 7.0 p-xylene ' 323 0.41. . . . 5.0 7.1 . . . . . . . . . 348 1.85 5.0 8.2 373 1.9 3.9 160 15 c~clohexane ' 423' 0.5' ....0.06 cis- 1,4-dimeth~c!cryclohexane 398 0.5 0 it may be easily shown (by using the series expressions for [3 cot 13 or [3 tan 13) that eqs. 9 or 14 reduce to a simple exponential decay:

C:expE]

m

(19)

Co

This is a good approximation for L < 0.5. The plot of In (C/Co) vs t then becomes a straight line through the origin with slope directly proportional to the purge flow rate. To avoid the region of equilibrium control it is desirable to make ZLC diffusion measurements under conditions such that L is greater than about 5. Operation at even higher L values has the advantage that for L > 10 [31 _~ n so the diffusional time constant may be estimated directly from the slope of the long time asymptote. Under these conditions the slope of the plot of In (C/Co) vs t becomes essentially independent of purge flow rate but the intercept decreases, approaching inverse proportionality with the flow rate at high L (where I ~ 2/L). Variation of the purge flow rate thus provides a simple experimental test for kinetic or equilibrium control. It is sometimes useful also to make measurements at very low flow rates (low L) within the equilibrium controlled regime, from which reliable values of the equilibrium parameter (KVs) can be determined. These values can then be compared with the values

194

100.

= l

--a_.._ 2 !

)

0.5

0.1

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

o.6r,

o;i

O.~S o;2

o.~ .... o;, ......o.~s

o:4 .....o.~s

ols

Figure 3. Plot of (1- c/c,,)/4Dt/R 2 vs 4 D t / R ~ calculated from the short time solution for the ZLC response curve showing the proposed method of extractin~ the time constant according to Eq. 17. From Brandani and Ruthven ().

1.E§ .

1.E-Ol

-:

.

......

0.1

;

-

0.2

X

,

,

~

9

_

,

0.3

L =

1E.o~

;

-

0.4

o

20

X : 0.0

__ 1

Figure 4.

. E . 0 3

1.

.

.

.

.

.

.

_

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

_

_

.

Theoretical response curves for a non-linear ZLC system showing that with increasing isotherm non-linearity the intercept decreases but the slope remains essentially constant. The parameter ~. = qdqs = bco/(l+bco) measures the degree of isotherm non-linearity in accordance with the Langrnuir model. From Brandani (6).

195

derived from measurements at higher flow rates within the kinetic regime thus providing a check on the validity of the high flow rate measurements. 3.4 Fluid Phase Hold-Up (2' s) In the simple model discussed above the hold-up of sorbate in the fluid phase within the cell is neglected. A more accurate analysis taking account of fluid phase holdup leads to the following expressions (in place of Eqs. 4 and 5):

c

Co

exp(-/32DtSR2 .

= 2L~.,~176 n=l

[tiff + (L - 1 - y'fl~)2 + L - 1 + yfl2 ]

ft. cotfl. + L - l - y f l ~

=0

(20)

(21)

where the parameter y = Vf/3 KVs characterizes the ratio of external to internal hold-up. Clearly for Y --4 0 Eqns. 20 and 21 revert to Eqs. 9 and 10. Direct comparison of the response curves shows that for 7 < 0.1 the effect of the extra particle hold-up is negligible. This conditions is almost always fulfilled for vapor phase ZLC measurements but it is generally not fulfilled for liquid systems for which a proper allowance for extra particle hold-up is essential. 3.5 Isotherm Non-Linearity The effects of a non-linear equilibrium relationship on the ZLC response have been investigated in detail by Brandani (6). From the practical point of view the important conclusion from this analysis is that non-linearity affects the intercept of the In (C/Co) vs t plot but has very little effect on the slope (see fig. 4). The asymptote of the response curve is well approximated by the following expression:

ln (c / Co) = lnO - 2,)- 2,

pZyr + -~r~-(LTr-1

2L )

+ In( fl( + L(L - 1) - f12 Do t / R 2

(22)

For strongly adsorbed species it is not always easy to make measurements at low enough concentrations to ensure accurate isotherm linearity. Eq. 22 thus provides a practically useful way to extract the diffusional time constant from the response curves for such systems, even when the concentration level is outside the Henry's Law range.

196 4. PRACTICAL REALIZATION A schematic of the experimental system is shown in figure 5. In order to minimize the intrusion of thermal effects and extra-particle resistance to mass transfer the adsorbent quantity should be as small as possible consistent with adequate sensitivity of the detector response. The zero length column is conveniently formed by sandwiching a few adsorbent particles (typically < 1 mg) between two sinter discs held within a Swagelok fitting. Under conditions of kinetic control (L > 10) the limiting slope of the ZLC response curve should be invariant with the sample quantity (which affects only L and therefore the intercept). Varying the particle size has a direct effect on the time constant and thus provides direct experimental confirmation of kinetic control. Since extracrystalline resistances to both heat and mass transfer depend on the nature of the purge gas whereas intracrystalline diffusional resistance is not affected by the nature of the purge gas, replicate experiments with, for example He and Ar (or N2) as carrier provide a convenient experimental test for the intrusion of extracrystalline resistance. This test is most useful for ZLC micropore diffusion measurements. Since the macropore diffusivity may vary with the nature of the carrier (which affects the gas phase diffusivity) invariance of the response to changes in carrier is not necessarily to be expected for macro diffusion controlled systems.

Figure 5.

Schematic diagram of experimental set-up for ZLC measurements. For NZLC measurements the on-line mass spectrometer may be replaced by a standard chromatographic detector (TCD or FID).

197 (b) 0.1

't

. . . .

O.Ol~

7

"O

d

%w m

0111111 o

".m m

0

Io

II II ii

~o

9 9 9 9 N~, 3.2 m8

He3.2m g

9

61111

OO . OO /1 o.s

i

1~s

~ ImO) ~

,~mple

s

&

3.S ,,

ll~ 9 N3, He - 1.3 mg &j 13 N~ He-0.6mg

mt

o

Im

~

Figure 6. (a) Experimental ZLC response curves, and (b) Apparent diffusional time constants for benzene in 50 9m NaX crystals showing the effect of changing sample quantity and the nature of the purge gas. From Brandani et al. (7).

,

C/Co

^. c^..,E.,

I0"

10-2

0

500 TIME

($ECS)

1000

1500

Figure 7. Experimental ZLC response curves for the o-xylene in large NaX zeolite crystals showing the effect of purge flow rate, crystal size and the effect of changing the nature of the purge gas. From Ruthven and Eic (s).

198 Representative ZLC response curves showing the effects of changes in particle size, purge gas flow rate, the nature of the purge gas and the adsorbent quantity are shown in figures 6 and 7 (7). It is clear that for benzene in large crystals of NaX the response is impacted by extracrystalline resistances when the sample quantity is greater than about 1.5 mg, leading to a lower apparent time constant and a difference in the response curves for He and N2 carriers. However, with a sufficiently small sample the response becomes independent of zeolite quantity and the response curves for He and N2 converge, indicating that the basic assumptions of the model are then valid. The effects of varying the crystal size and purge flow rate are shown (for o-xylene - NaX) in figure 7. At 30 cm3/min purge rate with 50 ~tm crystals the response is close to the equilibrium controlled regime (Eq. 19) but at higher flow rates the curves have the characteristic form for kinetic control; there is little difference between the response with He and Ar and a dramatic difference in the responses for 50~tm and 100 ~tm crystals. The good agreement between the ZLC diffusivities and the values determined from gravimetric measurements with large NaX crystals is shown in figure 8.

10"s

10"6L:'-

~ c~

~

~

~'~.

~ ' ~ NMR-Benzene(1)

~

~

...

NMR-O-Xylene(11

10"

c~ [

\o Benzene 9Uptake 9Tracer

104 I 10"9 1.9

eo~ O- Xylene 2:1

213

215

217

103/T (K'*)

t .2.9

, 3.1

Figure 8. Arrhenius plot showing comparison of ZLC diffusivities with Do values determined from gravimetric uptake rate measurements with large (100 ~tm and 250 ~tm) crystals of NaX. From Ruthven and Eic (8).

199

4.1 Heat Effects

A ZLC experiment is carried out in the presence of a relatively high flow of carrier gas and this should aid heat transfer and ensure near isothermal operation. However heats of sorption can be relatively large so, in certain situations, there can be a perceptible thermal effect. This possibility has been examined in detail by Brandani et al. ~9) who showed that for a non-isothermal ZLC a rich variety of desorption curves is possible. A simple criterion for negligible thermal effects was developed in terms of the dimensionless parameter characterizing the heat and mass transfer process. This criterion may be represented approximately by the inequality:

( ~ I ) 2Ryc~ 3KoD - ~ ha R2

(23)

As a conservative approximation we may take h _~ Lg/R corresponding to Nu = 2.0) and for spherical particles a = 3/R reducing eq. 23 to:

KoD
0.8 ~//

Source

~

09

0.4 2

3

H/A

4

5

Figure 6. Nitrogen/Oxygen selectivity and separation factor in graphitic slit pores at 298K from DCV GCMD simulation. The squares are separation factors (permeability ratios). Up triangles are the equilibrium selectivity (SN/o) in the source region, down triangles are SN/o in the sink region. since they can always be related to the phenomenological coefficients, L,m, (cf equation (52) and (53)) and thus to equilibrium correlation functions, but this is a very arduous task [27]. Some idea of the magnitudes of D~l and D22 can be obtained if separate pure component DCV GCMD simulations are performed in which the pressure drops involved are identical to the partial pressure drop of the same component in the mixture. Working backwards, one may then obtain an estimate of D12 and D2~ in the mixture [97]. Dynamic separation factors, defined as the ratio of permeabilities, should be compared with the equilibrium selectivities if conclusions are to be drawn regarding the separation mechanism. The equilibrium selectivities are available from the same DCV GCMD simulation used to calculate the mass fluxes. The GCMC data from the source and sink control volumes gives the mole fractions of the two components in the adsorbed phase. A typical mixture simulation will be conducted at a given pressure drop, temperature and composition. Since the input parameters are the activities of the two species in the control volumes, it is necessary to have a relation between pressure, composition and activity for the bulk gas mixture. If such a relation is unavailable for the particular choice of model, the relevant data can be found from a series of separate bulk isothermal-isobaric Monte Carlo simulations at the target pressure, temperature and composition and the activities calculated by the Widom insertion method [98]. Mass flow may be studied as a function of composition, temperature and pore width. If the pore widths or the pressure gradients are large, the viscous flow contribution may become significant. In this case one would have to resort to the viscous subtraction method [56] which so far has only been applied to pure components. It is also possible to simulate mass flow in the absence of a pressure gradient [28]. If more than two components are present in the gas mixture the expressions for the component fluxes become increasingly cumbersome (see section 2.3). However, the viscous flow contribution can be eliminated since, with more than two components, it is possible to set up component flows in the absence of a pressure gradient. Figure 6 shows the behaviour of the dynamic separation factor (defined as the ratio of nitrogen and oxygen permeabilities) and equilibrium separation as a function of pore width for the

291 nitrogen/oxygen mixtures in graphitic slit pores at 298K [95]. In these simulations the mixture had an external gas phase composition of 80 mole percent nitrogen at ambient temperature. The source and sink pressures were fixed at 15 and 10 bar respectively, and selectivity was calculated at a series of pore widths using DCV GCMD simulation. The dynamic separation factor and equilibrium selectivities both oscillate with pore width. The larger pores favour nitrogen over oxygen, but selectivity is reversed in the smallest pore (H=2A) where the smaller size of the oxygen molecules relative to nitrogen becomes advantageous. The selectivity of nitrogen to oxygen is lower in the source control volume than in the sink control volume, since the higher pressure in the source volume favours oxygen packing. It is interesting to note that the equilibrium selectivity is a good approximation to the dynamic separation factor in general agreement with results for carbon dioxide/methane mixtures [96]. On the other hand selectivity for oxygen between 3 and 30 has been reported for industrial separations with carbon molecular sieves [99]. On the basis of a more elaborate pore model than those discussed here, it has been argued [36,100] that pore length may be an important variable in real materials. As mentioned in section 4.2 this is likely to be the case where a single file type of hindrance plays a part in controlling the transport process. 5.0 CONCLUSIONS

The frictional coefficient approach to transport is a valuable framework in which to construct transport equations. The statistical mechanical theories pioneered by Kirkwood and co-workers (see for example [19]), although complete, lead to complicated expressions for the phenomenological coefficients which are not usable for practical purposes. Furthermore, although the theory is formally comprehensive enough to account for transport of fluids in confined spaces, it does not do so explicitly. The more heuristic development outlined here [16, 18] is directly related to the Stefan-Maxwell equations, and is readily transformed into an irreversible thermodynamic formalism. The price that is paid is that no molecular interpretation of the phenomenological coefficients in relation to friction coefficients emerges from the theory. Nevertheless, the content of the Fickian diffusion coefficients in terms of self diffusion, viscosity coefficients etc is revealed, and all the phenomenological coefficients can, in principle, be separately evaluated from computer simulation. Thus simulation provides the means to understand the molecular mechanisms that operate in mixture transport through confined spaces. In the specific context of mixture separations, the ultimate goal is the relative permeability of the fluid species. It is clear that predictive expressions, relating this property to temperature, density and pore size, not to mention the complications of network structure discussed in Chapter 2.3, are difficult to obtain without considerable approximation. Adsorbates differ from bulk fluids because they are non-uniform, and because their mean density can vary very widely, depending on the pressure of the external gas phase and the temperature of adsorption. Thus for example, processes carried out in microporous materials at ambient temperatures, under pressures of a few bar, may relate to states of matter that have no counterpart in uniform bulk fluids. The phenomenological coefficients obtained, for example from experiment or from most simulation studies, are therefore averages with respect to a mean density. With the rapid advance of computing power, it has become relatively simple to obtain self diffusion coefficients, furthermore, collective diffusion coefficients and viscosity are now within the range of relatively modest resources. From the standpoint of membrane separation, the most interesting development of recent years is the extension of NEMD methods to the DCV-GCMD technique which attempts to mimic the membrane process directly. Especially when supplemented by EMD and the viscous subtraction method (VSM), this approach seems particularly promising. There are several problems that are outstanding at the present time, which we may mention

292 briefly: It is clear from the simulations already made that the modelling of the dynamic interaction of the fluid molecules with the wall can be crucially important. In simple systems, the specular, diffuse and cosine law models all have weaknesses, even though each respects detailed balancing [40]. More realistic models must include allowance for incomplete momentum accommodation with a solid in which phonons can develop, and this implies at least an order of magnitude increase in the size of the calculations. It is relatively easy to deduce that the contribution from viscous flow increases as the density of the adsorbate is increased, and/or the pore size increases. However, there is presently no detailed understanding of how the crossover from diffusion dominated, to viscous dominated, flow relates to variables such as temperature, density and pore size, even for single component fluids. Moreover, it is clear that when pore width varies from point to point in a real material, there will be an exchange of flux between different modes of flow. The viscous flow of mixtures raises further questions; generally viscous flow is considered to be non-separative, but it is a physically reasonable to surmise that this may not be the case in specific systems, as discussed in section 2.2. In the context of adsorbates, intriguing possibilities may arise since the adsorbate can be severely nonuniform, and may simultaneously contain both dense and rarefied regions, and since the viscous behaviour of gases and liquids is quite different. A third area that has received little attention is the influence of temperature gradients. The adsorption process is exotheimic, and temperature gradients may be set up in real processes, even though they are apparently run under constant temperature conditions. Thus thermally driven fluxes could exist in membrane pores, and these can couple to isothermal diffusion fluxes (since the phenomenological coefficients are of the same tensorial class [21 ]). More complex phenomena relating to viscous flow can also occur - not least because the viscosity coefficients are temperature dependent. Computer simulation seems to offer the best chance to unravel the complexity of transport processes in confined spaces. With improved understanding, it will become clearer how to create more effective separation processes by exploiting this complexity. We wish to thank the CEC for support under grant BRPR-CT98-0722. REFERENCES 1. J. Karger and D. M. Ruthven, Diffusion in Zeolites and Other Porous Materials, Wiley Interscience, New York, 1992 2. F. Rodriguez-Reinoso et al (Eds) Studies in Surface Science and Catalysis, Characterisation of Porous Solids II, 87(1991), J. Rouquerol et al.(eds) Studies in Surface Science and Catalysis, Characterisation of Porous Solids III, 87(1994), B. McEnaney et al.(eds), Characterisation of Porous Solids IV, Royal Society of Chemistry (1997), F. Rouquerol, F. Rouquerol and K. S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, London, 1999. 3.S. Yashonath and P. Santikary, J. Chem. Phys., 100 (1994) 4013. 4.R.M. Barrer, J. Chem. Soc. Faraday Trans., 86(1990)1123, 88 (1992) 1463, Catalysis and Adsorption by Zeolites, G. Ohlman et al (eds), Elsevier, Amsterdam, 1990. 5.R.F. Cracknell, D. Nicholson and N. Quirke, Molecular Simulation, 13 (1994) 161. 6.H. Jobic, M. Bee, J. Caro, M. Bulow and J. Karger, J. Chem. Soc. Faraday Trans., 85 (1989) 4201., H. Jobic, M. Bee and J. Caro, International Zeolite Conf, 9th, (1992) 121., H. Jobic, M. Bee, J. Karger, R. Sh. Vartapetyan, C. Balzer and A. Julbe, J. Membrane Sci., 108 (1995) 71.;

293 H. Jobic, M. Bee, J. Karger, C. Balzer and A. Julbe, Adsorption, 1 (1995) 197.; H. Jobic, M. Bee and G. J. Kearley, Zeolites, 12 (1992) 146. 7.J.M.D. MacElroy, J. Chem. Phys., 101 (1994) 5274; J. M. D. MacElroy and K. Raghavan, J. Chem. Soc. Faraday Trans., 87 (1991) 1971. 8. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases, Cambridge University Press, London, 1970. 9. E. A. Mason, A. P. Malinauskas and R. B. Evans, III, J. Chem. Phys., 46(1967)3199. 10. E. H. Kennard, Kinetic Theory of Gases, McGraw-Hill, New York, 1938. 11. M. Knudsen, Ann. Phys. 28(1909)75. 12.R.M. Barrer in The Solid Gas Interface, Chapter 19, vol. 2, E. A. Flood (ed), Marcel Dekker, (1967). 13. S. T. Hwang and K. Kammermeyer, Can. J. Chem. Eng., 44 (1966) 82; D. Nicholson, J. Petrou, and J. Petropoulos, J. Coll. and Interf. Sci., 71 (1979) 570; D. Nicholson and J. Petropoulos, J. Mem. Sci., 71 (1979) 570; 14.R.T. Yang, Gas separation by Adsorption Processes, Imperial College Press, London, 1997. 15. E. N. Lightfoot, Transport Phenomena in Living Systems, Wiley, New York (1974). 16. E. A. Mason and L. A. Viehland, J. Chem. Phys., 68 (1978) 3562. 17. E. A. Mason and H. K. Lonsdale, J. Membrane Sci., 51 (1990) 1. 18. R. Krishna and J. A. Wesselingh, Chem. Eng. Sci., 52 (1997) 861. 19. R. J. Bearman and J. G. Kirkwood, J. Chem. Phys., 28 (1958) 136. 20. E. A. Mason and L. F. del Castillo, J. Membrane Sci., 23 (1985) 199. 21. H. J. M. Hanley, Transport Phenomena in Fluids, Marcel Dekker, New York, 1969. 22. D. Nicholson, J. Mem. Sci. 129 (1997) 209. 23. P. Hansen and I. R. McDonald, Theory of Simple Liquids, Academic Press, 1986. 24. K. P. Travis, B. D. Todd and D. J. Evans, Phys Rev. E., 55 No 4 (1997) 4288. 25. D. Nicholson and N. G. Parsonage, Molecular Simulation and the Theory of Physical Adsorption, Academic Press, London, 1982. 26. Bitsanis, M. Tirrell and H. T. Davis, J. Chem. Phys., 87 (1987) 1733. 27. J. M. D. MacElroy and S.-H. Suh, Mol. Phys., 60 (1987) 475; J.M.D. MacElroy and S.H. Suh, Molecular Simulation, 2 (1989) 313. 28. J. M. D. MacElroy and M. J. Boyle, Chem. Eng. J., 74 (1999) 85. 29. F. K. Katsaros, T. A. Steriotis, A. K. Stubos, A. Mitropoulos, N. K. Kanellopoulos and S. R. Tennison, Microporous Materials, 8 (1997) 171; J. E. Koresh and A. Softer, J. Chem. Soc. Faraday Trans., 82 (1986) 2057; T. A. Steriotis, F. K. Katsaros, A. Mitropoulos, A. K. Stubos, P. Galiatsatou, N. Zouridakis and N. K. Kanellopoulos, Rev. of Sci. Instruments, (1997); S. Butler, thesis, Imperial College, London, (1987). 30. E. Akhmatskaya, B. D. Todd, P. J. Daivis, D. J. Evans, K. E. Gubbins and L. A. Pozhar, J. Chem. Phys., 106 (1997) 4684; G. Mo and F. Rosenberger, Phys. Rev. A, 42 (1990) 4688; U. Heinbuch and J. Fischer, Phys. Rev. A, 40 (1989) 1144; M. Sun and C. Ebner, Phys. Rev. A, 46 (1992) 4813; I. Bitsanis, S. A. Somers, H. T. Davis and M. Tirrell, J. Chem. Phys., 93 (1990) 3427; M. Sun and C. Ebner, Phys. Rev. Lett., 69 (1992) 3491; L. Hannon, G. C. Lie and E. Clementi, Phys. Letts A, 119 (1986) 174. 31. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Oxford University Press, Oxford, 1987. 32. D. Frenkel and B. Smit, Understanding Molecular Simulation, Academic Press, San Diego, 1996. 33. J. G. Powles, S. Murad and P. V. Ravi, Chem. Phys. Lett., 188 (1992) 21.

294 34. J. Tersoff, Phys. Rev. B, 37 (1988) 6991; Phys. Rev. Lett, 61 (1988) 2879; D. Brenner, Phys. Rev. B, 42 (1990) 9458. 35. W. A. Steele, The interaction of gases with solid surfaces, Pergamon, Oxford, 1974. 36. J. M. D. MaeElroy, N. A. Seaton and S. P. Friedman, Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid surfaces; Eds. W. Rudzinski and W. Steele, Elsevier (1998). 37. J. M. D. MaeElroy, S. P. Friedman and N. A. Seaton, Chem. Eng. Sci, 54, 1015-1027 (1999). 38. R. F. Craeknell, D. Nieholson and N. Quirke, Phys. Rev. Lett, 74 (1995), 2463. 39. S-H. Suh and J. M. D. MaeElroy, Mol. Phys. 58, 445 (1986); 60 (1987) 475. 40. J. P. Valleau, D. J. Diestler, J. H. Cushman, M. Sehoen, A. W. Hertzner and M. E. Riley, J. Chem. Phys., 95 (1991) 6194. 41. H. Jonsson and J. H. Weare, Faraday Discussions Chem. Soe., 80 (1985); V. Chirita, B. A. Pailthrope and R. E. Collins, J. Phys D: Appl. Phys., 26 (1993) 133; B. Jackson, J. Chem. Phys., 108 (1998) 1131. 42. P. J. Daivis and D. J. Evans, Chem. Phys., 198 (1995) 25; K. P. Travis, P. J. Daivis and D. J. Evans, J. Chem. Phys., 103 (1995) 1109. 43. E. J. Maginn, A. T. Bell and D. N. Theodorou, J. Phys. Chem., 97 (1993) 4173. 44. D. A. MaeQuarrie, Statistial Mechanics, Harper Collins, New York (1976); A. A. Chialvo and P. G. Debenedetti, Phys. Rev. A, 43 (1991) 4289. 45. M. P. Allen and A. J. Masters, Mol. Phys., 79, (1993) 435; M. P. Allen, D. Brown and A. J. Masters, Phys. Rev. E, 49 (1994) 2488; M. P. Allen Phys. Rev. E, 50 (1994) 3277., 46. W. M. Visseher, Phys. Rev., Ser A, 10 (1974) 246; J. W. Dut~y and M. J. Lindenfeld, J. Stat. Phys., 20 (1979), 259; E. G. D. Cohen, Physiea, 118A (1983) 17; G. P. Morriss and D. J. Evans, Phys. Rev., Ser. A, 35 (1987) 792; D. J. Evans and G. P. Morriss, Phys. Rev. Set. A, 38(1988)4142. 47. J. Petravie and D. J. Evans, Phys. Rev. Lett., 78 (1997), 1199; Phys. Rev. E., 56 (1997), 1207. 48. B. D. Todd, Phys. Rev. E., 56 (1997) 6723. 49. D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids, Academic Press, San Diego, 1990. 50.C. Cielinski, MS thesis, University of Maine, (1985); R. F. Cracknell, D. Nicholson and N. Quirke, Phys Rev Lett 74 (1995) 4362. 51. G. S. Heffelfinger and D. M. Ford, Mol. Phys., 94 (1998), 659. 52. D. Ford and G. S. Heffelfinger, Mol. Phys., 94 (1998) 673. 53.N. Quirke, private communication. 54. Ford, D. M. and Glandt, E. D. J. Phys. Chem. 99 (1995) 11543; J. Membrane Sci., 107 (1995) 47; S.-H. Suh, D. Nicholson and J. M. D. MacElroy, Bull. Korean Chem. Soc., 19 (1998) 1145. 55. R. M. Barrer, J. Chem. Soc. Faraday Trans., 86 (1990) 1123; R. M. Barrer, J. Chem. Soc. Faraday Trans., 88 (1992) 1463. 56. K. P. Travis and K. E. Gubbins, J. Chem. Phys., In Press (1999). 57. B. D. Todd, P. J. Daivis and D. J. Evans, Phys. Rev. E, 51 (1995) 4362. 58. B. D. Todd and D. J. Evans, J. Chem. Phys., 103 (1995) 9804. 59. G. Ciccotti, G. Jaccuci and I. R. MacDonald, J. Stat. Phys., 21(1979) 1; D. McGowan, Phys. Rev. A, 36 (1987) 1367; J. J. Erpenbeck, Phys. Rev. A, 39 (1989) 4718; R. Vogelsang and C. Hoheisel, J. Chem. Phys., 89 (1988) 1588; R. Vogelsang, C. Hoheisel, G. V. Paolini and

295 G. Ciccotti, Phys. Rev. A, 36 (1987) 3964; P. J. Gardner, D. M. Heyes and S. R. Preston, Mol. Phys., 73 (1991) 141. 60. D. M. McGowan and D. J. Evans, Phys. Rev. A, 34 (1986) 2133; D. J. Evans and D. McGowan, lbid, 36 (1987) 948; D. J. Evans and P. T. Cummings, Mol. Phys., 72 (1991) 893. 61. S. Sarman and D. J. Evans, Phys. Rev. A, 45 (1992) 2370; Phys. Rev. A, 46 (1992) 1960. 62. B. Hafskjold and T. Ikeshoji, Molecular Simulation, 16 (1996) 139. 63. D. J. Evans and G. P. Morriss, Phys. Rev., Ser. A, 30 (1984) 1528. 64. J. J. Erpenbeek, Phys. Rev. Lett., 52 (1984), 1333; R. A. Gray, et al., Proe. R. Soc. Lond. A, 448 (1995), 113; D. M. Heyes, Mol. Phys., 57 (1986), 1265. 65. D. J. Evans and G. P. Morriss, Phys. Rev. Lett., 56 (1986) 2172; D. J. Evans, S. T. Cui, H. J. Hanley and G. C. Straty, Phys. Rev. A, 46 (1992) 6731; K. P. Travis, P. J. Daivis and D. J. Evans, J. Chem. Phys., 103 (1995) 10638; K. P. Travis and D. J. Evans, Mol. Sim., 17 (1996) 157. 66. P. J. Daivis, K. P. Travis and B. D. Todd, J. Chem. Phys., 104 (1996) 9651. 67. B. D. Todd, D. J. Evans and P. J. Daivis, Phys. Rev. E, 52 (1995) 1627. 68. T. Demi and D. Nicholson, Molecular Simulation, 5 (1991) 363. 69. J. J. Magda, M. Tirrell and H. T. Davis, J. Chem. Phys., 83 (1985) 1888. ; J. J. Magda, M. Tirrell and H. T. Davis, J. Chem. Phys., 88 (1988) I207. 70. M. Schoen, J. H. Cushman, D. J. Diestler and C. L. Rhykerd, J. Chem. Phys., 88 (1988) 1394; 71. R. F. Crackndl, D. Nicholson and K. E. Gubbins, J. Chem. Soc. Faraday Trans., 91 (1995) 1337. 72. D. Nicholson, R. W. Adams, R. F. Cracknell, and G. K. Papadopoulos, Charaeterisation of Porous Solids IV, Royal Society of Chemistry, Eds. B. MacEnaney, et al. (1997) 53. 73. D. Nicholson, Carbon, 36 (1998) 1511. 74.T. Demi and D. Nicholson, Molecular Simulation, 7 (1991) 121; T. Demi and D. Nicholson, Langmuir, 7 (1991) 2342; T. Demi and D. Nieholson, J. Chem. Soc. Faraday Trans., 87 (1991) 3791; T. Demi, J. Chem. Phys., 95 (1991) 9242. 75 R. L. June, A. T. Bell and D. N. Theodorou, J. Phys. Chem., 94 (1990) 1508 76. R. F. Cracknell and K. E. Gubbins, Langmuir, 9 (1993) 824. 77. G. K. Papadopoulos, D. Nicholson, and S-H Suh, Mol. Simulation, 22 (1999) 237. 78. D. Nieholson, Supramoleeular Science, 5 (1998) 275. 79. T. K. Vanderlick and H. T. Davis, J. Chem. Phys., 87 (1987) 1791. 80. S. A. Somers and H. T. Davis, J. Chem. Phys., 96 (1992) 5389. 81 D. Keffer, A. V. McCormick and H. T. Davis, Mol. Phys., 87 (1996) 367. 82. K. Hahn and J. K~ger, J. Phys. Chem., 100 (1996) 316; K. Hahn and J. K~,rger, J. phys A. Math Gen., 28 (1995) 3061; J. K~.rger, M. Petzold, H. Pfeifer, S. Ernst and J. Weitkamp, J. Catalysis, 130 (1992) 283. 83. J. M. D. MaeElroy and S-H. Suh, J. Chem. Phys. 106 (1997)8595. 84. K. Hahn and J. K~rger J. Phys. Chem. B, 102 (1998) 5766. 85. M. Sehoen, J. H. Cushman and D. J. Diestler, Mol. Phys., 81 (1994) 475. 86. K. P. Travis, B. D. Todd and D. J. Evans, Phys. Rev. E, 55 (1997) 4288. 87. A. Baranyai, D. J. Evans and P. J. Daivis, Phys. Rev. A, 46 (1992) 7593. 88. B. D. Todd and D. J. Evans, Phys. Rev. E, 55 (1997) 2800. 89. G. Ayton, O. Jepps and D. J. Evans, Mol. Phys., 96 (1999) 915. 90. H. H. Rugh, Phys. Rev. Lett., 78 (1997) 772.

296 91. H. Grad, Commun. Pure App. Math., 5 (1952) 455; R. F. Snider and K. S. Lewchuk, J. Chem. Phys., 46 (1967) 3163; D. J. Evans and W. B. Streett, Mol. Phys., 36 (1978) 161. 92. A. C. Eringen, Contributions to Mechanics (Pergamon, New York 1969). 93. K. P. Travis and D. J. Evans, Phys. Rev. E, 55 (1997) 1566. 94. D. Nicholson, in preparation. 95. K. P. Travis and K. E. Gubbins, Lartgmuir, 15 (1999) 6050. 96. L. Xu, T. Tsotsis and M. Sahimi, J. Chem. Phys., 111 (1999) 3252. 97. K. P. Travis and K. E. Gubbins, J. Chem. Phys. Submitted (2000). 98. B. Widom, The Journal of Chemical Physics, 39 No 11 (1963) 2808. 99. H. JOntgen, K. Knoblauch, and K. Harder, Fuel, 68 (1981) 817. 100. J. M. D. MacElroy, S. P. Friedman and N. A. Seaton, Chem. Eng. Sci., in press (2000)

RecentAdvancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) o 2000 ElsevierScienceB.V.All rightsreserved.

297

Simulation of Gas Transport in a "Network of Micropores". The effect of Pore Structure on Transport Properties E.S. Kikkinides "'b, M.E. Kainourgiakis a and N.K. Kanellopoulos a aMembranes for Environmental Separations Laboratory, Institute of Physical Chemistry, N.C.S.R."DEMOKRITOS", 15310 Ag. Paraskevi Attikis, Athens, Greece bChemical Process Engineering Research Institute,P.O. Box 361, Thermi-Thessaloniki 57001, Greece *(current address)

I.

Introduction

The study of transport of gases through the pore space of membranes is a subject of great importance in the development of membrane-based separation processes [1,2]. The resistance that a gas encounters as it is transported through the pore space of a membrane is a function of its molecular properties, its interaction with the material that makes up the walls of the pores and the pore structure of the membrane. Since the early 50's, a voluminous number of theoretical and experimental studies have appeared in the literature, concerning transport in porous media and the dependence of the transport coefficients on the main structural parameters of the media [3]. However, this connection has proven to be difficult and frequently controversial, not only because of the complexity of the different transport mechanisms in many fluid-solid systems, but also because of the great difficulty in representing accurately the complicated and tortuous nature of a porous medium. Transport in the pores can take place through various mechanisms, depending on the strength of the interaction of the gas molecules with the pore walls, and by the relative magnitudes of three different length scales characterizing, the size of the molecules, the distance between the pore walls and the fluid density in the pores, respectively [4]. The description of the pore space, on the other hand, is frequently complicated by the existence of distribution pore sizes and shapes in the same material, the degree of correlation and interconnectivity among neighboring pores [5]. Furthermore, if the solid matrix of the porous medium is deformable or if the flowing fluid is reactive then the pore structure of the medium may change during flow or any other transport phenomenon [6]. Hence the accurate prediction of the transport coefficients in disordered media still remains a challenging problem of scientific and practical interest, since membrane performance for gas separations is directly related to transportdependent properties, such as permeability and perm-selectivity [1,2,4,7,8]. Since the analysis of the various diffusion mechanisms that take place during the transport of gas molecules through a single pore is the subject of a previous chapter (chapter 2.1) the present chapter will be focused primarily on the effect of pore structure on transport through the membrane. Hence the main concern here will be concentrated in the various efforts that have been made towards an accurate representation of the porous matrix of a membrane. The

298 evolution of the modeling approaches to the above problem, over the last three decades, from the simplified serial pore models to the more sophisticated, yet still limited, network models [9-14], is a result of advances in theory and experimental techniques as well as in computational power. In the network models, the effective diffusivity or permeability of the porous medium is determined by solving the mass balance equation written at every pore intersection defined as a site in the network. A common assumption made in these models is that the sites contribute negligibly to the diffusion process [11,13], an assumption that is shown to break down in many cases [ 14]. A third class of models involves the solution of the transport equations, either by solving the appropriate diffusion and/or flow equations in the continuum limit, or by Monte Carlo/ random walk methods, in arrays of solid objects arranged in various configurations [15-29]. Random walk methods have the advantage of estimating diffusion coefficients of inert gases quite accurately not only in the continuum molecular diffusion regime, but in addition at the intermediate and Knudsen regimes, where the collisions between the molecules and the solid interface dominate over the intermolecular interactions [27]. Thus the remaining problem in employing this approach is to be able to represent properly the geometry of the domain, e.g. by reconstructing a three-dimensional image that describes accurately the morphology and the topology of the porous medium. Note that Monte Carlo methods can in certain cases (e.g. Knudsen diffusion) be employed in different types of network models so that a direct comparison to the mass solution can be made [ 14]. Recent studies in the field of petroleum engineering deal with the development of a method that generates reconstructed structures from serial thin sections of actual porous media, based on information regarding the first two moments of the phase function of these media, namely the porosity and correlation function [29-30]. Since these efforts, several alternative reconstruction methods have been proposed for the reconstruction of different classes of porous media [31-36]. Unfortunately, serial-tomography techniques cannot be easily employed in mesoporous and microporous materials due to the considerably higher resolution required in such small length scales. Instead, information on the aforementioned properties of these materials can be obtained directly from SEM or TEM images or indirectly by Small Angle Scattering Techniques (SAS) [37-40]. A completely different approach was recently presented [41 ], in which controlled porous glasses (CPG's) were generated through a dynamic simulation of the actual spinodal decomposition process which is believed to be the main mechanism responsible for the formation of these materials [42]. This reconstruction method although more sound from a physical point of view, suffers from severe computational requirements and is limited to the specific material considered. Along the same lines (although using a more phenomenological and thus less computationally intensive approach) is the grain consolidation model [43], which focuses in the modeling of diagenetic processes. Despite the great progress in modeling complicated transport mechanisms of real gases in confined spaces, these confined domains have been limited in ideal geometries of cylinders, slits, etc. In the last decade a few attempts have been made to simulate transport of real gases in pore networks or model pore structures [44-51]. Since the main focus in this chapter is to investigate the effect of the complexity of the pore space on diffusion we will limit our study to as simple diffusion mechanisms as possible. For this reason we shall focus our attention to the simple mechanism of Knudsen diffusion a mechanism responsible for the transport of

299 rarefied gases in mesoporous or even microporous media of average size of >1 nm. It is believed that the basic features on the effect of the pore space topology and accessibility found for this simple type of diffusion should hold at least qualitatively for the case of networks of microporous media, where in many cases the strong adsorbate-adsorbent interactions are quite difficult to be represented in the whole porous matrix [3,51]. Furthermore, in many porous catalysts and sorbents the microrpores are surrounded by mesoporous networks, whose structure can influence the whole diffusion process inside the porous solids. Finally, there still exist quite a few gas separations using inorganic membranes that are based solely upon the Knudsen mechanism [1]. An additional advantage of this mechanism is the high permeability value that can be achieved [ 1]. 2. Theory

2.1 Knudsen Diffusion In many applications involving the transport of rarefied gases through a porous solid, the mean free path of the gas molecules, ~, defined as the mean distance between moleculemolecule collisions, is much larger than the average pore size. In this case, moleculemolecule collisions in the gas phase are rare and transport takes place through collisions of the diffusing molecules with the pore walls [ 1] (Figure 1). Since the driving force for transport is the partial pressure of the gas species, Knudsen transport can occur either by concentration or by pressure gradients. In the former case the process is called Knudsen diffusion while in the later case it is called Knudsen flow [4], while very often the term diffusion is used to characterize both cases. For the case of Knudsen diffusion in a single long cylindrical pore, the diffusivity is known to be proportional to the pore diameter, dp, and to the mean thermal speed of the gas molecules, Uo [1]:

DpI~ : (1/3)dp uo

(1)

Where Uo=(8RgT/n'M) ~, Rg being the universal gas constant, T the ambient temperature and M the molecular weight of the gas. Equation (1) indicates that the perm-selectivity of a membrane for a binary mixture in the Knudsen regime is equal to the square root of the inverse of the molecular weight ratio of the gases.

I

!

I

I

Fig. 1: Knudsen Diffusion in a rectangular slit

300

2.2 Representation of the Pore Space 2.2.1 Capillary Network Models The most common approach of representing the highly interconnecting nature of porous solid is that of a network model (Figure 2). It is evident that, under the same conditions, diffusion in a random pore network will be slower than diffusion in a set of straight cylindrical capillaries. The random orientation will result in an increase of the length of the diffusion path and a corresponding reduction in the concentration gradient, while connectivity will lead to further reduction of the flux. The simplest way to account for such effects is by the introduction of the empirical tortuosity factor, z, so that the diffusivity of the porous matrix is given by:

De = eDp/r

(2)

where Dp is the diffusivity of a straight cylindrical pore of the same diameter, and e is the porosity of the matrix. For the case of Knudsen diffusion Dp=DpK, given by eq. (1). ||||]~;;|||;;

.i l .i l.l l.l i.U.l.l l.l i.i . . . . . .

~ il li ii ll ll ll ll li ll il il ll il il ll ii ll ll ll ll ll nl l ll ii ll il l lu uluiuil limil ll iimnl l imnnimil li nlnlulnnimiiilllmliniunl uiliiulnnninuuni m u m u n m m m n n n

nnummuummunnnummunnnnmumnmiu |iliminmlliliimlmimlilimuiml uinuuuunnummnununuuuunmunnnn nmmmmmmmmmmmummmunnnmmmmmmmm nmamuumnmmmmuummmmmiauuumumm ummnununnnmnnnunnuunnnummunu nnnmnmnnnininnmnnninnunuuuuu nnnnnuunnununnnunnnnunnunnun nunnunnnnnnnnnnuuunnunnunnuu nmmmmmmmmmmmmmmmmmmmmmmmmnmm umuumuulumnmumnnnmmnnnuuuumm nmnmmnunuuuuuuninnunmnnmmunn nmnmnmmnmmmmnnimmmmmmmmmmmmm nunmmuunumnmumumnunmnmunuuuu nulunnniuuuunnuuuunniuuuunnu umnnmnnnnmnuinummunnnnummmnm umnunnmnmuuuununumunnnnnuuni uuinmnninmmnuiuuununnumuunnn nmnunmnuuuunuuuunnnnuuumnuin

unnnuunnnununnnnununnunnunnn iaaaaliniaaiaalilnaaellallul mnnnnnnmnannlinnnnimnnmninim

Fig. 2" Example of a capillary 2D network Obviously the approximation that all network effects can be lumped into a single tortuosity factor is oversimplified since it depends on the implicit assumption that the effects of pore structure are the same regardless of the pore size distribution and diffusion mechanism. For this reason it was realized quite early that the use of a network of capillary models should give a more adequate representation of the porous matrix [52]. Consider a three dimensional regular network of capillaries with radii r, randomly selected from a distribution functionf(r), defined in the range [ra, rb]. Following the approach of Nicholson and Petropoulos, [52] three-dimensional regular networks of connectivity 18, 12, 8, 6 and 4 can be constructed. Details on the network construction can be found elsewhere [52,53]. The flux expression for an open cylindrical pore (bond) of the network connecting two nodes (sites), i and j, in the Knudsen regime can be written as follows (assuming long capillaries, as in eq. (1)):

301

Jr=

3 \~M)

1

(3)

where r~ is the radius of the capillary and I is the length of the capillary pore (assumed to be the same for all network pores). Writing the material balance equation at each pore junction results in a set of linear algebraic equations that can be solved for the nodal pressures using successive over-relaxation methods. The network permeability is then determined from the total flux, J, obtained for a given pressure drop across the network [ 11]. 2.2.2 Effective Medium Approximation Effective medium approximation (EMA) is a phenomenological method for determining the effective properties of a disordered medium, in which the medium is replaced by a hypothetical homogeneous one with unknown physical constants (for a review on the method see [6] and the references cited there in). For the case of resistor networks Kirkpatrick showed that for a regular network of coordination number, z, EMA determines the effective conductivity of the network by solving a simple integral equation [54]. It is straightforward to transform this equation for the case of gas flow through a network of cylindrical capillaries [ 11, 53]. The resulting equation is:

~ (Pe M - j(r)), f(r) ~r~ j (r ) + (z ] 5 Sl) :-~eM dr = O

(4)

where PeM is the effective medium permeability which is determined by the solution of the above integral equation. The function j(r) corresponds to the type of flow in each pore of radius r. For the case of Knudsen diffusion in a cylindrical capillary this function is given by eq (3). 2.2.3 Bethe Networks In contrast to regular networks (where there is an infinite number of distinct continuous pathways of bonds between any pair of sites), in Bethe networks there is one and only one pathway of bonds connecting any given sites [55,56]. In this respect, regular networks appear to be more realistic models of porous media than Bethe networks since they predict highly interconnected pore space. Nevertheless the simplicity of a Bethe network makes its topological properties mathematically tractable resulting in analytical or simplified expressions for several important lattice properties [55,57,58]. Theoretical studies in transport processes [53, 59-62] have been all based on the use of Bethe trees to provide significant insight into the intricate effects of pore structure on the performance of such processes. 2.2.4 Chamber and Throat Network models The common assumption made in the capillary network models is the lack of volume in the junctions between different nodes. Such an approximation combined with the assumption of infinitely long capillaries leads to the additional assumption that the pore junction connecting different capillaries does not contribute significantly to the diffusion process [ 14].

302 Unfortunately in many real porous materials the assumption of pore junctions of zero volume or of infinitely long capillaries often breaks down, such as in compacts made from primary non-porous spherical particles. In such cases the majority of the pore space is in the pore junctions represented by large spherical chambers, connected by cylindrical throats of much smaller size (Figure 3). Since these throats can no longer be considered of infinite length, a new type of pore network is obtained that is capable of representing a variety of porous solids. Such models have been extensively used to represent the void space of macroporous media in oil recovery and mercury porosimetry studies [63-65].

t

l

J

t

Fig. 3: Example of a chamber and throat 2D network Chamber and throat network models can be employed in the same manner as the simpler capillary networks to determine Knudsen permeabilities [13]. However, it has been recently shown [14] that this analysis gives inaccurate results for "short" throats, where edge effects are no longer negligible. In such cases Knudsen permeabilities should be calculated by molecular simulation methods in the whole network and not in individual pores [ 14]. 2.2.5 Stochastic Reconstruction There exist several methods of reconstructing porous media based on measurements of the first two moments of the phase function of this material, namely the porosity and the correlation function [29-34]. Consider an experimentally obtained 2-D image of a section of a porous medium as the one shown in Figure 2. Using standard techniques [66,67], this section can be described by a 2-D matrix of binary pixels, which take the values of 0 and 1 in the solid and pore phases, respectively (Figure 4). Accordingly, the phase function of the binary medium shown in Figure 4 is defined as follows:

ifx belongs to the pore space

zx,:fl

(5) otherwise

303

Fig. 4: Digitized image of a 2d section of a porous medium (black color represents pore space and gray color represents solid phase). where x is the position vector from an arbitrary origin. The porosity, e, and the auto-correlation function Rz(u) can be defined by the statistical averages [29-34,66] g = (Z(x))

Rz (.)-

(6a)

,).6"--8 2 +.)- ,))

(6b)

Note that indicates spatial average. For an isotropic medium, Rz(U) becomes onedimensional as it is only a function of u-lul [29-34]. Ideally, a representative reconstruction of a medium in three dimensions should have the same correlation properties as those measured on a single two-dimensional section, expressed properly by the various moments of the phase function. In practice, matching of the first-two moments, that is, porosity and autocorrelation function, has been customarily pursued. This simplification is often shown to be invalid as one can find examples of porous media exhibiting quite different morphological properties while sharing the same Rz(u). In this case one should try to much multi-point correlation functions. Such an approach is however, quite tedious making the whole exercise quite difficult to handle. Instead, determination of the chord length distribution function, p(1), which gives the probability a chord of length 1, to lie in the pore space of the medium, is often pursued [33,67]. Such a property is related to the multi-point correlation functions and can be easily determined in digitized biphasic media. The orientationally averaged etfective diffusivity of an inert gas in the reconstructed digitized medium, is determined from the mean-square displacement , of a statistically sufficient number of identical particles injected in the void space of the medium, according to the well known equation [1 ]:

304

D = l i m (r ,--,0~ 6t

(7a)

where t is the travel time of the particles. Following the projection of displacements on the three directions x,y, and z, one obtains the diagonal terms of the diffusion tensor [26]: Dl,=lim/2t

i=x,y, or z

(7b)

The displacement is monitored throughout the distance, s, traveled by the particles assuming that they move at a constant speed equal to the mean thermal speed Uo, defined above, as indicated in similar studies [15-27]. For a reliable determination of the macroscopic diffusivities, the travel time has to be large enough to ensure that the particles actually feel the effect of all the structural details of the porous medium as it is illustrated in Figure 5, below. In this sense, the material can be considered as macroscopically homogeneous in terms of its structural and diffusion characteristics.

Fig. 5: Knudsen Diffusion of a point-like gas molecule through a digitized porous medium (gray color represents pore space and black color represents solid phase). Using the expression in eq. (1), for the Knudsen diffusivity through an infinitely long capillary of diameter le one can non-dimensionalize diffusivity. The resulting expression for diffusivity calculations are (substituting also t=S/Uoin equation (7)) [26,27]: D

_ lim

(~2Jl~}

or for the respective diagonal terms of the diffusion tensor:

(8a)

305

D~

Dk (l e )

= lim

s/l,-*~

2 s/l e

i=x,y,z

(8b)

A final point has to be made regarding the calculation of diffusivity. In general, diffusivity calculations are based on the motion of the fluid in the pore space. Nevertheless, in many cases effective diffusivity results have been reported in the literature [68, 69], which are basically diffusivities multiplied by the porosity of the material. These effective diffusivities are also known as permeability values for the case of inert gases [68,70,71], as it is also the case in the present work. Finally, the calculated Knudsen permeabilities in the dry Vycor at different degrees of pore filling, are normalised by the value that corresponds to the case of dry vycor. 3. Use of Dynamic Studies to Estimate Structural Properties: The Gas Relative Permeability Method Gas relative permeability measurement, PR, is defined as the permeability of an inert gas through a porous medium partially blocked by a second fluid, normalized by the permeability through the same porous solid, when the pore space is free of this second fluid [72]. In most cases, the gas permeability diminishes at the "percolation threshold", at which a significant portion of the pores are still conducting; however in the simple bundle of capillaries model the percolation threshold arises only when all the pores are blocked by sorption and condensation. In comparison, the network model can provide a satisfactory analysis of percolation threshold problem, without, as noted earlier, increasing the number of the model parameters. An explicit approximate analytical relation between the relative permeability and the two network parameters, namely the pore network connectivity, z, and the first four moments of the pore size distribution, f(r), has been develeped, based on the Effective Medium Theory Approximation (EMA) [53,73]. Bethe networks, can also be considered since they give simplified expressions for several properties of the porous medium, while at the same time retain most features of percolation theory [53]. Application of stochastic reconstruction models to study gas relative permeability is currently limited by the inability to model sorption in such complicated domains. The analysis, which will be presented below, is based on mesoporous materials where the theory of capillary condensation is valid [74]. Although this theory is expected to break down for pore sizes below 1 nm, the basic principles regarding the effect of pore blocking on permeation as dictated by the development of non-conducting clusters in the pore network will be still present and only the mechanism of formation of these clusters is expected to change. Typically the adsorbate is at equilibrium with bulk vapor at a relative pressure P/Po and consists of a capillary condensed liquid filling the pores with radii smaller than the Kelvin radius, rK (subcritical pores, r ~ rx) and an adsorbed layer of thickness t coveting the walls of the supercritical pores (r > rK). For the classic case of N2 sorption on a mesoporous medium at 77 K, there exist standard expressions which have been successfully employed in the literature [74, 53]: The flux expression for an open cylindrical pore (bond) of the network connecting two nodes (sites), i and j, is given by eq. (3) from above, where rij has been now replaced by xo=r~-t, which is the open core radius of a capillary partly filled with adsorbate of

306 thickness t. Employing standard resistor network analysis [ 11, 53] the Knudsen permeability of the network is determined at different degrees of pore filling by the adsorbate. The above computation scheme is repeated for a range of values of P/Po between zero and unity and the

4 0)

relative permeability PR - d(0) is determined as a function of the relative pressure the normalized adsorbed volume

P/Po or

Vs. This volume is calculated by the following expression: (9)

EZx

Vs= -ZE4 Application of EMA for the determination

1- fb +i (Pem-xS)" f(x) /

,. x

of Pn gives [53, 73]: (10)

0

where PeM is the dimensionless effective medium permeability which is determined by the solution of the integral equation, x=r-t andj~ is the number fraction of the open (supercritical) pores at a certain value of P/Po. Vs is related to3~ through the following expression: Vs = 1--fb'@

(11)

where ~(P/Po) is a complicated function of P/Po and contains first and second moments of the distribution functions f(r) and f(x)=f(r-O. The exact relation between .g and Vs can be found elsewhere [73]. Thus for a certain value of P/Po, the quantities Vs, fb and PR = Peru (P/Po;Vsfb)/Pem (0;0,1) are determined from the above equations. It is important to note that when f6=2/z then Vs = Vsc and PR=0 according to EMA. This result, although generally accurate in two-dimensional networks, totally breaks down for the case of three-dimensional networks [75-77] and other methods should be employed in such a case [76]. In Figure 6a relative permeability curves computed by the network model are plotted for z=4,6,8 and 18. EMA results are also shown in this figure, for comparison purposes. It appears that as z increases the Ps curve becomes broader as it approaches the percolation threshold, Vsc. In all cases EMA is in very good agreement with the network solution, except in the neighborhood of Vsc. In that region, the EMA predicted PR curve decreases linearly with Vs, while the network solution results in a non-linear behavior and reaches a higher percolation threshold, Vso This is because Vsc predicted by the network model corresponds to the theoretical ft~ predicted by percolation theory (fbc.-.1.5/z, see also [77]), while Vsc found by EMA corresponds to fbc=2/z [54]. A similar picture is obtained in figure 6b, where PR is plotted as a function of the fraction of the open pores,.g. It can be seen that for all z, near the percolation threshold, EMA shows a linear decrease of PR with ~. On the other hand, network results indicate that, in the same region, PR decreases withj~ according to a power law as dictated by percolation theory:

307

NETWORK

O.8 _1 0.6

EMA

-

~ . . Z=18 .4

~-

Z=4

0.2--

Z=6

0

I

0

0.2

0.4

0.6

0.8

1

Vs Fig. 6a: Relative permeability, PR, as a function of the amount adsorbed, Vs, for different values of network connectivity, z.

0.8

tr

IX

-

NETWORK . . . . EMA

0.6z=8

0.4

z=18

0.2

%

~.

0

\ z=6

z=4

I

-T

1

I

0.2

0.4

0.6

0.8

1

Fig. 6b: Relative permeability, PR, as a function of the fraction of open pores, J~, for different values of network connectivity, z.

308

P.

i,c)'

(12)

where t is a universal critical exponent that depends only on the dimensionality of the network. For a three-dimensional lattice, ~ 2 [6, 75]. Note that for a network of size LxLxL finite size scaling effects are expected to influence the above behavior (See [75] for more discussion on the matter, and [54], on details on the treatment of PR, in this case). Thus it appears that relative permeability curves follow percolation theory, since they satisfy both the theoretical percolation threshold and the scaling law for three-dimensional networks [77]. More importantly, relative permeability curves of different connectivity exhibit the same behavior with J;-J~c as.Ac is approached [53]. The same conclusion is valid for different pore size distribution functions fir) provided that f3< = [76]. Hence one can use relative permeability curves to determine the percolation threshold and from there the average connectivity, z, of the pore network. 4. Simulation of Pore Structure and Knudsen Diffusion in Model Membranes 4.1 Vycor Porous Glass Vycor porous glass is a well-known mesoporous material which, apart from its practical application in many physical processes, is considered as a model system to study equilibrium and dynamic properties [78-82]. Vycor 7930 glass (Coming Glass Works) is produced by a spinodal phase separation [42] and a leaching process, in which the sodium borosilicate glass is thermally treated below the liquidus temperature to induce separation into continuous phases, and the borate phase is leached out by acid solutions. This porous material is a typical example of an interfacial system with an internal surface that fills the space in a complex way. Recent developments in reconstructing 3-D images of this material based on structural information obtained from SAS [35,36] have opened up the possibility of employing more sophisticated diffusion simulations in such structures [27, 36, 50]. A completely different approach has been followed by Gelb and Gubbins [41] who have generated Vycor porous glass through a dynamic simulation of the actual spinodal decomposition process, which is believed to be the main mechanism responsible for the formation of these materials. 4.1.1 Structure Generation and Characterization The reconstruction technique proposed by Crossley et al [36], has been adopted in the present study, since it is relatively simple, while it gives an excellent fit of the whole SANS spectrum and thus the correlation function of the material. Note also, that other reconstruction methods such as the one proposed by Levitz and coworkers [36, 50], provide excellent fits of the SAXS spectrum of Vycor porous glass. The reconstructed Vycor image is generated by starting with an initial three-dimensional random number array lo(x,y,z) from a uniform probability distribution in [0,1]. The initial random image becomes correlated through a convolution with a Laplacian-Gaussian Kernel, K(x,y,z;co) which introduces a correlation length co:

309 o0

o0

o0

l(x,y,z)= ~ ~ ~KL~(x-x/,y- y/,z-z/)lo(x/,y/,z/) d.x/dy/dz /

(13a)

-0o--00-o0

where KL~ is given by:

KL~(x,y,z)=(_6+4(x 2 + y2 +z2)/co2)• exp(_(x 2 + y2 +z2)/co 2) Finally the correlated array I(x,y,z) is binarised by thresholding with

(13b)

the porosity of the material. The 3-D binary media generated by the reconstruction process described above, are characterized by the same porosity and correlation function as the original Vycor porous glass sample while leading to structure factors that satisfy the scaling analysis at long wavelengths [36]. A 2-D image of the reconstructed Vycor porous glass at porosity e=0.3 is presented in Figure 7 for 09=5.

Fig. 7: 2D digitized section of Reconstructed Vycor porous glass (0)=5) In Figure 8a, the auto-correlation function measured on the generated image is plotted as a function of the actual distance. In the same Figure, the auto-correlation function obtained from a TEM picture of the material [39] is also included. By matching the correlation curves of the simulated medium and the TEM image, one finds the actual pixel size of the generated medium, le. It is evident that the agreement between the correlation function of the reconstructed and the actual medium is excellent. Additional calculations for different 2-D sections of the same 3-D reconstructed image, have produced correlation functions that do not show any significant deviations from those included in Figure 8a. This result ensures the isotropy of the generated 3-D medium, as expected from the reconstruction procedure. In Figure 8b we present the pore chord length distribution functions determined in the original and reconstructed material. Once again, the agreement is excellent indicating the ability of the reconstruction model to satisfy higher order statistical properties of the material.

310

10-

0 020,

0.8'

r

1~=15A

--o-- 8EM image

0015

9 Experimental (TEM)

06,

---.e--- 3D image, le=15A "" w..,~-

0.4

c~

0 010

0 005 v

~

,

=61OOOOOOgl==A .......... 0000

-02

0

100

200

0

200

400

600

~0

1000

u(A)

5 0

400

(a)

(b)

Fig. 8: (a) Auto-correlation function and (b) pore chord length distribution function of actual and reconstructed Vycor. An interesting structural property of a porous medium is its internal surface area per unit volume, Sv. For the case of a random binary medium, it has been recently shown that this property can be estimated analytically [26]. For correlated media, Sv can be determined either from the slope of the correlation function at zero distance [66], or computed by a simple algorithm that counts the pixel faces that belong to the solid-void interface and divides them by the total volume of the sample. In this work, the second approach has been selected since it is inherent in the reconstruction procedure followed. The results in the form of Sv vs e-(1-e), for three different resolutions, are presented in Figure 9. It can be seen that Sv varies linearly with e.(1-e) as in the case of a random porous medium, but with a different slope and a nonzero ordinate. Furthermore, it is evident that for le

10-9

9 86.C 83.Z 86.E 87.(

85.E

86.7

40

tr

o

~0 10-10 10-11

, 0.2

8,~.~,.

20 , 0.3

,

, 0.4

,

, 0.5

, 0.6

'

0

Kinetic diameter (nm)

I 5e ......i ......

0

9

19

30

Oxidation period (day) P~ H

E] C

E]

~(k~

6.o i.....:..~..~.,.,:,. I

Heat-treatment in N 2 at 600~ N Q O

Fig. 3. Effect of oxidation on permeances Per-

Fig. 4. C h a n g e s in m a s s and elemen-

closed circle

tal distribution of m e m b r a n e s d u r i h g

= as formed, open circle = oxidized in O 2

stability tests. The initial m a s s is as-

at 300~

s u m e d to be unity. (From H a y a s h i et

of m e m b r a n e carbonized at 700~ meation temperature = 65~

[26])

for 3 h. (From H a y a s h i et al.

al. [26])

329 in Figure 6. The precursor hollow fiber was spun from polyimide which was synthesized from BPDA and a r o m a t i c diamines. The dried fiber w a s 0.40 m m O.D. and 0.12 m m I.D. It was h e a t - t r e a t e d in air at 400~ for 30 min and t h e n pyrolyzed at 600-1000~

for 3.6 min. The fiber was s h r u n k to 0.35-0.28 m m O.D. and 0.11-0.09

Heat-treatment period (h) 0

1

2

3

4

10-7 ~ ' l " ~ ~ ' 'He . . ~. . . . . . . . ..._ .

----

2E ~

V1

10-9

10 "10

t--

~ lo-ll ix. 10-12

0

10 20

'' 30

''

' .....

Oxidation time (day)

Fig. 5. Effects of exposure to air at 100~ a t m o s p h e r e at 600~ 700~

an d post h e a t - t r e a t m e n t in a nitrogen

for 4 h on p e r m e a n c e s of carbon m e m b r a n e carbonized at

P e r m e a t i o n t e m p e r a t u r e = 65~

(From H a y a s h i et al. [26])

electric tube furnace

,ake-up-bobb,n

r-'-i

quartz glass pipe

fiber

r feed-bobbin

N2

exhaust gas

N2

Fig. 6. Schematic d i a g r a m of the continuous carbonization of an a s y m m e t r i c hollow fiber. (From Kusuki et al. [13])

330 m m I.D., depending on carbonization t e m p e r a t u r e . Figure 7 shows the fractured face of an asymmetric carbon m e m b r a n e with a skin layer. This structure realizes the flexibility of the carbon fiber. Carbonization t e m p e r a t u r e greatly affects permeances of the produced membranes. As shown in Figure 8, the permeance to hydrogen was the highest when the fiber was carbonized at 700~

but the H2/CH 4 selectivity reached a m a x i m u m at

carbonization t e m p e r a t u r e of 850~

In order to examine the stability of the hollow

fiber carbon m e m b r a n e prepared at 750~

toluene vapor was mixed in the feed of

an equimolar of H 2 and CH 4. Both the carbon m e m b r a n e and the initial polyimide m e m b r a n e were then subjected to permeation tests [34]. As shown in Figure 9, the H 2 and CH 4 permeances of the polyimide m e m b r a n e decreased with increasing toluene concentration to 1/7 and 1/4 of the initial values at a toluene concentration of 8000 ppm. After the feed was switched to the dry m i x t u r e of the gases, the CH 4 permeance was recovered to the initial value, but the H 2 permeance was recovered only to h a l f the initial value. On the contrary, the H 2 and CH 4 permeances of the carbon m e m b r a n e were higher t h a n those of the polyimide membrane, and the H 2 and CH 4 permeances were unchanged. This suggests t h a t the self-supporting carbon hollow fiber m e m b r a n e was much more stable t h a n the precursor polyimide membrane. Yoshinaga et al. [8] showed t h a t permeances of the self-supporting car-

Fig. 7. F r a c t u r e d section of carbonized asymmetric hollow fiber membrane. (From Kusuki et al. [13])

331

-

eo

i

I

.-i

10-2

i

I

i

I

i

I

. 1000

i

A

100 :~

_.o

%

-

E o 1 0-3 -"

"1-

-

10

I-09

E

~ 10-4

ZX

or

-

~

-

12.

9 10-5

i

I

200

I

400

I

I

I

600

I

I

800

I

1000

1200

Heat-treatment temperature (~

Fig. 8. Effect of carbonization t e m p e r a t u r e on H 2 a n d CH 4 perrpeances a n d H2/CH 4 selectivity at 80~

Feed p r e s s u r e = 1 MPa. (From K u s u k i et al. [13]) Dry feed

Dry feed (Regenerated)

(initial)

~ #

'

i

........ ,,m

' /' ~ :11000

_

= ............

"1~"~m=-~

" I

.__. "-->" ,,=,

-

V

[]

o

100

-1-

~m "l-

E

%

~," 10-3 E o

12. I-O)

cq -1-

10 e-.-.-.-~=~-..-.: . . . . . =, . . . . :__~__

9!

~-" 10.4 E o o e-

~ 10-5 ID

I

o

II

I

IOOO

,

,

,

,

,,,,I

J/

n

IOOOO

Toluene concentration (ppm)

i

o

Fig. 9. Effect of toluene v a p o r c o n c e n t r a t i o n in t h e feed on H 2 p e r m e a n c e a n d H2/ CH 4 selectivity. O p e n symbols = a s y m m e t r i c hollow fiber polyimide m e m b r a n e , close symbols = a s y m m e t r i c hollow fiber carbon m e m b r a n e . (From T a n i h a r a et al. [36])

332 bon m e m b r a n e s were increased by the t r e a t m e n t in an oxidative atmosphere. Jones and Koros [30, 31] reported t h a t permeances to 02 and N 2 for an asymmetric hollow fiber carbon m e m b r a n e , which had been carbonized at 500-550~

were

decreased to 0.4-0.5 of the initial value after the m e m b r a n e was exposed to air humidified to relative humidities of 23-85% at ambient temperature. The stability of the carbon m e m b r a n e was improved by coating the m e m b r a n e using perfluoro2,2'-dimethyl-l,3-dioxole or tetrafluoroethylene.

4. P E R M E A T I O N M E C H A N I S M OF C A R B O N M E M B R A N E S Kusakabe et al. [28] reported t h a t the C O i N 2 selectivity of a carbon m e m b r a n e was 40 for single component gases at room t e m p e r a t u r e , and t h a t the selectivity increased to 51 for an equimolar mixture of CO 2 and N 2. No effect of carrier gas was observed. This suggests t h a t the carbon m e m b r a n e has slit-like pores, the shorter w i d t h of which could be 0.4-0.6 nm. Thus, molecules could pass one a n o t h e r by moving to the longer width of the slit, but CO 2 molecules cannot be concentrated on the pore wall because of the small slit width. Thus the CO~IN2 selectivity would not be expected to be greatly increased for a mixed feed. This m e c h a n i s m is different from t h a t of Y-type zeolite [37] and silica m e m b r a n e s [38]. For Y-type zeolite membranes, CO 2 molecules are adsorbed on the zeolite surface and t h e n t r a n s p o r t e d into the pore via a surface diffusion m e c h a n i s m . The pore size of Y-type zeolite m e m b r a n e s is 0.7-0.8 nm, and CO 2 molecules are concentrated on the surface of the pore. The concentration of N 2 molecules inside the pore is lower t h a n t h a t on the outside, and CO 2 molecules, which m i g r a t e along the pore wall, o u t r u n N 2 molecules, which are located in the core region of the pore. The Y-type zeolite membrane showed a CO~]N 2 selectivity of 3 at a permeation t e m p e r a t u r e of 30~ when permeances were determined using pure gases. When a mixture of CO 2 and N 2 was fed, however, the selectivity increased to 80 [37]. The type of carrier gases on the p e r m e a t e side h a d no effect on permeances. In the pore of the silica m e m b r a n e , molecules are not able to pass one another. The CO~]N 2 selectivity for a mixed feed is then determined by the slowest-moving species and is lower t h a n t h a t for pure gases [38]. E x p e r i m e n t a l data relative to carbon m e m b r a n e s were rationalized by computer simulations [39-41].

333

5. CONCLUSIONS Molecular sieving carbon membranes are produced by carbonizing precursor membranes which can be prepared from a variety of polymers. When carbonization conditions, such as temperature and time, are properly selected, permeation properties and stabilities of the precursor membranes are greatly improved. Controlled oxidation at elevated temperatures can increase permeances of the carbon membranes. However, permeances may be decreased by exposing the membranes to an oxidative or humidified atmosphere at temperatures below 100~ This appears to be caused by formation or adsorption of oxygen-containing functionalities in pores. The permeances can be recovered without damaging selectivities by heat-treating the membranes in an inert atmosphere. REFERENCES

1. J.E. Koresh and A. Sofer, Sep. Sci. Technol., 18 (1983) 723. 2. Y.D. Chen and R.T. Yang, Ind. Eng. Chem. Res., 33 (1994) 3146. 3. M.B. Rao and S. Sircar, J. Memb. Sci., 85 (1993) 253. 4. S. Wang, M. Zeng and Z. Wang, Sep. Sci. Technol., 31 (1996) 2299. 5. F.K. Katsaros, T.A. Steriotis, A.K. Stubos, A. Mitropoulos, N.K. Kanellopoulos and S. Tennison, Microporous Mater., 8 (1997) 171. 6. T.A. Centeno and A.B. Fuertes, J. Memb. Sci., 160 (1999) 201. 7. V.M. Linkov, R.D. Sanderson and E.P. Jacobs, J. Memb. Sci., 95 (1994) 93. 8. T. Yoshinaga, H. Shimazaki, Y. Kusuki and Y. Sumiyama (Ube Industries Ltd.), Asymmetric hollow filamentary carbon membrane and process for producing same, Eur. Pat.No. 0 459 623 B1 (1991). 9. H. Hatori, Y, Yamada, M. Shiraishi, H. Nakata and S. Yoshitomi, Carbon, 30 (1992) 305. 10. C.W. Jones and W.J. Koros, Carbon, 32 (1994) 1419. 11. J.-i. Hayashi, M. Yamamoto, K. Kusakabe and S. Morooka, Ind. Eng. Chem. Res., 34 (1995) 4364. 12. H. Suda and K. Haraya, J. Chem. Soc., Chem. Commun., (1995) 1179. 13. Y. Kusuki, H. Shimazaki, N. Tanihara, S. Nakanishi and T. Yoshinaga, J. Memb. Sci., 134 (1997) 245. 14. J. Petersen, M. Matsuda and K. Haraya, J. Memb. Sci., 131 (1997) 85. 15. M. Yamamoto, K. Kusakabe, J.-i. Hayashi and S. Morooka, J. Memb. Sci., 133

334 (1997) 195. 16. A.B. Fuertes and T.A. Centeno, J. Memb. Sci., 144 (1998) 105. 17. M. Ogawa and Y. Nakano, J. Memb. Sci., 162 (1999) 189. 18. H. Kita, M. Yoshino, K. Tanaka and K. Okamoto, Chem. Commun. (1997) 1051. 19. A.B. Fuertes and T.A. Centeno, Microporous Mesoporous Mater., 26 (1998) 23. 20. K. Kusakabe, S. Gohgi and S. Morooka, Ind. Eng. Chem. Res., 37 (1998) 4262. 21. J.Y. Park and D.R. Paul, J. Memb. Sci., 125 (1997) 23. 22. M.B. Rao and S. Sircar, J. Memb. Sci., 110 (1996) 109. 23. M. Anand, M. Langsam, M.B. Rao and S. Sircar, J. Memb. Sci., 123 (1997) 17. 24. J.-i. Hayashi, H. Mizuta, M. Yamamoto, K. Kusakabe, S. Morooka and S.-H. Suh, Ind. Eng. Chem. Res., 35 (1996) 4176. 25. J.-i. Hayashi, H. Mizuta, M. Yamamoto, K. Kusakabe and S. Morooka, J. Membrane Sci., 124 (1997) 243. 26. J.-i. Hayashi, M. Yamamoto, K. Kusakabe and S. Morooka, Ind. Eng. Chem. Res., 36 (1997) 2134. 27. T. Naheiri, K.A. Ludwig, M. Anand, M.B. Rao and S. Sircar, Sep. Sci. Technol., 32 (1997) 1589. 28. K. Kusakabe, M. Yamamoto and S. Morooka, J. Memb. Sci., 149 (1998) 59. 29. J.E. Koresh and A. Softer, Sep. Sci. Technol., 22 (1987) 973. 30. C.W. Jones and W.J. Koros, Ind. Eng. Chem. Res., 34 (1995) 158. 31. C.W. Jones and W.J. Koros, Ind. Eng. Chem. Res., 34 (1995) 164. 32. K. Haraya, H. Suda, H. Yanagishita and S. Matsuda, J. Chem. Soc., Chem. Commun., (1995) 1781. 33. V.C. Geiszler and W.J. Koros, Ind. Eng. Chem. Res., 35 (1996) 2999. 34. S.A. McKelvey, D.T. Clausi and W.J. Koros, J. Memb. Sci., 124 (1997) 223. 35. S. Akiyama, H. Mizuta, H. Anzai, K. Kusakabe and S. Morooka, Proc. 5th Intern. Conf. On Inorganic Membranes, P-111, Nagoya (1998). 36. N. Tanihara, H. Shimagaki, Y. Hirayama, S. Nakanishi, T. Yoshinaga and Y. Kusuki, J. Memb. Sci., 160 (1999) 179. 37. K. Kusakabe, T. Kuroda, A. Murata and S. Morooka, Ind. Eng. Chem. Res., 36 (1997) 649. 38. 39. 40. 41.

B.-K. Sea, K. Kusakabe and S. Morooka, J. Memb. Sci., 130 (1997) 41. S. Furukawa, T. Shigeta and T. Nitta, J. Chem. Eng. Japan, 29 (1996) 725. S. Furukawa and T. Nitta, J. Chem. Eng. Japan, 30 (1997) 116. S. Furukawa, K. Hayashi and T. Nitta, J. Chem. Eng. Japan, 30 (1997) 1107.

Recent Advances in Gas Separationby Microporous Ceramic Membranes N.K. Kanellopoulos(Editor) e 2000 Elsevier Science B.V. All rights reserved.

335

Microporous Silica Membranes

Nieck Benes, Arian Nijmeijer and Henk Verweij

Laboratory of Inorganic Materials Science, Department of Chemical Technology, University of Twente, PO Box 217, 7500AE Enschede, the Netherlands

Introduction

Microporous silica membranes have a high potential for gas separation and pervaporation at high temperatures in chemically aggressive environments. Well-prepared silica membranes show high fluxes for small gas molecules such as H2, CO2 and O2 and considerable selectivities for these gases with respect to larger gas molecules such as SF6 and hydrocarbons [ 1,2]. This offers perspectives on applications such as natural gas purification, molecular air filtration, selective CO2 removal and industrial 1-12 purification. A specific application for these membranes is the use in high temperature membrane reactors in which silica membranes can be of particular use to remove Ha selectively with high fluxes to acieve conversion enhancement in thermodynamically limited reactions. Examples of such reactions can be found in steam reforming, the water-gas shift process, dehydrogenation of hydrocarbons and coal gasification [3,4]. Two different types of molecular sieving silica membranes can be distinguished: 9

Chemical Vapour Infiltrated (CVI) membranes, which are commercially available*.

9

Sol-gel silica membranes, which are not commercially available yet.

CVI membranes are produced by reacting a gaseous silica precursor such as Tetra-Ethyl-Ortho-Silicate (TEOS) with an oxidising agent inside the pores of a macro- or mesoporous support [5,6]. These membranes normally have very high permselectivities towards hydrogen, values as high as 3000 have been measured for H2/N2. A large drawback of such membranes is, however, their relatively low permeance (2-4x 10s mol/m2sPa at 200~

due to the presence of the nearly dense silica plugs inside the

pores of the supporting system. By changing reaction conditions it is possible to obtain a higher hydrogen permeance, but at the expense of selectivity. CVI membranes recently developed in our group have a H2/N2 permselectivity of 43, but with a H2 permeance of 1.7x 10-7 mol/m2sPa at 200~ [6]. An possible advantage of CVI membranes, however, is that the vulnerable separative silica layer is located inside the pores of the supporting system, where it is to some extent protected to aggressive environments. Sol-gel coated silica membranes have a separative layer that is coated on top of a supporting

Media and Process TechnologyInc. (MPT), Pittsburgh, PA, USA.

336

system and show fluxes that are again a factor of 10 higher than the above-mentioned CVI membranes and hence in the range of 1-2x 10-6 mol/m2sPa. With such high permeances the supporting system may very well become the limiting factor instead of the active membrane layer. Compared to polymeric membranes, inorganic microporous membranes with molecular sieve-like properties have a good chemical, mechanical and thermal stability [7]. Nevertheless, the stability of silica membranes towards water and water vapour at elevated temperatures and how they affect the membrane performance is not yet elucidated. The issue of thermal and chemical resistance is not only relevant during applications but also in membrane cleaning procedures which often specify strong acids and bases. A general rule is that more acidic metal oxides or ceramics show greater resistance towards acids but are more prone to attack by bases and vice versa [8]. For example, alumina or zirconia membranes generally are more stable than silica when exposed to alkaline solutions. On the other hand, silica membranes have better acidic resistance than most other metal oxide membranes. Recently some interesting self-organising mesoporous silica structures which can be used for membrane purposes have been realised by the group of Brinker [9,10]. By templating methods, using small molecules, they were also able to prepare microporous silica membranes with a controlled pore-size [11,12]. For those ceramic membranes, which contain two oxides, the chemical resistance towards acids and bases often lies between those of the constituents. Even within a given metal oxide system, the chemical resistance may vary with the particular phase. For example, ct-alumina is very stable towards strong acids and bases, the "/-alumina phase however has been known to be subject to some attack at high and low pH. The objective of this chapter is to describe recent developents in synthesis, thermochemical stability and transport properties of supported silica membranes. We did not attempt to provide a complete literature survey on the subject but instead, focused on recent results obtained in the 'Inorganic Materials Science' group of the University of Twente.

Synthesis

The microporous silica membranes prepared in our group consist of three layers. First a support is prepared from or-alumina powder with a fiat or tubular shape. Flat supports are prepared by either die pressing [2] or colloidal filtration [13] and the tubular supports are prepared by the centrifugal casting technique [14]. The use of colloidal processing techniques such as filtration and centrifugal casting come more and more into scope because they result in an extremely homogeneous and hence strong porous structure and a high surface quality. The latter is of importance to be able to apply very thin

337

defect-free membrane layers. On top of the supports a 7-alumina intermediate layer is coated under clean-room conditions. Finally on top of this intermediate layer the final molecular sieving silica top layer is coated. In this section all synthesis steps to obtain a supported microporous silica membrane will be treated, starting with the silica top layer. After that some highlights on 7-alumina intermediate layers, such as pore-sizes and stability, will be given and finally the preparation of flat and tubular supports will be described in detail.

Silica top layer

Two types of silica top layers are of interest, the conventional hydrophilic layers and the newly developed hydrophobic silica top layers [ 15]. These layers are prepared by dipping supported y-A1203 membranes in polymeric silica dip solution, followed by drying and calcining. A standard silica sol is prepared by acid-catalysed hydrolysis and condensation of tetra-ethyl-ortho-silicate (TEOS)* in ethanol. A mixture of acid and water is carefully added to a mixture of TEOS and ethanol under vigorous stirring. During the addition of the acid/water mixture the TEOS/ethanol mixture is placed in an ice-bath to avoid premature (partial) hydrolysis. After the addition is complete the reaction mixture is refluxed for 3 hours at 60~ in a water bath under continuous stirring. The reaction mixture had a final molar TEOS/ethanol/water/acid ratio of 1/3.8/6.4/0.085 in agreement with the "standard" recipe of silica sol preparation, as defined in [ 16]. The reacted mixture was cooled and diluted 19 times with ethanol to obtain the final dip solution. After dipping the membranes were calcined at 400~ for 3 hours in air with a heating and cooling rate of 0.5~

The whole process of dipping and calcining can be repeated once again to repair any de-

fects in the first silica membrane layer. Recent results showed, however, that this second coating step is not absolutely necessary anymore if one works under class 100 cleanroom conditions. The membranes are henceforth referred to as "Si(400) membranes". Another type of membranes was prepared by the same procedure as described above but with the only difference that the calcination temperature was 600~

These membranes will be referred to as "Si(600) membranes". More recently the first de-

fect-free silica membranes "Si(800)" were prepared with a firing temperature of 800~ Hydrophobic silica layers [ 1,15] To make the silica membrane material more hydrophobic, methyl-tri-ethoxy-silane (MTES) "r is incorporated at a certain stage of sol preparation. The hydrolysis/condensation rate at room temperature of MTES is --7 times higher than that of TEOS [ 17]. This implies that the reaction time of MTES should

P.a. grade, Aldrich ChemicalCompanyInc., Milwaukee(WI), USA. *P.a. grade, Aldrich ChemicalCompanyInc., Milwaukee(WI), USA.

338

be ---7 times shorter to obtain silica polymers with dimensions similar to those obtained with hydrolysis and condensation of TEOS. This simple consideration led us to the idea to start with a "standard" silica sol solution preparation and add MTES after 6/7 of the normal total reaction time at least. If MTES was added earlier, for instance after 2/3 of the total reaction time, more "bulky" polymers were formed, visible through light scattering in the sol solution. This implied that in that case the polymer particles formed had dimensions of >10 nm, hampering the formation of a microporous membrane structure in a later stage of the process. The complete sol preparation procedure for hydrophobic membranes was as follows: TEOS was mixed with ethanol and placed in an ice-bath to avoid premature (partial) hydrolysis. A mixture of acid and water was added under vigorous stirring. After addition the reaction mixture was heated for 2 90hr at 60~ in a water bath under continuous stirring. The reaction mixture had a molar ratio (based on unreacted components) TEOS/ethanol/water/acid of 1/3.8/6.4/0.085. MTES was mixed with ethanol in the ratio of 1:3.8 and placed in an ice-bath. This mixture was added to the TEOS reaction mixture that has refluxed 2 90hr. The resulting MTES/TEOS reaction mixture obtained was heated for another 15 min. at 60~

The mixture then had a molar ratio MTES/TEOS/ethanol/water/acid (based on unreacted

components) of 1/1/7.6/6.4/0.085. Subsequently, the resulting sol was cooled and diluted 19-fold with ethanol to obtain the final dip-coat solution. After coating the membranes were calcined at 400~ for 3 hrs in pure N2 using a heating and cooling rate of 0.5~

Some active coal pellets' were placed in

the vicinity of the membranes to capture traces of oxygen in the N2 stream. Calcination was performed under a constant nitrogen flow (instead of air for the standard membranes) to avoid premature oxidation of the CH3 groups. The whole process of dipping and calcining was repeated once to repair any defects in the first silica membrane layer. The membranes obtained in this way are henceforth referred to as "MeSi(400) membranes". Unsupported silica material Unsupported microporous silica material was made for characterisation by means of physical sorption measurements as follows [2]: 60 cm 3 of 19x ethanol-diluted, hydrolysed silica sol was allowed to evaporate in a 10 cm O petri-dish at room temperature, so that 0.1-0.3 mm thick silica gel flakes were obtained overnight. These flakes were calcined at 400~

or 600~

for 3 hours with a heating and

cooling rate of 0.5~ The unsupported (microporous silica) membrane material was characterised with Ar physical sorption at 87K to determine its micropore volume, porosity and pore size distribution t. Nitrogen sorption measuraments were performed to investigate the amount of hydroxyl groups present in microporous

Norit RGM 0.8, QualityA3687, Norit N.V., Amersfoort, The Netherlands. t Sorptomatic 1900, Carlo Erba Instruments, Milan, Italy.

339

materials. The physical gas sorption set-up was provided with a turbo molecular pump system* and an extra pressure transducer for the low-pressure range (10 -3 Torr to 10 Torr) to be able to determine microporosity. This was checked with measuring zeolites [ 18]. All samples were degassed at 300~ for 24 hours prior to the sorption experiments. The pore size distribution is calculated according to the Horvfith-Kawazoe method [ 19], combined with the 10:4 Lennard-Jones potential functions for sorption of Ar on SiO> Hydrophobicity The hydrophobicity of the unsupported membrane material is determined by measuring the hydrophobicity index H I = Xoc,a,,Jx,,a,e,. as described in [20,21 ]. For that purpose the sample was dried first for 12 hrs at 250~ in a pure Ar stream. After that an Ar stream containing defined and equal concentrations of water and octane was used to load the sample until saturation at a temperature of 30~

The

Ar, water and octane flow rates were controlled by mass flow controllers. The breakthrough curves of the individual components were obtained by on-line gas chromatography. Numerical integration of the normalised breakthrough curves provided the sample loading of water, Xwater, and octane, Xoctane. These values were corrected for background signals, originating from the reactor. Measurement of breakthrough curves of water and octane resulted in/-//--0.3 for the unsupported Si(400) material and HI=3.0 for the MeSi(400) material [1,15]. The methylated unsupported membrane material is thus very hydrophobic whiie the standard silica material is strongly hydrophilic. The value of HI=3.0 for amorphous microporous silica is similar to a value of HI=2.9 found by Klein et al for a methylated silica-titania hybrid material [20]. For zeolites, however, higher values are measured such as H I = 1 0 . 3 for Silicalite I [21 ] which offers perspectives for further improvement of our silica material.

*Turbotronik, NT50 Leybold,Germany

340

Figure 1:

Drop of water on (A) MeSi(400) and (B) Si(400) membrane [1,15]

An impression of the difference in hydrophobicity of the membranes could also be obtained directly by putting a drop of water on both membrane types and observing the difference in curvature of the drops. As can be seen in Figure la water drop becomes more spread out on top of a Si(400) membrane than on a MeSi(400) membrane. This confirms that the MeSi(400) membranes are more hydrophobic than the Si(400) membranes. Thermogravimetric analysis Thermogravimetric analysis (TGA)* was performed on unsupported silica material to obtain a qualitative impression of the amount of hydroxyl groups at the surface. The TGA samples were stored in normal air at room temperature and hence at normal relative humidity before measurement. Unsupported material, made from the standard dip solution [Si(400)], but not calcined was examined by TGA to determine the burnout of the organic groups. The TGA experiments were performed with a heating rate of 1~

to 800~ in a pure N2 stream with a water and oxygen content less than 5 ppm.

The thermogravimetric experiments demonstrated a clear difference between the thermochemical properties of Si(400) and MeSi(400) materials as can be seen in Figure 4.

*Type 1136, Setaram, Lyon, France.

341

100 MeSi(400)~

98

A

U)

o

.,(=

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

96

o~

94

.~

92

~

9O

88

Figure 2:

Si(nr

,,,

0

I

,,

200

I

I

I

400 600 Temperature (~

800

,

1000

TGA, relative weight loss vs T for MeSi(400), Si(400) and dried silica sol [1,15]

MeSi(400) material does not show any weight loss up to 500~ starts to loose weight below 100~

while the Si(400) material already

This low-T weight loss of Si(400) is ascribed, as usual, to evapo-

ration of physisorbed water [22,23]. The lack of such a low-temperature weight loss for the MeSi(400) material indicates that in this material water sorption from ambient air hardly occurs. The total weight loss of both materials is quite different as well. Si(400) shows a weight loss of about 2%, caused by the loss of adsorbed water and surface hydroxyls at elevated temperatures. MeSi(400) shows a weight loss starting at much higher temperatures that saturates at 4% around 800~ cluded to be thermochemically stable until-500~

Hence MeSi(400) is con-

in pure N2. The weight loss of MeSi(400) in N2 at

higher temperatures might be due to the loss of incorporated methyl groups with the formation of CH4 or H2. Theoretically a weight loss of 12% is expected if all methyl groups, that are initially introduced in the synthesis, are removed in this way. It was found that after the TGA experiments the MeSi(400) material had turned black while the Si(400) material remained white. This led us to the conclusion that after the TGA run not all carbon atoms of the CH3 groups were removed from the MeSi(400) material and that it is likely that thermally induced condensation of methyl groups had occurred, for instance by:

~Si~CH

3 +

H3C~si"

/

~

~

~Si~CH2~Si~

~

4"

OH4

(1)

If, for instance, every two methyl groups combine, as happens in reaction (1), a maximum weight loss of 6.4% is expected. The fact that the actual weight loss observed is much less than 6.4% can be ex-

342

plained by the rather low concentration of methyl groups. This makes it unlikely that all methyl groups can participate in a reaction such as (1). Infra-Red Spectroscopy The presence of methyl groups in the microporous silica structure of the hydrophobic membrane material was demonstrated with infrared (FTIR) spectroscopy'. For that purpose, a KBr pellet was made of 20 mg unsupported material and 200 mg KBr. The pellet was heated in a pure Ar stream in an IR-cell t with KBr windows at 400~

for 20 hrs to remove water and weakly bound surface hydroxyls. The

spectra were recorded at 30~ (200 Scans) in the diffuse reflectance mode and represented by application of the Kubelka-Munk-function [24]. In Figure 3 the IR-spectra are given of unsupported Si(400) and MeSi(400) material. In the methylated material a sharp extra absorption peak is found around 1280 cm ~. This peak is ascribed to a symmetric deformation vibration of the CH3 groups [24].

*IFS 46, Bruker, Ettlingen, Germany. t HVC/diffuse reflectance unit DRA-XX, Harrick Scientific Corporation, Ossining (NY), USA.

343

O0

MeSi(400) m

mm

C

C

1,0

m

m

|

'

9

9

m

CH3

tt~

t~ m

03

r

0

m

!

1500

1400

1300

1200

1100

Wavenumber Figure 3

1000

900

I

800

c m "1

IR spectraof MeSi(400) and Si(400) [1,15]

?,-Alumina intermediate layer ),-Alumina membranes are prepared by dip coating sintered a-alumina supports (either flat or tubular) in a home-made boehmite (),-A1OOH) sol. The boehmite sol is prepared by the colloidal sol-gel route as follows: 70 moles of double-distilled water are heated to about 90~

and 0.5 mole of alumin-

ium-tri-sec-butoxide (ATSB)* is added drop-wise under a nitrogen flow to avoid premature hydrolysis. The temperature of the reaction mixture should at least be 80~ to prevent the formation of bayerite (AI(OH)3) [25]. After the addition of ATSB is complete, the mixture is kept at 90~ to evaporate the formed butanol. Subsequently, the solution is cooled down to about 60~

at which temperature the

boehmite mixture is peptised with HNO3t at pH of 2.5. During the full synthesis the mixture is stirred

Acros, 97% purity, Belgium. +E. Merck, Darmstadt,Germany.

344

vigorously. The peptised boehmite mixture is refluxed for 20 hours at 90~ resulting in a homogeneous and stable 0.5 molar boehmite sol. During refluxing the pH increases to 3.5. If the sol is peptised at pH of 3.5 before the 20 hours of refluxing, the final pH will be about 4.4. This will result in fast aggregation of boehmite particles and subsequent precipitation of part of the boehmite from the sol. This lowers the concentration of the remaining sol, thus making it unusable for membrane preparation. Before dipping the sol is mixed with a PVA" solution of 3 grams PVA per 100 ml 0.05 HNO3., prepared at 80~

This "dip solution" has a PVA : boehmite ratio of 2:3.

Dip coating is performed under class 100 cleanroom conditions in order to minimise particle contamination of the membrane layer. After dipping, the membranes are dried in a climate chamber* at 40~ and 60% R.H. that is situated inside the cleanroom. The drying rate at such conditions is sufficiently low to avoid any crack formation in the boehmite layer [26]. Standard )'-alumina membranes are formed by firing at 600~

for 3 hours in air with a heating and cooling rate of l~

The total

,/-alumina layer thickness is in the order of 3 ~m, with an average Kelvin radius of 2.0 nm, as determined by permporometry [27,28]. Hydrothermally stable )'-alumina membranes An important drawback of the "standard" )'-alumina membranes described above is that they are not stable towards steam atmospheres that are, for example, used in steam reforming. For a membrane steam reformer, normal operation conditions are: 600~

30 bar gas pressure with a ratio H20:CH4 =

1:3, these conditions are further indicated as SASRA (Simulated Ambient Steam Reforming Atmospheres). SASRA conditions were found to be highly detrimental to our standard ~/-alumina membranes: the complete ),-alumina layer peeled-off within several hours. It was discovered that the peeling-off of the ),-alumina layer is due to insufficient adherence of the layer to the a-alumina support. The use of supports with a less smooth surface, to enhance mechanical anchoring, can not solve this problem. Hence a chemical "anchoring" material is coated onto the a-alumina support before coating the ,/-alumina layer. This treatment leads to )'-alumina membranes that do not show any degradation under steam reforming conditions anymore [29]. The treatment is performed as follows: A Mono-Aluminium Phosphate (MAP) layer is coated on the supports according to the following procedure: A commercial 50 wt-% MAP solution s is diluted either 10 or 20 times, further indicated as MAP 10 and MAP20, respectively. The shiny surface of a flat support is brought in contact with this solution for 3 seconds, after which it is dried. Next to this pre-treatment, the supports are coated under class 100 clean room conditions with either pure or doped 0.5M boehmite sols as described above.

*MW 72.000 (g/mol)P.a., Merck, Darmstadt, Germany. *Heraeus V0tsch, Balingen, Germany. ~tAlfa, Johnson Matthey GmbH, Karslruhe, Germany.

345

The extent of degradation of the membranes is related to the tensile strength at the or/y-interface at which peeling-off or blistering is observed. Membrane degradation (peeling-off or blistering) was here tested by the so-called Scotch Tape Test [31 ]. In this test a piece of Scotch Tape is stuck onto the membrane surface and torn off rapidly. If the layer is of good quality it will not be torn off together with the tape. For the membranes with sufficient adherence, the change in pore-size during steamreforming treatment is measured with permporometry Standard y-alumina membrane-layers on ~-A1203 supports always came off in the Scotch Tape Test after SASRA treatment. When the support was treated with MAP, however, after SASRA treatment no delamination was observed. We suggest that the beneficial effect of MAP treatment results from chemical bonding between the membrane-layer and the support. The concentration of the MAP solution is found to be critical. Treatment with 5 wt-% MAP-solution gave good adherence, while a 2.5 wt-% solution resulted in some delamination, possibly due to insufficient phosphate on the surface of the supports. To reduce possible pore growth during the steam reforming treatment, the y-alumina membranes are sintered at temperatures much higher than usual. Such high temperatures, even up to 1000~

are pos-

sible provided an appropriate amount of lanthanum doping is present. The stabilising effect of lanthanum doping is well known [32,33]. Doping of the boehmite sol is performed by thorough mixing with the appropriate amount of a 0.3M lanthanum nitrate solution. The mixing is done directly before coating to avoid possible ageing effects that have been reported in the literature, for example by Lin and Burggraaf [32]. No such ageing studies are, however, performed in the present work. After the pore-size is established, the membranes are SASRA treated in a steel reactor. Heating and cooling is performed in an argon atmosphere at the same total pressure at a rate of 1~

In a few

experiments a pure steam treatment is carried out at 0.2 MPa total pressure at 150~ or 300~ in the same manner as for SASRA treatment. A pure CO2 treatment is done likewise, but at 500~

at

1.2 MPa pressure. Table 1 summarises the most important results from the investigation of metal doping. In this table the results of MAP treatment are combined with effects of firing temperature and doping. As can be seen in Table 1, y-alumina membranes with pore radii as low as 2.0 nm (Kelvin radius) may be obtained after firing at 600~

Note that, since an instrumental standard error of 0.5 nm (90% reliability) is

common in permporometry this technique should only be used for comparison purposes and to obtain a qualitative impression of the pore-size and pore-size distribution of the material under investigation.

346

Support Treatment

Tcalc(oc)

Test conditions

rKe,v,, (nm)

None

600

None

2.0

None

825

None

3.6

None

100(

None

8.7

MAP 10

825

None

4.2

MAP 10

825

SASRA

6.2

MAP 10

825

2xSASRA

7.5

y +3La

None

825

None

3.3

V+ 3La

MAP 10

100r

None

8.4

y+ 3La

MAP 10

100s

SASRA

9.3

y + 6La

MAP 10

100(~

None

6.0

y + 6La

MAP 10

1000

SASRA

6.1

~,+ 6La

MAP 10

1000

150~ steam

6.0

y + 6La

MAP 10

1000

300~ steam

6.0

? + 6La

MAP 10

1000

C02

6.3

V+ 9La

MAP 10

1000

None

8.6

Membrane

Table 1

Influence of support treatment, y-alumina doping, membrane firing temperature and SASRA-treatment on the pore-size of y-alumina. MAP 10 indicates a 10 times diluted standard MAP solution, which results in an effective MAP concentration of 5 mol-%., 3La indicates a 3 mol-% La-doped membrane, 6La indicates a 6 mol-% La doped membrane.

The pore-growth o f undoped "/-alumina strongly depends on temperature with a large increase in poresize between 825 and 1000~ 825~

The MAP-treated membranes have somewhat larger pores after firing at

The cause o f this effect is not clear yet. For undoped '/-alumina membranes, the pores g r o w

during S A S R A from 4.2 to 6.2 nm, and after a second S A S R A treatment to 7.5 nm. Thus, it appears that the pore-growth continues within the time scale o f our S A S R A treatment experiments. C o m p a r e d to undoped materials, 3 mol-% lanthanum doping gives hardly any beneficial effects on stability (Table 1). A significant improvement is found, however, for 6 mol-% lanthanum doping. For this case a pore-size o f only 6.0 nm is found after firing at 1000~

and no pore growth during S A S R A

347

treatment is observed at all. Additionally, after SASRA treatment, the pore-size distribution of a 6 mol-% doped y-alumina membrane is still very narrow, as can be seen in Figure 4.

6.E+17 In (D

5.E+17_

8v

4.E+17 _

"6 3.E+17

_

t_

,I2

2.E+17 1.E+17

t

0.E+00_

A

.4k A

0

10

A

4k

IA

20

30

Kelvin radius (nm)

Figure 4

Pore size distribution of a SASRA-treated,/-aluminamembrane. The support was treated with 5 mol-% MAP (MAP 10). The ,{-aluminawas doped with 6 mol-% La and sintered at 1000~ for three hours.

As one can see from Table 1, a spin-off result of this work is a list of recipes for the preparation of membranes with different amounts of doping, covering a complete range of pore-sizes with a resolution of 1-2 nm. This shows that we are now able to produce membranes with a tailor-made pore-size, which may be important for retaining certain large molecules by high-flux nanofiltration.

Flat supports

Flat supports are relatively easy to prepare. In our group two different methods are used. The first method is die pressing of a commercially available spray dried m-alumina powder*. The resulting disk is then pressed isostatically at 4000 bar. Final sintering is performed at 1260~ for 3 hours. The second method is the so-called colloidal filtration method. In this method a colloidal suspension is made of pure alumina powder [AKP30 or AKP-15t]. A 50wt-% suspension is obtained by dispersing the a-alumina powder in a 0.02M nitric acid solution [for AKP-30 powder] or a 0.02M nitric acid solution, mixed with Poly Vinyl Alcohol PVA ~ (5 g/l) [for AKP-15 powder] and using of ultrasonic

*PAI, Philips, Uden, The Netherlands t Sumitomo Chemical Company,Ltd, Tokyo, Japan. E. Merck, Darmstadt, Germany.

348

treatment* for 15 minutes. The resulting suspension is filtered over polyester filters t, consisting of a biological mixture of cellulose nitrate and cellulose acetate, with a pore size of 0.8 ~tm using a waterjet evacuation. The resulting filter cake (cast) is dried overnight at ambient temperature and fired at 1100~

[AKP-30] or 1150~ [AKP-15] for 1 hour. After firing the supports are machined to the re-

quired dimensions and polished until a shiny surface is obtained. Support pore-diameters obtained are 80 nm for the AKP-30 supports, 120 nm for the die-pressed supports and 160 nm for the AKP- 15 supports.

Tubular supports The single-bore tube geometry is currently most-well known in inorganic membrane technology. However to enhance area/volume ratios, multi-bore tubes and hollow fibres have emerged. All large membrane producing companies, such as US Filter, Noritake and Mitsui are able to deliver multi-bore tubes with various geometries. More recently, hollow fibre [34] supports consisting of porous or-alumina ceramics have been developed by TNO/CTK in Eindhoven. In a number of cases multibore may be less suitable due to limitations on reactor lay-out and the possible complications with high temperature sealing. Sealing problems can be expected for the hollow fibre geometry as wellbut the largest difficulty that must still be overcome is finding suitable techniques for the application of separative layers inside the hollow fiber. Coating a layer on the outside of the fibre is much easier but has the drawback that such a layer is much more subject to damage. Hence for hollow fibres supports, application of permselective layers by CVI seems to be the most suitable technique. Porous ct-A1203 tubes are frequently used as support for inorganic membranes. The normal way of producing such tubes is by extrusion or isostatic pressing followed by sintering. These techniques are fully accepted for the production of dense ceramic tubes, but may be less suitable for the production of porous membrane supports. Especially the occurrence of unroundness, inhomogeneities and a considerable surface roughness may impose problems. For the application of defect-poor meso- and microporous membrane layers for gas separation [ 16,35] a very smooth inner surface together with a narrow pore-size distribution of the membrane support tube is needed as well [36]. To meet increasing demands on roundness, homogeneity and surface quality ceramic tubes can be made by centrifugal casting (CC) of colloidal particles [37,38,39]. In this process a ceramic powder is dispersed in a liquid with a stabilising agent, followed by rotating for some time in a cylindrical mould around its axis. The resulting cast is dried, released from the mould and slightly sintered. If particles are used with a narrow size distribution and a low degree of agglomeration one may expect the forma-

*Model 250 Sonifier, BransonUltrasonicsCorporation,Danbury, USA. t ME 27, Schleicher& Schuell, Dassel, Germany.

349

tion of a nearly random-close-packed (RCP) green compact [40]. This requires the use of a proper colloidal stabiliser at a concentration such that the particles stay well dispersed in the liquid but form a coherent rigid structure in the compact. Examples of possible stabilisers are nitric acid [41,42,43] or polyacrylate-based products [39,44,45]. If the concentration of stabiliser is too low the particles will already flock in the liquid and form a low-density compact that will exhibit a rough surface. At higher stabiliser concentrations the dispersion may become too stable so that the compact remains fluid-like [46] and redispersion might occur as soon as the rotation stops. At optimum conditions the compact shape will closely follow the cylindrical mould shape which can be made with roundness near to perfection. In addition the surface roughness of the inside surface of the compact can be expected to be of the order of the particle size. Sintering mainly serves to obtain sufficient strength by the formation of necks without significant grain growth and shrinkage. The starting ot-A1203 powders were the above-mentioned AKP-30 and AKP-15 with a mean particle size of 0.40 and 0.62 ~tm and a BET surface of 6.2

m2/gand 3.5 m2/g respectively. Both powders have

narrow particle size distributions of(1.5% 10.6 mol/m2*s*Pa) as has been summerized by Coronas et al (9). However the values cannot be correlated with the thicknesses of the zeolite layers which have been reported (in the range - 1 to 500 ~tm). These discrepancies have been ascribed to the effects of transport resistance through the support, and differences in the location of the zeolite layer (e.g. outside or inside the pores of the support). Vroon (90), Kapteyn (91) and Burggraaf (5) have discussed in more detail the discrepancies between calculated and experimental flux values for other gases. They conclude that the grain size and grain boundaries, as well as pores between crystals may dominate the flux behaviour observed. 3.2 Separation and Permeation of Gas Mixtures The permeation of gas mixtures is complex and it is generally not possible to make predictions of behaviour from measurements made with the separate components. Detailed treatments have been given by K~ger and Ruthven (81) and Barrer (82) to describe the diffusion mechanisms which may occur with gas mixtures in zeolites and other microporous media where strong adsorption and condensation may occur. To rationalize the behaviour of binary gas mixtures, Burggraaff (5) has distinguished each component according to the strength of adsorption viz. either weak (w) or strong (s). Generally for a combination of

389

weakly adsorbed gases the separation factors, ct, are similar to the permselectivity values, although the permeance values in the mixture are somewhat lower than the single gas permeances. For mixtures of more strongly sorbed gases, the situation is more complex. For example with MFI, shape selective effects can occur with linear and branched hydrocarbons (viz. n/i-butane mixtures). Selectivities of 27 at 295 K and 23 at 403 K were found by Bakker et al (92), despite only a small difference in the adsorption of each isomer. Such differences have been ascribed to the preferential location of the branched hydrocarbon at the intersections of the channel systems in MFI. More remarkable separation effects have been observed with mixtures containing a weakly and a strongly sorbed gas. This is illustrated by the results of Kapteijn et al (5) for the separation of hydrogen and n-butane over a range of temperatures (Figure 12.). Here the permeation behaviour of n-butane is similar to that for the single component. However the permeation of hydrogen is drastically reduced at lower temperature due to "poreblocking" by n-butane. In contrast to the single gas behaviour, the H2 permeation, then increases with temperature. This increase follows a decrease in the pore filling of the n-butane at higher temperature. Such "pore-blocking" effects have been reported and analysed by Barrer (82) over 30 years ago in studies of gas separation with microporous carbon plugs. The mechanisms of the process, although similar, is likely to be more complex with zeolites due to the more specific interactions of the strongly sorbed component within the zeolite pores. The effects of blocking by a more strongly sorbed component, as observed with H2/n-butane mixtures, have been reported for several other two component systems e.g. H2/CO2 and O2/MeOH (44).

25-

en

'~

15

~

10

4(.

I

300

'

i

400

'

I

500

'

I

600

Temperature / K Figure 12. Separation behaviour of a H2/n-butane (1" 1) mixture as a function of temperature by a silicalite membrane at 100 kPa (after Kapteijn et al (5)).

390 In these cases the permeance of the weakly sorbed component (1-12,02) increases with the rise in temperature. With mixtures of weakly sorbed gases several examples of molecular sieving have been reported with MFI type membranes. These include the separation of H2/SF6 mixtures (93), where the permeances were similar to those of the single components. Here a selectivity of-- 9 was found, which could be ascribed to the differences in kinetic diameter (viz. 2.9 and 5.5 A respectively). Other examples of sieving with MFI include HJCH4 (37), O2/N2 (68). Separation effects with CO2/CH4 (84) and COJN2 (68) on MFI have also been reported, however here the stronger quadrupolar interaction of the CO2 with the zeolite is likely to have a role. This effect is evidently the explanation for the separation of the CO2/N2 mixtures with NaY zeolite membranes as reported by Kusakabe et al (60). Here separation selectivities of 50-75 were reported at 303 K, which cannot be ascribed to molecular sieving with this zeolite (pore size 7.4 A), since the kinetic diameter of CO2 is 3.3 A. Separations have been reported for H2/N2 mixtures with NaA membranes (48). This zeolite has a smaller pore size (4.1 A) and sieving effects may indeed occur. There are several reports of the size exclusion with MFI membranes for two component gases, particularly with hydrocarbon isomer mixtures. These include n-hexane/2-2 dimethyl butane (94, 55, 90) and p/o-xylene mixtures (90) for example. In contrast to work with membranes with the MFI structure there are few reports of separations with membranes of other types of zeolite. Separation of organic mixtures have however been observed with NaY for benzene/p-xylene (96) and ferierite for cyclohexane/benzene and xylene isomers (97). A comprehensive bibliography of gas separations performed with zeolite membranes has recently been published by Coronas et al (9). This also includes a review of different separations performed by pervaporation of liquid mixtures with zeolite membranes, a topic which is not covered in the present review.

4. CONCLUSIONS It is evident from this review that research activity on zeolite membranes has expanded enormously within the last ten years. This activity has been stimulated by potentially novel applications. These include on the one hand those concerned with gas separation and catalytic membrane reactors. Here the unique molecular sieving properties of zeolites may be exploited using membranes in continous processes at elevated temperature, with high efficiency and savings in energy. The other emerging field concerns the application of zeolite films, as selective sensors and optoelectronic devices for example. Both of these areas are technically challenging, and require membranes which are free of defects, stable at high temperature, and have controlled microstructure. The various routes which have been used to synthesize such zeolite membranes have been described here. Furthermore the structure and properties of these membranes in gas separation applications have been treated in detail. Some general conclusions and indications where further research will be required in the future can be made. The most numerous applications of zeolite membranes have been in separations involving the pervaporation of liquids (e.g. water/alcohol mixtures). These membranes have generally been of the polymer matrix variety, in which a range of different zeolites (silicalite, NaX, NaY) have been incorporated. The more recent and successful applications of zeolite membranes in gas separations have been predominantly with MFI-type membranes.

391 These have usually been prepared by in-situ hydrothermal routes, generally using either porous alumina of stainless-steel supports. These routes have been optimised to minimise defects in the membranes. Potential sources of such defects, and methods for their elimination, have already been discussed. Nevertheless it is evident that the more successful gas separations have been achieved with mixtures containing either two condensible gases or a condensible gas and a non-condensed gas. The mechanisms of these separations have often involved preferential sorption effects and "pore blocking" processes. In such separation processes, the elimination of defects is less crucial, as the defects (mesoporous) may also be "blocked" by capillary condensate. There have been far fewer reports of successful separations of non-condensable gas mixtures. The separation of mixtures such as N2/CO 2, H2/CO2, and NJO 2, which are of particular commercial importance, are likely to be achived by molecular sieving or size exclusion mechanisms. Consequently further research is required in the development of membranes containing smaller pore zeolites (e.g. zeolite A, chabazite, sodalite), which are defect free. Progress in the synthesis of these membranes, having alumino-silicate structures, is more likely to be achieved using secondary growth processes. The in-situ hydrothermal batch process, which has been successful previously for silicalite 1 membranes, seems less appropriate. A particular advance may be achieved using colloidal zeolite crystals. This is an active area of current development as has been discussed. It is also possible that techniques, developed previously in sol-gel processing for the deposition of porous thin films of oxides and catalytic coatings on ceramic and metallic substrates (74, 98, 99) could be applied here. These techniques may be readily adapted for the coating of membrane support modules with colloidal zeolites on a commercial scale in the future.

5. ACKNOWLEDGEMENTS We are indebted to many colleagues for helpful discussions, and in particular Drs. N.K. Kanellopoulos and E.S. Kikkinides. Financial support by the European Community under the Industrial and Materials Technologies Programme (Brite-Euram III; Contract No. BRDPRCT96-313) is gratefully acknowledged.

5. REFERENCES 1. R.M. Barrer, Zeolites and Clay Minerals and Sorbents and Molecular Sieves, Academic Press, NY (1978) 2. D.W. Breck, Zeolite Molecular Sieves: Structure Chemistry and use. Wiley, New York, 1974 3. H. van Bekkum, E.M. Flauigan and J.C. Jansen (eds.), Introduction to Zeolite Science and Practice. Studies in Surface Science and Catalysis, Vol. 58, Elsevier, Amsterdam, 1991 4. W.M. Meier and D.H. Olson, Atlas of Zeolite Structure Types, Butterworth-Heinemann, 3rd edn. London, 1992 5. A.J. Burggraaf, "Transport and Separation Properties of Membranes with Gases and Vapours", in Fundamentals of Inorganic Membrane Science and Technology, A.J. Burggraafand L. Cot (eds.) p. 331, Elsevier Science B.V. Amsterdam, 1996

392 6. V.N. Burganos (ed.) in: MRS Bulletin "Membranes and Membranes Processes", 24 (1999) 19 7. J.L. Falconer, R.D. Noble and D.S. Sperry, in "Membrane Separation Technology. Principles and Applications", R.D. Noble and S.A. Stem, eds., p. 669 Elsevier Science B.V. Amsterdam, 1995 8. Y. Yan, M. Ysapatsis, G.R. Gavalas, M.E. Davis, J. Chem. Soc., Chem. Commun. (1995) 227 9. J. Coronas and J. Santamaria, Separation and Purification Methods, 28 (1999) 127 10. G.A. Ozin, A. Kuperman and A. Stein, Angew. Chem. 128 (1998) 359 11. M.E. Davis, Ind. Eng. Chem. Res., 30 (1991) 1675 12. Y. Yah, T. Bein, J. Phys. Chem., 96 (1992) 9387 13. Y. Sun, E. Hao, X. Zhang, B. Yang, J. Shen, L. Chi, and H. Fuchs, Langmuir, 13 (1997) 5168 14. J. Hedlund, B.J. Schoeman, J. Sterte, Progress in "Zeolite and Microporous Materials", Studies in Surface Science and Catalysis, Vol. 105c, H. Chou, S.-K. Ihm and Y.S. Uh (eds.) Elsevier Science, Amsterdam, 1997 p. 2203 15. G. Cho, J.S. Lee, D.T. Glatzhofer, B.M. Fung, W.L. Yan and E.A. O'Rear, Adv. Mater., 11 (1999) 497 16. M. Tsapatsis and G.R. Gavalas, "Synthesis of Porous Inorganic Membranes", MRS Bulletin, Membranes and Membrane Processes, V.N. Burganos (ed.), 24 (1999) 30 17. R.M. Barrer, Hydrothermal Chemistry of Zeolites, Academic Press, London, 1982 18. R.M. Barrer, in "Zeolite Synthesis", in M.L. Occeli and H.E. Robson, ACS Symp. Ser. 398 (1989) 11 19. U. Mtiller and K. Unger, Zeolites, 8 (1988) 154 20. A.E. Person, B.J. Schoeman, J. Sterte a,d J.E. Otterstedt, Zeolites, 14 (1994) 557 21. B.J. Schoeman, J. Sterte and J.E. Otterstedt, Zeolites, 14 (1994) 110 22. B.J. Schoeman, J. Sterte and J.E. Otterstedt, Zeolites, 14 (1994) 208 23. B.J. Schoeman, J. Sterte and J.E. Otterstedt, J. Colloid and Interface Sci., 170 (1995) 449 24. W.H. Dokter, T.P.M. Beelen, H.F. Van Garderen, C.P.J. Rummens, R.A. Van Santen and J.D.F.Ramsay, Colloids Surf. A. : Physicochem Eng. Aspects, 85 (1994) 89 25. P.-P.E.A. de Moor, T.P.M. Beelen, B.U. Komanschek, O. Diat, R.A. Van Santen, J. Phys. Chem. B 101 (1997) 11077 26. C.E.A. Kirschhock, R. Ravishankar, F. Verseurt, P.J. Grobet, P.A. Jacobs and J.A. Martens, J. Phys. Chem. B. 103 (1999) 4965 27. R.M. Barrer and S.D. James, J. Phys. Chem., 64 (1960) 417 28. D.R. Paul and D.R. Kemp, J. Polym. Sci. Symp., 41 (1973) 79 29. H.J.C. te Hennepe, W.B.F. Boswerger, D. Bargeman, M.H.V. Milder and C.A. Smolders, J. Membrane Sci., 89 (1994) 185 30. M.G. Stier, N. Baq and L. Yilmaz, J. Membrane Sci., 91 (1994) 77 31. T. Bein, K. Brown, and C.J. Brinker, "Molecular Sieve Films from Zeolite-Silica Microcomposites", in Zeolites: Facts, Figures and Future, P.A. Jacobs and R.A. van Santen (eds.), Elsevier Science Publishers, Amsterdam, 1989. 32. R. Le van Mao, E. Rutinduka, C. Detellier, P. Gougay, V. Hascoet, S. Tavakolyan, S.V. Hoa, and T. Matsura, J. Mater. Chem., 9 (1999) 783 33. P. K(ilsch, D. Venzke, M. Noack, P. Toussaint and J. Caro, J. Chem. Soc. Chem. Commun., (1994) 2491

393 34. P. K61sch, D. Venzke, M. Noack, E. Lieske, P. Toussaint and J. Caro, in: Studies in Surface Science and Catalysis, Vol. 84 B, 1075, J. Weitkamp et al. (eds.), 1994 35. D. Uzio, J. Peureux, A. Giroir-Fendler, J.A. Dalmon annd J.D.F. Ramsay, in Studies in Surface Science and Catalysis, Vol. 87, 411, Rouquerol et al. (eds.), 1994 36. J.D.F. Ramsay, A. Giroir-Fendler, A. Julbe and J.A. Dalmon, Fr. Patent 94-05562 (1994) 37. E.R. Geus, M.J. den Exter and H. van Bekkum, J. Chem. Soc. Faraday Trans., 88 (1992) 3103 38. E.R. Geus, H. van Bekkum, W.J.W. Bakker and J.A. Moulijn, Microp. Mat., 1 (1993) 131 39. Y. Yan., M. Tsapatsis, G.R. Gavalas and M.E. Davis, J. Chem. Soc., Chem. Commun., (1995) 227 40. Y.H. Chiou, T.G. Tsai, S.L. Sung, H.C. Shih, C.N. Wu and K.J. Chao, J. Chem. Soc., Faraday Trans., 92 (1996) 1061 41. K. Kusakabe, S. Yoneshige, A. Murata and S. Morooka, J. Membr. Sci. 116 (1996) 39 42. Z.A.E.P. Vroon, K. Keizer, M.J. Gilde, H. Verweij and A.J. Burggraaf, J. Membrane Sci., (1996) 127 43. M.D. Jia, B. Chen, R.D. Noble and J.C. Falconer, J. Membrane Sci., 90 (1994) 1 44. E. Piera, A. Giroir-Fendler, H. Moueddeb, J.A. Dalmon, J. Coronas, M. Menendez and Santamaria, J. Membrane Sci., 142 (1998) 97 45. G.J. Myatt, P.M. Budd, C. Price and S.W. Carr, J. Mater. Chem. 2 (1992) 1103 46. S. Yamazaki and K. Tsutsumi, Microp. Mater. 4 (1995) 205 47. H. Kita, K. Horii, Y. Ohtoshi and K. Okamoto, J. Mater. Sci. Lett., 14 (1995) 206 48. K. Aoki, K. Kasukabe and S. Marooka, J. Membr. Sci., 141 (1998) 197 49. H. Kita, T. Inoue, H. Asamura, K. Tanaka and K. Okamoto, Chem. Commun, (1997) 45 50. E. Piera, M.A. Salomon, J. Coronas, M. Mendez and J. Santamaria, J. Membrane Sci., 149 (1998) 99 51. J. Dong and Y.S. Lin, Ind. Eng. Chem. Res., 37 (1998) 2404 52. T. Sano, F. Kiyozumi, K. Maeda, M. Toba, S. Niwa and F. Mizukami, J. Mol. Catal., 77 (1992) 19 53. J.C. Poshusta, T.A. vu, J.L. Falconer and R.D. Noble, Ind. Eng. Chem. Res., 37 (1998) 3924 54. J. Coronas, J.L. Falconer and R.D. Noble, Ind. Eng. Chem. Res., 37 (1998) 166 55. A. Giroir-Fendler, J. Pereux, H. Mozzanega a,d J.A. Dalmon, Stud. Surf. Sci. Catal., 111 (1996) 127 56. G.E. Romanos, E.S. Kikkinides, N.K. Kanellopoulos, J.D.F. Ramsay, P. Langlois and S. Kallus, in "Fundamentals of Adsorption- 6", p. 1077, F. Meunier (ed.), Elsevier, Amsterdam, 1998. 57. M.J. den Exter, H. van Bekkum, C.J.M. Rijn, F. Kapteijn, J.A. Moulijn, H. Schellevis and C.I.N. Beenakker, Zeolites, 19 (1997) 13 58. H.S. Oh, M.H. Kim and H.K. Rhee, Studies in Surface Sci. and Catalysis, 105 (1997) 2217 59. S. Kallus and J.D.F. Ramsay, unpub, work 60. K. Kusakabe, T. Kuroda, A. Murata and S. Morooka, Ind. Eng. Chem. Res., 36 (1997) 649 61. R. Lai and G.R. Gavalas, Ind. Eng. Chem. Res., 37 (1998) 4275 62. Y. Yan, M.E. Davis and G.R. Gavalas, J. Membrane Sci., 123 (1997) 95 63. M. Nomura, T. Yamaguchi and S. Nakao, Ind. Eng? Chem. Res., 36 (1997) 95 64. G. Tzeng, K.J. Chao, Adv. Mater., 9 (1997) 1154

394 65. Y. Han, H. Ma, S. Qiu, F.-S. Xiao, Microporous and Mesoporous Materials, 30 (1999) 321 66. Lovallo and Tsapatsis, "Nano-crystalline Zeolites: Synthesis, Characterization, and Application with Emphasis on Zeolite-L Nanoclusters", in Advanced Techniques in Catalyst Synthesis, W. Moser (ed.) Academic Press, 1996 67. M.C. Lovallo and M. Tsapatsis, AIChE J. 42 (1996) 3020 68. M.C. Lovallo, A. Gouzinis and M. Tsapatsis, AIChE J. 44 (1998) 1903 69. L.C. Boudreou and M. Tsapatsis, Chem. Mater., 9 (1997) 1705 70. M.C. Lavallo, M. Tsaptsis and T. Okubo, Chem. Mater. 8 (1996) 1579 71. K.J. Balkus and M.E. Gimon-Kinsel, Chem. Mater., 10 (1998) 464 72. G. Xomeritakis, A. Gouzinis, S. Nair, T. Okubo, M. He, R.M. Ovemey and M. Tsapatsis, Chem. Eng. Sci., 54 (1999) 3521 73. A. Gouzinis and M. Tsapatsis, Chem. Mater. 10 (1998) 2497 74. C.J. Brinker and G.W. Scherer, Sol Gel Science, Academic Press, San Diego, 1990 75. G. Cho, J.-S. Lee, D.T. Glatzhofer, B.M. Fung, W.L. Yuan and E.A. O'Rear, Adv. Mater., 11 (1999) 497 76. S. Kallus, P. Langlois, G.E. Romanos, Th. Steriotis, E.S. Kikkinides, N.K. Kanellopoulos and J.D.F. Ramsay, "Zeolite Membranes - Characterisation and Application in Gas Separations", Proc. Characterisation of Porous Solids-V, Heidelberg, 1999 (in press "Studies in Surface Sci. and Catalysis"). 77. K.J. Balkus, T. Mufioz and M.E. Gimon-Kinsel, Chem. Mater., 10 (1998) 464 78. K.J. Balkus, L. Ball, B.E. Gnade and J.M. Anthony, Chem. Mater., 9 (1997) 380 79. C.C. FreyhardtM. Tsapatsis, R.F. Lobo, K.J. Balkus, M.E. Davis, Nature, 381 (1996) 295 80. T. Mufioz and K.J. Balkus, J. Amer. Chem. Soc., 121 (1999) 139 81. J. Karger and D.M. Ruthven, "Diffusion in Zeolites and other Microporous Solids",Wiley, New York, 1992 82. R.M. Barrer, "Surface and Volume Flow in Porous Media" in "The Solid Gas Interface", Vol 2, p. 557, E.A. Flood (ed.), E. Arnold Ltd., London, 1967 83. R.M. Barrer, "Porous Crystal Membranes", J. Chem. Soc. Faraday Trans., 86 (1990) 1123 84. M.B. Rao and S. Sircar, J. Membr. Sci., 85 (1993) 253 85. J.E. Koresh and A. Softer, Sep. Sci. Technol., 22 (1987) 972 86. A.B. Shelekhin, A.G. Dixon and Y.H. Ma, J. Membr. Sci., 75 (1992) 233 87. R.S.A. de Lange, J.H.A. Hekkink, K. Keiser and A.J. Burggraaf, J. Membr. Sci, 99 (1995) 57 88. J.M. van de Graaf, F. Kapteijn and J. Moulijn, AIChE J., 45 (1999) 497 89. W.J.W. Bakker, L.P.J. van den Broeke, F. Kapteijn and J. Moulijn, AIChE J., 43 (1997) 2203 90. Z.A.E.P. Vroon, K. Keizer, M.J.Gilde, M. Verweij and A.J. Burggraaf, J. Membrane Sci., 113 (1996) 293 91. F. Kapteijn, W.J. Bakker, G. Zheng and J. Moulijn, Microporous Mater., 3 (1994) 227 92. W.J.W. Bakker, F. Kapteijn, J. Poppe and J.A. Moulijn, J. Membrane Sci., 117 (1996) 57 93. C. Bai, M.D. Jia, R.D. Noble and J.L. Falconer, J. Membrane Sci., 141 (1995) 79 94. J.G. Tsikoyiannis and W.O. Haag, Zeolites 12 (1992) 126 95. H. Kita, T. Horita, H. Asamura, K. Tanaka and K. Okamoto, Proc. ICIM '98, Nagoya, Proc. p. 536 96. N. Nishiyama, K. Ueyama and M. Matsukata, J. Chem. Soc., Chem. Commun., (1995) 1967

395 97. W. Wishiyama, K. Ueyama and M. Matsukata, Stud. Surf. Sci. Catal., 105 (1997) 2195 98. R.L. Nelson, J.D.F. Ramsay, J.L. Woodhead, J.A. Cairns and J.A.A. Crossley, Thin Solid Films, 81 (1981) 329 99. J.D.F. Ramsay, "Synthesis of Porous Ceramics by Sol-Gel Processes", in Sol-Gel Processing of Advanced Ceramics, F.D. Gnanam (ed.), p. 47, Oxford IBH Publ. Co., New Delhi, 1996


RecentAdvancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) 2000 ElsevierScienceB.V. All rightsreserved.

397

Chemical Vapor Deposition Membranes M. Tsapatsis ", G.R. Gavalas b, and G. Xomeritakis a a Department of Chemical Engineering, 159 Goessmann Laboratory, University of Massachusetts, Amherst, MA 01003-3110 h Division of Chemistry and Chemical Engineering, 210-41, California Institute of Technology, Pasadena, CA 91125 This chapter is divided into four sections the first of which treats issues of general relevance to Chemical Vapor Deposition (CVD) of membranes, the second reviews work on dense silica membranes, the third is devoted to Y203-stabilized ZrO2 (YSZ) membranes, and the fourth treats CVD of Pd membranes. 1. INTRODUCTION Inorganic membranes are used in various liquid filtration processes but unlike polymeric membranes they have not yet been industrially applied to gas separations. Because of their high cost, these membranes are potentially useful only in separations where they offer some essential advantage such as high selectivity, or thermal and chemical stability. Very high selectivities, not possible with polymeric membranes, are offered by metal or silica membranes for hydrogen separation, by ion conducting ceramic membranes for oxygen separation, and by zeolite membranes for hydrocarbon separations. Moreover, being thermally stable, inorganic membranes are essential for membrane reactor applications to hydrocarbon catalytic dehydrogenations, isomerizations and partial oxidations. Inorganic membranes are classified into unsupported and supported types. The former are generally uniform throughout their thickness while the latter are composites of thin films having the separating layer deposited on thicker porous substrates, or supports, providing mechanical strength. Unsupported membranes are usually made by extrusion or tape casting from a suspension of precursor particles, followed by calcination. Supported membranes are made by depositing the separation layer from suitable precursors suspended in a liquid or gaseous medium. Deposition from the liquid phase involves techniques such as dip-coating in polymeric or particulate suspensions used for making silica and carbon membranes, hydrothermal synthesis used for making zeolite membranes, and electroless deposition used for making palladium membranes. Membrane formation from gas phase precursors by chemical vapor deposition (CVD), the subject of this article, is also quite versatile and has been used to make several types of membranes as will be reviewed in subsequent sections. Another classification of inorganic membranes is into dense or microporous (pore diameter below 2 nm). The microporous category is the broadest one, tbr it includes carbon, zeolite, and amorphous oxide membranes. These membranes have pore size between 0.4 and 1 mn and owe their separation properties to molecular sieving, selective adsorption or a combination of the two properties. As a result, microporous membranes are suitable for separation of a wide variety of gas mixtures. The dense category includes Pd alloy and other metal membranes, ionic (or mixed ionicelectronic) conducting oxide membranes and dense silica membranes. Dense membranes

398 made by CVD are limited to separations of mixtures containing hydrogen or oxygen. Such separations, however, are essential in the refining, petrochemical, and energy generation industries. Hydrogen separation, for example, has potential applications to membrane reactors for many important catalytic dehydrogenations, hydrogen production, and fuel cells. Membrane oxygen separation has potential application to membrane reactors for hydrocarbon partial oxidations, among which the partial oxidation of methane to synthesis gas is currently pursued in several industrial laboratories. 2. QUALITATIVE PRINCIPLES OF MEMBRANE CVD CVD signifies the growth of a solid product, usually in the form of a film, from gaseous reactants. The product can be grown on fiat substrates, fibers, or particles for different types of applications. The mechanisms of CVD reactions involve gas phase reactions, and reactions taking place on the solid surface. Some common CVD reactions employed in semiconductor fabrication have been studied in detail by surface spectroscopies and other surface science techniques. CVD of membrane films have not been studied in such detail but conditions for growing good quality membranes have been identified empirically. Nevertheless, some qualitative principles are useful for guiding the experimental effort. For this purpose we consider the simplified reaction sequence: A (g) B (s) B (s) + B (s) B2 ts) + B ~) B2 (g) + B2 (g) etc,

--) --) ")' --) --)'

B (s) + C (s) S (~) B2 (s) B3 is) B4 (8)

(1) (2) (3) (4) (5)

where B, the--ae~e gas phase intermediate, can react on the solid and can also form oligomers in the gas phase. The oligomerization reactions (3)-(5) can be purely physical, reversible events akin to vapor condensation, or can involve bond formation. In the first case the growth of particles follows a nucleation path and will be very sensitive to the concentration and temperature that control supersaturation. In the second case the tbrmation of particles also depends on concentration and temperature but the growth is not quite as sensitive to these parameters. In both cases, lowering the reactants' concentration will reduce linearly the first order steps (1) and (2) and more strongly the oligomer and particle forming steps (3)-(5 ). For CVD reactions involving two gaseous reactants, C and D, one possible scheme similar to (1)-(5) is C(s ) + D(g) --) E~s)+ F(s ) (6) E(s) + E(s) ") E2(s) (7) E (s) --) E (~) (8) etc. Whether deriving from gas phase or liquid phase deposition, the membrane pore structure depends on two major factors. One is the size and shape of the molecules or particles responsible for film growth. The other is the transformation that the nascent film undergoes

399 in subsequent drying and heat treatment operations. As outlined above, the growth species can be the unconverted feed, A, the species B formed by decomposition of A, small oligomers or clusters, or even particles. Once adsorbed on the surface these species can undergo further reactions. For example, in deposition of SiO2 by alternating reactions with SIC14 and H20, the species adsorbing and reacting on the surface is the unaltered feed, SIC14 or H20 (Kim and Gavalas, 1993). In deposition of SiO2 from tetraethylorthosilicate (TEOS), on the other hand, the entity adsorbing and reacting on the surface is a molecule resulting from gas phase TEOS decomposition (Yah et al., 1994). In deposition of A1N from A1C13 and NH3 reactants the molecules adsorbing and reacting on the surface were identified as A1C13.(NH3)• complexes (Kim et al., 1991). If attention is focused on the first of the aforementioned two factors, namely the size and shape of the growth species, the crucial issue is the size distribution in the vicinity of the porous support. When particle formation is delayed or suppressed the deposit grows by reaction (2) taking place on the external surface and inside the pores of the support. Clearly, ~ along with the monomer B, dimers and other clusters also react in the same fashion. Deposition in the pores will cease when the pore mouths have narrowed to the point where the growth species can no longer penetrate. In principle this limiting pore size is approximately the kinetic diameter of the growth species but reactions and diffusion in subsequent heat treatment will generally increase or decrease that pore size. Thus, the resulting membrane will be dense or microporous, depending on these latter solid state processes that are highly material specific and have not been systematically studied in the context of membrane formation. After the pore mouths are closed to the growth species, deposition will continue and extend the membrane layer outside of the support. The time to pore closure depends on the support pore size, or, more precisely, on the pore size distribution. According to the wellknown relations for reaction and pore diffusion, the depth of deposit penetration into the pores is approximately proportional to the square root of the ratio of reaction rate constant and pore diffusion coefficient. The density of this internal deposit layer is not uniform; it is maximum at the pore entrance and gradually diminishes with distance from the surface. This issue will be discussed in some detail in the section on silica and YSZ deposition. At higher concentrations of the reactant A and longer residence times of the reactants prior to contacting the membrane support that are long enough to allow substantial particle formation, the kinetics of deposition and the structure of the deposit layer is far more difficult to describe. Particle nucleation, growth, agglomeration and mass transfer and adhesion to the surface, as well as surface reactions like (2) are all involved in the deposit growth which is now much faster than in the case of purely gaseous growth species. The resulting membrane may be dense or porous depending on the particle size distribution and on the relative rates of convective or diffusive particle accumulation on the one hand, and growth of the already deposited particles on the other hand. The particle size distribution, in turn, depends on the feed concentration and temperature-time history of the reactant gases. A quantitative description of film growth under these conditions would obviously be very involved and require rate parameters that are rarely known. Particle-enhanced deposition has been studied as a means of increasing the film growth rate on nonporous substrates (Allendorf et al., 1993; Komiyama and Osawa, 1985). Control of the reaction conditions is essential for high quality membranes. Making a dense membrane obviously requires suppression of particle formation so that growth proceeds

400 strictly by reaction (2) or similar reactions involving small clusters. For this purpose the concentration of B must be kept low and growth will be slow. These conditions are appropriate for growth on mesoporous supports with pore size 2-10 nm. For membrane growth on supports with larger pore size, carrying out the deposition in the absence of particles would take long time to pore-closure and pore penetration will be deep on account of the larger diffusion coefficient. Thus, CVD on macroporous supports must generally utilize combined deposition by particles as well as gaseous species. The reaction conditions must be more delicately balanced to achieve a particle size appropriate for the particular pore size of the support. Particle deposition is essential in this case, but it must be supplemented by heterogeneous reaction in the deposit if the interparticle voids are to be closed. 3. CVD OF SILICA MEMBRANES Microporous or dense silica membranes prepared by CVD have been studied extensively for applications in selective hydrogen separations and less commonly for other molecular sieve separations like nitrogen or air/hydrocarbon separations. Vycor glass is the most often used support because in spite of its relative low permeability that effectively sets the upper limit for hydrogen fluxes through the composite membranes it has a rather narrow mesopore size distribution. It can also be argued that it is in principle compatible with SiO2 in terms of thermal expansion coefficients and therefore is expected to suffer less by cracking due to thermal cycling. Moreover, the surface chemistry of Vycor glass is rather well studied and therefore heterogeneous deposition schemes can be devised at least at the qualitative level allowing for better control of the CVD process. More recently, other supports like a-alumina or y-alumina coated a-alumina tubes have been used successfully as supports. The objective of most of the SiO2-CVD processes reported is to close the pores of the support over a narrow range enabling selective hydrogen separation. Over the last decade several successful demonstrations of this idea have been reported, however, flux and stability improvements especially in the presence of water vapor are needed tbr industrial applications. The earlier attempt on the preparation of silica membranes by CVD is that reported by Okubo and Inoue (1989a). These workers introduced vapors of TEOS inside a tubular glass support (pore size 4 nm) at 200~ and 1 atm and decomposed the silicon precursor near the pore mouths of the support so that the permselectivity between He and 02 was improved from 3.0 of the support to --6.0 after modification. The permeation properties of these membranes were studied in more detail in a subsequent publication and include a H2 permeance of 5xl 0-9 mol/m2-s-Pa at 200~ with H2/N2 ratio of-~l 1 (Okubo and Inoue, 1989b). At this point, it is believed that the partial success of these workers can be attributed to the low temperature of deposition employed, imposed by the difficulty of sealing the porous glass support inside their reactor at higher temperatures. More systematic efforts on the preparation of silica membranes by CVD and very high permselectivities were reported shortly after by the group of Gavalas in a number of publications. The support employed by this group was porous Vycor glass tubes of pore size 4 nm (supplied by Coming), welded at both ends with non-porous quartz tubes, so that it could be conveniently mounted inside a tubular reactor and operated at temperatures up to 800~ In their first attempt, the oxidation reaction of silane (Sill4) with 02 was employed with the two reactants introduced from opposite sides of the tubular support at a total pressure of 1 atm (Gavalas et al., 1989). Pore plugging was achieved at a narrow temperature range of 450~

401 since reaction was too slow at lower temperatures whereas decomposition of silane to silicon was prohibiting operation at higher temperatures. These membranes, when heated at higher temperature, suffered from densification with substantial loss of 1-I2 permeance. At the synthesis temperature, these membranes exhibited a H2/N2 ratio as high as 3000 with a rather low 1-12permeance of 0.18 cc/cm2-min-atm. Due to the difficulties encountered with the SiH4/O2 system, these workers switched to hydrolysis of SiCI4 as means of SiO2 deposition, a reaction which could be operated at temperatures as high as 800~ resulting in membranes with better thermal stability and lower susceptibility to densification (Tsapatsis et al., 1991). Hydrogen-permselective membranes could be formed by either opposing or one-sided deposition, but the latter membranes had higher H2 permeance. For the membranes prepared in that study, H2 permeance ranged between 0.28-0.43 cc/cm2-min-atm at 450-600~ with H2/N2 permselectivity of 600-4000. Subsequent publications from this group focused on stability" studies and microstructural characterization of silica membranes formed by one-sided deposition (Tsapatsis and Gavalas, 1994) and improvement of the deposition process by employing alternating reaction between the chloride and water vapor (Kim and Gavalas, 1995). Tsapatsis and Gavalas (1994) found that during one-sided hydrolysis of SiCI4, silica membranes were mechanically stable only when they were confined inside the support pores but cracks could form when deposition was extended substantially on the support surface. Deposit confinement in the support can be easily achieved in relatively short Vycor tubes (10-15 cm) however, in longer supports this is rather difficult to achieve due to axial reactants depletion and the resulting deposition rate variation. This problem can be circumvented by using deposition by sequential introduction of SiCI4 and H20. Due to the heterogeneous reaction mechanism deposit building in a layer by layer fashion can be achieved according to the sequential scheme: Si-OH r + SIC14r --) Si-O-Si-Cls cs) + HC1 ~g) Si-C1 r + H20 r ---) Si-OH r + HC1 cg) accompanied with densification reactions The use of removable diffusion barriers can be further combined with these deposition schemes to reduce film thickness (Jiang et al., 1995). The alternating-reactant deposition scheme proved quite satisfactory for securing a uniform deposition along lengthy tubular supports but had the disadvantage of requiting numerous repetitions until a H2-permselective membrane was formed. In the opposing reactants geometry the deposit is formed in the interior of the support and therefore crack formation problems can be eliminated even for long support with no need for elaborate one-by-one reactant introduction and/or barrier formation. However, this is achieved at the expense of lower permeances as a result of thicker deposits. The alternating-reactant deposition scheme proved quite satisfactory for securing a uniform deposition along lengthy tubular supports but had the disadvantage of requiring numerous repetitions until a H2permselective membrane was formed. Additional work on silica membrane formation by CVD in Vycor tubes was also reported by former collaborators of Gavalas. Megiris and Glezer (1992) employed oxidation of triisopropylsilane (TPS) at 750~ in the opposing reactant geometry and obtained SiO2/C composite membranes that exhibited rather modest permselectivity of 30 for H2/]q2 with H2

402 permeance of-0.25 cc/cm2-min-atm. Nam and coworkers (Ha et al., 1993) employed TEOS and succeeded in plugging pores of the support tube at T>600~ (>400~ in the absence (presence) of 02. At 600~ their membrane exhibited H2 permeance and H2/N2 selectivity of 0.235 cc/cm2-min-atm and 880, respectively. Despite the intensive efforts by all the above workers, the permeance of the composite SiO2/Vycor membranes made by CVD was limited by the high resistance of the support and could not exceed the rather low value of 0.4 cc/cm 2min-atm, despite the higher intrinsic permeance of the (usually submicron-thick) silica permselective layer. CVD synthesis of H2-permselective silica membranes in more practical alumina-based tubular supports of much lower permeation resistance was extensively documented by Morooka and coworkers. These workers typically employed TEOS decomposition at T>600~ with the reactant introduced from the outer surface of the tubular support and forced through the support wall by evacuating the inside of the support. The ultimate pressure achieved in the bore of the tube was used as a measure of the pore plugging process by this workers. Successful deposition was demonstrated in either as-received a-alumina support tubes (pore size 0.15 lam, supplied by NOK Corp.) or y-alumina layers (pore size 7 nm) coated on the aalumina supports by the sol-gel process. When extensive deposition was carried out, the resulting membranes exhibited a H2 permeance in the range 1-2x10 -8 mol/m2-s-Pa with H2/N2 ratio of--1000 (Yan et al., 1994a; Morooka et al., 1995a, 1996). The HE permeance of this silica membrane could be increased in the 10-7 mol/mE-s-Pa range with a sacrifice of selectivity (100-200) only when deposition was carried out for shorter times inside 7-alumina layers, but not inside as-received a-alumina tubes, (Sea et al., 1996, 1998) or when phenylsubstituted TEOS precursors of larger molecular diameter were employed (Sea et al., 1997). In the latter case, the obtained membranes showed permselectivity for larger molecules, e.g. n-butane/isobutane >10, apparently because of the larger pore size of these membranes. For the as-received a-alumina tubes, it appears that significant amount of silica was necessary to plug their macropores and hence the H2 permeance could not exceed the l0 8 mol/mE-s-Pa range in this case. Besides the extensive work published by the groups of Gavalas and Morooka, some limited studies on modification of porous supports by CVD of silica for the purpose of obtaining high HE-permselectivity were presented by some other workers as well. Liu and coworkers (Lin et al., 1994; Wu et al., 1994) modified 7-alumina top layers (pore size 4 nm) of asymmetric alumina tubes (supplied by US-Filter) by CVD of TEOS and obtained either porous membranes with pore size 6-15 A or denser membranes (3-5 A) that could exhibit HE/N2 permselectivity above the Knudsen limit. For their best membranes, H2/N2ratio ranged from 28-36 and HE permeance was 2-10 cc/cm2-min-atm at 300-600~ Hwang and coworkers (Hwang et al., 1999, 2000) employed TEOS decomposition with evacuation to modify 7alumina or a-alumina top layers of support tubes (supplied by Noritake) for the purpose of obtaining membranes that could separate H2 from a HE-H20-HI gaseous mixture at elevated temperatures. Their best membranes exhibited a H2 permeance and HE/qNI2permselectivity that did not exceed 10.8 mol/mE-s-Pa and 228, respectively, measured at 600~ However, their less selective membranes exhibited HE permeance as high as l0 -7 mol/mE-s-Pa at 300-600~ with mixture separation factors as high as 10 for HE/H20 and 1000 for HE/HI. Finally, Nijmeijer et al. (1998) modified 7-alumina top layers of support disks by decomposition of silicon-tetraacetate !SiAc4) at 275~ in the presence of 02, obtaining membranes with a H2 permeance of 4xl 0 mol/mE-s-Pa and HE/N2 of 43 at 250~

403

Table 1 summarizes the synthesis and permeation properties of silica membranes made by CVD in porous supports. Table 1. CVD Synthesis and properties of Silica Membranes. Workers

Support a

pore size

'

Reaction Scheme

DePosition temp. and tp

H2 permeance [mol/m2-s-Pa]

5x10 -9 Okubo & vycor, TEOS 200~ 40 h !noue (1989) 4nm (at200~ 10-8 Gavalas et Yycor, SiH4+O2 45o~ I ~al. (1998) 4nm (at450~ 15min 2x10 -8 Tsapatsis et 'Vycor, siC14+H20 400.800oc, 4rim i al. (1991) (at600~ 1 0 - 1 0 0 min 2x10 -s Megiris Vycor, 750~ s+o2 (1992) 4nm (at750~ 90 min l_2x10 "8 Ha et al. Vycor, TZOS(+o2) 400-700~ (.!.993) 4nm (at600~ 30 min .... , 1 0 . 8 Morooka et 600-650~ ct-A1203, al. (1995) (at600~ 3h 150 nm 2xlO -s Yan et al. TEOS ' 600-650~ ~-A1203, (1994) 3-4 h (at600~ 7nm 1.3x10 "7 Sea et al. TEOS 600-650~ 7-A1203, (1996) (at 600~ 7nm 4.7x10 -7 Sea et al. 600-650~ y-A1203, TEOS,PTES (1997) , DPDES (at 600~ 7 nm ,,, 200o(2 1.5.9.0Xi0 "7 Wu et al, TEOS y-A1203, Lin et a1('94) (300-600~ 4nm 0.6-3.0x10 8 Hwang et al. y/~-AI203, TEOS 600~ (1999-2000) 10-100 nm F ,, (at 600~ 2-7 h 4.0x10 -7 Nijmeijer et '~-A1203, 275~ PdAc4+O2 al. (!998) 4 nm 45 min (at 250~ PTE S=phenyltriethoxysilarte; DPDES=diphenyldiethoxysilane

Selectivity H2/N2 'i .......

3000 600-4000 30-100

i000 1000 1000 100 70-300 28-36 10-230 43

For the case of membrane CVD using chloride hydrolysis in Vycor, detailed models result in very good quantitative agreement with experiment once the heterogeneous deposition mechanism is taken into account and the evolution of pore structure and diffusivitiy are properly described using percolation theory. An important point here is that quasi-steady-state kinetics (QSSK) to express the growth rate only as a function of the gaseous species (chloride and water) cannot be employed since even the in absence of 1-120, metal chloride vapors can react with the Vycor surface. A clear demonstration of this issue is given experimentally by Tsapatsis and Gavalas (1992, 1997). In these studies the Vycor support is first treated with the metal chloride in order to render all OH" groups to CI groups. Under subsequent identical deposition conditions, it is found that a different deposit position and shape is formed as compared to that formed in the non-chlorinated support. A model using QSSK for surface species cannot capture these effects.

404

4. CVD OF YSZ MEMBRANES

4.1 Experimental results Dense ceramic membranes that exhibit oxygen ion (02-) conductivity as a result of a high oxygen vacancy concentration in their lattice can become O2-semipermeable at elevated temperatures when a pressure gradient of O2 is imposed across their thickness. Most wellknown oxygen ionic-conductors are stabilized zirconia (ZrO2) and bismuth oxide (Bi203) with a fluorite-type structure, while mixed conductors with a perovskite structure such as SrCoyFel_ yO3-8, etc. exhibit high ionic as well as electronic conductivity due to the partial substitution of A and B site cations of the ideal ABO3 perovskite structure by other metal cations with lower valence (Boivin and Mairesse, 1998). Dense membranes comprising of these (mixed) ionicconducting materials are highly desirable since they may find applications as oxygen separators and sensors, solid electrolytes for fuel cells and membrane reactors for partial oxidation reactions. Major limitation of the dense ceramic membranes is their low oxygen permeation flux, especially for the fluorite-type ionic conductors since electronic conductivity is very low compared to the ionic conductivity. For this reason, CVD has been proposed as an attractive method for the preparation of thin ( 500 A) are both time-consuming to prepare and can be sometimes generated by other techniques as well. For example, in the case of polymeric precursors the spin coating and phase inversion ~6 routes may generate selective layers with a thickness in the 500-1000 A range; thin ceramic layers can be obtained subsequently e.g. by oxidation (case of a siloxanic polymer) or carbonization (case of a high carbon yield organic polymer). Nevertheless, spinnability and ability for LB transfer need not exhibit the same trends and, in addition, the deposited layers can exhibit markedly different molecular arrangements and, thus, yield (after plasma treatment) quite different final structures.

lll.c. Choice of LB substances A composite structure consisting of a stack of LB layers transferred on an appropriate porous substrate may serve either as a final asymmetric membrane or as an asymmetric membrane precursor. When an asymmetric ceramic membrane is desirable, a modification should normally follow the LB deposition. As most of the LB materials transferred have an organic part, the modification can take the form of oxygen treatment, so that the organic part will be removed by oxidation; this oxidation can be achieved in a quite controlled manner via oxygen plasma treatment. However, for certain deposited substances a non-oxygen plasma treatment may be appropriate. It is sometimes assumed that the ability of a substance to form an LB layer can be judged on the basis of the ability of the same substance to form a thermotropic 3-D mesophase, which nevertheless strictly speaking is neither a necessary nor a sufficient condition; for example, PDMS (polydimethylsiloxane) does form an LB film but not a mesophase, while the opposite is true for PDES (polydiethylsiloxane) ~7.

424 Polymers that can be successfully and repeatedly transferred as LB films on solid substrates, most often consist of a flexible backbone with amphiphilic side chains, or a rigid backbone with flexible hydrophobic side chains 18'19, though our experience with sesquioxanes (see below) suggests that a broader range of polymers may be transferred successfully. When the intended end product is an asymmetric carbon membrane, a high carbon yield is certainly a positive polymer feature (For carbon yields see, for example, the review of Fitzer2~ A polymer that during heating/carbonization can form 3-D structures before melting may also be preferable. Unfortunately, the most obvious polymer candidate, polyacronitrile (PAN) does not form monolayers 4. A non-oxidizing plasma should be applied when the desired end product is a carbonaceous layer and a carbon or carbonizable substrate, such as a porous novolac 21, may be preferable to avoid stresses. In addition to appropriate high carbon yield polymers, other candidate precursors for a carbon top layer are pitch products and a number of commercial products have been tested; LB transfer on a porous substrate appears to be possible though with some difficulty 22. So far, most LB/plasma membrane research has been conducted with LB substances that require oxygen plasma processing. Appropriate LB substances include the metal salts of fatty acids and siloxane-based polymers. When the metal salt of a fatty acid (e.g. steatic, arachidic or palmitic acid) is LB transferred on a ceramic substrate, a subsequent plasma oxidation would remove the C and H species of the substance and yield the metal oxide. In this manner, oxides of divalent (e.g. Mg, Cd, Ca) and trivalent metals (e.g. Fe) can be deposited on top of a ceramic substrate. In the case of polymers containing siloxanic bonds, a LB transfer and subsequent plasma oxidation will generate a SiO2 deposition. Siloxanes are the obvious candidates for this deposition. Nevertheless, in the case of the simplest of the siloxanes (polydimethylsioxane, PDMS) the LB transfer is limited to a maximum of 3 to 4 layers, at least at temperatures higher than 0~

while the rest of the linear siloxanes are

incapable of forming an LB monolayer 23. The deposition of 2-4 layers is usually insufficient for the formation of a continuous, at least over macroscopic distances, film.

425 The limited LB transfer of PDMS appears to be the result of a near isotropic fluid-like behavior of the polymer following the deposition of 2-3 layers (which is understandable, given that

Tm-

-3 5~ for bulk PDMS) 9.

Because of the intractability of linear siloxanes, we have focused our attention on silsesquioxanes. Silsesquioxanes are ladder siloxanic polymers; each silicon atom participates in three instead of two siloxanic bonds. Work with polymethylsilsesquioxane has shown that this polymer (actually an oligomer) can be transferred easily and repeatedly on both anodic alumina and Vycor substrates (with the aforementioned limitation for the degree of transfer for Vycor)9. The mesophase-forming cyclolinear polyorganosiloxanes which are LB film formers as well 24 are also good candidates for LB precursor-based asymmetric ceramic membranes. Conceivably, it may be of interest, at least for certain combinations of substrate and deposited oxides, to subject the composite membrane to heat treatment that may allow for an intimate blending of the top oxide and the substrate (note for example the ability of SiO2 to dissolve a wide range of inorganic oxides). Except for SiO2 and single metal oxides of divalent and trivalent atoms, one may also be able to deposit more complicated ceramic compositions, e.g. by alternating LB deposition of two metal salts. In addition to the fatty acid salt route, and at least in principle, metal oxides can be LB/plasma deposited from appropriate metal-containing polymeric precursors 25. Finally, ceramic non-oxide thin layers may also be deposited by an appropriate choice of LB and/or plasma substances. Silicon carbide (SIC) and nitrogen or phosphorous containing ceramic layers may be developed in this manner. Routes for the formation of SiC and

Si3N 4 from

appropriate polymeric precursors have been

reviewed by Atwel126.

llI.d. Potential routes to SA-based membranes

In order to generate an asymmetric ceramic membrane through an SA technique, the SA film formation should be limited to the substrate surface (or its immediate neighborhood), by techniques such as the following: (1) Use of a temporary barrier that blocks the bulk of the membrane and limits deposition near the surface. A polymeric barrier subsequently carbonized may well serve that

426 purpose. Formation and carbonization of a polymer within Vycor was studied by Elmer et al. ~7 within a different context and more recently by Jiang et al. 28 for the purpose of limiting a Chemical Vapor Deposition (CVD) to a portion of a porous membrane. Following the formation of the carbon barrier, the carbon deposition may be removed from the membrane

surface through an appropriate plasma treatment. SA surface

deposition and another plasma treatment for the conversion of the deposited matter to a ceramic layer may follow. Finally, the carbon in the bulk of the membrane can be removed by burning. (2) Use of bulky SA substances that will not penetrate or penetrate rather slowly the interior of the membrane. This approach may helpful when the starting membrane is a nanoporous one and the SA substance contains bulky groups or is an oligomer with many active sites, so that the bulk of the membrane will be excluded from modification. (3) A nice example of another SA-based route aiming at creating an asymmetric membrane is provided by the work of Sugarawa et al. 29. An organotrichlorosiloxane dissolved in n-heptane forms a SA, stabilized by >A1-OH + C1-Si- ~ >A1-O-Si- + H20 condensations, at the surface of the pores of an alumina membrane. Due to the large pore diameter this SA monolayer formation does not affect considerably the pore diameter. Water, which is immiscible with n-heptane, is introduced from the other side of the membrane. Near the water side of the membrane, water hydrolyzes all accessible Si-C1 bonds, which includes Si-CI bonds of the SA pore wall film near the water side, as well as all Si-C1 bonds of RSiCI3 found at the water / n-heptane interface. The final result is a siloxane polymer network, formed near the alumina surface (water side) and ultimately attached to the alumina pore walls. Due to the presence of the organic R group, the generated asymmetric membrane has an upper use temperature of 200~

which is typical

of silicones, but a plasma oxidation of this or similar products may lead to a high temperature all-ceramic asymmetric membrane. In addition to employing chlorosilanes the aminosilane/porous silica substrate SA route also appears to be of interest 3~

427 IV. LB/PLASMA MEMBRANE STUDIES IV.a. Membrane formation.

Table I contains the most important results regarding the formation of precursor membranes from fatty acid salts, linear and ladder siloxanes and pitch LB substances and Anopore and Vycor substrates. We report the maximum degree of deposition (Da,max), which is equal to the area of the transferred film divided by the area of the substrate, and the values of nm~x, the maximum number of layers deposited (nmax = OCindicates that a minimum of 20 layers were deposited without signs of decay for the Da,max value). Detailed data regarding pH, spreading solution and subphase composition, and temperatures and n of deposition for fatty acid salt LB substances can be found in Soterakou at al. 7. LB substances" 1) Fatty acid salts. Stearic and arachidic acids were >99% pure and

obtained from Aldrich. Salts used were CdC12 > 99.99 % pure (Aldrich), MgClz.6H20 99% pure (Janssen Chimica) and, for pH adjustment, Na2CO3 > 99.5% pure (Aldrich). 2) Siloxane polymers. A series of 13 polydimethylsiloxanes with a number average molecular weight ranging from 1,000 to 75,000 were obtained from Aldrich. Methylsesquioxane with an estimated molecular weight in the 1,500 range was obtained from UCT. 3) Pitch. The reported data were obtained with a Mitsubishi Oil Co. pitch product showing a softening point of 285~

(similar products are described in a US

Patent3~). Substrates: Anopore alumina disc substrates have a 25 mm diameter and a thickness of

0.065ram, while the Vycor tubes used have a diameter of ca. 7ram, a wall thickness of 1. l mm and a typical length of 25 ram. Pore dimensions are indicated in Table I. Plasma treatment: This treatment was performed under the conditions described in

Section II.b. A cross section of a plasma-oxidized (fully ceramic) composite membrane prepared with the 0.21~m Anopore substrate is presented in Figure 3.

IV.b. Structural studies

The LB-plasma derived membranes studied in most detail so far s are those based on a model Cd arachidate/Vycor precursor for a number of layers (n) varying from 4 to 19.

428

T A B L E I" LB deposition on porous substrates

LB substance Mg Stearate Cd Arachidate Porous substrate

Dd,max

nmax Dd,max

Vycor(40A)

0.6+0.1

Anopore(200A)

-'1

Anopore (lO00/20o0A)

--1

PDMS

Methyls esquioxane

nmax Dd,rnax nmax

gd,rnax

nrnax

0.6+0.05

6

429 Integral permeability of a host of gases and vapors with molecular diameters ranging from 2.55 .~ (He) to 8.5 A (mesitylene) has been studied at temperatures in the 295-395 K range. Relative permeability has been studied for the He/H20 pair, while differential CO2 permeability for pressures up to 55 bars was performed with slightly supercritical CO2 (measurement at T=35~

while Tc.co2=3I~

For a review of the techniques used for

structural characterization see the work of Mitropoulos et al. 32. The structural picture that has emerged from the above studies is synopsized as follows: (a) The porous microstructure of the top layer is a complicated function of n. Few deposited precursor layers (e.g. n = 4-7) lead to small pores but some surface defects are also present. A moderate number of layers (e.g. n = 10-15) leads to larger pores, while surface defects are still present. A large number of deposited precursor layers (e.g. n = 19) practically eliminates surface defects and, at least the average pore size of the surface layer, is the smallest of all studied membranes (n = 4-19 range). (b) All small pores of the surface layer belong to the moderate sized micropore range (e.g. lower limit in the 5-6 A range and upper limit in the 10-12 A range). The surface defect population is relatively small and disappears for a large number of deposited layers. Differential permeability vs. pressure plots for n=4 Vycor and plain Vycor are shown in Figure 4 (Data replotted from Soterakou et al.8). The peak at 55 bars is indicative of flow control by unmodified Vycor mesopores (d=40 A). After the LB deposition and plasma treatment of only four layers the mesopore peak is reduced substantially and, in addition, a major microporous peak appears in the 1 bar range. The latter peak is a clear indication 32 of the presence of a dominant micropore population. It may be noted that in the case of a less effective ceramic surface modification of Vycor by a different deposition method ~3 the micropore peak was found in the 10 to 25 bar range (reflecting the presence of large micropores vs. small to moderate micropores for the LB/plasma case). Integral permeability data for an n--10 sample are shown in Figure 5 (data replotted from Soterakou et al. 8). k is measure of the deviation from Knusden flow, though a k vaule close to 1 does not guarantee that the flow is of near-Knusden character 8. For each gas or vapor, an 'ideal' integral permeability is calculated on the basis of actual

430

-e-n=4

9

vycor

JL

3,00E-03

2,50E-03

0,14

0,12

2,00E-03

0,08

0,06

1,50E-03

_

_ f - O

--......

1,00E-03

0,04

0,0"2

5,00E-04

0 0

10

20

30

40

50

60

P (bar)

F_.jKure 4. Comparison of carbon dioxide differential permeability vs. pressure data for a plain Vycor membrane and an n=4 Cd arachidate/Vycor LB/plasma membrane. Right permeance (Pe) axis: plain Vycor. Left permeance axis: modified Vycor. The large peak at ca. 55 bar for plain Vycor corresponds to d=40 .~ pores. In the case of modified Vycor the d=40 A peak has been reduced drastically and Pe increases with decreasing pressure to peak at approximately 1 bar, an observation which reflects the presence of a dominant micropore population.

permeability at the same temperatm-e and the Knusden ratio (square root of the ratio of molecular weights), k is the actual permeability of each gas or vapor over its 'ideal' Knusden value. Figure 5 is a plot of k vs. TJT, where Tr is the critical temperature of the gas or vapor examined and T is the temperature of the permeability measurement, for seven gases and vapors (helium, nitrogen, methane, carbon dioxide, propane, o-xylene and mesitylene). The plot shows a strong tendency for k to increase with T c and then to suddenly drop. The drop may be due to a full prevention of flow by the micropores (while defects remain conductive), or to a significant obstruction to flow. If the former interpretation applies, then for n=l 0:5.1 A < d~icropore P " ; (b) calculation of normalized ion current lx/ls from ref. [ 11 ] for different values of S, with h = 4 ~tm, Ld = 100 ~tm, 1-~ = 0.69 and rs - 1.16.

Similarly, in oxidative catalytic reactions using heterogeneous oxide catalysts, metal nanoparticles are present at the surface of the oxide catalyst acting as active sites for oxygen surface exchange with the gas phase. In semiconducting gas sensors it is generally accepted that negatively charged oxygen adsorbates, such as O2, O , and O 2, cover the surface of semiconductive metal oxides in air. O- are considered as the most reactive species in the temperature range of 300-500~ and play an important role in detecting gases such as H2 or CO. More interesting for the present discussion is the mechanism of charge transfer responsible for variations of resistance on which is based gas detection. In the case of n-type semiconductive metal oxides like SnO2, a space-charge region exists at the surface of the metal-oxide grains due to the formation of oxygen adsorbates, Figure 5a. Then an electron-depleted surface layer results from electron transfer from grain surfaces to the oxygen adsorbates.

445

O - O- 0 - 0 . semi-conduetive ~ metal-oxide grain ~.f--

O- O- O Ong 3re

space-charge re~ion (t)" grain boundary grain boundary

(a)

(b)

Fig. 5. Space charge region occurring at the surface of semi-conductive ceramic grains due to oxygen adsorbates (a); resulting potential profiles at grain boundaries in oxidative or reducing atmosphere (b).

The depth of the space-charge region (/) is a function of the surface coverage of oxygen adsorbates and intrinsic electron concentration in the bulk. If the oxidative atmosphere in contact with the metal-oxide surface changes to a reductive atmosphere, the electrons trapped in the oxygen adsorbate layer will return to the bulk, leading to a decrease of the potential barrier height (Figure 5b) and then in a drop in the resistance of the semiconductive material. Let see now the influence of the size of nanocrystallites forming the material. Drastic changes in the resistance of pure SnO2 sensors have been evidenced as a function of grain sizes [12]. In the nanometric range the material resistance slightly decreases as the grain sizes (d) are decreased down to a value (6 nm for SnO2 crystallites) for which the resistance sharply increases. This has been explained by the increasing amount of oxygen adsorbates as the grain sizes decrease (higher specific surface area) until the space-charge region occupies the totality of the grains. This is the case for d = 6 nm, when the space-charge region thickness l is calculated to be equal to 3 nm. It has been concluded from this work that when d >> 2l the dominant conductivity mechanism is under grain-boundary control; when d > 21, the spacecharge region controls electron transfer at the grain interfaces and the electrical resistance becomes highly sensitive to an oxidizing or reducing atmosphere; finally when d < 21 a fully grain control of electron transfer is achieved. In other respects, the addition of an appropriate amount of metal has been shown to improve the detection of various kinds of gases i.e. the minimum partial pressure at which a gas can be detected. Insertion of noble metal nanoparticles at the surface or in the sub-layer of the semiconductive material (TPB concept) results in a decrease of electron concentration in the oxide surface layer. This corresponds to an increase of l as a result of electron transfer from the metal oxide to the metallic particles. Then at high temperature the oxygen adsorbates extract electrons from the metal, which in turn extract electron from the metal oxide, leading to a further increase in l. It can be concluded, that due to reduced grain sizes in nanocrystalline materials, the depletion layer can attain dimensions similar to the particle sizes. Under these conditions, oxygen adsorption will result in metal oxide grains that are fully depleted of conduction electrons leading to a drastic change in resistivity. Therefore, if

446 these materials are potentially attractive for producing highly sensitive films, since the presence of very low gas concentrations will have a profound effect on intergrain conduction, they may cause problems in MIEC membranes. In other words, if the average grain sizes in a porous MIEC membrane is too small (typically less than 10 nm), this may lead to a depletion in electronic conductivity in the solid phase and to a simultaneous decrease of ion current. In metal oxide catalytic materials used in heterogeneous catalysis, the dispersion of very fine metallic particles (Rh, Pd, Pt, Ni, Co, Ru, Ir ...) greatly enhances oxygen exchanges and oxygen mobility at the surface of metal oxide grains. Research in this field includes metal oxide materials with high oxygen surface mobility and high thermal stability (> 1000~ like CeO2. Using the TPB concept, oxygen exchange mechanisms with the gas phase via the metallic particles as well as the oxygen adsorbates diffusivity at the surface of the oxide have been evidenced through the isotopic exchange I802(gas)/Z60(oxide) as shown in Figure 6 [14,15]. Adsorption-desorption of 1802 on the metal (steps 1 and 1') typically occurs in the temperature range 200-500~ then there is an exchange of 180 between the metal and the oxide support (step 2), migration of oxygen adsorbate 18O at the surface of the support (step 3), and finally oxygen exchange 180/160 with the oxide (step 4). Direct adsorption of oxygen on the oxide surface (step 5) has been proved to be negligible. Moreover it has been shown that oxygen adsorption via metallic nanoparticles is 10~ faster on CeO2 than on A1203 [16]. The remarkable behavior of CeO2 compared to A1203 can be attributed to the rapid electronic transfer Ce3+/Ce4§ but also to the presence of oxygen vacancies generally encountered in fluorite-based structures.

Fig. 6. Oxygen exchange mechanism between material via metallic particles [ 15].

1802 in

the gas phase and

160 in

the oxide

In such nanocomposites consisting of both metal oxide nanocrystallites and metallic nanoparticles, we must also consider the possibility of electron transfer between metallic nanoparticles. When small electronic conducting particles with a few nanometers size (typically in the sub-lO nm range) are isolated in the solid phase, no electron transfer can occur between these particles. If they are arranged within a small spatial distance of approximately 1 nm, ttmnel junctions with electrical capacitances of less than 10qs F can be

447 generated [17]. This allows the one-by-one transfer of electrons by sequential quantum tunneling. The probability of a tunneling event is determined by the external voltage or current source applied, as well as by the actual distribution of charges over the constituting sites. Finally, if the particles come in contact in order to form an infinitely continuous network, they will give rise to a percolative composite material in which the transport of electronic charge carriers will occur through an electronic conductive phase then balancing the oxygen ions transport through the ionic conductive ceramic phase [ 18]. Taking into account the crucial role of metallic particles in enhancing oxygen exchange with an oxide surface, one can expect significant improvement of surface reaction limited transport in porous MIEC membranes by introducing metallic nanoparticles in their porous structure. Current work in our group is intended to the preparation by the sol-gel process of such perovskite-based nanophase materials with finely dispersed metallic particles. For example, nanophase ceramics in the system SrFeO3.8, containing uniformly distributed Pt nanoparticles, were prepared by the sol-gel process at 850~ The metal was directly incorporated in the sol as a metal-organic precursor. Such method allows an homogeneous insertion of noble metals up to 20% while maintaining a nanophase structure for the composite material. One can see on the micrograph, Figure 7, corresponding to a composite material with 18wt% Pt that the nanostructure of the material is a combination of the structures presented in Figures 4 and 6. SrFeO3.8 particle sizes of about 70 nm form a mesoporous structure with mean pore diameters of 40 nm. The brownmillerite structure Sr2Fe205 formed at 400~ during the heat treatment of the xerogel and then was transformed in a quadratic perovskite phase at 700~ Normally when this compotmd is prepared by conventional methods, reversible structural transformations occur with temperature giving rise to three specific structural domains [41]: the brownmillerite domain at T < 350~ a two phase domain for 350~ _< T < 850~ in which both the brownmillerite and the tetragonal perovskite phase coexist; a cubic perovskite domain above 850~ with apparition of a disordered state of the vacancies. A remarkable result in the present sol-gel derived SrFeO3_8 material is that the quadratic phase which formed at 700~ is stabilized at room temperature.

Figure 7. SEM micrograph of a sol-gel derived nanophase ceramic structure prepared at 850~ in the system SrFeO3.8, and containing a distribution of Pt particles.

448 As far as this quadratic phase can keep a good ion conduction, this result is in favor of ion conductive materials able to work at intermediate temperatures, namely 500-700~ It can be concluded that the nanophase ceramic approach in oxygen ion conductive ceramics can lead to CICM able to work at lower temperatures than those prepared by conventional ways. Moreover, the insertion of noble metal nanoparticles can greatly enhance oxygen exchange with the gas phase. Nevertheless, depending on the concentration and particle sizes of the metallic phase in MIEC membranes, the role of the metal will be different. Enhancement of oxygen exchange at the gas/oxide interface can be expected from isolated metal particles while a combined effect on oxygen exchange and electronic charge carrier transport is supposed to happen for high metal concentrations leading to a percolative network.

3. PRESENT STATUS AND EXPECTED DEVELOPMENTS FOR OXYGEN ION CONDUCTIVE CERAMIC MATERIALS 3.1. Fluorite-based oxide ion conductors Among the fluorite-related structures used as solid electrolytes for oxygen transport, YSZ has been the most extensively investigated solid solution and used practically. It is considered to be the most reliable candidate for SOFC applications so far. Nevertheless many studies have been done on alternative materials with the aim to overpass a number of limitations for zirconia-based electrolytes [4]. In particular the limiting magnitude of electrical conductivity and the high operating temperature (1000~ required create serious technological problems in terms of interface reactions and stability of the different components (electrodes and connectors) of the cell. A number of other oxides possess the fluorite structure in the pure state (ThO2, CeO2, PRO2, UO2 and PuO2) whereas ZrO2 and HfO2 are stabilized to the fluorite structure by doping with divalent or trivalent oxides. For example, because Zr4+ and In 3+ ions exhibit a radius ratio close to 1, tetragonal ZrO2-In205 solid solutions were investigated for their potentially high ionic conduction [19]. However they revealed inferior to ZrO2-Y203, probably due to different defect arrangements in the structure. Ceria has collected much attention as an alternative oxide to zirconia. Thus electrical conductivity of gadolinia-stabilized ceria has been found to be about one order of magnitude larger (10 -~ S.cm "z at 800~ than for YSZ electrolytes. In fact the magnitude of electrical conductivity and the stability under reductive atmospheres for ceria-based oxides are greatly dependent on the kind and quantity of doping elements. In a review on ceria-based solid electrolytes [9], the authors went to the following conclusions: the diffusion constants of ceria-based oxides can be considered to be almost the highest among the fluorite oxides; nevertheless the increase of the electrolyte conduction domain under a wide range of oxygen pressures for doped ceria remains an important problem because it is apt to be reduced and electronic conduction becomes significant at low oxygen partial pressures. As far as some improvements can be expected from rare earth doping in fluorite oxides, the most serious problem would be the homogeneity of the material, since electrical conduction is much dependent on the concentration and location of rare earth elements in the structure. Compounds in the system 8-Bi203, in which Bi is substituted by Th, also must be mentioned as excellent mixed conductors with ionic transferance numbers to = 0.74 at 650~ and to = 0.85 at 800~ [20]. More recently, nanocrystalline solid solutions of

449 (CeO2)l.x(BiOi.5)x were obtained using an hydrothermal preparation method [21 ]. Because the ion conductivity of these materials is one of the highest to date, such oxide solutions with incorporation of 5-Bi203 in CeO2 are expected to lead to a novel electrolyte with improved ion transport at lower temperature. Oxide pyrochlores (A2B207) are closely related to the fluorite structure with one eight of the oxygen sites vacant [22]. The problem with pyrochlore structures is the difficult prediction of the anion disorder degree as well as the high temperatures required for the disordering process. For example Gd2Zr207 disorders at around 1550~ to a defective fluorite system. It has not been proven so far that pychlore-based materials can really compete with existing solid electrolytes. 3.2. Perovskite-based ion conductors

Because of the serious limitation due to the high temperature, generally near 1000~ required to achieve efficient ion conductivity in oxygen separation devices based on solid oxide electrolytes, there is a great deal of interest in developing new materials that exhibit high ion conductivity (10 l to 10.2 S.cm "l) at lower temperature (400-800~ Ceramic oxides with perovskite-based structures are attractive as alternative materials to the conventional fluorite oxides as far as they can exhibit high conductivity and chemical stability under oxygen partial pressure [23]. The idealized perovskite structure does not contain oxygen vacancies but is subjected to important structural variations able to provide a large concentration of oxygen vacancies as in brownmillerite oxides. The perovskite structure with the general formula ABO3 can accommodate a wide range of cations and exhibit conductivity behaviors ranging from predominantly electronic to almost purely ionic. The basic structure is a simple cubic system as shown in Figure 8a. The B cation (transition metal cation) is octahedrally coordinated to six oxygen and these octahedra are corner shared. The A cations (alkali, alkaline earth or rare earth ion) occupies the space between eight octaedra and has twelve neighbor oxygens.

Fig. 8. Idealized structures of perovskite ABO3 (a) and brownmillerite A2B205 (b). O represents the A cations. Oxygen vacancies l-I in the brownmillerite-type structure are in the [ 101 ] direction.

450 The idealized brownmillerite structure is orthorombic and the related oxides have the composition AzB'B"Os. The stucture can be viewed as a perovskite with oxygen vacancies ordered along the [101] direction in alternative layers (Figure 8b). This vacancy ordering results in an increased unit cell for the brownmillerite (B) compared to the perovskite (P): a8 = v/2 al,, b8 = 4bp, c8 = v/2 ce. If the B' and B" cations are identical, the perovskite related structure is known for the composition A2B205 like Ba2In205 which has received significant attention as an oxide ion conductor [24-26]. Examples of compounds indexed to a brownmillerite orthorombic structure from their X-ray diffraction patterns are: Ca2Fe205, Sr2Fe205, Sr2In205, Ba2T12Os. Brownmillerite-perovskite intergrowths are also possible with ordered or disordered structures of the type (AB'O2.5)x(AB"O3)y. Example of ordered intergrowth were described in the literature for the CaTiO3-Ca2Fe205 system [27,28]. The systems Ba3In2MO8 (M = Zr, Hf and Ce) was characterized as having an intergrowth structure in which two octaedral layers alternate with one tetrahedral layer along the c-axis [29]. Other brownmillerite-based layered structures in the system BaBiaTi3MO14.5 (M = Sc, In and Ga) have been mentioned as a new class of oxygen conductors which have intrinsic oxygen vacancies and undergo order-disorder transitions [30]. Another category of compound, Bi4V2Oll, with intergrowth structures has been identified as leading to fast Oz ion conduction at T< 400~ [31,32]. These compounds consist of Bi2022+ layers alternating with perovskite blocks along the c-axis. Normally the txBiaV2Oll phase existing at room temperature transforms through a fl-phase 450 ~tm) for the ion conductive material in order to meet the conditions described in Section 2.4 for new nanophase-based CICM. 4.3. Membrane characteristics and oxygen flux measurement

Historically, measurements of oxygen transport in CICM electrolytes have been made through the electrical conductivity using the dc four-probe method on sintered ceramic pellets. This can lead to errors because of effects due to the grain boundaries and electrodes, which may mask the true behavior of the bulk.

Rg

Rb

Re

I

II Cb

II Ce

Cg

(a)

T

frequency

Rb

Rg

fe

Re Z' (ohm)

,-'~

(b) Fig. 14. Complex plane impedance analysis of solid electrolytes, a) Idealized equivalent circuit of a dense sintered grained material, b) Complex impedance diagram with semicircles resulting from the contribution of bulk, grain boundary and electrode dispersion.

460 Later on, the reliability of the measurements has been improved by the use of the complex plane impedance analysis [72]. In this method, a complex impedance diagram is plotted from impedance measurements carried out at a large range of frequencies, usually from 10.3 to 106 Hz. The idealized circuit and the complex impedance diagram for a two phase ceramic electrolyte is shown in Figure 14. Bulk, grain boundary and electrode contribute successively to an equivalent circuit as RC elements (Figure 14a) giving rise to semicircles (Figure 14b) with a particular frequency f a t the top of each semicircle (f= 1/RC). For ceramic oxides the low-frequency semi-circle is due to electrode dispersion, the intermediate frequency circle is due to the grain boundaries and the high-frequency semicircle is due to the bulk behavior. Characterization of the bulk ionic conductivity of an electrolyte is usually made by using a two electrodes cell. Electrodes are in contact with the two planar and parallel surfaces of a pellet sample in order to get a well defined geometric factor. Three electrodes cells are preferred for electrode polarization studies. In this case, a direct current is superposed to an alternating current of low amplitude and variable frequency. Then, the voltage variation is measured between a working electrode and a reference electrode versus the direct current passing through the sample via an auxiliary electrode.

Downstream chamber .

Mass flow controller Furnace

Y

Membrane Upstream chamber Manometer ..~

V Vacuum

l_ ~"

--]

[ Gas [ Chromatograph

Fig. 15. Vertical high-temperature gas permeation system for flat disk MIEC membranes [73].

461 In the case of MIEC membranes, the oxygen flux can be measured directly by applying an oxygen pressure gradient across the membrane. The major technical problem in direct oxygen flux measurement of CICM derives from membrane sealing at high temperature. Appropriate devices are used for oxygen flux measurements depending on membrane geometry [43,44,7375]. A typical specific apparatus designed for fiat discs membranes is shown in Figure 15. Two tubular ceramic gas chambers are used, the upstream chamber being placed inside the downstream chamber. A tubular furnace is used for chambers heating up to the appropriate temperature at which oxygen flux is measured. A gas stream of pure oxygen or oxygen/nitrogen mixture is introduced in the upstream chamber with the aid of mass flow controllers. Helium is used as sweep gas in the downstream chamber which is connected to a gas chromatograph in order to analyze the concentration of oxygen and/or nitrogen in the sweep gas stream. Aside from direct measurements of conductivity or oxygen flux in CICM, some other techniques could be of interest for the characterization of CICM materials in relation with their oxygen transport and redox properties. Among them, transient TGA (gravimetric) and temperature-programmed methods are of particular interest. One of the major difficulties in measuring oxygen permeation flux through thin MIEC membrane (typically < 100gm) is the sealing at high temperature. In other respects, understanding of the surface reactions for oxygen transport is a very important aspect because it becomes the rate limiting step for thin membranes. The transient TGA (gravimetric) method already used for gas transport studies in the case of microporous solids as zeolites has been successfully used for oxygen surface reaction investigation with ionic conductive ceramics [76]. A La0.2Sr0.sCaO3.5 membrane (crushed in small grains) was tested according to the TGA method providing information on oxygen adsorption and desorption rates as a function of instantaneous change of activity of oxygen in the gas phase. A mathematical model considering surface reaction as the rate-limiting step is presented in this work to describe the oxygen transport through the membrane material and employed to obtain the reaction rate constants. A simple correlation between the oxygen flux calculated from the TGA method is proposed which showed to be consistent with the data measured by a permeation method on the La0.2Sr0.sCaO3_5membrane. Temperature-programmed (TP) techniques are also of interest to characterize ion conductive ceramics, in particular when they are used as anode where oxygen ions react with the fuel to produce oxidation products and electrons. Practically ceramic powder samples are placed in a furnace equipped microreactor and heated under a reductive or oxidative controlled atmosphere in the temperature range 0-1000~ A proportional, integral and differential control temperature programmer is used to adjust power supply to the furnace. During an experiment gas exiting the reactor is analyzed using a mass spectrometer analysis technique. Different configurations: temperature-programmed reduction (TPRd), reaction (TPRx) or oxidation (TPO) can be implemented allowing the investigation of redox behavior as well as catalytic activity of the samples. As an example, the perovskite oxide La0.sCa0.2CrO3 was studied for application as a direct methane oxidation anode in SFOCs using TP techniques [77].

462 5. CURRENT APPLICATIONS AND FUTURE TRENDS FOR CERAMIC OXYGEN TRANSPORT MEMBRANES Today there are many examples of commercial processes using oxygen or oxygen-enriched atmospheres. The global market for pure oxygen is huge with large production scale demands in metallurgical or petrochemical industries. On the other hand, the utilization of oxygenenriched atmospheres results in higher efficiency and lower emission in any process involving combustion of a hydrocarbon fuel. Oxygen is also consumed in smaller quantities in aerospace or medical life support applications [1]. Conventional units currently used for oxygen separation from air are the cryogenic distillation, the pressure swing adsorption and the vacuum swing adsorption. Over the past two decades, gas separation membranes based on amorphous polymers have been thoroughly investigated with significant improvement of their permeability and selectivity characteristics. The permeation of simple gases such as the noble gases, hydrogen, oxygen, nitrogen, carbon dioxide, and methane through glassy polymers with a high glass-transition temperature (Tg) are now considered for industrial applications [78]. However, these membranes exhibit limited oxygen separation performance and do not satisfy high temperature and chemical resistance requirements for many potential applications. New processes based on gas tight CICM have distinct advantages over the aforementioned technologies as far as they can produce high purity oxygen in a single operation and provide at the same time a physical barrier to contaminants present in the feed stream. For example, production of pure oxygen in fuel cell technology is a major concern for new power generation systems able to compete with the well established energy production plants based on combustion or nuclear processes [2]. Depending on required oxygen quality and production scale, CICM can be implemented in oxygen separation devices following two ways. First, the same electrically driven configuration can be used for fuel cells and electrocatalytic devices in which a dense layer separates a porous anode and cathode. The role of the dense layer is to block the direct passage of gas molecules between the electrodes whereas sole ionic oxygen species are allowed to pass. The other way consists in a pressure driven configuration in which both ionic species and electrons are transported through a dense membrane under an oxygen partial pressure gradient. Oxygen generators and catalytic membrane reactors are the main applications for this later configuration. 5.1. Solid oxide fuel cells Special attention must be paid to fuel cell applications for which selective oxygen transport materials have been one of the keys of the important technical breakthrough recently achieved in this area. Fuel cells are particularly attractive as they allow to bypass the conventional burning process as a link between fuel and electric power: fuel can be converted into electricity and is not subject to Camot limitation. An other important characteristic of the fuel cell compared to more conventional methods of electricity generation is its environmental impact: the fuel cell produces less waste, a lower level of emissions and nearly no noise. It is possible to describe the fuel cell as an inverted electrolysis apparatus in which oxygen and hydrogen are converted into water and at the same time an electric current is generated. The central component of the fuel cell is the electrolyte through which 02 or H2 selectively permeates under an ionic form. In addition, the electrodes (anode and cathode) are important components which allow both the transformation of transported ionic species and the fuel oxidation with simultaneous generation of electrons.

463 Relatively large SOFC systems (> 1 MW) are now envisaged for stationary power generation with an efficiency approaching 70%. For the seek of comparison the most technologically advanced combined cycle gas turbines (IGCC) are able to generate electricity with a maximum efficiency of 50-52%. Fuel cell vehicles (FCVs) for transportation applications are also under development. A FCV powered by hydrogen offers the zero emission benefits of battery powered vehicles but avoids the range, recharging, weight and cost penalties associated with batteries. Nevertheless, because of hazards caused by hydrogen supplies, a number of fuels are being considered as alternatives to pure hydrogen. Methanol and gasoline are options under development but these fuels require an on-board fuel processor to extract hydrogen from the fuel. Though, the development of membrane reactors (reformers) based on CICM is a major concern of FCV technologies. FCVs are projected to reach efficiencies of 3 5-40% after thermal and parasitic power losses.

Fig. 16. Typical operation scheme of a solid oxide fuel cell showing examples of utilization for oxygen ion conductive materials.

Conventional fuel cells based on ceramic oxygen conductive electrolytes operate at high temperature (about 1000~ for YSZ) and generate electricity (electrons) from air and hydrogen or hydrocarbon fuel [79]. As shown in Figure 16, a flow of negative oxygen ions is generated at the cathode which is exposed to air, and transported to the anode through the electrolyte material. At the anode, migrant oxygen ions react with hydrogen and/or hydrocarbon to produce water and carbon dioxide. These reactions generate electrons which are collected. The amount of electricity produced and the temperature for a maximum efficiency greatly depend on the resistance of the electrolyte to the migration of oxygen ions. Unfortunately, at temperatures lower than 1000~ the ionic resistance of YSZ is too high, and cell performance is reduced to uneconomical levels. Current developments in SOFC technology are based on two cell configurations, tubular or planar, with specific advantages and disadvantages for both of them [2]. New cell designs or alternative electrolytes are needed to fully realize the economic promise of SOFCs. As already mentioned in Section 4, a large number of ion conductive materials are under investigation from which effective ion conduction at temperatures lower than for YSZ are expected. Actually, new cell designs in conjunction with new electrolytes are considered for future SOFCs development. Reducing

464 the thickness of the electrolyte is certainly the most obvious approach to maintain SOFC performance at lower temperatures. However the thin film approach is inherently difficult as far as an electrolyte thickness of about 10 ~tm is needed for an efficient conduction at 650800~ and such thickness is typically in the flux limitation range due to oxygen surface reactions. Moreover, to prevent short circuits between anode and cathode, the films must be dense and free of cracks or pinhole defects. Increasing the contact surface between electrodes is an alternative means for maintaining power densities and cell efficiency at lower operating temperatures. In fact, increasing the surface area increases the number of ions reacting at the anode, offsetting the reduced migration rate caused by lower operating temperatures. The power density of conventional SOFCs can be potentially increased by 3-5 times using anode/electrolyte interfaces with millimeter-scale corrugations. Single component SOFCs are being explored which consist of electrolytes with specific chemical and structural modifications on opposite sides to generate anode- and cathode-like surfaces. Electrical and physical mismatches between electrodes and electrolyte materials would thus be minimized. For example, such a fuel cell would consist of a conventional YSZ electrolyte with anode and cathode surfaces created by doping with titania and terbia respectively. Finally electrolytes that conduct protons instead of negative ions could provide a novel basis for cost effective, low temperature SOFCs [79]. In this case the fuel cell would operate with hydrogen ions flowing from the anode to the cathode and with water production shifted at the cathode, diluting air instead of fuel. A better efficiency can be expected from this concept as far as air could be supplied in excess of stoechiometry for cooling, whereas this is not possible on fuel side in conventional SOFCs. To date, little is known on hydrogen ion conductors compared to their oxygen ion counterparts and they are being explored at the laboratory scale [45,80]. 5.2. Ceramic oxygen pumps and generators Pressure driven devices based on MIEC membranes offer certainly the simplest design for ceramic oxygen generators. The driving force for oxygen transport is the differential oxygen partial pressure across the membrane. The membrane is electrically isolated and the membrane material therefore needs to be a good electronic conductor to provide a return path for the electrons balancing the current of oxygen ions. Most of these MIEC materials have an electronic conductivity much higher that their ionic counterparts. Consequently, oxygen transport parameters determine oxygen fluxes [ 1]. Oxygen pumps and generators, based on electrically driven devices, operate in a reverse way compared to solid oxide fuel cells. As these devices have many common design principles, a technological spin-off for membranes can be expected from current developments of SOFCs. In oxygen pumps and generators, an electrical potential is applied across an oxygen conducting electrolyte membrane via electrodes. The oxygen flux produced . . . . 2 is directly proportional to the current passing through the electrolyte (1 A/cm = 3.5 ml O2/min) and is governed by the membrane electrical resistance. The advantages of such an electrical driven device is that it is possible to achieve large oxygen fluxes per unit area and at a higher pressure than the air feedstock. An electrochemical oxygen pump allows the control of oxygen partial pressure by delivering or extracting pure oxygen in/from a gaseous atmosphere. A typical apparatus design, Figure 17, consists of an YSZ gas tight tube coated with platinum and placed in an oven in order to achieve operating temperatures close to those used for SOFCs. Depending on the way in which the internal electrode is operated, anode or cathode, oxygen is either supplied from air to a gas stream or extracted from a gas atmosphere

465 and rejected to air. YSZ-based oxygen sensors used in many high temperature applications operate in the same way [12].

YSZ gas tight tube

] (~) (~)

(~) (~)AIR (~)

(~) (~)

(~)

I

> GAS r------> GAS ~ l ~._~-.._~-._~._~._:~_~._~-._._~.._~.:._~.._~._~..~..~-.~..~ ~ ~-.~.~,.~.~.~.~.~.~-.~~ ~,.~~ I 1 Porous Pt coating

AIR

@ @ @ @ @ @ @ @

%--

] Electrical generator generator Oven

Fig. 17. Schematic principle of an electrically driven oxygen pump.

Other devices derived from SOFC technology have been proposed for membrane oxygen separation and membrane reactor applications. One example concerns the preparation of bilayer structures consisting of an electrolyte dense film bonded to the surface of a porous electrode substrate [57]. These bilayer structures offer specific advantage of being gas tight with little interfacial resistance.

5.3. Catalytic membrane reactors There is now a large interest for CICM in catalytic applications, in particular for partial oxidation reactions. Actually, membrane reactors (MRs) as a concept, dates back to 1960s and the interest of inorganic membranes has been emphasized for many catalytic processes of industrial importance (classically using fixed, fluidized or trickle bed reactors) and involving the combination of high temperature and chemically harsh environments [81-83]. Inorganic membranes for MRs can be inert or catalytically active, they can be either dense or porous, made from metals, carbon, glass or ceramics. MR configurations can be classified in three groups, related to the role of the membrane in the process [60]: (i) as an extractor for the removal of product(s) in order to increase the reaction conversion by shifting the reaction equilibrium; (ii) as a distributor for the controlled addition of reactant(s) in order to limit side reactions; (iii) as an active contactor for the controlled diffusion of reactant(s) and for the creation of an engineered catalytic reaction zone. CICM are of particular interest in MRs because they can combine the functions of distributor and contactor in the same device. This is typically the case in new SOFCs designs for which the successive steps of fuel (methane, methanol, gasoline ...) conversion, hydrogen and oxygen delivery at the anode and conversion to water are controlled by an integrated membrane reactor system.

466

Fig. 18. Two possible membrane reactor configurations using perovskite-based MIEC membranes: (a) tubular geometry for the partial oxidation of methane to syngas [43]; (b) planar geometry for the oxidative coupling of methane [75].

Two types of membrane reactors can be implemented with CICM depending on electrical transport properties of the involved ceramic membrane material: pressure driven devices for MIEC membranes or electrically driven devices for oxide ionic conductor-based membranes. The two main applications investigated to date for MIEC perovskite-based membrane reactors have been the partial oxidation of methane to syngas (CO + H2) and the oxidative coupling of methane for ethylene and ethane (C2 products) production. In the case of partial oxidation of methane to syngas [43], the perovskite membrane serves as an oxygen distributor in order to provide optimum oxygen partial pressure in the axial direction of a tubular reactor as shown in Figure 18a. A methane conversion larger than 98% with a CO selectivity of 90% was reported for such a membrane reactor with an operating temperature of 850~ A similar role was described for a perovskite-based membrane implemented in a fiat membrane reactor, Figure 18b, for the oxidative coupling of methane [75]. One membrane surface is exposed to O2fN2 mixture stream and the other to He/CH4 mixture stream. High C2 selectivity (70-90%) and yield (10-18%) were achieved at temperatures higher than 850~ However, the C2 selectivity drastically dropped as the He/CH4 ratio decreased too much, typically to values lower than 20. It was concluded that the surface catalytic properties of the membrane were strongly dependent on the oxygen activity at the surface exposed to methane stream. These results relate to the genetic problem of the thermo-structural stability encountered with MIEC perovskite-based membranes in contact with low oxygen partial pressures [78,85]. An electrochemical membrane reactor for the partial oxidation of hydrocarbons was described as an other possible utilization of perovskite-based MIEC membrane reactors [86]. The same concept has also been proposed as an efficient, economical and simplified methane conversion process, compared with the conventional steam reforming way [87]. Basic operation principle of this electrochemical cell is shown in Figure 19. In this system, syngas production is achieved at 900~ at the anode -coated with the appropriate catalyst, whereas

467

02 separation from air is performed at the cathode. For a current density of 30 mA/cm 2, i.e. 0.267 mmol/h.cm 2 of oxygen flux, formation rates of CO, H2 and CO2 were 0.431, 0.796 and 0.018 mmol/h.cm 2 respectively. Selectivity to CO was 97%, based on converted CH4 (10.7%).

Fig. 19. Principle of CH4 oxidation to syngas with air using an electrochemical membrane reactor [87].

Due to their high selectivity for delivery of highly reactive oxygen species, further development can be expected for CICM-based reactors. For example, the reduction of NOx in N2 using a brownmillerite oxide based catalyst [87] or the combustion of volatile organic compounds on perovskite-loaded catalytic membranes [62] can be mentioned as other possible applications of MIEC derived membranes.

6. CONCLUSION Although an enormous potential market for oxygen separation membranes has been predicted for the oncoming years, separation devices able to work from ambient temperature up to 1000~ remain a major technological challenge. CICM with a high ionic oxygen conduction at intermediate temperatures, and exhibiting high chemical and thermal stability under low oxygen partial pressures are still under investigation. In fact only YSZ has shown reliable properties and has been used at an industrial scale so far. Unfortunately, a significant ionic conduction of YSZ is attained for temperatures > 900~ Other fluorite or perovskite derived materials used as electrodes or thin supported membranes did not satisfy entirely until now all the requirements for sustainable industrial developments. This certainly explains the

468 considerably increasing number of studies on the search for new compounds with better stability and conductivity at temperatures < 800~ Some very promising materials have been already identified. Several of them have been studied in details and tested for their thermochemical stability and integrity upon aging and use. Results show that the synthesis and shaping methods greatly influence the performance and stability of these materials. Then, beside the very active research for new compounds, an R&D effort put on structure formation and shaping methods of existing materials can greatly benefit to the development of these technologies. Preparation of less electrically resistant thin membranes with an ultrastructure allowing a faster conversion of gazeous oxygen to ionic species is one of the directions liable to improve significantly the performance of oxygen separation devices. Nanophase porous ceramics and metal-ceramic nanocomposites have been described in this chapter as very promising materials for CICM applications. It has been shown that oxide nanocrystallites and metal nanoparticles prepared by the sol-gel process can be stabilized up to 800~ and are able to promote enhanced oxygen conversion to active species as well as faster ionic transport. Moreover the sol-gel process is well adapted to the fabrication of supported layers with a controlled porosity, obtained either as thin surface films or infiltrated layers. Today, one can say that the concept of ceramic oxygen generator has been scientifically proven and a number of candidate materials for CICM applications now exists. The construction of demonstrators followed by prototype plants can be expected in a next future thank to the utilization of new concepts in membrane design, ceramic ultrastructure, and shaping methods.

REFERENCES

1. 2. 3. 4. 5. 6. 7.

J. Kilner, S. Benson, J. Lane and D. Waller, Chem. Ind., 17 November (1997) 907. B. Steele, C.R. Acad. Sci. Pads, t.1, Serie IIc (1998) 533. R.W. Siegel, MRS Bull., October (1990) 60. B.C.H. Steele, Material Science and Engineering, B 13 (1992) 79. B.C.H. Steele, Current Opinion in Solid State & Material Science, 1 (1996) 684. B.C.H. Steele, Solid State Ionics, 75 (1995) 157. H.J.M. Bouwmeester and A.J. Burggraaf, in Fundamentals of Inorganic Membrane Science and Technology, A.J. Burggraaf and L. Cot (eds.), Elsevier, Amsterdam, 1996, pp. 435-528. 8. A. Manthiram, J.F. Kuo and J.B. Goodenough, Solid State Ionics, 62 (1993) 225. 9. H. Inaba and H. Tagawa, Solid State Ionics, 83 (1996) 1. 10. C.S. Chen, H. Kruidhof, H.J.M. Bouwmeester and A.J. Burggraaf, J. Appl. Electrochemistry, 27 (1997) 71. 11. H. Deng, M. Zhou and B. Abeles, Solid State Ionics, 74 (1994) 75. 12. J. Watson and K. Ihokura (eds.), Gas Sensing Materials, MRS Bulletin, 24 No. 6 (1999) pp. 14-59. 13. A. Kapoor, R.T. Yang and C. Wong, Catal. Rev.-Sci. Eng., 31 (1989) 1. 14. D. Duprez, Stud. Surf. Sci. Catal., 112 (1997) 13. 15. D. Duprez, M. Colin and M. P~lissier, Stud. Surf. Sci. Catal., 112 (1997) 303. 16. D. Martin and D. Duprez, J. Phys. Chem., 101 (1997) 4428. 17. U. Simon, Adv. Mater., 10, No. 17 (1998) 1483.

469 18. T.J. Mazanec, T.L. Cable and J.G. Frye Jr, Solid State Ionics, 53-56 (1992) 111. 19. A.P. Sellars and B.C.H. Steele, Mat. Sci. Forum., 34-36 (1988) 255. 20. I.C. Vinke, B.A. Boukamp, K.J. de Vries and A.J. Burggraaf, Solid State Ionics, 57 (1992) 91. 21. G. Li, L. Li, S. Feng, M. Wang, L. Zhang and X. Yao, Adv. Mater., 11, No. 2 (1999) 146. 22. H.L. Tuller and P.K. Moon, Mat. Sci. Eng. B-Solid State M., 1 (1988) 171. 23. K.R. Kendall, C. Navas, J.K. Thomas and H-C zur Loye, Solid State Ionics, 82 (1995) 215. 24. J.B. Goodenough, J.E. Ruiz-Diaz and Y.S. Zhen, Solid State Ionics, 44 (1990) 21. 25. G.B. Zhang and D.M. Smyth, Solid State Ionics, 82 (1995) 161. 26. C.A.J. Fisher, M.S. Islam and R.J. Brook, J. Solid State Chem., 128 (1997) 137. 27. J.C. Grenier, F. Menil, M. Pouchard and P. Hagenmuller, Mater. Res. Bull., 13 (1978) 329. 28. T.R.S. Prasanna and A. Navrotsky, J. Mater. Res., 9-12 (1994) 3121. 29. J.B. Goodenough, A. Manthiram, P. Paranthaman and Y.S. Zhen, Solid State Ionics, 52 (1992) 105. 30. J.K. Thomas, K.R. Kendall and H.-C. zur Loye, Solid State Ionics, 70/71 (1994) 225. 31. J. Rodriguez-Carvajal, M. Vallet-Regi and J.M. Gonzalez Calbet, Mater. Res. Bull., 24 (1989) 423. 32. K. Mader and Hk. Mtiller-Bushbaum, J. Less Common Met., 157 (1990) 71. 33. F. Abraham, J.C. Boivin, G. Mairesse and G. Nowogrocki, Solid State Ionics, 40-41 (1990) 934. 34. M.T. Anderson, J.T. Vaughey and K.R. Poeppelmeier, Chem. Mat., 5 (1993) 151. 35. M. Schwartz, B.F. Link and A..F. Sammells, J. Electrochem. Soc., 140-4 (1993) L62. 36. S. Wil3mann and K.D. Becker, Solid State Ionics, 85 (1996) 279. 37. Y. Nakahara, S. Kato M. Sugai, Y. Ohshima and K. Makino, Materials Letters, 30 (1997) 163. 38. K. Ktinstler, H.-J. Lang, A. Maiwald and G. Tomandl, Solid State Ionics, 107 (1998) 221. 39. O. H. Hansteen, H. Fjellvag and B. C. Hauback, J. Mater. Chem., 8-9 (1998) 2081. 40. S. Shin, M. Yonemura and H. Ikawa, Bull. Chem. Soc. Japan, 52-3 (1979) 947. 41. J-C Grenier, N. Ea, M. Pouchard and P. Hagenmuller, J. Solid State Chem., 58 (1985) 243. 42. Y. Teraoka, H.M. Zhang, K. Okamoto and N. Yamazoe, Mat. Res. Bull., 23 (1988) 51. 43. U. Balachandran, J.T. Dusek, R.L. Mieville, R.B. Poeppel, M.S. Kleefisch, S. Pei, T.P. Kobylinski, C.A. Udovich and A.C. Bose, Applied Catalysis A: General, 133 (1995) 19. 44. L.Qiu, T.H. lee, L.-M. Liu, Y.L. Yang and A.J. Jacobson, Solid State Ionics, 76 (1995) 321. 45. U. Balachandran, B. Ma, P.S. Maiya, R.L. Mieville, J.T. Dusek, J.J. Picciolo, J. Guan, S.E. Dorris and M. Liu, Solid State Ionics, 108 (1998) 363. 46. S. Kim, Y.L. Yang, R. Christoffersen and A.J. Jacobson, Solid State Ionics, 104 (1997) 57. 47. H. Yamamura, Y. Yamada, T. Mori and T. Atake, Solid State Ionics, 108 (1998) 377. 48. V.V. Kharton, A.P. Viskup, E.N. Naumovich and L.M. Lapchuk, Solid State Ionics, 104 (1997) 67. 49. T. Ishihara, T. shibayama, M. Honda, H. Nishigushi and Y. Takita, Chem. Commun., (1999) 1227.

470 50. C.S. Chen, B.A. Boukamp, H.J.M. Bouwmeester, G.Z. Cao, H. Kruidhof, A.J.A. Winnubst and A.J. Burggraaf, Solid State Ionics, 76 (1995) 23. 51. A. Ziehfreund, U. Simon and W.F. Maier, Adv. Mater., 8, No. 5 (1998) 424. 52. A.O. Isenberg, Solid State Ionies, 3/4 (1981) 431. 53. L.S. Wang and S.A. Barnett, J. Electrochem. Soc., 139 (1992) L89. 54. A. Negishi, K. Nozaki and T. Ozawa, Solid State Ionics, 3/4 (1981) 431. 55. N. Minh, J. Am. Ceram. Soc., 76 (1993) 563. 56. J. Luyten, A. Buekenhoudt, H. Weyten, W. Adriensens, J. Cooymans and R. Leysen, in S. Nakao (Ed), Proc ICIM5 (Inorganic Membranes), Nagoya, Japan (1998) p. 96. 57. C.P. Jacobson, S.J. Visco and L.C. De Jonghe, Electrochem. Soc. Proc., 97/94 (1998) 726. 58. J. Kim and Y.S. Lin, J. Am. Ceram. Soc., 82 (1999) 2641. 59. M. Fai Ng, T.L. Reichert, R.W. Schwartz and J.P. Collins, in D.E. Fain (Ed), Proc ICIM4 (Inorganic Membranes), Gatlinburg, Tennessee, 1996, p. 313. 60. A. Julbe, D. Farrusseng and C. Guizard, to be published in J. Membr. Sci. 61. J.C.S. Wu, H. Sabol, G.W. Smith, D.L. Flowers and P.K.T. Liu, J. Membr. Sci., 96 (1994) 275. 62. S. Irusta, M.P. Pina, M. Menendez and J. Santamaria, Catalysis Letters, 54 (1998) 69. 63. A. Julbe, C. Guizard, A. Larbot, L. Cot and A. Giroir-Fendler, J. Membr. Sci., 77 (1993) 137. 64. C. Guizard, in Fundamentals of Inorganic Membrane Science and Technology, A.J. Burggraaf and L. Cot (eds), Elsevier, Amsterdam, 1996, p.227. 65. A. Larbot, J.P. Fabre, C. Guizard, L. Cot and J. Gillot, J. Am. Ceram. Soc., 72 [2] (1989) 257-261. 66. C. Guizard, A. Julbe and A. Ayral, J. Mater. Chem., 9 (1999) 55. 67. R. Vacassy,C. Guizard, V. Thoraval and L. Cot, J. Membr. Sci., 132 (1997) 109. 68. G. Xiong, Z-L Zhi, X. Yang, L. Lu and X. Wang, J. Mater. Sci. Letters, 16 (1997) 1064. 69. Y. Shimizu and T. Murata, J. Am. Ceram. Soc., 80[ 10] (1997) 2702. 70. C. Chen, H.J.M. bouwmeester, H. Kruidhof, J.E. ten Elshof and A.J. Burggraaf, J. Mater. Chem., 6-5 (1996) 815. 71. R. Chiba, F. Yoshimura and J. Yamaki, Mat. Res. Soc. Symp. Proc., 496 (1998) 185. 72. J.A. Kilner and C.D. Waiters, Solid State Ionics, 6 (1982) 253. 73. J. Han, Y. Zeng and Y.S. Lin, J. Membr. Sci., 132 (1997) 235. 74. S.J. Xu and W.J. Thomson, Chem. Eng. Sci., 54 (1999) 3839. 75. Y. Zeng, Y.S. Lin and S.L. Swartz, J. Membr. Sci., 150 (1998) 87. 76. Y. Zeng and Y.S. Lin, Solid State Ionics, 110 (1998) 209. 77. R.T. Baker and I.S. Metcalfe, Applied Catalysis A: General, 126 (1995) 297. 78. G. Maier., Angew. Chem. Int. Ed., 37 (1998) 2960. 79. N.Q. Minh, J. Am. Ceram. Soc., 76[3] (1993) 563. 80. A.C. Bose, G.J. Stiegel and A. Sammells, in S. Nakao (Ed), Proc ICIM5 (Inorganic Membranes), Nagoya, Japan (1998) p. 6. 81. M.P. Harold, C. Lee, A.J. Burggraaf, K. Keizer, V.T. Zaspalis and R.S.A. de Lange, MRS Bulletin, April (1994) 34. 82. J.N. Armor, J. Membr. Sci., 147 (1998) 217. 83. A.G. Dixon, Specialist Periodical Reports. Catalysis, 14 (1999) 40. 84. Y.H. Ma, MRS Bulletin, March (1999) 46. 85. S. Hamakawa, K. Sato, T. Hayakawa, A.P.E. Yoek, T. Tsunoda, K. Suzuki, M. Shimisu and K. Takehira, J. Electrochem. Soc., 144 (1997) 1.

471 86. S. Hamakawa, T. Hayakawa, K. Suzuki, K. Murata and K. Takehira, in S. Nakao (Ed), Proc ICIM5 (Inorganic Membranes), Nagoya, Japan (1998) p. 350. 87. T. Ori, H. Yamamura, H. Ogino, H. Kobayashi and T. Mitamura, J. Am. Ceram. Sot., 77 [10](1994)2771.


RecentAdvancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) e 2000 ElsevierScienceB.V.All rightsreserved.

NANOPOROUS

CARBON MEMBRANES

473

FOR GAS SEPARATION

S. Sircar* and M. B. R a o Air Products and Chemicals, I n c . 7201 Hamilton Boulevard Allentown, PA 18195-1501 ABSTRACT Two types of nanoporous carbon membranes (NCM) having pore diameters in the range of 3-10A can be produced by judicious pyrolysis of polymeric films. One variety called the molecular sieve carbon (MSC) membrane preferentially allows the smaller molecules of a feed gas mixture to enter the carbon pores as adsorbed molecules followed by their surface diffusion to the lower pressure side of the membrane. The other type called the selective surface flow (SSF) membrane preferentially permeates the more polar and/or larger molecules of the feed gas mixtttte by their selective adsorption and surface diffusion on the pore walls to the lower pressure side. The pores of the MSC membrane are generally smaller in size than those of the SSF membranes. The formation and the separation characteristics of these membranes depend on the choice of the precursor polymer, and the conditions of pyrolysis and post treatment. Both MSC and SSF membranes can simultaneously offer high flux and transport selectivity for the preferentially permeated molecules. The comparative advantages between these two membranes and their potential applications in industrial gas separation are reviewed. Examples of actual separation performance of these membranes are provided. The pore size and surface polarity of a NCM can be altered by thermal treatment and controlled oxidation of pore walls. Thus, these membranes can be tailor made for a desired separation. Today's technology, however, does not allow quantitative physico-chemical characterization of the nanopores. Measurement of methane diffusivity through a NCM may provide a relative estimation of the pore size.

INTRODUCTION Separation of gas mixtures by selective permeation of their components through a polymeric membrane is an established industrial practice [1-5]. A large variety of non-porous and porous polymeric materials has been fabricated and used in the spiral wound and hollow fiber membrane forms for many different gas separation applications during the last thirty years. Numerous membrane operation schemes have also been developed for optimizing the separation performance.

474 The basic principle of gas separation by these polymeric membranes is known as the solutiondiffusion mechanism. The transport of a component of a gas mixture through the polymer matrix occurs under a gas phase partial pressure (or chemical potential) gradient of that component across the membrane. The feed gas components dissolve into the polymer at the high pressure side of the membrane and then they diffuse through the polymer structure to the low pressure side of the membrane where they vaporize into the gas phase. The two key properties for characterizing the gas separation performance by these membranes are (a) the permeability (P,) of component i and (b) the selectivity of transport (permselectivity, otij) of component i over component j of the gas mixture. The permeability is generally defined by ji = A . ( ~ _ 1 .[pH _pL]

(1)

where Ji is the steady state flow rate of component i across a membrane of area A and thickness g when each side of the membrane is exposed to gas mixtures at constant but different partial pressures of that component. The variables p~(= pHyH) and piL(= pLy~) are the partial pressures of component i in the high and low pressure sides of the membrane, respectively. The corresponding total gas pressures are given by pH and pL, and the mole fractions of component i are given by yin and y~. The ideal selectivity of transport (oqj) is defined by c~ij-- Pi/Pj

(2)

A steady state diffusivity (Di) for component i which is not a function of composition within the polymer matrix can also be defined by Ji=A'(-~/"[CH-

CL]

(3)

where Cin and C~ are, respectively, the steady state concentrations of component i within the membrane at the high and low pressure sides. For many gas-polymer systems, the gas solubility in the membrane is a linear function of its gas phase partial pressure" - s,p

' ;

- sipt

(4)

where S, is the solubility coefficient for pure component i in the polymer at the system temperature. It follows from equations (1)-(4) that

Pi = Si "Di,

~ij =

(5)

475 Equation (5) shows that the permeability and the permselectivity of a component of a gas mixture are determined by its relative solubility coefficient in the polymer and its relative diffusivity through the polymer. For many gas-polymer systems, Si and Di are found to be independent of the gas phase pressures and compositions. Thus, Pi and o~ij can be treated as constants for the design of the membrane systems. In fact, Equations (1) and (2) are frequently used (with constant Pi and ocij) to describe the steady state fluxes of components through a polymeric membrane in writing the overall component mass balance equations for process design. However, the gas phase partial pressures of the components vary along the length on both sides of the membrane. These equations are then integrated using the appropriate boundary conditions to obtain the overall separation performance by the membrane module. The constancy of Pi and ctij even allows analytical solutions of governing equations for estimating membrane performance under several simplified conditions [6,7]. High permeability and high transport selectivity for component i under the design conditions are the preferred properties if the separation scheme demands that component i be enriched in the low pressure side of the membrane. Unfortunately, most polymeric membranes exhibit a reciprocal relationship between Pi and ~ij. High permeability is generally accompanied by low transport selectivity. An example of this phenomenon is shown by Figure 1 for separation of O2-N2 mixtures [8]. The 02 is selectively permeated over N2 by all polymers described in the figure. ,...NANOPOROUS CARBON ,,MEMBRA.NES (NCM) In view of the above described limitation of most polymeric membranes for gas separation, research at various academic and industrial laboratories around the world has been focused during the last fifteen years to find new membrane materials which can simultaneously provide relatively high permeability and transport selectivity for the components of interest. Nanoporous carbon membranes constitute one class of such materials. These membranes consist of a thin layer (

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