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
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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
MESL, Institute of Physical Chemistry, NCSR "Demokritos", 15310 Aghia Paraskevi Attikis, Greece
T. Stubos
MESL, Institute of Physical Chemistry, NCSR "Demokritos", 15310 Aghia Paraskevi Attikis, Greece
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
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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
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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<0.05)~), Dg (and P) is independent of the pressure gradient. Thus, the existence of membrane defects can be detected by examining
Dg is
whether
constant over a range of pressure gradients or not. A typical example is
presented by Romanos et al. (2) for two zeolite membranes on supports of different porous size (0.08 ~m and 0.15ktm) synthesised at the same hydrothemal conditions. The membranes were examined by helium differential permeability experiments at 308 K and exhibited a typical crack (macropore) free behaviour. From Figure 3a it is clear that the change from molecular to viscous flow, for both membranes, occurs at approximatelly 12 bar, where the mean free path of helium for the aforementioned temperature is 168 ,~. By making the usual assumption that Knudsen regime changes to viscous when 0.01
7
7 Wb o
i
~"
~
.
~ O
7
I
~ oO
o
~
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o
o o
support 0 . 1 5 ~
'~
az
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x
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8 ----0
--0
support O.081a m I 3 ~------~ 0 5
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15
20
, 25
30
35
0
0.5
Pressure (bar)
(a)
1
1.5
Pressure (bar)
(b)
Figure 3. Helium differential permeances at 308K of the zeolite membranes on ct-A1203 substrates with mean pore diameters (a) 0.08 ~tm and 0.15 ~tm, (b) 0.08 ~tm and 9 ~tm.
Additionally, the structure factor kg (the ratio of the experimentally measured Dg over the theoretical one for cylindrical pores), introduced by Barrer and co-workers (11,12), can easily be calculated from experimental helium permeability values. The magnitude of this factor, in combination with other available structural information (porosity, inhomogeneity) leads to some general conclusions about the pore network geometry (12,13), as in the case of mesoporous alumina and microporous carbon membranes. The measured helium permeability values were constant for both membranes over a wide range of pressure heads (10-900 mbar) ensuring that the membranes were crack-flee and that mass transport occurred in the Knudsen regime (14). The value of kg (0.51), calculated for the alumina membrane, was higher than the expected ideal value of 1/3 for an isotropic, homoporous medium. This can be attributed to deviations from the cylindrical geometry (flattened pores) and/or the assumption of random reflection of molecules (15). On the other hand the structural factor kg for the asymmetric carbon membrane was estimated (1) to be in the range of 8xl 05. Such an extremely low value for a carbon membrane having a skin with a microporosity of approximately 0.38, may signify an unusually long (tortuous) path necessary for permeability and therefore, the porous structure should be in the vicinity of its percolation threshold. As the percolation threshold should be near 0.15 for a three dimensional pore arrangement and near 0.50 for a two dimensional arrangement, a percolation threshold in the vicinity of 0.38 indicates that the pore arrangement has a partial two dimensional character. Nevertheless, an alternative explanation for the observed very low structure factor is the presence of constrictions. To this end, with the aid of information obtained from SAS and N2 adsorption, structural models for the carbon membrane have been developed (16). Furthermore, the dependence of Dg on temperature is of major importance mainly in microporous systems, revealing whether diffusion is activated or not. Activated diffusion takes place when the molecules must surmount an energy barrier, usually produced by constrictions at the pore mouths. For alumina and Vycor the Knudsen mechanism was supported by measurements of helium permeability at different temperatures (Dg oc T~), while for all the microporous membranes the temperature dependence of the integral permeance of helium was not Knudsen. The process was found to be activated and activation energies were derived assuming an Arrhenius type (PoceEa/Rx)of behaviour. The activation energies, E~, can
-16.5
o~ -16.7
support 0.15Ix
[-.. -16.9 r~ "~
-17.1
o ~
-17.3 x
~"
support 0.08Ix -17.5 -177 2.4
2.6
2.8
3
3.2
3.4
3.6
1000/T (K l )
Figure 4. Calculation of Ea for helium on zeolite composite membranes.
be easily calculated from the slope of the In Pe vs. 1/T curves (Figure 4). The activation energy for the carbon membrane was 4 kJ/mol, while in the case of zeolite membranes, although the permeability values were different, Ea was 6 kJ/mol for both of them (Figure 4). These values imply that the pore network of the carbon membrane is constricted while the zeolite porous system, developed during synthesis, is the same in the two substrates (in terms of pore size, connectivity, constrictions etc.). The latter can only happen if the membranes are defect free and transport occurs only through silicalite-1 channels (2). On the other hand, differential permeability measurements of adsorbable gases or vapours through mesoporous media, performed at relative pressures (P/P0) ranging from 0 to 1, exhibit a maximum at a certain P/Po. This fact is attributed to the occurrence of capillary condensation in the mesopores and by using appropriate models, structural characteristics of the porous media can be deduced (17). Differential permeability experiments of CO2 on microporous carbon membranes (1) at slightly supercritical conditions (T=35 ~
have shown
that at a pressure of about 35 bar a peak analogous to the mesopore case appears (Figure 5). Further experimentation with nanoporous Vycor membranes having their surface modified by various types of continuous or near continuous microporous layers, show that for materials with similar physical chemical characteristics the maximum appears to shift to smaller values with smaller pore sizes (18). Thus, the technique may eventually lead to a method appropriate
for the assessment of the pore structure of microporous membranes. However, the correlation of such peaks with the pore structure is, at present, rather qualitative, due to the limited knowledge regarding the behaviour of the fluid in micropores. The sharp maxima which are observed can be attributed to the special arrangement of the CO2 molecules inside the micropores. Simulation studies have predicted an orientational ordering transition of the molecular axis of supercritical CO2, inside individual pore models, with size of the order of few molecular diameters (19). To this end recently (20), neutron diffraction experiments in conjunction with in situ adsorption are used to monitor changes in the nature of the adsorbed gas.
350
300 25O
~g 2:~
200 150
100
0
10
20
30
40
50
60
Pm (bar)
Figure 5. Differential CO2 permeability curve at 308 K for the composite carbon membrane.
A qualitative explanation for the observed maxima can also be given following Nicholson et al. (21). The flux in the x-direction is given by the expression:
J=Jo +Jv =--~--
1] ~,Ox)
(1)
10 with Jo : diffusive flux, driven by the chemical potential, tg~t/c~, Jv : viscous flux, driven by the pressure gradient, c~/o~x, c : molecular concentration inside the pore space, Do : diffusion coefficient, k : the Boltzmann constant, T : absolute temperature, B0 : geometrical term and 1"1 :the viscosity coefficient. Non Equilibrium Molecular Dynamics (NEMD) studies revealed that for certain micropores viscous contribution is activated above a critical density (and therefore pressure) of the fluid inside the pores. At lower pressures the diffusive flux is predominant, while in higher pressures the viscosity coefficient increases rapidly. This situation will eventually lead to a maximum in the permeability, as predicted for the permeability of supercritical CH4 through a 0.95 nm width slit-shaped carbon micropore (21). On the other hand a Monte Carlo (MC) simulation (9) for carbon dioxide in supercritical conditions is currently used to estimate the density profile (and, as a result, the mean density) of the fluid inside carbon slits at various pressures (Figure 6). We expect that ultimately a combination of such NEMD and MC simulations will permit the determination of pore width from the high-pressure differential permeability data.
c
i
A o
6
O
;
i
E v 2
0 0
t
~
,.+
t
t
t
I
10
20
30
40
50
60
70
p (bar)
Figure 6. Mean density of CO2 at 308 K inside micropores vs. pressure (Monte Carlo simulation) A. pore width = 7.5 A, B. pore width = 10.5 A, C. pore width = 15.5 A
Finally, for pores smaller than approximately 10 A, the membrane pore size may also be assessed with the help of a series of organic probe molecules. In the case of zeolites the pores are part of the crystal and their dimensions determined from crystallography. To this end the measurement of the permeability of a large probe molecule (that cannot fit in the zeolite pores) provides an accurate method to check whether transport occurs through cracks or intra crystalline voids. For example such experiments were performed for silicalite-1 membranes (2) via the Wicke~Kallenbach method. Nitrogen was used as sweep gas, flowing on the substrate side, while the zeolite side was fed with a mixture of helium and SF 6 (50%). Both sides were kept at atmospheric pressure. The lowest calculable permeance value, limited by the analytical ability of the thermal conductivity (TCD) detector, at the specific set up, was 1.4xl 0 -14 (m3/m2 sec kPa). Under the above conditions, no flux of SF 6 was detected or else, its permeance was lower than the aforementioned limit. However, it should be noted that in principle the permeability of vapours of appropriate substances would require a continuous path of pores having a minimum dimension larger than the diameter of the probe molecules. A complication that often arises in practice is that the microporous structure contains paths that allow certain probe molecules j to enter the one side of the membrane but not to exit from the other. Subsequent degassing may then become rather cumbersome and in situ burning of the probe molecules is, in general, not possible as the membranes are usually sealed and held in place with the help of an organic resin.
2.3. Small Angle Scattering Small angle scattering~(SAS) method either with neutrons (SANS) or X-rays (SAXS) provides structural information about inhomogeneities of scattering objects, such as pores, in the size range from 1-200 nm. In addition, for the study of larger inhomogeneities (up to 1 gm or even more), the area is covered by Double Crystal Diffractometers, a special kind of SANS instruments. As a result, SAS measurements are ideal for the study of mesoporous and macroporous materials. On the other hand, SAS technique although improper for the study of microporous media, is not worthless. One reason being that microporous materials have sizes less than 2 nm whereas SAS is general applicable for sizes larger than 1 nm. This means that there is an overlapping range between 1-2 nm detectable by this method. In addition, porous
12 media commonly refer to a wide range of pore sizes. For instance, coal contains all classes of pores (i.e. micro-meso and macro pores). Therefore SAS method may provide critical information for these mixed class porous systems (22-26). Again, pore network effects referring to microporous necks controlling the entrances of larger pores is another example which can successfully be studied by SAS. Finally, we may note that SAS may detect both open (either conducting or not) and closed pores. The basic principles of SAS are described in Chapter 1.2 of this book.
3. COMBINATIONS OF METHODS 3.1 Permeability in conjunction with Adsorption (Relative Permeability) Permeability in conjunction with Adsorption or Relative Permeability (PR), is a technique, which combines dynamic (permeability) with static measurements (adsorption) in a systematic manner and can become a source of detailed porous structure information (13). The method was introduced by Professor R.M. Barrer and his group, who were the first to measure
PRof He and H2 through membranes formed by compaction of carbolac, blocked by sorbed SO2 and NH 3 (27,28). Very few measurements have been reported thereafter due to experimental complications (13). In order to overcome these difficulties, a new simplified relative permeability technique has been demonstrated recently by Steriotis el al. (29). A similar technique, known as permoporometry, which is developed by Eyraud (30), Katz (31) and Cuperus (32), is based on counter diffusion measurement through the partially blocked membrane. Finally, time saving multiple membrane figs, with the unique capability to perform a broad range of characterisation and evaluation measurements, can be used (33). The relative permeability technique is based on the monitoring of the permeability, P, of a weakly adsorbed gas, such as helium, through a porous membrane partially blocked by a second dense adsorbate phase. The plot of P, normalised to the permeability at zero content, versus the volume adsorbed (normalised with respect to maximum content), or the equilibrium (relative) pressure is the PR curve. Upon adsorption of a gas or vapour on a mesoporous membrane, a layer of adsorbate is building up on the walls of the pores and, when condensation occurs additionally, all the pores with radii smaller than a critical value, given
13 by the Kelvin equation are blocked. Thus, by following the mechanism of "narrowing" and consequently "blocking" larger pores, along the PR curve, the influence of different sizes of pores on the flow properties of the medium is revealed. The data, if analyzed, can offer important structural information, relevant to the evaluation of performance of membranes, provided that an appropriate pore structural model is used for the data interpretation. The most widely used model for the membrane pore structure simulation is the heteroporous model. The pore structure is represented as a bundle of tortuous capillaries with radii obeying the pore size distribution fir) and having effective length Leer, along the axis of the flow. The model is completely defined by the f(r) and the tortuosity factor, x= Lee/L, where L is the straight distance in the direction of the flow. Alternatively, the capillary network model constitute a significant improvement over the aforementioned mentioned tortuosity model, since it can provide realistic modeling, especially for systems involving membranes partially blocked by condensed vapours. In this model the degree of connectivity of the pores, nT, is replacing the less tangible tortuosity factor x. In most cases, the gas permeability diminishes at the "percolation threshold", at which a significant portion of the pores are still not blocked; however in the heteroporous tortuous capillary model gas permeability diminishes only when all the pores are blocked by sorption and condensation, unless constrictions in the capillaries are introduced. 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. Since the tortuosity model is unable to reproduce the percolation threshold, a simple network model, introduced by Nicholson and Petropoulos (34-36) can be used instead. For the gas relative permeability, an explicit approximate analytical relation between the relative permeability and the two network parameters, namely nT and the first four moments of the pore size distribution, f(r), has been developed, based on the Effective Medium Theory Approximation (EMA) (29,37). In the Effective Medium Approximation, the actual network is replaced by an "effective" alternate network of uniform radius. The "effective" radius is estimated by requiring equal flux to result from both the effective and the actual networks at the same pressure difference. Upon adsorption the pores follow a probability distribution ftmction f(x)
14 with x=r-t (r is the pore radius and t is the thickness of the adsorbed layer). When condensation occurs, all the pores with radii smaller than a critical value Xk(Xk=rk-t) are blocked (filled with condensed vapour) so that the probability distribution function is Xk
fc(x)=fa'8(x)+f(Xk<X
is the fraction
0 of the blocked pores. From EMA,
oo
f(Pm - c " x3)" fc(x)dx
o
c-x
3
+ vP m
nT
with v = ~ - I
,
= 0
(2)
nT: connectivity (2 < ~ n T
Knudsen regime). By moment expansion of the aforementioned EMA equation the relative permeability can be related explicitly to the relevant microstructural network parameters, namely the suitable moments of the pore size distribution and the network connectivity. The relative permeability, PR, is then given as :
PR = ~c3 .(1 + al); f__b_-.(_a_Ml+ aM2 ) .(fb , ~ ' ] ~c3((1 + a l ) . a M
~, I-~.
(3)
where the relevant parameters (a and ~.) are functions of nT and the moments of psd defined in oO
(29,37) fb is the fraction of conducting pores (fb= 1-fa), Xe = ~ x. f(x) dx is the average radius of Xl, fb oo
the open pores and re = ~r. f(r)dr is the average radius of the network.
0 A typical application of this model is the calculation of the pore connectivity, as in the case of the mesoporous alumina membrane. Figure 7 illustrates the helium PR versus the amount of the adsorbed water. It becomes clear that when the amount adsorbed is between 0 and 30% of the total pore volume there is a sharp decrease in PR while for adsorbed fractions
15 over 30% the drop in
PRis smoother and approaches 0 before saturation (at Vs/Vt ~0.83). At
this point (percolation threshold) the last open continuous path of the membrane system is blocked and no flow through the system occurs. Figure 7 shows also the EMA model
PR
curves for nT=2, 8 and 20. By using the best fitting simulation curve the actual pore connectivity (nT=8 for alumina) can be estimated (29). We may also note that an EMA model has recently been developed for the condensed vapour differential permeability (17). It is shown that these measurements are very sensitive to the structural characteristics of the membrane (10) and a complementary dynamic method for the determination of nT can be based thereon. On the other hand the dominant feature of packings of spheroidal particles (as in the case of alumina pellets) is the constrictions between the tetrahedral cavities formed by the microspheres. A more realistic picture, based on the random sphere packing models, is thus required. Such models are obviously more complex. Conversely, they permit a more realistic representation of the pore space among the spheroidal particles. A preliminary model has been reported for sorption (38) and relative
permeability PR (39). A more realistic model of the sorption and permeability at different porosities has been developed. The model aims at predicting the sorption and the condensed phase permeabilities, given the porosity and the spheroidal particle size distribution (40). Another application of the relative permeability technique is the monitoring of changes in the physicochemical properties of the surfaces, brought by adsorption (or reaction). We here present in detail an example of the effect of surface geometry on transport properties as monitored with the aid of PRmeasurements on the Vycor diaphragm. The measurements were carried out or in a high-pressure multi-component apparatus described elsewhere (40). After the measurement of helium permeability, the Vycor diaphragm was loaded either with water or with CH2Br2 vapor at various relative pressures (P/Po). At each equilibrium point, helium permeabilities were recorded and the two relative permeability curves were drawn.
16 A
0.9 0.8 0.7 0.6
~, 0.5
\
0.4 +
nx=2.01
i
0.3+ 0.2~0"1T O,
0
~
b
t
0.2
0.4
0.6
,.. 0.8
1
Figure 7. Relative permeability curve for the alumina membrane (lines: PR curves calculated from EMA). For a smooth cylindrical pore in classical Knudsen theory (41) the diffusion coefficient Og is given by:
2 12RT Dg =-~d ~M
(4)
where d is the pore diameter, and M is the mass of the diffusing molecule. On the other hand, when the surface is rough, the movement of diffused molecules may be affected by surface irregularities. For a pore tunnel having a fractal pore wall, with a fractal dimension Ds, Coppens and Froment (42) suggested the following expression:
Dg
16
- ~ 3cAcc
./RTA/
8
-2
)D~
V-2-~-M- 'SMAX
(5)
17 where A is the cross sectional area of the capillary, 6 is the diameter of the diffusing molecule, ~SMAXis the upper cutoff for surface fractality, and CA, Cc are respectively a proportionality constant for the area/perimeter relationship and a factor correcting the surface curvature. Figure 8 shows the PR-CUrve whereas the adjusted drawings portray the cross section of a pore tunnel in three different stages (I. dry and fractally rough, IIa. H20 loaded and smooth, IIb. CH2Br2 loaded and fractally rough). The shape of the 1-120 PR curve suggests a maximum at p/p0=0.3. The PR-maximum can not be resolved by a trivial application of Knudsen theory. As adsorption progresses an amount of adsorbed water is deposited on the pore walls. Therefore, the radius of the pores will decrease by a value t corresponding to the thickness of the adsorbed film. Consequently, if Eq. (4) was valid,
Dg (and thus
P) should
constantly decrease as P/P0 increases, as in the case of CH2Br2. This is not the case for H20 however. Helium permeabilities through a) a dry Vycor diaphragm and b) a Vycor diaphragm loaded with H20 at p/p0=0.3 are measured equal to 0.84x10 3 and 1.70x10 3 cm%ec respectively (43). The adsorption of helium at ambient temperatures and other effects, such as helium interaction with dry or wet Vycor surfaces, are practically negligible and thus not sufficient to explain this large difference in P. A possible explanation is the following: when the Vycor sample is dry (Figure 8, stage I) the pore walls are not smooth and therefore Eq. (4) is not valid. Instead, Eq. (5) is more appropriate to describe the molecular movements within the pore network. As the amount of adsorbed water increases however (stage II), the surface geometry of Vycor changes from a rough to a smooth configuration. According to previously published data (44) at p/p0=0.3 defractalization of the system takes place. The internal surface of dry Vycor is probably disturbed by a number of silicate entities which give rise to a fractal character and affect the movements of the diffusing molecules. When H20 loaded, silicate entities fall dawn rendering the surface smooth (Stage IIa). As a result a maximum appears on the H20 PR" curve. In the case of CH2Br2 there is only a partial coverage of the silicate entities at p/p0=0.3 (Stage IIb), while defractalization occurs at p/p0=0.76 (45). In Eq. (5), CA is in general quite independent from the shape of the perimeter. For a smooth cylindrical pore CA--3.5449 and for a Koch-type fractally rough perimeter CA-3.7816 (42). Thus, an average value of CA--3.6 may be accepted. Again, at early adsorption stages the
18 tortuosity factor may be considered as invariant. By assuming the following parameters: CcM (42), 8MAx--20%,8He--2.18%, d'-40%, D-2.5 (45), porosity-0.3, and obtaining volume adsorbed and t from adsorption isotherms (Vycor and non porous SiO2 at p/p0=0.3), a ratio of effective d i f f u s i v i t i e s Dg~
~ --- 0.5 is calculated for water w h i l e Dg~
~ ,-~ 2 for CH2Br2. The results
are in excellent agreement with experimental data (see Figure 8).
Figure 8.
PR c u r v e s for He/H20 and He/CH2Br2. The insets illustrate the cross section of a pore ttmnel. Stage I: dry; Stage II: p/p0=0.3 (a) H20 loaded (b) CH2Br2 loaded.
In the case of microporous materials, relative permeability technique can as a first approach be used as an easy and quick test for defect-free membranes as pointed out by Steriotis et al. (14). In Figure 9 the relative permeability curves of two carbon membranes (C1 and C2) are presented. The membranes were equilibrated to various relative pressures of benzene vapours and helium permeability was measured at each equilibrium point. Of course the adsorption isotherm could not be assessed due to the composite nature of the adsorbent
19 (part of the vapour was adsorbed by the macroporous substrate). The shape of the relative permeability curve for C1 indictes the presence of cracks while C2 reveals a crack free behaviour.
1.0 I~,
7
0,9 0,8 defects
"
"
-- I I
0,7 0.6 - -It- - C 1
"
05 0.4
0.3 0.2
0.1 0.0 0
0.2
0.4
0.6
0.8
P/ p0
Figure 9. Defect (C 1) and defect free (C2) behaviour of two carbon membranes via PR curves for He/benzene at 25 ~
Additionally, the quality of produced zeolite membrane and the defect (macropore) free growth of the zeolite layer can be certified via COJHe relative permeability experiments at elevated pressures (2). As an example, an experiment performed in a high pressure WickeKallenbach selectivity apparatus (46) at 308 K (just above the critical temperature of carbon dioxide), is presented. The membrane was fed with 10 ml/min helium on the support side, while 10 ml/min carbon dioxide were flowing past the zeolite layer. The steady state helium permeances were measured for all the successive increments of pressure (both sides) from 1 to 10 bars. No helium was detected at the zeolite layer side when the pressure reached the value of 8 bars, which corresponds to the complete filling of pores, as indicated by the carbon dioxide isotherm at 308 K (Figure 10). We may conclude that relative permeability can be used for the characterisation of microporous membranes, since one can progressively block the micropores (Starting equilibrium at p/p0=l x 105) and study the effect of pore blocking on the permeability of the
20 microporous medium. Nevertheless, a systematic use of this test may have to wait for the development of a quantitative interpretation of micropore adsorption based on NonEquilibrium Molecular Dynamics (NEMD) modelling. 1.0 A
0 ~0 O
0.8 ~ , ,
O0 ~
~ 06
~
cro~ ~
y
oo0-
, o
2
4 Pressure
6
8
(bar)
Figure 10. Defect free behaviour of zeolite membrane via PR curves for H e / C O 2 at 3 5 ~ (PR is the relative permeability, Vs/V, is the adsorbed volume normalised to the total uptake).
3.2. Adsorption in Conjunction with SAS Adsorption in conjunction with SAS is powerful technique for providing information about adsorption mechanisms (filling of micropores, growth of adsorbed multilayers, capillary condensation, formation of fractal-like networks, physicochemical properties of the surface etc.) in porous media (44-45,47-50). According to SAS theory (51), the intensity I(Q) scattered by a two phase system is related to the corresponding electron densities (or scattering length densities, sld) p~ and P2 of the phases in terms of the expression
I(Q) oc (Pl - [32)2
(6)
Apparently, when a porous medium is fully saturated with a condensed liquid adsorbate having similar electron density (sld) with the solid matrix (pl=p2), complete contrast matching will be reached. As a result the scattering is zero and the sample becomes transparent to X-rays (neutrons). In the case of SANS, an appropriate mixture of molecules of
different hydrogen isotopes (e.g. H20/D20 or C6H6/C6D6) may be used as a contrast matching adsorbate for a wide range of materials, whereas a case-specific substance having an electron density similar to that of the solid is required for SAXS. When the sample is partially saturated, the pores filled with condensate will cease to act as scatterers and only the remaining empty pores will produce a measurable intensity. Since the electron density of pores is zero (Ppore=0) and complete contrast matching is attained (Pso~ia=Padsorbate=P),then Plp2=p. Therefore, a correlation between the scattered intensity and the amount adsorbed can be deduced. As a first approach, simple mathematical expressions have been derived based on the general case of the scattering theory. For an isotropic porous medium the spherically averaged intensity, I(Q), may be represented by the integral
| sinQrQr dr I(Q) = 4np2~(1-e)V~r27(r)
(7)
0
where V is the volume of the sample, p is the electron density or the sld, ~,(r) is the correlation function at point r, and e is the fraction of the pore volume; Q is the scattering vector (Q=4nsin0/~ where 20 is the scattering angle and ~ the wavelength). A Fourier inversion of Eq. (7) gives
1
~(1-~)7(r)=2n292V
i Q2I(Q) sinQr Qr dQ
(8)
At r=0, Eq. (8) gives the Porod invariant
oo
= ~Q2I(Q)dQ = 2nzpzve(1 - e) 0
(9)
22
Eq. (9) depends only on the porosity of the specimen and not on the form of the pores. A convenient way to quantify Eq. (9) is to plot the scattering data as a function of Q2 I(Q) vs Q and then to consider the area under the curves. According to adsorption theory, two mechanisms may result to a change in that area. One is the deposition of an adsorbed film on the surface of the pore walls, and the other is the condensation in an entire class of pores. In both cases, an apparent increase in the solid volume fraction of the dry sample, (l-e), by ~x (where ~x is the volume fraction of the amount adsorbed at p/p0--x) and an equal decrease in the pore volume fraction, e, will be observed. Relating Eq. (9) for p/p0=0 and x, the following expression can easily be deduced
(10)
q)2x + ( I - 2 ~ ) ( p x + ~ ( I - ~)(oe x - I ) -- 0
where txx = q-z-~- and 0<%<e. From Eq. (10) the amount % may be calculated and normalized q0 to u~=%/e. However, a computational error may arise due to the fact that the integral in Eq. (9) is infinite, whereas the estimation of the area under the curve requires a defined Q interval. In particular, Eq. (9) can be approximated by the relation
oo
Qmax
j'Q2I(Q)dQ ~ 0
Qmin
j" Q2I(Q)dQ + Qmin
j" Q2I(Q)dQ+ 0
oo
j'Q2I(Q)dQ
(11)
Qmax
According to Patel and Schmidt (52), the second and third terms on the right hand of Eq. (11) introduce errors of about 1 and 10% respectively. If the scattering intensity
n e a r Qmax
is proportional to Q-a, I(Q) can be approximated by the empirical expression I(Q)=K,Q%K2 where K1 and I(2 are constants. Thus, the third term equals to Kz/Qm~,. If, however, I(Q) is independent of Q
n e a r Qmax the
third term accounts only for the background. The second term
can, in general, be considered negligible.
23 Another source of errors may arise from the evaluation of the first term on the right hand of Eq. (11), especially, when the effect of the absorption of x-rays by the adsorbate fluid is appreciable. As adsorption progresses this error can become significant. According to the linear absorption theory (53) of x-rays the observed scattered intensity lobs is related to the absorption coefficient, Ix, and the path thickness, t, by the expression: Iobs=I(Q)e-"t . Assuming that IXdoes not depend on Q in the small-angle region, Eq. (10) becomes
q)2x + (1- 2e)q~x + ~(1- e)[((z x)obsexp(q~,dao,lx*t) - 1]
(12)
where IX* is the mass absorption coefficient and dad s is the liquid density of the adsorbate. By plotting Ux vs P/P0 (Eq. (10) or Eq. (12)), a reconstruction of the adsorption isotherm may be obtained (26,45). For the case of incomplete contrast matching, Eq. (7) is not valid (Psolid:C-Padsorbat~)and a scattering contrast between the solid/film and film/pore interfaces is detected. A development of a theory on incomplete CM can be justified by the following three reasons: 9 CM may not be possible if heterogeneities, other than pores, are present within the solid matrix; 9 Proton exchange can result to a drift in CM; 9 At high P/P0 where capillary condensation usually commences, CM will dramatically reduce the scattered intensity, resulting in an increase of the statistical error. For a ternary system the Porod invariant qx may be written as follows,
~x = SQ2I(Q)dQ = 2n2 (Ap2)x V o
where (Ap2/ /
/ X
(13)
is the mean square fluctuation of the contrast. Assuming that the electron
densities within the individual phases are constant and the electron density of the pores pp is negligible, this fluctuation can be written as (54):
24
AP 2
) X
=(Ps-Px)
2
2 2 +Pxq~x(~Pp-qgx)+Psq~s(q)p-q)x)
r
(14)
In this expression Ps and Px are the electron densities of the solid and the adsorbate respectively, q0s is the volume fraction occupied by the solid, q0pis the fraction occupied by the pores when the sample is dry (q0s+q)p=l) and (Px is the fraction of the amount adsorbed at p/p0-x. As adsorption progresses, q)x increases due to: (a) the deposition of an adsorbed film on the solid surface, and (b) capillary condensation. At p/p0=0 and p/p0--1, the system is binary and Eq. (14)reduces to x,(Ap2/o
= los2(ps(Pp
and ,,(Ap2/I = (Ps-Px )2 (Ps(Dp respectively.
Therefore,
q____~_=x 1 - Px
2
//2
9q~ + 1 - q)____~+x Px
q'p -PTsj
q~
1-
r
(15)
1.0 0.8 .. 0.6-~ ~
0.4 0.2 0.0 0
0.2
0.4
0.6
0.8
1
P/P0 Figure 11. The adsorption isotherm of water for an alumina membrane and the reconstruction of the adsorption isotherm from SANS data. (o) adsorption and (o) desorption branches from SANS; (m) adsorption and (cl) desorption branches volumetrically. Eq. (15) allows the calculation of q0x from SAS spectra. Figure 11 illustrates the adsorption isotherm of water for a mesoporous alumina membrane and the reconstruction of the isotherm
25 from SANS data (55). Within the limits of experimental uncertainty, the agreement between the two curves is good. In the following, we will describe a few recent applications for the characterisation of porous media by combining in situ adsorption and SAS.
(a) Calculation of co-ordination number Adsorption in conjunction with SAS can provide information regarding the film areas for each relative pressure. This may be attained by calculating the surface area via the Porod formula and by assuming that the fraction of pores that are closed is negligible. This is a quite reasonable assumption for the case of an alumina porous pellet produced via symmetric compaction of particles with a narrow distribution and a final porosity comparable to that of a random close packing (rcp) or a loose close packing (lcp) of spheres (0.36-0.40 vs. 0.40). Since symmetric (i.e. rather homogenous) compression leads to porosities similar to those of rcp or lcp structures and, in addition, the alumina material can not flow (e.g. the way a polymer particle may do upon compression), it is rather safe to postulate that the pore network of the compressed alumina structure should not differ in its coarse features from that of the rcp and lcp structures. Since the latter contain no closed pores we will assume that the fraction of closed pores in the compressed alumina is not significant. By applying appropriate models, such as those postulated by Kamaukhov and Kiselev (56) or Wade (57,58) the co-ordination number of the alumina membrane may be obtained. Although our experimental technique (adsorption in conjunction with SANS) was completely different from that of Wade, for similar samples the two results are comparable and a Cn --10 was estimated for the alumina membrane (59).
(b) Defractalization process Adsorption in conjunction with SAS may provide a detailed information about the geometrical nature of internal surface of a porous material. Such information is of interest as in many cases the nature of the internal surface itself- in addition to the porosity level - is of critical importance for a porous material application (e.g. catalysis). According to the Bale and Schmidt formula (60), at large Q values, the fractal dimension, D s, of the surface is related
26 to the scattered intensity through the expression:
I(Q) oc QDs-6. When the slope is equal to -4,
a smooth surface is exhibited, and Ds=2; i.e. it is Euclidean. When 2
27
Figure 12. SANS spectra from Vycor/H20 system at p/p0-0 (upper curve) and 0.28 (lower curve) and the corresponding cross section of a pore tunnel (I(Q) is multiplied by an arbitrary
factor). On the other hand, the SAXS data suggest that CH2Br2 defractalizes the Vycor surface rather slowly in terms of the following mechanism (Figure 13). At p/p0=0.34 (stage II), a tiling of CH2Br2 molecules occurs at the surface, causing a partial coverage of the silicate entities and the monolayer formed reduces slightly the fractal dimension (Ds=2.5). At p/p0=0.76 (stage III), the heights of the molecular tiles and largest silicate entities are equal and a smooth liquid/vapor interface is observed. Recently, Hoinkis (66) studied benzene adsorption, with in situ SANS measurements, on a porous
SiO 2
glass (CPG-10-75) with pore size 7.7 nm. He observed that the internal
surface of the dry sample is fractally rough with Ds=2.3. However, adsorption of a benzene film at p/p0--0.74 revealed a smooth liquid/vapor interface. One may note that in this discussion we have used the terms 'rough' and 'fractal' in somewhat interchangeable manner. In reality there is a physical distinction between a rough and a fractal surface, but it is very difficult to distinguish between the two via a SAS experiment. A detailed analysis of this point has been given in the pertinent literature (67). Nevertheless, this point does not affect the essence of our conclusions regarding the interaction of the adsorbate molecules with large protruding silicate entities of the internal surface.
28
Figure 13. SAXS spectra from Vycor/CH2Br 2 system at P/P0 (from top to bottom): 0, 0.34, 0.76 ) and the corresponding cross section of a pore tunnel (I(Q) is multiplied by an arbitrary factor).
(c) Size distributions A full correlation between adsorption and SAS requires a close monitoring of the Kelvin equation. Since the SAS data provide information about the average pore size of empty pores and the Kelvin equation furnishes the upper limit of pores filled with condensate, the relation between the Kelvin and SAS predictions is not straightforward and the help of appropriate models is required. As an example, the pore structure of an alumina membrane was studied by adsorption in conjunction with SANS (68). Contrast matching was achieved by using a 25% H20/D20 mixture. SANS data were modeled by assuming a system of polydisperse homogeneous permeable spheres (69,70) and pore size distributions were extracted at each pressure step according to the scattering of a rectangular distribution function (Figure 14). At low relative pressures, as the adsorption process progresses (0
29 distributions. At p/p0=0.94 there are still open pores of about 120 .~ acting as scatterers, probably due to the presence of positive and negative curvature effects (71).
0.02
dry
i"
p/pO=0.45 ---t- -
p/pO=O.
57
=_. p/pO=0.70 A
0.01
O. 0
'
--X--- p/pO=0.77
I
50
100
150
r(A) Figure 14. Predicted pore size distributions according to the scattering of a rectangular distribution function.
A simple method for evaluating average particle (pore) sizes from SAS by curved and fractal surfaces, has been developed (72). It is based on the extension of Porod and Kirste equation (73) from smooth to fractal surfaces. The scattered intensity, I(Q) can be expressed as"
I(Q) = Q6A_~,+ QsA_~s(6 - Ds)(5 - D~) ~ 1+ 3 1 1 12 qr2 8 \ r , - ~ j
(16)
where D is the fractal dimension of the surface, r] and r2 are the prime radii of curvature averaged over the intemal surface, AoocF(5-Ds)sin{n(3-Ds)/2. By introducing appropriate values for Ds and r], r2 the Porod's law, the Kirste and Porod correction, or the Bale and
30 Schmidt (60) formula may be recovered. By assuming an appropriate geometrical shape an estimation of the average particle (pore) size can be retained.
(d) Formation of pore percolation network with fractal geometry Li et al. (49) observed a very-low-Q scattering component (D=1.75), during desorption of matched water mixture (64% D20) in Vycor porous glass. This is a diffraction evidence for the
~ k.
P/Po=.O. P/Po = 9 5 %
t
interpore scale "percolation network" with fractal geometry. The correlation length is larger than 1000 A for the high humidity samples, a distance equivalent to about five times the average pore
~ , ~ - - . ~ a , , ] ~ , - -~--~
separation distance. The desorption process has been demonstrated with Monte Carlo calculations (Figure 15) by using a square 100 x 100 lattice. The pore neck sizes were distributed at random according to a given size distribution with the imposed constraint that only those pores connected to the vapor phase by sufficiently large neck channels may desorb. In this case, the percolation cluster of empty pores is clearly visible at high relative pressures (p/p0=0.95). When P/P0 is lowered (p/p0=0.75), the large-scale fractal structures penetrate deep into the bulk material. Theoretical studies suggest (74-76) that D should be 1.89 for
Figure 15. Monte Carlo simulations for desorption as a percolation process. The pores are situated on the lattice sites, with the empty pores represented as disks.
a two-dimensional cluster and 2.4 for a three-dimensional (3D) system and with little dependence on connectivity if pore has more than three connects. However, SANS measurements suggest that the real system is somewhat more complicated. The real difference may be due to the fact that Vycor is produced by spinodal decomposition followed by an etching process, which means that it has a spaghetti-like structure with very low connectivity (77).
4. CONCLUSIONS Three independent methods of membrane characterisation (adsorption, permeability, small-angle scattering) have been briefly surveyed with emphasis given to two combinations
31 of them, namely relative permeability and adsorption in conjunction with SAS. Additionally, examples of recent application of the methods to membrane materials were reported. Relative permeability provides a means of "on line" measurement of the fluid flow properties of a membrane during adsorption. Since these properties are closely connected with microstructural characteristics, such as pore shape, connectivity and size distribution, the interpretation of the results can lead to enhanced information concerning the porous network of the membrane under investigation. Furthermore, surface changes during adsorption can be easily monitored. On the other hand the technique is extremely useful for testing the existence of defects in microporous membranes. For quantitative information on the pore network structure of microporous materials the PR data must be coupled with sophisticated micropore adsorption models, such as Grand Canonical Monte Carlo and Non Equilibrium Molecular Dynamics. Small Angle Scattering is nowadays a widely used technique for the structural characterisation of porous media. Analysis of the SAS spectra provides information about the pore size and shape, as well as the surface properties. Consequently, by combining adsorption with SAS one can obtain the whole range of the aforementioned information at every equilibrium point. To this end, adsorption in conjunction with SAS becomes a powerful tool for the investigation of the adsorption mechanism in porous media. The amount adsorbed can be correlated in terms of the scattering theory and reconstruction of the adsorption isotherm can be attained. Furthermore, the technique can detect changes in the porous structure or in physicochemical properties of the surface during adsorption. We may conclude that the combination of equilibrium and dynamic characterisation methods leads to an enhanced spectrum of information for membrane materials, in terms of pore geometry and surface properties. Thus, by combining techniques it is possible to draw self-consistent conclusions, which are broader than those obtained from a single method.
5. ACKNOWLEDGMENTS We gratefully acknowledge the TMR program of the European Commission for providing financial support and access to Berlin Neutron Scattering Centre (Hahn Meitner Institut) and ISIS pulsed neutron source, Rutherford Appleton Laboratory, UK.
32 6. REFERENCES 1. F.K. Katsaros, T.A. Steriotis, A.K. Stubos, A.Ch. Mitropoulos, N.K. Kanellopoulos, and S. Tennison, Microporous Materials, 8 (1997) 171. 2. G.E. Romanos, Th.A. Steriotis, E.S. Kikkinides, N.K. Kanellopoulos, V. Kasselouri, J.D.F. Ramsay, P. Langlois, and S. Kallus, submitted to J. European Ceramic Society. 3. S. Brunauer, L.S. Deming, W.S. Deming, and E. Teller, J. Amer. Chem. Soc., 62 (1940) 1723. 4. S.J. Gregg, and K.S.W. Sing, Adsorption, Surface Area and Porosity, 2nd ed., Academic Press, London, 1982. 5. B.F. Roberts, J. Colloid Interface Sci., 23 (1967) 266. 6. M.M Dubinin, Russ. J. Phys. Chem., 39 (1965) 697. 7. D. Nicholson, and N.G. Parsonage, Computer Simulation and the Statistical Mechanics of Adsorption, Academic Press, 1982. 8. R.F. Cracknell, D. Nicholson, and N. Quirke, Mol. Phys., 80 (1993) 885. 9. S. Samios, A.K. Stubos, N.K. Kanellopoulos, R.F. Cracknell, G.K. Papadopoulos, and D. Nicholson, Langmuir, 13 (1997) 2795. 10. M.E. Kainourgiakis, A.K. Stubos, N.D. Konstantinou, N.K. Kanellopoulos, and V. Milisic, J. Membrane Sci., 114 (1996) 215. 11. R. Ash, R.W. Baker, and R.M. Barrer, Proc. R. Soc. London Ser. A, 299 (1967) 434. 12. R. Ash, R.M. Barrer and R.J. Sharma, J. Membrane Sci., 1 (1976) 17. 13. N.K. Kanellopoulos, and J.H. Petropoulos J. Chem. Soc. Faraday Trans., 1723 1, 79 (1983)517. 14. T.A Steriotis, F.K. Katsaros, A.K. Stubos, A.Ch. Mitropoulos, and N.K. Kanellopoulos, Measurements Sci. Technol., 8 (1997) 168. 15. R. M. Barrer, The solid-gas interface, vol. 2, E.A. Flood ed., Marcel Dekker Inc, NY, 1967. 16. Th. Steriotis, K. Beltsios, A.Ch. Mitropoulos, N. Kanellopoulos, S. Tennison, A. Wiedenman, and U. Keiderling, J. Appl. Polym. Sci., 64 (1997) 2323. 17. E.S Kikkinides, K.P. Tzevelekos, A.K. Stubos, M.E. Kainourgiakis, and N.K. Kanellopoulos, Chem. Eng. Sci., 52 (1997) 2837. 18. E Magoulianiti, K. Beltsios, D. Davazoglou, G. Romanos, and N.K. Kanellopoulos, Proceedings of the International Symposium on International Chemical Vapor Deposition: CVD-XIV and EUROCVD 11 Symposium, Paris, Proceedings Volume 97-25 (1997) 576. 19. G.K. Papadopoulos, and N.K. Kanellopoulos, unpublished work. 20. F.K. Katsaros, Th.A. Steriotis, K.L. Stefanopoulos, N.K. Kanellopoulos, A.Ch. Mitropoulos, M. Meissner, and A. Hoser, Physica B, in press. 21. D. Nicholson, and R. Cracknell, Langmuir, 12 (1996) 4050. 22. M. Kalliat, C.W. Kwak, and P.W. Schmidt, ACS Symp. Ser., 169 (1983) 3. 23. O.P. Mahajan, Powder Technol., 40 (1984) 1. 24. P.L. Walker, Philos. Trans. R. Soc. London Ser. A, 300 (1981) 65. 25. A.Ch. Mitropoulos, J.M. Haynes, R.M. Richardson, T.A. Steriotis, A.K. Stubos, and N.K. Kanellopoulos, Carbon, 34 (1996) 775.
33 26. A.Ch. Mitropoulos, K.L. Stefanopoulos, and N.K. Kanellopoulos, Microporous and Mesoporous Mat., 24 (1998) 29. 27. R. Ash, R.M. Barrer, and C.G. Pope, Proc. R. Soc. London Ser. A, 271 (1963) 19. 28. R. Ash, R.M. Barrer, and R.T. Lowson, J. Chem. Soc. Faraday Trans., 1 (1973) 2166. 29. Th. Steriotis, F.K. Katsaros, A. Mitropoulos, A.K. Stubos, and N.K. Kanellopoulos, J. Porous Mat., 2 (1995) 73. 30. C. Eyraud, Application of gas-liquid permoporometry to characterisation of inorganic ultrafilters, E. Dridi, and M. Nakagaki ed., Proc. Eur.-JPN Cong. Memb. Processes, 1984, 629. 31. M.G. Katz and G. Baruch, Desalination, 58 (1986) 199. 32. F.P. Cuperus, D. Bargeman, and C.A. Smolders, J. Membrane. Sci., 71 (1992) 57. 33. T.A. Steriotis, F. Katsaros, A.K. Stubos, A.Ch. Mitropoulos, P. Galiatsatou, and N.K. Kanellopoulos, Rev. Scient. Instrum., 67 (1996) 2545. 34. D. Nicholson, J.K Petrou, and J.H. Petropoulos, Chem. Eng. Sci., 43 (1988) 1385. 35. D. Nicholson, and J.H. Petropoulos, J. Chem. Soc. Faraday Trans., 80 (1988) 1069. 36. N.K. Kanellopoulos, and J.K. Petrou, J. Membrane Sci., 37 (1988) 1. 37. J.H. Petropoulos, J.K. Petrou, and N.K. Kanellopoulos, Chem Eng. Sci., 44 (1989) 2967. 38. N.K. Kanellopoulos, J.K. Petrou, and J.H. Petropoulos, J. Colloid Interface Sci., 96 (1983) 90. 39. N.K. Kanellopoulos, J.K. Petrou, and J.H. Petropoulos, J. Colloid Interface Sci., 96 (1983) 101. 40. S.A. Sasloglou, J.K. Petrou, N.K. Kanellopoulos, and G.P. Androutsopoulos, J. Microporous Mesoporous Mat., in press. 41. S. Dushman, Scientific Foundation of Vacuum Technique, John Wiley, NY, 1949. 42. Coppens, and G.F. Froment, Chem. Eng. Sci., 50 (1995) 1027. 43. P.K. Makri, G. Romanos, T. Steriotis, N.K. Kanellopoulos, and A. Ch. Mitropoulos, J. Colloid Interface Sci., 206 (1998) 605. 44. A.Ch. Mitropoulos, P.K. Makri, N.K. Kanellopoulos, U. Keiderling, and A. Wiedenmann, J. Colloid Interface Sci., 193 (1997) 137. 45. A.Ch. Mitropoulos, J.M. Haynes, R.M. Richardson, and N.K. Kanellopoulos, Phys. Rev. B, 52 (1995) 10035. 46. F.K. Katsaros, Th.A. Steriotis, A.K. Stubos, and N.K. Kanellopoulos, in preparation. 47. E. Hoinkis, and A.J. Allen, J. Colloid Interface Sci., 141 (1991) 540. 48. J.D.F. Ramsay, and G. Wing, J. Colloid Interface Sci., 141 (1991) 475. 49. J.C. Li, D.K. Ross, L.D. Howe, K.L. Stefanopoulos, J.P.A. Fairclough, R. Heenan, and K. Ibel, Phys. Rev. B, 49 (1994) 5911. 50. J.C. Li, D.K. Ross, and M.J. Benham, J. Appl. Cryst., 24 (1991) 794. 51. A. Guinier, and G.Foumet, Small-angle scattering of x-rays, Wiley, NY, 1955. 52. I.S. Patel, and P.W. Schmidt, J. Appl. Cryst., 4 (1970) 50. 53. B.D. Culity, Elements of X-ray Diffraction, Addison-Wesley, Reading, MA, 1967. 54. L.A. Feigin, and D.I. Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum Press, NY, 1987. 55. A.Ch. Mitropoulos, T.A. Steriotis, F.K. Katsaros, K.P. Tzevelekos, N.K. Kanellopoulos, U. Keiderling, A. Sturm, and A. Wiedenmann, J. Membrane Sci., 129 (1997) 289. 56. A.P. Kamaukhov, and A.V. Kiselev, Russ. J. Phys. Chem., 34 (1960) 1019.
34 57. W.H. Wade, J. Phys. Chem., 68 (1964) 1029. 58. W.H. Wade, J. Phys. Chem., 69 (1965) 1395. 59. Th. Steriotis, A. Mitropoulos, N. Kanellopoulos, U. Keiderling, and A. Wiedenmann, Physica B, 234-236 (1997) 1016. 60. H.D. Bale, and P.W. Schmidt, Phys. Rev. Lett., 53 (1984) 596. 61. E. Cheng, M.W. Cole, and P. Pfeifer, Phys. Rev. B, 39 (1989) 12962. 62. F. Katsaros, P. Makri, A. Mitropoulos, N. Kanellopoulos, U. Keiderling, and A. Wiedenmann, Physica B, 234-236 (1997) 402. 63. P. Levitz, G. Ehret, S.K. Sinha, and J.M. Drake, J. Chem. Phys., 95 (1991) 6151. 64. M.J. Benham, J.C. Cook, J.C. Li, D.K. Ross, P.L. Hall, and B. Sarkissian, Phys. Rev. B, 39 (1989) 633. 65. D.W. Schaefer, B.C. Bunker, and J.P. Wilcoxon, Phys. Rev. Lett., 58 (1987) 284. 66. E. Hoinkis, Adv. Colloid Interface Sci., 76-77 (1998) 39. 67. P. Wong, Phys. Rev. B, 32 (1985) 7417. 68. K.L. Stefanopoulos, G.E. Romanos, A.Ch. Mitropoulos, N.K. Kanellopoulos, and R.K. Heenan, J. Membrane Sci., 153 (1999) 1. 69. M. Kotlarchyk, and S.H. Chen, J. Chem. Phys., 79 (1983) 2461. 70. L. Blum, and G. Stell, J. Chem. Phys., 71 (1979) 42. 71. D.H. Everett, Colston Res. Soc., 10 (1958) 95. 72. A.Ch. Mitropoulos, N.K. Kanellopoulos, K.L. Stefanopoulos, and R.K. Heenan, J. Colloid Interface Sci., 203 (1998) 229. 73. R. Kirste, and G. Porod, Kolloid-Z. Z. Polym., 184 (1962) 1. 74. V.K.S. Shante, and S. Kirkpatrick, Adv. Phys., 20 (1971) 325. 75. M. Parlar, and Y.C. Yortsos, J. Colloid Interface Sci., 124 (1988) 162. 76. A.U. Netmaann, and S. Havlin, J. Stat. Phys., 52 (1988) 203. 77. G. Mason, Proc. R. Soc. London Ser. A, 415 (1988) 453.
Recent Advancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) o 2000 ElsevierScienceB.V. All rightsreserved.
35
In situ X-ray diffraction studies on micropore filling T. Iiyama*, T. Ohkubo, and K. Kaneko Physical Chemistry, Material Science, Graduate School of Natural Science and Technology, Chiba University, Yayoi, Inage, Chiba, 263-8522 Japan The molecular level picture of micropore filling mechanism in carbon micropores was summarized and the necessity of the structural study on molecules confined in carbon micropores with in situ X-ray diffraction is described. The detailed explanation of in situ X-ray diffraction technique for adsorption studies is given. The effectiveness of the in situ X-ray diffraction for elucidation of structures of molecules filled in micropore is shown for CCI4, water, and alcohol molecules. In situ X-ray diffraction studies shows the presence of organized structure inherent to an adsorbate molecule, although only adsorption measurement cannot distinguish the molecular state different from the bulk liquid.
1. INTRODUCTON Human welfare has been giving a great perturbation to earth. Energy saving technology has been requested in every industrial field in order to preserve the global environments.. Porous materials, in particular, microporous solids have a hopeful potential to develop new energy saving technology. Microporous solids have been helpful for efficient separation, concentration, purification, and removal through an intensive adsorption of gases in micropores. Consequently, more understanding of the adsorption of gases in micropores has been strongly required. Pores whose pore width w is less than 2 nm are called micropores according to the IUPAC classification [1]. Representative microporous solids are activated carbon and zeolite. Zeolite is a crystalline solid having well-described micropores. Activated carbon is basically ill-crystalline, because activated carbon has a random structure of nano-order graphitic units having two to four stacking layers. The void spaces between thin graphitic units provide slit-shaped micropores. However, activated carbon fiber ACF and KOH-activated carbon have considerably uniform micropores and great pore volume. Granulated activated carbon which has a wide pore size *Present address: Department of Chemistry, Faculty of Science, Shinshu University, Asahi, Matsumoto, Nagano, Japan
36 distribution from micropores to macropores, has been widely used in a variety of industries. A better understanding of micropore structures and adsorption mechanism should contribute to realize the energy saving technologies. The adsorption of vapor in micropores is called micropore filling. Originally Dubinin et al introduced the concept of micropore filling for adsorption on activated carbon [2]. They considered that mechanism of pore filling can describe the adsorption on activated carbon in a better way compared with the mechanism of successive layer formation so called BET mechanism. They assumed that the filling ratio r at an equilibrium pressure P, which is the fraction of the micropore volume occupied by adsorbed molecules, is a function of the Polanyi adsorption potential A and the parameter n associating with the distribution of the adsorption potential. A = RT In (Po/P)
(1)
Here Po is the saturated vapor pressure and A is reduced by the characteristic energy E. They chose the following Weibull distribution function to get the so-called DubininAstakhov equation. r = exp [- (A/E) n ]
(2)
r
(3)
W /Wo
where W and W o are the volume occupied by molecules at P and the micropore volume, respectively, n - 2 gives Dubinin-Radushkevich (DR) equation. Stoeckli et al took into account the pore size distribution and extended the above approach to describe adsorption in micropores even for polar molecules [3]. Sing et al [4] introduced ct s-plot to analyze the adsorption isotherm, proposing the two-stage mechanism of primary and cooperative (or secondary) fillings. However, they did not analyze sufficiently the adsorption isotherm below cts = 0.5, which is essentially important in micropore filling. Then, no clear physical model for the twostage mechanism was given. Kaneko et al [5,6] introduced the high resolution ct splot over the wide ct s ranges from 0.01 to 2.4 using the adsorption isotherm from P/Po = 1 0 -5 -- 1 0 6 . They showed the presence of two upward deviations from the linear ct splot below as = 1.0. The upward deviations from the linearity below and above ct s = 0.5 are called filling and cooperative swings, respectively. The filling swing is ascribed to an enhanced monolayer adsorption on micropore walls and cooperative swing comes from filling in the residual space between the monolayer on both micropore walls. Also Kaneko et al showed accelerated bilayer adsorption in micropore filling of He at 4.2 K [7,8], pore entrance-enriched micropore filling of n-nonane [9], dipole interaction mediated micropore filling of SO2 [11], and cluster mediated filling of water [11] on the
37 basis of the detailed analysis of their adsorption isotherms. These mechanisms of micropore filling have no physical evidences except for adsorption isotherms, although molecular simulation can be referred in some cases. We need direct physical information on the mechanism of micropore filling. As activated carbon can absorb efficiently light from ultraviolet to infra-red region, ordinary molecular spectroscopies cannot be applied to the carbon system. However, X-ray can penetrate carbon walls and thereby X-ray technique such as X-ray diffraction and small angle X-ray scattering SAXS can be applied to study micropore filling in activated carbon. This review describes assembly structures of molecules adsorbed in micropores of activated carbon, mainly ACF, which is obtained from in situ X-ray diffraction examinations and gives structural pictures on micropore filling. Although in situ Xray diffraction is powerful to elucidate the structure of the molecular assembly in micropores, it is not necessarily effective to understand the mechanism of micropore filling. The integrated information with in situ SAXS can provide a more perfect description on the micropore filling mechanism in future.
2. MICROPORE FILLING MECHANISM AND MOLECULAR PROPERTIES We will discuss the interaction of a molecule with the graphitic slit pore of the micropore model of activated carbon. The interaction between a molecule and a surface atom as a function O(r) of the distance r between them can be expressed by the Lennard-Jones potential, 9 (r) = 4 e sf[( Crsf/r)'2-( Crsf/r)6 ]
(4)
where crse and Crsfare the well depth and effective diameter for the molecule-graphitic carbon atom. These cross parameters are calculated according to the Lorentz-Berthelot _ )1/2 rules, e ~f ( t~ ss t~ ff ; O'sf = ( O'ss "[" O'ff)/2. Here, (O'ss, e ss) and (O'er, eff ) are the Lennard-Jones parameters for a surface atom and a molecule, respectively. The interaction potential O(z) for a molecule and a single graphite slab is given by the Steele 10-4-3 potential [12], (I) (Z) = 2 7~" tO C ~ sf O's? A {(2/5)( O"sJz)l~
4- 0"s4/[3 A (0.61 A +z)3]}
(5)
where z is the vertical distance of the molecule above the surface, A is the separation between graphite layers (=0.335 rim), p c is the number density of carbon atom in a graphite layer (=114 /nm3). As the micropores of activated carbon can be approximated by the slit spaces between the predominant basal planes of nanographitic units, the whole interaction potential 9 (Z)p of a molecule with the micropore of an inter-graphite surface distance H can be given by eq. (6).
38 (1)(Z)p ----- (1)(Z) + (1)(H-z)
(6)
Consequently, we can evaluate the potential profile of the molecule adsorbed in the graphitic micropore. Here H is not the effective pore width w determined by the adsorption experiment. The difference between H and w is a function of o'sf and cr~ [13]. H-w = 1.60
O'sf--
(7)
O'ff
Figurel shows potential profiles of N 2 in a slit-shaped graphite pore as a function of w using the one-center approximation. Here, the molecular position in Figure 1 is expressed by a vertical distance z from the central plane between two surfaces. The potential profile of an N2 molecule in the graphitic slit pore of w > 0.6 nm has double minima, indicating the presence of monolayer adsorption on each microporewall. As the barrier height between the double minima of the micropore of w > 0.7 nm is greater than 77 K, a distinct monolayer adsorption on each pore-wall occurs in micropores of w > 0.7 nm. The predominant monolayer adsorption occurs at the low P/Po region, compared with the monolayer adsorption on the fiat surface, because the N2-graphitic surface interaction in micropores is greater than that on the flat surface. In the case of micropores having w > 1 nm, N2 molecules should be adsorbed in the space between monolayers on both micropore-walls after monolayer adsorption. Then, we can presume that in micropore filling of N 2 by micropores of w > 1 nm, there are two elementary processes - monolayer adsorption on each micropore-wall and filling in the residual space between the opposite monolayers on micropore-walls. The separation
1000
\ -1000
= 1.5nm
t,q 0.8 nm
-2000 \
07nm
\
0.5 nm
-3000
I -0.8
o'4
o
o14
z/nm
Figure 1. Potential profile of
a n N 2 molecule
with a graphitic slit space.
39 of these elementary processes depends on the height of the potential barrier between double minima. In the micropores of w < 0.7 nm, which are called ultramicropores, a single layer or double layers can be formed between two graphitic walls. The multistage micropore filling process on the real activated carbon having pore size distribution was observed. The Grand Canonical Monte-Carlo (GCMC) simulation studies support this two-stage model of micropore filling of N 2 [14,15]. Very recently Ohba et al [16] showed clearly the role of preformed monolayer in the further adsorption by use of GCMC simulation. Figure 2(A) shows the potential profiles of a n N 2 molecule at the second layer in the monolayer-coated graphite slit pore of w = 1.24 nm. The potential depth of the second layer molecule corresponds to 60 % of that of the monolayer molecule. As the interaction potential of the second layer molecule with the monolayer is more than 70 % of the total molecular potential, adsorption of molecules at the second layer position should stem mainly from the adsorbate-adsorbate interaction. Figure 2(B) shows the simulated N 2 adsorption isotherms for monolayer and second layer formation at 77 K. Adsorption at the second layer positions occurs steeply at a narrow relative pressure region. This filling is not the capillary condensation, but this should be designated cooperative filling, as suggested by Sing et al [4,17]. The above simulation results coincide well with experimental data from the high resolution ct ~-plot by Kaneko et al [17,18]. The basic mechanism of micropore filling of vapor molecules which interact strongly with the graphitic walls is almost understood, as described above. However, still microscopic molecular states and structures are not elucidated. We need to introduce a structural technique to adsorption in micropores. As the low temperature limit of the in situ X-ray diffraction experiment is 140 K, so far we cannot apply this method to N2 adsorption at 77 K. In stead of nitrogen molecules, we must choose an appropriate vapor molecule which satisfies the following requirements: The probe molecule is a nonpolar molecule of a spherical shape and it has a great X-ray scattering ability in 1ooo m
"7 ' i A ) !!!
500
~-
I I !
I
0
! | | I
-500
9
9 9
9
II 0fO
- 1000
-1500
I!
i
k -0.4
!
.~ 500 (B) ,,.., o E '~
30o
l
1
Z
t e
t o
o
t
- - -~i! - ''~176176
_t 06
0
t
200 100
l
,, ,, . . . . . . . . . . . . .
400
0.4
-5
-4
-3
-2
-1
0
l o g ( P / P 0)
Figurer 2. (A) Potential profile of a n N 2 molecule in the monolayer-coated micropore of w =1.24 nm. The solid curve is the potential due to monolayer molecule. (B) Simulated N 2 adsorption isotherms for monolayer and second layer adsorption in micropore of w=1.24 nm at 77 K. Broken curve: monolayer, solid curve: second layer.
40
order to get a good contrast against graphitic walls. A CC14 molecule has a high symmetry of T~ which can be approximated by the spherical shape. Also the atomic number of a chlorine atom is much greater than that of the carbon atom, giving rise to a distinct electron density difference. Accordingly a CCI 4 molecule was chosen as the representative of the nonpolar vapor molecule. The basic picture on the micropore filling of nonpolar vapor in carbon micropores should have a good similarity for other vapor molecules of spherical shape. Then, X-ray diffraction study on micropore filling of CC14 will be shown in this review. The mechanism of micropore filling can be estimated from the molecular simulation studies on N2 adsorption in graphite slit pore. The basic feature of the micropore filling of N2 can be applied to that of CCI 4. Recently Suzuki et al [19] showed that CC14 molecules are adsorbed in micropores at 303 K in a similar way to N 2 at 77 K. However, the CC14 molecule is greater than the N2 molecule, inducing a specific structure formation in smaller micropores. The adsorption of water on activated carbon is not clearly understood. We have a question why water molecules can be adsorbed in hydrophobic carbon micropores. A water molecule cannot interact strongly with the graphite surface, because the induced images in the graphite surface from the permanent dipole of a water molecule is not stable under the random orientation of physisorbed molecules. Hence, the electrostatic interaction is not great and also the dispersion interaction of a water molecule with the graphite surface is not predominant, leading to very small interaction energy. Therefore, water molecules are not adsorbed on the graphite surface and even in graphitic micropores at the low P/P0 region. It is well-known that water molecules form the dimer or clusters even in the gas phase. In carbon micropores, highly concentrated Table 1 Molecular properties of adsorbed molecules N2 O'ff / A 3.798 e ff/ka / K 71.4 O'se / A 36.0 e sJka / K 45.0 3-D size / A3 2.6x2.6x3.8 D-pole / D none Q-pole -4.9 / 1040 Cm -2
Polarizability / 10 .24 cm 3
1.7403
CC14 5.947 322.7 4.67 95.6 5.43 none none
10.5-11.2
H20 CH3OH C2HsOH 2.614 3.626 4.530 809.1 489.1 362.6 3.01 3.51 3.97 151.3 116.8 101.3 2.6x2.8x3.6 3.6x3.9x4.4 3.9x4.2x6.0 1.854 1.70 1.69 8.7(xx) ..... -8.3(yy) -0.4(zz) 1.45 3.29-3.32 5.11-5.51
Here O'sf and e se are obtained from Lorentz and Berthelot rules and [s] denotes an carbon atom. 3-D size, D-pole, and Q-pole are 3-dimensional size, dipole moment, and quadruple moment, respectively.
41
O
H20 O o
(H20)5
O
~](H,O)n Molecular position
Figure 3. Hypothetical potential profile of a water molecule in graphitic micropores.
e~0
A AAAA 9
800
o
600 o ,.0 o r~
400 A
9
(3 .~i~3 O AC) 9 9
o
200 -
o 9 o~
o
<
o ~a___e~~-" 0
0.2
~
"
0.4 P/P
,
,
0.6
0.8
1
0
Figure 4. Water adsorption isotherms of P5 and P20 at 303 K. O: P5-adsorption, O: P5-desorption, A- P20-adsorption, A: P20-desorption water clusters such as the pentamer ( H 2 0 ) 5 of which size is about 0.5 nm must be formed due to the compressed conditions [20]. Water molecules are bonded with each other using hydrogen bonds in the cluster and thereby the electrostatic charge of the water molecule should be more compensated, inducing a strong Lennard-Jones type interaction with the graphitic rnicropore-walls. Figure 3 shows hypothetical interaction potential profiles of a water molecule in a graphite slit pore. For a single water molecule, the interaction is very weak, but the cluster in which point charges are used for the hydrogen bonding formation can have a deeper potential well through the
42 dispersion interaction. The cluster fitting for the micropore geometry has a deeper potential well. Consequently, water adsorption begins suddenly above the medium P/Po where the clusters grow. In case of a small alcohol molecule, more or less similar situation can be applied to adsorption in graphitic micropores. Then, we can check phenomenologically this aspect using adsorption of alcohol. As the relationship between the micropore filling mechanism and molecular interaction is not sufficiently established yet, the factors of molecules in Table 1 must be taken into account. Here the Lennard - Jones parameters ,~ ff and e sf indicate the intermolecular interaction and the molecule - graphite wall interaction, respectively. The e n of a water molecule is quite great due to the hydrogen bonding, giving a large O'sf through the Lorentz Berthelot rule. However, the O'sf for a water molecule is not a good measure. This situation holds for a methanol molecule having a strong hydrogen bonding ability. Figure 4 shows adsorption isotherms of water on two kinds of ACFs at 303 K. Here P20 and P5 have the average pore widths of 1.1 and 0.75 nm, respectively. The adsorption isotherms are of Type V. Almost no water is adsorbed below P/P0 = 0.5, while a predominant adsorption begins above P/P0 = 0.5. The rising relative pressure of P20 is higher than that of P5. The rising relative pressure of P20 treated at 1273 K in H2 which has almost no surface functional groups according to the X-ray photoelectron spectroscopy, shifts to a higher value [21]. The adsorption isotherm of P20 has a noticeable hysteresis, while that of P5 has almost no hysteresis. The adsorption hysteresis of the water adsorption isotherm is not caused by capillary condensation [22]. On the course of adsorption, water molecules are adsorbed through the above-mentioned cluster mediated filling mechanism to form a uniform adsorbed layer in micropores. On the other hand, molecules and/or small clusters are evolved from the interface between the adsorbed layer and gas phase. This different processes should provide the adsorption hysteresis. Iiyama et al is now trying to elucidate the mechanism of the cluster-mediated filling of water and the adsorption hysteresis with in situ SAXS [23].
3. A P P L I C A T I O N O F E L E C T R O N M E T H O D TO C O N F I N E D FLUIDS
RADIAL D I S T R I B U T I O N
FUNCTION
The dimension of molecular assemblies confined in carbon micropores is limited to less than 2 nm in the width direction at least. Then, the observed X-ray diffraction of confined fluids is very broad. We need an effective analysis for the broad X-ray diffraction pattern in order to get an important information on the structure of adsorbed molecules. The electron radial distribution function (ERDF) method [24] is applied to the analysis of confined fluids. This method can extract the information on the intermolecular structure from broad X-ray diffraction patterns. The electron radial distribution function shows the average molecular number or molecular density p at a
43 distance r from a central molecule. This method was developed by distinguished pioneers such as Warren in 1930's [25]. Narten had studied liquid structures systematically with ERDF method [26]. Nishikawa et al improved the electron radial distribution function method for liquid systems [24]. We applied this improved method for the confined systems. However, we need careful corrections for accurate ERDF conclusions. 3.1. X-ray intensity correction The observed X-ray scattering intensity at s, lobs(S), of the carbon sample having adsorbed molecules is given by [27]
Io,,s(S) = I,o,(S) "P(O) "G(O) "a(O, p ) +
"A(O, p )
Here I,o,(S) is the X-ray scattering intensity of the sample at s. parameter s can be expressed, 4;rsinO s- ~ A
(8) The scattering
(9)
Here 2 tY is the scattering angle, A is the wavelength of X-ray in experiments. All of correction factors, P(tY), G(t7), A(6~,p), and Ib~ck(S) depend on the experimental arrangements. The experimental arrangement of the X-ray diffraction in this paper is shown in Figure 5. The polarization factor, P(6~), is given by [27],
e(o) =
1+
2a" cos 2 20 1 + cos2 2a
cos 2
(10)
Here 2 a' is the scattering angle on the monochrometer. The geometrical factor, G(tY), for a normalization of X-ray irradiating volume is simply given by
G(O) -
1 cos0
(11)
The Ib, ck(S) is the parasitic scattering that is mainly attributed to the scattering by windows of the sample cell. It can be determined experimentally by the measurement of the sample cell without sample in vacuo. The X-ray absorption factor, A(tY,p), depends on both of the scattering angle 2 6? and extent of molecular adsorption. It is given by,
44
A(O, p) - exp.
_ tt~ (p)'l.____.._~ cosO
- ~r (p)'lg
} (12)
where /~s(P) and /'['8(P) are the linear X-ray absorption coefficients of the sample and the gas phase which are the function of the pressure p and X-ray path length. The notation ls and Ig are the X-ray path lengths in the sample and gas phase, respectively. The first term in the exponent of eq. (12) expresses the X-ray absorption by the carbon sample and adsorbed molecules, and the second term stems from absorption by gaseous molecules in the sample chamber. The first term is much greater than the second one under these experimental conditions. Further, /z~(p) l~ can be expressed by,
Ia
t~g (p)" ts - log--~o - t,~g (p) "lg
(13)
Here Ia is the transmitting X-ray intensity with the sample and Io is that without the sample at 6? = 0 deg. Both of la and Io were measured at 20kV and 10mA using an aluminum plate of 2mm in thickness as the X-ray attenuator. The /_zg is calculated with the following equation.
,14, g
Here, (/z//O)g is the mass X-ray absorption coefficient which is calculated from the literature values [28], and M r is the molecular weight of adsorbed gas, R and T are the gas constant and the measuring temperature.
3.2. Effect of small-angle X-ray scattering Figure 5 shows the X-ray diffraction pattern of pitch-based activated carbon fiber (P20). The strong X-ray scattering is observed in a small angle region of s < 2A -~, which is a common feature of porous carbons. The X-ray scattering near s =0 ( tY= 0 ~ ) is known as small-angle X-ray scattering (SAXS). A non-uniform structure of different electron densities leads to the SAXS. The SAXS contains valuable information on mesoscopic structures of the system, elucidating latent pore structures [29,30]. However, the SAXS has a strong influence on the transformation of the X-ray diffraction data to the electron radial distribution function especially in porous carbon. The false sign curve whose wavelength is 1.5 - 2.0nm superimposes on the electron radial distribution function. Then we must remove the effect of small-angle X-ray
45
4000
3000
:~
.,. r~
2000
1000
I
I
I
I
2
4
6
8
s/A
10
1
Figure 5. X-ray diffraction pattern of pitch-based ACF (P20) in vacuo.
scattering. We assume that the total X-ray intensity, I,o,(S), can be expressed by the additive form, !
I,o , (s) = Ito t (s) + I,~ (s)
(15)
Here I,~x(S) is the small-angle scattering and Ito,' is the corrected total intensity. The porous carbons and confined fluid molecules do not have a long-range periodic structure. Therefore, corrected total intensity, I,o,' has no peak at less than 1.5z~-1. The X-ray scattering intensity at s < 1.5z~-1 can be attributed to the small-angle X-ray scattering. A log-log plot of X-ray diffraction intensity versus scattering parameter of porous carbon and confined fluid system give a straight line. Therefore, the smallangle X-ray scattering is expressed as,
ln(/,~ (s))-- a ' l n s + b
(16)
The constants a and b are determined by the least-squares method. The corrected total intensity, I,o,'(s), is derived by subtraction of the I, ax(S). The influence of the correction method of the SAXS for the ERDFs of adsorbed CC14in micropores was examined. The best method was used for further analysis.
3.3. Determination of scattering intensity of confined fluids The scattering intensity of only adsorbed molecular assembly must be extracted from
46
the observed X-ray scattering intensity Itot(S). We assume the additive form of scatterings by carbon walls (ItotC(s)) and by adsorbed molecules (Ito~a(s)), and by interference term due to adsorbed molecules and carbon walls (Imt(S)) , a s described by
I,o , (s) = I,o, c (s) + I,o," (s) + Imt (S)
(17)
Although nanographitic structures of cellulose-based ACF are effected by water adsorption [31], it is expected that adsorption of non-polar molecules does not change the structure [31,32]. Although the adsorption of polar molecules can affect the interlayer spacing of the micrographites, we assume no change of the micrographitic structures in this analysis. As the contribution of adsorbed molecules to the total diffraction is predominant, this assumption should be reasonable. Hence, the first term, I,o,C(s), can be obtained experimentally from the diffraction data of the carbon only.
lobs c (S) - I,o, c (s) " P(O) "G(O) "A(O, p = O) + Ib,,,:k(s) " A(O, p = O)
(18)
Here IobsC(s) is the observed X-ray diffraction intensity of the carbon without adsorbed fluids. These correcting factors, P(6~), G ( 8 ) , A( 8 , p), and /back(S), are already described above. The interference term is given by j,k
sin srjk
I,,,t (s) - Z Z ]'c L ~ l,k srlk
(19)
Here, fa is the molecular scattering factor of adsorbed molecules. It is calculated by atomic scattering factors of component atoms. For example, in C C I 4 case, fcc~ is approximated by, [CCI4 -'-"~/ # "J"4fc21
(20)
where fc and fcl are atomic scattering factors of carbon and chlorine atom, respectively. The rjk in eq. 19 is the distance between the j-th carbon atom and the k-th adsorbed molecule. The interference term, l,,,(s), is smaller than the second term of eq. 17 which is approximately proportional to fa" In this analysis, this interference term, Im,(s), is neglected. Therefore, I, ota(s), the scattering intensity of the adsorbed molecules can be determined as,
47
I,o, ~ (s) = I,o , (s) - I,o, c (s) .
(21)
3.4. Electron radial distribution function analysis The X-ray diffraction of the adsorbed molecular assembly, I~ota(s), consists of coherent and incoherent X-ray scatterings,
Itota(S)~le~coha(S)'l'~(s)'lmca(S)}
(22)
Here Icofl(s) and Iicoa(S) are coherent and incoherent X-ray scatterings, respectively. The coefficient 9 (s) is the ratio of the intensity observed by a detector to the incoherent scattering. This coefficient ~ (s) depends on the experimental conditions of the monochrometer. The wavelength of incoherent scattering X-ray, ~ ', increases with increase scattering angle, 2 tY. Ak, - k,'- k, = 0.024626(1- cos 20)
(23)
where 3.' and //. are wavelengths of incoherent scattering and incident X-rays, respectively, and ,4 3. is their difference. Eq. 23 can be expressed by the function of s. The monochrometer removes a part of incoherent scattering. The single crystal of graphite having a large Mosaic-Spread is used as the monochrometer in this study. However, a graphite ]nonochrometer cannot sufficiently remove the incoherent scattering in the wavelength region near the characteristic X-ray. The monochrometer removes completely the incoherent scattering when the wavelength of X-ray is far from that of the characteristic X-ray. The wavelength of X-ray which is completely removed by the monochrometer is denoted Awid. The coefficient, ~ (A//.), is given by,
[1-(IAzl/•wid)(whenlAZl ~ Zw., ) .I.(AZ) - ~ 0 (whenlAZ I > Zw., )
(24)
The wavelength Aw,d should depend on the scattering angle of the monochrometer, or, and the length of the Mosaic-Spread, Am. Am
Zw.~ = ~ tan a
(25)
48
The average length of the Mosaic-Spread on graphite single crystal is 7 " 1 0 -3 rad. Therefore, //'w,d= 0.0657 A. AS ,4 A is the function of s, eq. (26) is derived,
9 (s) -- 1-
2" 0.024626" 2,2. sZ 2
.
(26)
8,~ 'l~w,d We can use the literature value [28] for incoherent scattering, I,,fl(s), and correct numerically the incoherent scattering term, 9 (s) "l,,c(s). The coherent scattering, I, ofl (s), is fitted to the self scattering factor [28] at large s region to determine the normalization factor, le [33].
~ s
~ (27)
/ ~o~~ (Sm~x)
Here s,,,,x is a maximum of s in the experiment. In this study, we use the average of intensity over 6-12 ,~-1. Figure 6 shows the normalized, coherent, and corrected incoherent scatterings of P20.
60 50 40 ~9r
30
2 =
20
10
0
I
I
I
I
I
2
4
6
8
10
-
12
s l .~ Figure 6. The corrected X-ray diffraction intensities of P20. Fine solid line: coherent scattering intensity of carbon; dashed line: corrected incoherent scattering intensity of carbon; dotted line: sum of coherent and incoherent scattering intensities; and bold solid line: diffraction intensity of P20.
49 The electron radial distribution function (ERDF) analysis improved by Nishikawa and Iijima.[34] is applied to elucidate the structures of adsorbed molecular assembly in micropores.
The ERDF,
4 ~r2 ( ,o (r)- ,Oo), is obtained by the Fourier transformation of
the structure function, si(s). Here ,o(r) and /90 are the electron density at a distance r and the average density of adsorbed molecules, respectively. This function, 4 ~r2(,o
(r)-,Oo) ,
is a differential electron radial distribution function and
exact ERDE ERDF.
As ,0 o cannot be determined precisely,
47rr 2,0(r)
4 ~'r2(,o(r)- ioo) is
4srr2(p(r)- P~ - ~c~Z ,2 ~ si(s)'exp(-Bs2)'sin(sr)" As
where Zj is the electron number of a component atom j. distribution of the electron clouds.
Structure function,
is an
often used as
(28)
The ERDF expresses the
si(s), is given by
si(s) - s{Icoha(s) - ~ f, (s) 2}
(29)
Then ERDF can be obtained, as shown in Figure 7. Each peak in Figure 7 corresponds to the interatomic distance on graphitic structure of P20. The exponential term of exp(B sZ), is called the convergent factor that is used for reduction of Fourier noise. The Fourier noise decreased with increasing the constant B, but the position resolution of the ERDF decreased simultaneously.
B = 0.2 - 0.5 was the best for analysis. The
measuring time for getting reliable date can influence the reliability of the ERDF
10
o Q.
"~ -10
-20
' .... 0.5
' .... 1.0 r/nm
~ .... 1.5
2.0
Figure 7. Electron radial distribution function of P20.
50 because of weak X-ray beam. more than 8 h.
Necessary measuring time for the reliable analysis was
4. EXPERIMENTAL METHOD AND POROSITY OF ACTIVATED CARBON Pitch-based ACFs of P5, P10, and P20 (Osaka Gas Co.) were used as activated carbon samples. The micropore structures were determined by N2 adsorption isotherms over P/P0 = 106 to 1 at 77K. The micropore parameters of surface area, micropore volume, and average slit width w were determined from the subtracting pore effect (SPE) method using the high resolution as-plot. Table 2 shows the micropore parameters. The activated carbon samples have considerably uniform micropores. Adsorption isotherms of CC14, water, methanol, and ethanol on ACF samples were determined at 303 K after preheating at 383K and lmPa for 2h. The density of adsorbed molecular assembly in micropores was determined from the micropore volume obtained by N2 adsorption at 77 K and the amount of adsorption near the saturated vapor pressure. Table 3 collects the density of the molecular assembly in micropores of ACF at 303 K. The X-ray diffraction of molecules adsorbed in micropores of ACFs was measured by the transmission method using an angle-dispersive diffractometer (MXP3 system, MAC Science) in the scattering parameter s (=47rsin 8/A.) range of 0.7 to 12A1. The monochromatic MoKa at 50kV and 30mA was used for the diffraction measurement. The experimental arrangement of the X-ray diffraction is shown in Figure 8. The diameter of in situ X-ray diffraction chamber is 96mm. The sample holder is installed in the chamber. Mylar films are used for windows of the in situ measuring chamber and the sample holder. The sample chamber is connected to the vacuumadsorption system for controlling adsorption conditions. As the sample holder is open, gas molecules are adsorbed on carbon samples in the holder. Samples in the in situ x-ray chamber can be cooled by flowing liquid Nz down to 90K without condensation of adsorbate molecules using an indirect cooling device. The temperature of the sample is measured by a silicon diode on the sample holder. Here the distance between the silicon diode and the sample is 5mm. Table 2 Micropore structures of ACF samples Micropore volume Surface area ml.g 1 P5 P10 P20
0.336 0.622 0.971
m2.g1 900 1510 1770
External surface area m2-g-1
Pore width
5 25 44
0.75 0.82 1.13
nm
51 D
C
A
Figure 8. The schematic diagram of experimental arrangement. A: X-ray tube, B: sample, C: graphite monochrometer, D: scintillation counter, E: sample chamber, DS: dispersion slit (1.0 degree), SS: scattering slit (1.0 degree).
The in situ X-ray diffraction patterns were measured mainly at 303 K. The ground carbon samples are set in the sample holder and pre-heated at 383K and lmPa for 2h. Then X-ray diffraction of activated carbon samples in vacuo at 303K is measured which is used for correction of the diffraction contribution by carbon samples only. Then, adsorbate molecules are adsorbed and the X-ray diffraction of the molecule-adsorbed activated carbon is measured after a sufficient equilibration at P/Po = 0.9 and 303K. When the X-ray diffraction pattern of adsorbed carbon sample is measured at low temperature, the sample chamber is closed after the measurement at 303K. Only the X-ray diffraction of the water-adsorbed carbon samples is observed at 143 - 255K. The temperature of the sample is kept constant within __.0.1K for 303K and within __.5Kfor 143 - 255K during the X-ray diffraction measurement for 6h. The information on the adsorbed molecular structure is obtained as follows using the example of water: the X-ray diffraction intensity of microporous carbon with adsorbed molecules, Iais(s), expressed in terms of the additive form of the scatterings by carbon wall structures (the first term of eq.8), by adsorbed water (the second term of eq.8), and by the adsorbed water-carbon interface structures (the third term of eq.8), as given by eq.30.
X f2 + X ~ 2fw 2 sinsrk~k2 k 1 ~k9
I ~,, (s) = I
fc2 +
X J1 9 2
sr
SFklk 2
J132
+ ~.a
fc f~,
(30) sr
#
52 Here Ie is the standardization factor, and fc and fw are the atomic scattering factors of carbon and oxygen in water, respectively. The scattering caused by hydrogen atoms in water is neglected. The notation rj~ j2, rk~ k2 and rjk are the atomic distances. In this analysis, we neglect the scattering due to the adsorbed water-carbon interface. Hence, the X-ray diffraction of the adsorbed water is determined by subtraction of the first term in eq. 30 from the measured scattering. The similar procedure is applied to another adsorbate molecule. Some analytical results will be described below.
5. I M P E R F E C T PACKING STATES OF G E l 4 M O L E C U L E S The liquid structure of CC14 having Td symmetry was examined by Narten [26] and Egelstaff et al [40], suggesting a so-called bcc cluster model. Nishikawa and Murata [41] proposed the presence of a long range correlation even in a CC14 liquid state at room temperature. It is well-known that CCI 4 shows unique liquid-solid transition and it has three solid polymorphs [38]. Therefore, the molecular assembly structure of CC14 in micropores should be sensitive to the pore width. Also the study on CCI 4 confined in carbon micropores is the most reliable due to an clear contrast as mentioned before. All adsorption isotherms of CC14 were of Type I, indicating that CC14molecules are adsorbed by a representative micropore filling mechanism. As the interaction of CC14 with the graphitic micropore is stronger than that of N2, a noticeable adsorption of CC14 molecules begins at a very low pressure. The adsorption isotherms of CC14 were Table 3 The density of molecular assembly at 303 K Adsorbate
CC14
w / nm
Adsorbed density
Bulk liquid density
Bulk solid density
/ g cm -3
/ g cm -3
/ g cm -3
0.75
1.26
1.594
1.76(fcc) "1
1.1
1.43
1.87(monoclinic) .1 1.79 (Rhombohedral) .1
HzO
0.75
0.86
1.1
0.81
0.996
0.92(Ih) 0.92(Ic) .2 1.17(IceII, 123K) .2
CH3OH
0.75
0.67
0.98(113K)
C2HsOH
1.1 0.75
0.96 0.71
1.03(87K)
"J: ref.[37, 38]
1.1 ~2: ref.[39]
1.05
53
I
[[]
o 0.. i
P10 " Liquid [II] [IIIl
0
,,
0
0.5
1.0
I , , , ,
1.5
I , , ,
2.0
,I
,
2.5
,,,
3.0
r/nm Figure 9. Electron radial distribution functions of CCI 4 adsorbed on P10 and bulk liquid CC14 at 303 K. analyzed by the DR plots, leading to the adsorption capacity for CC14 in micropores. The density of adsorbed CC14 was determined using the adsorption capacity for CCla and the micropore volume determined by N2 adsorption at 77 K, as mentioned before. The density of adsorbed CCI 4 is shown in Table 3. The adsorbed density is much smaller than the bulk liquid density, indicating that the molecular size of CCI 4 is too great to fill the void space efficiently. Correspondingly, the adsorbed density of P5 (w = 0.7 nm) is smaller than that of P20 (w = 1.1 nm). The GCMC simulation study showed the same results on the density. The diffraction pattern of CCI 4 on P20 was close to that of bulk liquid, but their intensities were different from each other. The diffraction intensity of P5 was markedly weak, compared with those of P20 and the bulk liquid. The ERDFs of CC14 adsorbed in micropores of P10 and bulk liquid CC14 at 303K are shown in Figure 9. The ERDF of bulk CC14 liquid, which has main four [I], [II], [III], and [IV] peaks in the intermolecular region, is similar to the literature [40]. The [I] and [II] peaks are assigned to the nearest neighbors and second neighbors, respectively. The [I] peak of confined CC14 is the same as that of liquid CC14, while the [II] peak of the confined CCI 4 is situated at a shorter distance than that of bulk liquid. The intensities of [I] and [II] peaks are less than those of the bulk liquid. The [III] and [IV] peaks in the long-range of the confined CCI 4 are not attenuated regardless of the weak intensity compared with those of bulk liquid. Hence, the confined CCI 4 should have a more ordered longrange structure than bulk liquid regardless of the smaller adsorbed density. Figure 10 shows the ERDFs for confined CCI 4 in micropores of three kinds of ACFs. Each ACF has a different ERDF, indicating the inherent molecular arrangement. The
54
[I] peak position does not change with the pore width, while the [II] peak shifts to a smaller value with the decrease of the pore width. The [I] and [II] peak intensities decrease remarkably with the decrease in the pore width, suggesting that the serious geometrical restriction prohibits the perfect formation of the first nearest and second nearest neighbor structure around a central molecule in the narrower pore. Thus the short-range structure of the CC14 molecular assembly in the micropore is different from the bcc cluster type packing which is proposed for the bulk liquid. The confined CC14 molecules have a defective nearest neighbor structure, leading to the shorter side-shift of the second neighbors. Only the ERDF of P5 has a different peak structure in the distance range over 1.2 nm. The [II] and [III] peaks of P5 are markedly shifted from those of other ACFs in the opposite direction each other and there is an explicit new peak between [II] and [III] at 1.33 nm. This feature indicates the presence of the serious restriction of CC14 molecular packing in the narrowest pore and thereby molecules are packed in a different way from the bulk liquid. The average pore width of P5 corresponds to the 1.3 layer thickness of CCI 4. Accordingly, CC14 molecules cannot form the bcc cluster packing structure. The Grand Canonical Monte Carlo (GCMC) simulation provided the ERDF having the above features [19,42]. The CC14 molecules are packed in the narrow slit space to form an imperfect packing structure giving the observed ERDE Although the CC14 molecule can be approximated by a spherical molecule, it is noteworthy that the geometrical restriction provides the variety for the molecular packing [43,44].
, I
[II
P5 ~P10 . . . . . P20 [IIl
|
Q.. r
~
[III]
[IV]
g..
0
,
r
I: I
0
0.5
1.0
1.5
2.0
2.5
3.0
r/nm
Figure 10. Electron radial distribution functions of CC14 adsorbed on kinds of ACFs at 303 K.
three
55 4000 (A)
d
P20 " - - 303 . . . . . 223 ----143
3000 1 ~\ I~
6. d
2000
at 303 K K K K
(B)
0
1000
00
1
2
3
4
5
6
s/A;1 Figure 11. X-ray diffraction intensities of P20 at 303 K and water-adsorbed P20 as a function of temperature.
6. OREDERED STRUCTURES OF WATER IN HYDROPHOBIC MICROPORE The surface tension of water depends strongly on the curvature of the gas-liquid interface; the depression of the freezing point of water in a small space, which has been believed to be associated with biological and geological processes, is proportional to the reciprocal of the pore width [45,46]. The macroscopic properties of water confined in the small space are not sufficiently understood from the standpoint of molecular science yet. The enhanced intermolecular interaction in micropores should lead to an unusual behavior of the confined water. As the graphitic micropores of ACF can offer an excellent hydrophobic nanospaces, water confined in micropores of ACF was studied. Although adsorption of water by activated carbon has been studied for many years, the adsorption mechanism is not sufficiently established yet [47-52]. In adsorption of water on activated carbon, water molecules are presumed to form clusters prior to filling of micropores without any direct evidence. Then, X-ray diffraction study on adsorbed water has been strongly requested. The water adsorption isotherms at 303K are of Type V, as shown in Fig. 4. The saturated water adsorption amount of P5 and P20 are 290 and 790mgg 1, respectively. The fractional filling of water molecules on P5 and P-20 at 303K are 0.86 and 0.92 which are obtained using the density of the bulk liquid water at 303K and the bulk liquid N2 at 77K. The density values of water adsorbed on P5 and P20 are 0.86 and 0.81, respectively, which is smaller than that of bulk liquid and solid water. The water adsorption isotherm of P5 has almost no adsorption hysteresis, while P20 has a remarkable adsorption hysteresis.
56
(F)
........ 303 K - - 258 K ........ 223 K 143 K " . . . . Liquid
2 Q. ,
9
1
:
-1 -2 -3
0
0.5
1.0
1.5
2.0
r/nm Figure 12. Electron radial distribution functions of water adsorbed on P20 as a function of temperature and bulk liquid water at 303 K. X-ray diffraction patterns of water adsorbed P20 (w = 1.13nm) as a function of the temperature were measured, as shown in Figure 11. The X-ray diffraction patterns for all temperatures have broad peaks. In the bulk water case, the X-ray diffraction pattern changes drastically at melting point, giving sharp peaks below the melting point. X-ray diffraction patterns of bulk water at 303K and 233K are completely different from those predicted. In case of the adsorbed water there are no sharp peaks due to the bulk ice formation even at 143K. This result indicates that the water molecules in the carbon pore have only short-range order even at 143K because of space restrictions by pore walls. Both of the first peak (A) at s = 1.8 ,~-1and second peak (B) at s = 3.1/k 1 change gradually with temperature even across the freezing point of bulk water. However, Figure 13 cannot provide the detailed structure of adsorbed water itself. The ERDF analysis was also applied to this case. Figure 12 shows the ERDFs of water adsorbed in the 1.13nm-slit space at different temperatures.
The ERDF of bulk liquid water at 303K is also shown in Figure 14
for
comparison. Water adsorbed at 303K has the highest peak (F) and shoulder one (E) at 0.42 and 0.35nm, respectively. The feature at this region sensitively varies as lowering the temperature. The peak or shoulder (E) at 0.35nm is assigned to the nearest-neighbor water molecules, whereas peaks (F) and (G) are attributed to the second and third nearest-neighbor molecules, respectively.
Hence these three peaks provide the detailed
information on the short range structure of the water molecular assembly in the micropore. As bulk liquid water has an interstitial molecule at the nearest-neighbor position, and thereby the peak (E) is higher than the peak (F) in case of bulk liquid water. It is shown that the adsorbed water even at 303K has a more ordered structure
57 than bulk liquid. The ERDFs show the strong dependence with temperature. The shoulder (E) at 303K becomes a peak as lowering the temperature and at the same time the intensity decreases markedly. On the contrary, the intensity of the peak (F) increases with the decrease of the temperature. The position of the peak (E) shifts to a smaller value and the positions of the peaks (F) and (G) shift to a greater value with the decrease of temperature. The positions of peaks (E) and (F) at 143K are 0.282 and 0.456nm, respectively. These values are close to those of the bulk ice of Ih form, because the distances to the first and second nearest neighbor molecules in ice are 0.275nm and 0.449nm, respectively. The brief agreement indicates that the water molecular assembly in the 1.1nm-carbonaceous slit space has a similar structure to the bulk ice. The preliminary X-ray diffraction simulation suggests that the simulated diffraction patterns of nanocrystals having Ih and Ic structures do not coincide with the observed ones of water adsorbed in carbon micropores [53]. Also it should be stressed the fact that water molecules in micropores even at 143K have higher mobility than bulk ice, which is shown by broad peaks. The ERDF of water adsorbed at 143K has an ordered structure up to 1.3nm at best. This ordered structure range of the adsorbed water is plausible for the horizontal direction of the slit space. Although the structure of the water adsorbed was examined over the wide temperature range of 143K to 273K, we could not observe a clear phase transition behavior of water adsorbed in the micropore from X-ray diffraction. Figure 13 shows ERDFs of water adsorbed in micropores of 0.75nm in pore width as a function of the temperature and bulk liquid water at 303K. The peak intensities of (J) and (K) which are assigned to the second and third nearest-neighbor molecules increase slightly with the decrease of measuring temperature. The intensity difference between 143K and 303K is much smaller than that of the wide pore system of P20. Water molecules in P5 form a more ordered structure than in P20 and they cannot move easily even at 303K. The position of peak (J) shifts to a greater value as lowering temperature, while the position of peak (K) does not change. The first nearest neighbor molecule shows only the weak shoulder (I) near 0.3nm. Thus the structure of water adsorbed in P5 has a completely different temperature dependence from that in P20. This X-ray diffraction study clearly shows that water molecules confined in the hydrophobic nanospace have a solid like structure of the different molecular mobility. The ordering of the water molecular assembly structure depends sensitively on the pore width. We need the X-ray diffraction simulation in order to understand the water molecular assembly structure more precisely. This structural difference was ascertained by differential scanning calorimetry (DSC) [54]. The freezing DSC curve of water confined in micropores of P20 gave an exothermic peak at 220 K, whereas that of P5 had no peak. As the bulk water gave a single peak at 250 K, the DSC date were obtained under the supercooled conditions. Then, the marked depression of the freezing temperature occurs in water confined in micropores of
58
(J) (K) 2
0)
.
/~
!
......... 303 K ..... 223 K --143 K Liquid "
-
-
9 r
i
0 -1 -2 -3 L_______ 0 0.5
1.0 r/am
1.5
2.0
Figure 13. Electron radial distribution functions of water adsorbed on P5 as a function of temperature and bulk liquid water at 303 K.
P20, as observed in mesopores. Recently, GCMC simulation predicted that the freezing temperature of confined fluid in micropores depends on the pore-wall fluid interaction[55]. The freezing temperature of CC14 and benzene is noticeably elevated in micropores of ACF [56, 57]. Hence, we can conclude that even fluid confined in micropores can exhibit phase behavior. In case of water, water confined in the micropores of P20 exhibits the phase transition, whereas that of P5 does not, agreeing with the results of X-ray diffraction. Also the observed enthalpy change of water of P20 upon the phase transition was only 14 % of the bulk value. Hence, the thermodynamic state of the confined water in the carbon micropores of P20 is different from that of the bulk liquid. The confined liquid water is more stabilized due to a partial ordering and the confined solid is unstable owing to the serious restriction for formation of the perfect crystalline structure. Thus, water confined in the hydrophobic micropores of ACF has a special ordered structure[59-61].
7. ORIENTATIONAL FILLING OF A L C O H O L MOLECULES. An alcohol molecule has both of polar and nonpolar sites. The relationship between the amphilicity and the assembly structure in micropores is quite important to understand micropore filling mechanism of hydrophilic molecules. The balance between hydrophilicity and hydrophobicity can be controlled by the chain length of aliphatic group. Also alcohol molecules have hydroxyl group which can form
59 hydrogen bond.
Then, studies on alcohol confined in carbon micropores should be
helpful to understand the mechanism of water adsorption in carbon micropores.
Here,
the results on ethanol and methanol are described [61,62]. The adsorption isotherms of ethanol on ACF at 303 K are shown in Figure 14.
All
isotherms are of Type I , being analogous to the N2 adsorption isotherms. Hence ethanol molecules are adsorbed by micropore filling mechanism. The adsorption isotherm of methanol of P5 at 303 K is shown in Figure 15.
The adsorption isotherm
of ethanol on P5 at 303 K is also shown for comparison.
Although the adsorption
isotherm of ethanol has a remarkable uptake in a very low P/Po range, the adsorption isotherm of methanol has a gradual increase of adsorption below P/Po = 0.3. Therefore, the interaction of an ethanol molecule with the micropore is much greater than that of a methanol molecule. However, the methanol molecule can interact more strongly with the micropore-walls than a water molecule, because almost no water molecule is adsorbed below P/P0 = 0.3 [63]. Hence, the methanol molecule can play a role of the intermediate between water and ethanol molecules for carbon micropores. We can expect that the
-~
1000
""6
800
{
600
,~
400
"~ E <
2 0 0 ~ L~-~ ~ o
L] I} [-{-1
o
o
oo
,
,
,
0.6
0.8
P/P0
Figure
14. Adsorption
isotherms of
ethanol on ACFs at 303 K.
O" P5 and
[-l" P20
{
te eoooe o o~~ o
%
eo
D 0
"~ 100 D O
po o
was determined, as collected in Table 3. The adsorbed density of P20 is greater than that of P5 for both of ethanol and
50
methanol. The adsorbed density of P20 is almost equal to the bulk solid
0
density, but that of P5 is slightly
o
0.4
DR plots.
Then, the adsorbed density
o
L
_~ 150 8
methanol
o
0.2
different from those of water and ethanol. The saturated amounts of adsorption in micropores for ethanol and methanol were obtained from the
confined
o
0
200
of
-
O!/
is
structure
,j I'1 t !'I' II
0
I
i
I
I
0.2
0.4
0.6
0.8
1
P/P0
smaller than the bulk liquid density for
Figure 15. Adsorption isotherms of
both cases.
These adsorption data
methanol and ethanol on P5 at 303 K.
should
associated
O" methanol and 0 " ethanol
be
with
the
60
~0.27
,,
2 0 -2
0.5
1.0
1.5
2.0
r/nm Figure 16. ERDFs of ethanol adsorbed on P20 as a function of the fractional filling ~ at 303 K.
structures of alcohol molecules in micropores. The diffraction patterns of the ethanol-adsorbed ACF had a broad peak due to the adsorbed ethanol at s = 1.5 ,~-1. The difference of diffraction intensities between the ethanol-adsorbed ACF and ACF itself was assigned to the adsorbed ethanol molecular assemblies themselves. Figure 16 shows the ERDFs of ethanol in micropores of P20 at different fractional fillings. The ERDFs of bulk liquid ethanol is also shown for comparison. The intensity of the peak of adsorbed ethanol in the short range is higher than that of bulk liquid. The intensity of the peak in the short range for t~= 0.27 is the greatest. The adsorbed ethanol has greater amplitudes than bulk liquid in the range of 0.3 to 1.2 nm. The first and second nearest peaks at 0.5 and 0.9 nm shift to a shorter distance compared with those of the bulk liquid. The periodical structure above 1.5 nm is observed for the adsorbed ethanol. This long-range ordering suggests that adsorbed ethanol molecules form highly ordered structure. However the incomplete removal of the scattering between adsorbed molecules and pore-walls may contribute to the long periodical structure to some extent. The higher peak and the peak shift suggest that the immobile state of the adsorbed molecule and thereby that ethanol molecules adsorbed in micropores of P20 should have an ordered structure of less mobility. Figure 17 shows ERDFs of ethanol adsorbed on P5 and P20 at P/P0 = 1 and 303 K. The amplitudes of ERDFs of confined ethanol are greater than those of the bulk liquid ethanol. The peak positions of the confined ethanol shift from those of the bulk liquid. The ERDFs of confined ethanol depend on the pore width. We calculated the radial
61
"---P5
ZPTu d
1t I
%
-2
0
0.5
1.0
1.5
r/nm
Figure 17. ERDFs of ethanol adsorbed on ACFs at saturated pressure. Solid bars show each positions and intensities for crystalline ethanol.
distribution of the crystalline ethanol using the crystallographic data [64] and atomic scattering factors of carbon and oxygen atoms. As the crystalline structure gives a discontinuous distribution of the neighbor atoms, it is shown by vertical bars of which height is proportional to the coordination number. However, this calculated distribution is different from the average density. Hence, we will use this calculated distribution for a qualitative structure determination of the confined ethanol. Especially, the peak position of adsorbed ethanol at r = 0.49 nm for P20 is close to the peak position of the crystalline state at r = 0.47 nm. These results indicate that the solid-like structure is formed in the short distance. On the other hand, the peak of adsorbed ethanol at r = 0.44 nm for P5 suggests the strong confinement of ethanol molecules in narrower space and not to form the ordinary solid structure because of the serious confinement. The peak position increases with the pore width, approaching to that of bulk liquid. On the other hand, the peak intensity decreases with the pore width. These tendencies hold for both of the peaks of the first and second nearest neighbors. Both changes indicate that ethanol molecules should be confined strongly in narrower micropores. The adsorbed density of ethanol molecules in micropores of P20 is not close to that of bulk liquid, but that of bulk solid. Also the ERDF features strongly support the ordered structure formation. The ethanol molecule is a linear molecule and both groups of C2H5 and OH have completely different hydrophobicity and hydrophilicity,
62 respectively. The ethanol molecules should be associated with each other using hydrophobic and hydrophilic pairs. J6nsson examined the crystal structure of ethnaol and showed that ethanol molecules are joined by two kinds of hydrogen bonds to form infinite zigzag chains [64]. Morishige et al. showed that ethanol molecules adsorbed on the graphite surface have a hydrogen-bonded specific structure at low temperature [65]. Thus, the hydrogen bonding plays an important role in the structure of ethanol molecular assemblies. The stabilization by the hydrogen bonding is more than 20 kJ/mol [66]. In case of the ordered structure of ethanol molecules in micropores, the hydrogen bonds should play an essential role. We must take into account the adsorbed density, the crystal structure, and the possible hydrogen bonds for the ordered structure of ethanol molecules in micropores. Figure 18 shows the models of adsorbed ethanol in P5 and P20. The model structure for P20 was constructed from the crystal structure of the bulk solid ethanol. This model is consistent with the observed ERDF and the density of ethanol adsorbed in micropores of P20. On the contrary, micropores of P5 are too small to form the same structure. The molecular potential calculation showed that P5 has no double minima, but a single deep minimum on the central plane between both graphitic micropore-walls [67]. Then ethanol molecules should form a single sheet structure in which ethanol molecules are associated with hydrogen bonds. This single sheet structure gives the observed low density. Figure 19 shows ERDFs of methanol adsorbed on ACFs and bulk liquid methanol at 303 K. Briefly speaking, the ERDF of adsorbed methanol has similar peaks to that of liquid methanol; the peak positions of adsorbed methanol are close to those of liquid methanol. However, the nearest neighbor peak of the ERDF for liquid at 0.46 nm is slightly shifted to a smaller distance for P5 (at 0.44 nm), although the peak of P20 is the same as that of liquid. Also the nearest peak of P5 has a weak peak near 0.38 nm. Tauer and Lipscomb reported that the intermolecular distances between neighbor molecules in bulk solid methanol at 113 K are 0.364 nm for CH3-CH3, 0.41 and 0.42 nm for CH3-O , and 0.40 nm for O-O [68]. Accordingly, the peak of the ERDF for highly
Figure 18. Model of adsorbed ethanol in P5 (a) and P20 (b) at 303 K.
63
P5 P?O.
4 A I
2
Q-
0
I~
-2
-4 !
0
0.5
1.0 r/nm
1.5
2.O
Figure 19. ERDFs of methanol on ACFs and bulk liquid at 303 K.
ordered structure of confined methanol can have the fine structure in the nearest neighbor peak. Methanol confined in micropores of P5 should be more ordered than liquid methanol. Also, the amplitudes of ERDF of confined methanol are much greater than that of liquid methanol, indicating that methanol molecules in micropores are immobile compared with liquid. As P5 has greater peak intensities than P20, methanol molecules on P5 should be more immobile than those on P20 regardless of the small adsorbed density. Therefore, methanol molecules should form an ordered structure of the less packing density for the narrow micropores of P5 as well as ethanol adsorption. Consequently, even methanol molecules are too great to construct a quasi three-dimensional solid structure in the micropore of P5. On the contrary, only ERDF of P20 has an explicit peak at 1.15 n m , indicating the formation of the third nearest coordination structure which is not observed in bulk liquid. Thus, methanol confined in micropores of P20 should have a considerably long range order, agreeing with the adsorbed density value. Methanol molecules do not form the orientationally ordered structure similar to ethanol, but the position-ordered structure which is combined with weaker hydrogen bonds than confined ethanol. Methanol molecules confined in micropores should have more freedom of rotational motions than confined ethanol. Also methanol confined in narrow micropores of P5 must have the small adsorbed density and the highly ordered structure. The effectiveness of X-ray diffraction for study on micropore filling is described in this article. However, still we need the integrated analysis using several methods in addition to X-ray diffraction. Anyway we need the high resolution adsorption experiment in order to elucidate the micropore filling. In addition to the adsorption experiment, we must provide other physical measurements such as low temperature
64 magnetic susceptibility, direct calorimetry, NMR, and molecular spectroscopy in order to filling process of molecules [69-76]. Molecular simulation is also quite powerful to understand micropore filling phenomena [77-80]. Such studies are described in other chapters. In future we need to understand the micropore filling for supercritical gases, because storage of H2 and CH4 is quite important subject [81-83].
Acknowledgment This work was funded by the Grant in-Aid for Scientific Research on Priority Areas No. 288 "Carbon Alloys" from Japanese Government. We thank to Professor Keiko Nishikawa for her helpful discussion on ERDF analysis and Mr. Tomonori Ohba and Miss. Takako Kimura for their preparation of this manuscript.
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RecentAdvancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) 2000 ElsevierScienceB.V. All rightsreserved.
NEUTRON AND ION BEAM SCATTERING
67
TECHNIQUES
J.D.F. Ramsay Laboratoire des Mat6riaux et des Proc6d6s Membranaires, UMR CNRS 5635, Universit6 Montpellier II, 2 pl Eug6ne Bataillon, 34095 Montpellier, France
ABSTRACT Neutron coherent and incoherent scattering techniques can provide details of the microstructure of porous materials and the properties of sorbate molecules within micropores. Here the application of coherent scattering which includes, small angle neutron scattering (SANS), and diffraction are described. Two recent developments of SANS are illustrated. The first concerns the analysis of anisotropic porous materials (microporous carbon fibres, anodic alumina membranes). The second, concerns contrast variation methods, for the investigation of adsorption mechanisms (capillary condensation, micropore filling) in porous networks. Neutron diffraction can also provide information on the properties of sorbed phases conf'med in micropores, as illustrated by sorbed water in sol-gel oxides. The application of resonant ion (proton, a-particle) beam backscattering for the determination of pore size is illustrated by results obtained on meso and microporous oxide films; these films were deposited on substrates using sol-gel processes. Because a microfocussed beam is used with this technique, it is possible to obtain microstructural details, both as a function of depth (-~ 3 ~tm to - 100 ~tm) and across the sample (> 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 << 103). Such details can be obtained from the maxima in I(Q) which results from interference in the scattering with such an ordered system of uniform cylindrical pores. This is illustrated by the anisotropic isointensity plot in Figure 10. Here the maxima observed at Q---1.6"10 -3 A 1 correspond to a pore spacing of-~ 3.9"10 3 A, which is in satisfactory accord with the SEM results.
81
a) 10
9
9I ( Q n )
o
",0 0 O', 0
9I(Qv)
@, 0 @. ~ @6 O0
0.1
-
-.4
0.01 1E-3 ~.. 1E-4 1E-5
'
'
'
'
'
'
I
'
'
'
'
'
'
'
0.01
'
I
'
0.1 Q/A"
b) 109
Q
o
1
"I(Qv)
9i(Qv)
,j ,.0 -.0
0.1 0
cy 0.01
0
~
Oo o
1E-3
'%,. 0
1E-4 1E-5
0
'
'
'
'
'
'
I
~
O, 0 0
~ '
0.01
.
,
'
'
- I
o .I
'
'
Q/A" Figure 9. Anisotropic SANS results for an oriented alumina membrane (Anodisc). In (a) the orientation is perpendicular and in (b) parallel to the incident neutron beam respectively. I(Q~ and I(Qv) correspond to scattering along the horizontal and vertical axes of the 2D detector, respectively.
82
Figure 10. Anisotropic isointensity plot obtained by the SANS analysis of the Anodisc. 2.2.3 Contrast variation studies- adsorption processes Another recent and important development of SAS in the characterisation of porous solids has been the application of the contrast variation technique. Previously we have considered a two phase system, for simplicity, where the intensity of scattering, I(Q), is proportional to the contrast, i.e. the square of the scattering length difference between the two phases :
I ( Q ) ~ K ( p b ( I ) - p b ( 2 ) ) 2 = K ( A p b )2
(21)
For an evacuated porous solid, where pb(2) = pb(solid) the situation is simple since ]96(1) = O. However more detailed information may be derived if the pores are filled, or partially filled with an adsorbed vapour. Scattering from pores filled with a condensed liquid adsorbate may be eliminated if the scattering length, pb(1) is chosen to be the same as the solid, viz (Apb): = 0. This feature may be used to distinguish open and closed porosity, the latter being inaccessible to the adsorbate, for example. Using the same principal Hoinkis et al. (49) were able to measure the selective filling of micropores by exposing graphitic carbon to C6D6 at p/p0 ~ 0.25. In further applications of the contrast variation method, the filling of micropores, the growth of adsorbed multilayers and capillary condensation processes in micro and mesoporous oxide gels, have been investigated by SANS (50-53).
83 Other important developments have been made using SAXS and SANS in particular to probe the structure of the surfaces of porous materials which have a fractal character (54, 55). The majority of these earlier studies were made with samples which were pre-exposed to a fixed adsorbate pressure before the scattering measurement. This procedure, although simple, is limited for several reasons" firstly because of uncertainties in the equilibrium relative pressure due to temperature instabilities and containment problems, secondly due to irreproducibility between different solid samples, and thirdly the impossibility of making non-equilibrium and kinetic measurements. Advances have however been made recently (56) using SAXS with an in situ gravimetric system to study the isothermal adsorption of dibromethane (CH2Br2) on Vycor glass, both of which have comparable scattering length densities. The use of CH~Br2 in these investigations highlights the important limitation of SAXS compared with SANS. With SANS there is a wide flexibility in the choice of adsorbate (e.g. water, hydrocarbons alcohols, etc.) due to the control in Pb which can be achieved by substitution of H for D in the molecule (see Table 3). SAXS measurements have however been confmed to halogenated hydrocarbons since these have an electron density, Pc, which is sufficiently large to match that of porous solids, such as graphite and silica (see Table 3). This limitation precludes SAXS in studies of a wide range of simpler molecules, where evidentally adsorption is not dominated by the interaction of the halogen atoms with the surface. Recently the advantage of the SANS has been exploited using a specially designed apparatus which allows in situ measurements on thermostated samples under closely controlled relative vapour pressure of different adsorbates (57). Such an apparatus gives scope for equilibrium studies with mesoporous solids close to saturation vapour pressure and during an adsorption/desorption cycle. Furthermore measurements at very low P/P0, which are important in studies of microporous materials, are also feasible. Non-equilibrium and kinetic measurements, which are relevant to the rate of diffusion in the pore system are also possible. Table 3. Scattering length densities, pb, and electron densities, pc, of different materials. Substance pb/10 l~ cm2 pe/10 24 cm "3 H20 -0.56 0.334 D20 6.36 Benzene-h6 1.16 0.285 Benzene-d6 5.43 Cyclohexane-h 12 -0.28 0.268 Cyclohexane-dl 2 6.70 Silica 3.47 0.661 Graphite 7.67 0.683 Zirconia 5.25 1.568 We have recently applied the contrast variation technique using this apparatus in investigations of the adsorption of benzene in a mesoporous silica gels having different pore structures (53,58). In one case the gel was prepared by a sol-gel process, and had a welldefined model pore structure as had been established previously (59). To illustrate this investigation, the effect of progressive benzene (59 % C6D6) adsorption at 310 K on the SANS of the gel is shown in Figure 11. For the outgassed sample (P/p0 = 0) the scattering (full line, 11.(a)) is characteristic of a structure formed by the packing of spherical sol particles. Thus the pronounced maximum at Q of 0.025 A arises from the interference in the scattering from a partially ordered structure, where the interparticle separation is given approximately by
84 2x/Qmax viz. 24 nm. The inflexion at Q --- 0.045 A "l results from the form factor, P(Q), of the spherical particles. Thus for monodispersed spheres of radius R, the decay of P(Q) has a primary maximum at QR ~ 5.9. Although this feature is smeared here, the position correspondends to a particle diameter of 26 nm, in reasonable agreement with electron microscopy and SANS measurements on dilute sols. Beyond this inflexion, I(Q) decays linearly with Q-4 in accord with the Porod law. Changes in the SANS after equilibration with benzene having the same scattering length density as silica are shown for selected values of P/Po. At low relative pressure (P/Po ~ O.4) the scattering is little changed, but on further uptake progressive differences are noted: the almost total suppression of the interference peak is most striking. Less evident are the suppression of the inflexion due to the particle form factor, P(Q), and the reduction in intensity in the Porod region.
10 2
(b) i
I0
9
..
~.~
.'--
\\
~-4
9
XX \ f 10
\\
ooqo% ...
-1 -
10-2
10 -1
Q/A -1 Figure 11. SANS of silica gel (pore radius-~ 2.9 nm) exposed to contrast matched benzene at increasing relative vapour pressures, P/P0: (a), 0.0 ; (b), 0.42 ; (c), 0.50 ; (d), 0.55 ; (e), 0.60 ; (f), 0.67 and (g), 0.90.
85 The increase in I(Q) at low Q, associated with changes in the interference peak, can be ascribed to the growth of an adsorbed film and annular meniscus at the points of sphere contact (60) (see Figure 12.a). Such changes have been described previously for the SANS during water uptake in this gel system (50). For P/Po > 0.67 the changes become more marked and correspond to an enhanced uptake of benzene due to the development of capillary condensate at the sphere contact zones with increases in P/Po (Figure 12.b). This feature is illustrated in Figure 13, which shows the kinetics of the benzene adsorption after a stepwise increase of P/Po from 0.67 to 0.73. Here the SANS curves correspond to sequential measurements at intervals of-~ 5 min. At P/Po > 0.73 onset of the menisci coalescence in the pore throats occurs, leading to spontaneous pore filling. This results in the dramatic drop (by ~102) in scattered intensity observed at P/Po = 0.9. Other results showing the SANS on desorption, following the hysteresis loop have been described (53). More detailed theoretical analysis of such measurements can provide details of the mechanisms of capillary condensation and percolation in other model mesoporous structures of different geometry. This technique also offers future scope for investigations of both microporous and non-porous solids. In particular, details of the confinement and packing of sorbate molecules, either in micropores or monolayers on non-porous surface may in future be derived from measurements using different sorbates.
(a)
(b)
(c)
1 /
Figure 12. Depiction of adsorption and capillary condensation in sphere packings; (a) adsorbed film and annular meniscus at points of sphere contacts, (b) development at contact zone on progressive adsorption, and (c) onset of menisci coalescence in pore throat, leading to spontaneous filling (aider (60)).
86
0
"
"
["
"
I
.
.
.
.
.
.
.
.
.
I
"'"
"
"
I
.
.
.
.
!
.
.
.
.
~
.
.
.
.
(a)
60
(Y
30
(c
d) 0.00
0.02
0.04
0.06
Q/~-I Figure 13. Kinetics of benzene adsorption on silica gel after a stepwise increase of P/P0 from 0.67 to 0.73 at 310 K. Measurement time for each SANS curve was 305 s. The SANS for the outgassed gel is shown in (a) and for equilibrium at P/P0 of 0.67, 0.73 and 0.90 in (b), (c) and (d) respectively.
2.3 Neutron Diffraction- properties of sorbed phases As previously discussed, coherent neutron scattering has its counterpart in X-ray scattering which is an elastic scattering process. However the scattering cross sections of atoms for Xrays and neutrons are different (see Table 3). This feature has been exploited to investigate the mechanisms of adsorption in porous solids using both diffraction, as well as SANS, which we have already considered above.
87 Diffraction measurements can be used to distinguish the structural organisation of adsorbed atoms or molecules in porous media. This technique although not widely exploited has also been used to investigate water behaviour in meso and microporous oxides (61), as will be briefly described here. More recently neutron diffraction has been applied successfully by Rouquerol and coworkers (62-64) to study phase transition behaviour of different gases (argon, krypton, methane, nitrogen , carbon monoxide) in MFI-type zeolites. Other investigations include water in hydrated clay systems (65), and microporous carbon (38). The diffraction of bulk liquid water (D20) and ice are markedly different (see Figure 14.a and b). For ice the diffraction is characteristic of a hexagonal structure where there are four Hbonds associated with each oxygen atom as shown in Figure 15.a. The structure of liquid water is shown schematically in Figure 15.b. Here there are statistically between 3 and 4 Hbonds per oxygen atom. Although there is no long range order in liquid water there is however a short range structure, which fluctuates dynamically. This dynamic short range intermolecular structure is influenced by temperature in the bulk (66) and may be perturbed in a porous medium. It is well established that the freezing of water in mesoporous silica and other solids occurs at temperatures below 273 K - the bulk temperature. The depression of the freezing temperature is related to the pore dimension and this feature can indeed be used to determine pore size and shape (67). However when the size approaches the micropore range, -~2 nm, a regular H-bond network is unable to form in the confined pore space and the water remains in a supercooled non-crystalline state. This is demonstrated in Figure 16, which shows the effect of temperature on the neutron diffraction of hydrated porous silica (pore size -~2 nm). It will be noted that the band at 2 0 = 2 2 ~ narrows progressively, but even at 123 K the water remains non-crystalline and the diffraction is different from the bulk ice (cfFigure 14). Another application of neutron diffraction to determine the organisation of water in conf'med pore geometry has been demonstrated with smectite clay gels, such as montmorillonite and hectorite (65). Here the porous structure is formed by the parallel alignement of the thin (~ 1 nm) sheet like particles to give slit shaped pores. The interlayer zone in these structures contains water and as the uptake increases the sheet swell apart but remain highly oriented (43). It is indeed possible to examine the ordering of water molecules with respect to the clay surface as a function of interlayer spacing. In such neutron diffraction experiments the bulk samples are oriented with respect to the neutron beam (viz. either parallel or horizontal). Such investigations have shown that water molecules remain highly oriented to the clay surface to uptakes exceedings three layers.
88
(a)
3
c-"
I
>,, I1,,,,.
I
I
I
I
100
Ik=
F, f,,,.. >,,
I
I
(b) 002
15
o ,,,,,n
I/} c"
10
(c)
m
5-
0
I 10
I I I I I 20 30 40 2O/deg., X - 1.37 A
I 50
o
Figure 14. Neutron diffraction of (a) liquid D20 at 298 K (b) and (b) ice at 263 K. The peaks indexed in (b) correspond to the structure of hexagonal ice, Ih.
89 (b) WATER O OXYGEN
{a) ICE
9 HYDROGEN
. .....
l 9
v
l t
l |
i I
~
,
!
.z"~ i ,v~.,~-,4...._
,"
P
',,~---."~--L
~[
9
4. ! I
I ,
_
I ,
9
.,,S
Figure 15. Diagram depicting the hydrogen-bonded structure in (a) hexagonal ice and (b) liquid water.
8
)
(ct)
(c]
to 6 ~
c-
~>, 4 ~ 2
~
33 12I
~
8
r-.
-,-- 4 C
2 0
i 10
I 20
I 30
I 40
I // 50
I
I
10
20
I
I
30 40
I //
50
i
I
1
10
20
30
I
I
40 50
20/deg., X= 1.3655/~ Figure 16.Effects of temperature on the neutron diffraction of hydrated porous silica, SI (27% w/w D20). Temperatures (K) are" (a) 298 ; (b) 255 ; (c) 250 ; (d) 245 ; (e) 233 ; and (f) 123, respectively.
90 3. SCATTERING ION-BEAM SCATTERING TECHNIQUES The application of ion beam scattering techniques to determine pore size and pore volume, or density of thin silica gel layers was first described by Armitage and co-workers (68,69). These techniques are non-destructive, sensitive and ideally suited for the analysis of thin porous films such as membrane layers. However, apart from a more recent report on ion-beam analysis of sol-gel films (70) using Rutherford backscattering and forward recoil spectrometry, ion beam techniques have not been developed further despite their potential for membrane characterisation. This is probably due to the limited availability of ion beam sources, such as charged particle accelerators. The work of Armitage et al was carded out using both tandem Van der Graaff and linear accelerators as sources of focused proton and a-particle beams. The method involves observing the energy distribution of ions elastically backscattered after exciting a resonace in one of the nuclei of the sample. In this work the resonances for protons (2.66 MeV) and ctparticles (3.05 MeV) scattered from 160 were employed. An illustration of the experimental arrangement with an example of a spectrum obtained from porous SiO2 sample with 3.3 MeV a-particles is shown in Figure 17, together with the spectrum from a sample of non-porous SiO2 glass. It will be noted that the resonance peak for the porous sample is broader. This peak is associated with the 3.05 MeV resoncance arising from the elastic scattering of orparticles from 160. A full description is given in (69) of the methods of calculation of pore size from such backscattering data, with various assumptions of the pore and interpore path length distribution. Here only an outline of the theory can be given.
I
•
FOCUSSED_
.
i
I~eARTICLE
f,o.
SEAm
COLLIMATOR
RESONANCE'~
I0000
~ETECTOR SAMPLE]
PEAK 4,
Eo = 3.3 MeV
5000
I
"""
"~t. ~
I
SILICON
I ,, 1 2 ENERGY OF BACKSCATTERED PARTICLES (Mel0
Figure 17. Typical energy spectrum of a-particles backscattered from porous (full line) and non-porous silica thin films (dotted line). The inset shows the experimental arrangement. (after (69))
91
3.1 Theoretical principles Although details are not appropriate here, an outline of the principles of the method can be appreciated from the following simple description. The enhanced width of the oxygen resonance arises because individual backscattered ions pass through different numbers of pores before leaving the sample. Thus the total amount of solid material traversed by the ions, and hence the loss on emergence, is variable. Firstly we consider the case of an ion beam transmitted through a porous sample where the pore length through each pore is constant and equal to a. The resulting variance in path length through a random distribution of pores will be Na 2, where N is the mean number of pores encountered. The energy spread of the beam transmitted through the porous specimen will be increased over that obtained with a non porous specimen having the same areal density. The energy spectrum of the transmitted ions may be considered Gaussian so that the contribution of the pores to the measured fwhm = 2.35 (AE2) w, where (AE 2) is the corresponding variance in the energy distribution. Thusfwhm = 2.35 N1/2a dE/dx. We now consider the more complex case of backscattering from a porous sample. This arises when a beam of ions incident on the sample has an energy significantly higher than that of the resonance. If we ignore the effects of straggling, all the ions backscattered at the energy of the resonance will have penetrated the same thickness of solid material. However, the number of pores encountered will be variable with the result that the distribution of depths penetrated will have a variance Na:. After backscattering at the energy of resonance the ions will leave the surface having traversed a total distance in solid material whose variance is Na 2. The contribution of the pores to the width of the resonance follows from the transmission case, so that
fwhm = 2.35 (2Na2) m dE/dx
(23)
where dE/dx is evaluated at the emergent energy, Ed.
The total pore path length after scattering, Na, can be equated to the difference between the total path, to and the path through solid matter, te, viz.
Na = to- te
(24)
Since the porosity, e can be written as (to-te)/to we have
Na = [g/(1-6)]te
(24)
Furthermore it can be shown that
t~
= (E
r -
E a ) / dE / dR 1
where Er is the energy after scattering and dE~dR, is evaluated at 89 energy after scattering.
(25) i.e. the average
92 From the above we obtain
a=l[fwhm]2(1-o~] 2.35 ) k. 6-
l (dElr
(26)
The procedure then is to measure the fwhm of the resonance peak obtained with an equivalent non porous specimen, and to substract this in quadrature from the peak obtained from the porous sample. This ensures that the fwhm obtained in equation (26) is then free of any contributions arising from such effects as energy straggling, detector resolution, initial energy spread of the beam and natural width of the resonance. Values of dE/dR and dE/dR, can be obtained from range energy relationships (69). More sophisticated models to take account of the problem of the distribution of total path lengths through porous materials, based on the theory developed by Clement (71), were also described by Armitage et al. Such models to define pore path length dispersion were analysed on the basis of the known pore geometries of porous gels, which were formed by the packing of spherical particles, of almost uniform size.
3.2 Practical applications Armitage et al used models, as discussed above, to describe the distribution of the paths through and between the pores corresponding to the energy distribution of ions elastically backscattered from meso and microporous oxide gel films. This statistical description of the pore structure was shown to be in good agreement with pore size data obtained by other methods, such as gas adsorption isotherms. In the work with silica gels the pore structure was formed by the packing of spherical sol particles of different size and packing density to obtain samples with a range of pore size ( -- 20 to 100 nm). Other measurements were made on microporous oxide gels (e.g. titania, alumina) with pore size <2nm. These microporous gels had a known pore structure and were also formed by the packing of sol particles. However here interesting differences were observed which depended on the particle shape. Thus in the case of titania, where the gel was derived by drying a concentrated sol of relatively monodispersed rhombohedral shaped particles, the pore size parameter, a was found to be 1.9 nm. This was in accord with the size of the pore throats in such a packed structure, which had a pore geometry similar to the silica gels. However the hydrated alumina gel had a highly anisotropic structure composed of lamella shaped particles. Here the value of a determined was --3.8 nm, which was significantly greater than the known interlameUar spaceings.This difference was not unexpected, as it was noted that the average of the pore path lengths through parallel lamellae would be greater than that of the interlamellar spacing. This method, using a microfocused ion beam, has unique advantages over other techniques which could be very useful in membrane characterisation. Thus in the above work examples of measurements made on gel layers as a function of sampling depth (from-~3 ~tm to 100 ~tm) and as a function of distance across the sample were illustrated Figure 18. It will also be noted that the technique is equally appropriate for measurements in the microporous and mesoporous ranges.
93
9 x SAMPLE
E
c ,_..,
ALPHA
DATA
PROTON
DATA
---GAS ADSORPTION VALUE
B
-
"•'T l m"
.
50
X
LU N LU
r,-
0
O CL
-SAMPLE
C
Z .< LU
}-
50
=.
0--
I
1
1 1 I ! 111
1
10 to(DEPTH SAMPLED)[pm]
!
I
1 I I I1
100
Figure 18. Values of mean pore size (~2) in highly porous silica gel specimens obtained as a function of sampling depth. (after (60))
4. CONCLUSIONS In this review two different radiation scattering techniques have been described that can provide information on the microstructure of porous solids and the mechanisms of adsorption processes at surfaces and within pores. Although neutron scattering methods are relatively sophisticated, and not more readily accessible, they can give unique information which complements that available from more classical techniques of pore structure characterisation. This feature is illustrated here by two specialised applications of small angle neutron scattering which are currently under development. The first concerns the characterisation of anisotropic pore structures, where two examples are given, viz. microporous carbon and mesoporous anodic alumina membranes. The second illustrates the use of contrast matching methods to investigate the mechanisms of adsorption in porous networks. This development which is applicable to both micro and mesoporous media, may provide insight into the separation of gas mixtures in microporous membranes where either one or more components is a condensable phase. For example highly efficient separations involving pore "blocking" processes have been reported with microporous membranes (72). Although the mechanisms are still not fully understood, they are of considerable technical interest. Neutron diffraction may also provide information on the nature of the sorbed phase conf'med in micropores, as also discussed here, with reference to water in different microporous systems.
94 The other technique described- resonant ion beam backscattering, has received little development since its first application in pore structure characterisation. The method has the same advantages as SANS, by being an in-situ and non-destructive technique, which is equally appropriate for measurements on micro and meso porous materials. It does however have a unique advantage over other techniques, which could be very useful in the characterisation of microporous membranes. This results from the use of a microfocussed beam, which allows measurements as a function both of sampling depth (from-~3 ktm to 100 lam), and as a function of distance across the sample, as is illustrated here.
5. ACKNOWLEDGEMENTS Many of the neutron scattering experiments described here were carried out at the Institut Laue Langevin, Grenoble, the LLB, Saclay and the Hahn Meitner Institut, Berlin. Access and support at these facilities is gratefully acknowledged. This work was carried out with many colleagues to whom I much indebted. In particular these include Drs. L. Auvary, S. Kallus, and E. Hoinkis. Work on the ACF material was done in collaboration with Professor K. Kaneko and Dr. A. Matsumoto. 6. REFERENCES
1. A.J. Burggraaf and L. Cot (eds.), Fundamentals of Inorganic Membrane Science and Technology, Elsevier Science B.V., Amsterdam, 1996 2. V.N. Burganos (ed.) in: MRS Bulletin "Membranes and Membrane Processes", 24 (1999) 19 3. M.B. Rao and S. Sircar, J. Membr. Sci., 85 (1993) 253 4. A.B. Shelekhin, A.G. Dixon and Y.H. Ma, J. Membr. Sci., 75 (1992) 233 5. R.S.A. de Lange, J.H.A. Hekkink, K. Keizer and A.J. Burggraaf, J. Membr. Sci., 99 (1995) 57 6. R.M. de Vos and H. Verweij, Science, 279 (1998) 1710 7. R. Vacassy, C. Guizard, V. Thoraval and L. Cot, J. Membr. Sci., 132 (1997) 109 8. A.J. Burggraaf, "Transport and Separation Properties of Membranes with Gases and Vapours", in Fundamentals of Inorganic Membrane Science and Technology; A.J. Burggraaf and L. Cot (eds.), Elsevier Science B.V., Amsterdam, 1996 9. R.R. Bhave (ed.), "Inorganic Membranes, Synthesis, Characterisatics and Applications", Van Nostrand Rheinhold, New York, 1991 10. A. Julbe and J.D.F. Ramsay, "Methods for the Characterisation of Porous Structure in Membrane Materials", in Fundamentals of Inorganic Membrane Science and Technology, A.J. Burggraaf and L. Cot 8eds.) p. 67, Elsevier Science B.V., Amsterdam, 1996 11. J. Rouquerol, D. Avnir, C.W. Fairbridge, D.H. Everett, J.H. Haynes, N. Pernicone, J.D.F. Ramsay, K.W.S. Sing and K.K. Unger, Pure Appl. Chem. 66(8) (1994) 1739 12. S.J. Gregg and K.S.W. Sing in: "Adsorption, Surface Area and Porosity", Acad. Press, 2 nd Ed. London, 1982 13. K. Ibel (Ed.), Neutron Research Facilities at the ILL, ILL, Grenoble, 1994 14. J.W. White, C.G. Windsor, Rep. Prog. Phys. 47 (1984) 707 15. G.E. Bacon, Neutron Scattering in Chemistry, Butterworth, London, 1977
95 16. S.W. Lovesey, Theory of Neutron Scattering from Condensed Matter, vols. 1 and 2, Clarendon Press, Oxford, 1984 17. B.T.M. Willis (Ed.), Chemical Applications of Thermal Neutron Scattering, Oxford University Press, London, 1973 18. B. Jacrot, Rep. Prog. Phys. 39 (1976) 911 19. A. Guinier, G. Foumet, Small Angle Scattering of X-rays, Wiley, New York, 1955 20. B.O. Booth, J.D.F. Ramsay, in: J.M. Haynes, P. Rossi-Doria (Eds.), Principles and Applications of Pore Structural Characterisation, Arrowsmith, Bristol, 1985, p. 97 21. J.D.F. Ramsay, Neutron Scattering from Porous Solids, in K.K. Unger, J. Rouquerol, K.S.W. Sing, H. Kral (Eds.), Characterisation of Porous Solids, Studies in Surface Science and Catalysis, vol. 39, Elsevier, Amsterdam, 1988, p. 35 22. P.W. Schmidt, Small-angle scattering studies of porous solids, in: K.K. Unger, J. Rouquerol, K.S.W. Sing, H. Kral (Eds.), Characterisation of Porous Solids, Studies in Surface Science and Catalysis, vol. 39, Elsevier, Amsterdam, 1988, p. 35 23. G.G. Kostorz, in: H. Hermann (Ed.), A Treatise on Materials Science and Technology, Academic Press, New York, 1979, p. 227 24. R.H. Ottewill, in: J.W. Goodwin (ed.), Colloidal Dispersions, Royal Society of Chemistry, London, 1982, p. 143 25. J.D.F. Ramsay, Chem. Soc. Rev. 15 (1986) 335 26. J.S. Higgins, K. Ma, L.K. Nicholson, J.B. Hayter, K. Dodgson, J.A. Semlyen, Polymer Vol. 24 (1983) 793 27. O. Glatter, O. Kratky (Eds.), Small Angle X-ray Scattering, Academic Press, London, 1982 28. P. Debye, A. Bueche, J. Appl. Phys. 20 (1949) 518 29. G. Porod, Kolloidn Zh 124 (1951) 83 30. H.D. Bale, P.W. Schmidt, Phys. Rev. Lett. 53 (1983) 59b 31. J.K. Kjems, P. Schofield, in R. Pynn, A. Skeltorpe (eds.), Scaling Phenomena in Disordered Systems, Plenum, 1985, p. 141 32. J. Teixeira, J. Appl. Cryst. 21 (1988) 781 33. Lord Raleigh, Proc. R. Soc. London A90 (1914) 219 34. A. Guinier, Ann. Phys. 12 (1939) 161 35. A. Guinier, G. Fournet, Small Angle Scattering of X-rays, Wiley, New York, 1955 36. O. Kratky, G. Porod, J. Colloid Sci. 4 (1949) 35 37. M.H. Stacey, in: Studies in Surface Science and Catalysis, vol. 62, Elsevier, Amsterdam, 1991, p. 165 38. A. Matsumoto, K. Kaneko, J.D.F. Ramsay, in: Studies in Surface Science and Catalysis, vol. 80, Elsevier, Amsterdam, 1993, p. 405 39. L. Auvary, A. Ayral, T. Dabadie, L. Cot, C. Guizard, J.D.F. Ramsay, Faraday Discuss. Chem. Soc. 101 (1995) 235 40. L. Auvray, S. Kallus, G. Golemme, G. Nabias and J.D.F. Ramsay, Proc. of Characterisation of Porous Solids-V, Heidelberg, 1999, to be published in: Studies in Surface Science and Catalysis. 41. B.J. Olivier, R.R. Lagasse, D.W. Schaefer, J.D. Barnes, G.G. Long, Macromolecules 29 (1996) 28615 42. K. Kaneko, K. Kakei, T. Suzuki, Langmuir 5 (1989) 879 43. J.D.F. Ramsay, S.W. Swanton, J. Brunce, J. Chem. Soc. Faraday Trans. 79 (1990) 3919 44. T.P. Hoare and N.F. Mott, J. Phys. Chem. Solids, 9 (1959) 97
96 45. J.P. O'Sullivan and G.C. Wood, Proc. Roy. Soc. Lond. A, 371 (1970) 511 46. A.W. Smith, J. Electrochem. Soc., 120 (1973) 1068 47. G.E. Thompson, R.C. Fumeaux, G.C. Wood, J.A. Richardson and J.S. Goode, Nature, 272 (1978) 433 48. R.C. Furneaux and M.C. Thornton, Brit. Ceram. Proc., No. 43 (1988) 49. E. Hoinkis, A.J. Allen, J. Colloid Interface Sci. 145 (1991) 540 50. J.D.F. Ramsay, G. Wing, J. Colloid Interface Sci. 141 (1991) 475 51. J.-C. Li, D.K. Ross, M.J. Benham, J. Appl. Cryst. 24 (1991) 794 52. M.Y. Lin, S.K. Sinha, J.S. Huang, B. Abeles, J.W. Johnson, J.M. Drake, G.J. Glinka, Mater. Res. Soc. Proc. 166 (1990) 449 53. J.D.F. Ramsay, E. Hoinkis, in Proceedings of Characterisation of Porous Solids IV, Royal Society of Chemistry, London, 1997, p. 33 54. D.W. Hua, J.V.D. Souza, P.W. Schmidt, D.M. Smith, in: J. Rouquerol, F. RodriguezReinoso, K.S.W. Sing, K.K. Unger (Eds.), Studies in Surface Science and Catalysis. Characterisation of Porous Solids III, vol. 87, Elsevier, Amsterdam, 1994, p. 255 55. C.J. Glinka, L.C. Sander, S.A. Wise, N.F. Breck, Mater. Res. Proc. 166 (1990) 415 56. A. Ch. Mitropoulos, J.M. Haynes, R.M. Richardson, N.K. Kannelopoulos, Phys. Rev. B 52 (1995) 10035 57. E. Hoinkis, Langmuir 12 (1996) 4299 58. J.D.F. Ramsay, S. Kallus and E. Hoinkis, Proc. of Characterisation of Porous Solids-V, Heidelberg, 1999, to be published in: Studies in Surface Science and Catalysis: 59. J.D.F. Ramsay, B.O. Booth, J. Chem. Soc. Faraday Trans. 79 (1983) 173 60. B.G. Aristov, A.P. Kamaukhof, A.V. Kiselev, Russ. J. Phys. Chem. 36 (1962) 1159 61. J.D.F. Ramsay, Stud. Surf. Sci. Catal. 87 (1994) 235 62. P.L. Lewellyn, J.P. Coulomb, Y. Grillet, J. Patarin, H. Lauter, H. Reichert, J. Rouquerol, Langmuir 9 (1993) 1846 63. P.L. Lewellyn, J.P. Coulomb, Y. Grillet, J. Patarin, G. Andre, J. Rouquerol, Langmuir 9 (1993) 1852 64. H. Reichert, U. Mialler, K.K. Unger, Y. Grillet, F. Rouquerol, J. Rouquerol, J.P. Coulomb, Stud. Surface Sci. Catal. 62 (1991) 535 65. J.D.F. Ramsay, unpublished work 66. D. Eisenberg, W. Kauzmann, The Structure and Properties of Water, Oxford, 1969 67. M. Brun, A. Lallemand, J.F. Quinson, C. Eyraud, Thermochim. Acta 21 (1977) 59 68. C.D. McKenzie and B.H. Armitage, Nucl. Instr. and Meth. 133 (1976) 489 69. B.H. Armitage, J.D.F. Ramsay and F.P. Brady, Nucl. Instr. and Meth. 149 (1978) 329 70. J.L. Keddie and E.P. Giannelis, J. Am. Ceram. Soc., 73 (1990) 3106 71. C.F. Clement, J. Phys. D: Appl. Phys., 5 (1972) 793 72. 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
Recent Advancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) o 2000 ElsevierScienceB.V. All rightsreserved.
97
Application of pulsed field gradient NMR to characterize the transport properties of microporous membranes W. Heink, J. K[irger and S.Vasenkov Fakult~it fiir Physik und Geowissenschaften, Universit[it Leipzig, Linn6stra6e 5, D-04103 Leipzig, Germany The potentials of pulsed field gradient (PFG) NMR in elucidating molecular transport in microporous membranes are presented. Particular emphasis is given to structure-correlated diffusion anisotropy and single-file diffusion. First results of PFG NMR studies with A type zeolite membranes are presented.
1. FUNDAMENTALS OF PFG NMR Diffusion measurements by the pulsed field gradient (PFG) NMR method are based on the fact that most nuclei posses a non-vanishing magnetic moment. By appropriate sequences of radio frequency (rf) pulses, under the influence of a constant magnetic field, these magnetic moments may give rise to a transient M R signal, the so-called spin echo. The intensity of this signal is reduced if during the rf pulse sequence, over two short time intervals, the constant magnetic field is superimposed by an inhomogeneous field
Baaa = gz,
(1)
the so-called field gradient pulses. The signal attenuation obeys the relation ~ ( S g , t ) = exp(-y262g2D,)
(2)
where 6 and t denote the duration and the separation of the field gradient pulses, y stands for the gyromagnetic ratio which is a characteristic quantity for the given nucleus (e.g. 2.675 x 108 T 1 s1 for protons, i.e. the nucleus of hydrogen). For simplicity, it is assumed that the duration of the field gradient pulses is sufficiently small in comparison with their separation (6/3 << t) and that molecular diffusion- with the self-diffusivity (or coefficient of self-diffusion) D - is isotropic. Einstein's relation (rZ(t)) = 6 Dt
(3)
correlates the self-diffusivity D with the mean square displacement (r2(t)) of the molecules under study during the (observation) time t. Using this relation, eq. (2) may be transferred into
= e.p(-
It))' 6).
(4)
98 Eq. (4) helps to intuitivley understand the principle of diffusion measurement by NMR: If during the two field gradient pulses the individual nuclei (and hence the atoms and molecules containing these nuclei) occupy different positions, as indicated by the mean square distance (r2(t)) they do not exactly obey one and the same resonance condition. This difference in the resonance conditions leads to a signal attenuation. In the case of diffusion anisotropy, only molecular displacements in the direction of the magnetic field gradient (which by eq. (1) was chosen to be given by the z coordinate) is relevant. In this case, eq. (4) has to be replaced by ~(~g, t ) : exp(- ?'282g2 (z2(t))/2).
(5)
In more complex systems, where the intrinsic molecular transport does not follow anymore normal diffusion as characterized by eq. (3), the PFG NMR spin echo attenuation may be described by the more general relation
~(gg, t) :
~P(z,t)exp(izSgr)dz
(6)
with P (z, t) denoting the propagator, i.e. the probability (density) that during a time inerval t an arbitrarily selected molecule is shifted over a distance z in the direction of the field gradient pulses. Under the conditions of normal (i.e. Fickian) diffusion, the propagator is a Gaussian
P(z,t) = (4rcDt) - ~ exp(- z 2/4Dt)
(7)
being exclusively controlled by the coefficient of self-diffusion. Inserting eq. (7) into eq. (6) clearly yields eq. (2). A detailed description of the fundamentals of PFG NMR may be found in the literature [1-3].
2. SELF-DIFFUSION AND MOLECULAR TRANSPORT IN MEMBRANES The utility of microporous membranes is based on their permeation properties. The flux density through a membrane is determined by Fick's first law
J = _Dr(c) dc dx'
(8)
where dc/dx denotes the concentration gradient in the direction of the diffusion flux (x-direction) within the membrane. Dr(c) stands for the transport diffusivity. The term transport has been introduced [1] for clearer distinction from the self-diffusivity D. The self-diffusivity may be defined either by eq. (3) or by a modification of Fick's law (eq. (8)):
99
j
*9
~
dx,
(9)
where one considers a flux of labelled molecules (/'*) generated by their concentration gradient (dc*/dx), under the condition that the total concentration c (i.e. the sum of the concentrations of the labelled and unlabelled molecules) is uniform over the sample. Both definitions are equivalent [1]. For non-interacting molecules, i.e. in the limit of sufficiently small concentrations, the coefficients of transport diffusion and self-diffusion have to coincide (being independent of concentration). For larger concentrations, transport and self-diffusion are generally assumed to be related to each other by a Darken-type equation [ 1, 4]
DT ( C) = D( c) . d ln p
dln-----~'
(10)
where p(c) denotes the gas pressure necessary for maintaining the adsorbate at concentration c. The limits of the applicability of eq. (10) are still a subject of discussion [5-7]. Combining eqs. (8) and (10) the flux through a membrane is found to depend on three different quantities, viz. the permeate concentration gradient (being determined by the pressure difference and the adsorption potential), the "thermodynamic factor" dlnp/dlnc which is a measure of the deviation from proportionality between pressure and adsorbate concentration, and the molecular mobility in the membrane as represented by the self-diffusivity D(c). It is this latter quantity which is investigated by the PFG NMR method.
3. PECULIARITIES OF MOLECULAR DIFFUSION IN MICROPOROUS MATERIALS The intimate contact between the permeate molecules and the intemal surface of the membrane material leads to a number of special features in molecular diffusion which do not occur in bulk fluids. These peculiarities are particularly pronounced in zeolite membranes, as a consequence of their well-defined pore structure. Zeolite membranes combine the general advantages of inorganic membranes (temperature stability, solvent resistance) with a perfect shape selectivity [8, 9]. In this section, we are going to illustrate two features of zeolitic diffusion which are of immediate relevance for molecular transport in zeolite membranes. 3.1. S t r u c t u r e - C o r r e l a t e d D i f f u s i o n A n i s o t r o p y
Most of the so far manufactured zeolite membranes are of MFI type, i.e. of type silicalite or ZSM-5 [8-11]. The reasons possibly explaining this situation include the high level of accumulated knowledge in MFI synthesis, the relative ease of preparation, the suitable pore diameter of 0.55 nm which is interesting for industrial application and the high thermal and chemical stability [9]. As a special structural feature, MFI type zeolites are traversed by two types of channels, viz. straight channels in y-direction and sinusoidal ones in x-direction. There is no channel system in z-direction, and molecular transport in z-direction has to be accompolished, therefore, by interchanging periods of migration along the channel segments in x- and y-direction. As a unique feature of molecular diffusion in zeolites, there must exist, therefore, a correlation between the
100 principal elements of the diffusion tensor, i.e. between the diffusivities in x-, y- and z-direction. Under the assumption that molecular propagation from channel intersection to channel intersection via the individual channel segments may be considered as a random walk, the diffusivities may be shown to obey the relation [ 12, 13]
c2/Dz=a2/Dx+b2/Dy,
(11)
with a (~, 2 nm), b (z 2 nm) and c (~ 1.34 nm) denoting the unit cell dimension of an MFI framework in x-, y- and z-direction, respectively. It has been demonstrated by uptake measurements on macroscopic ensembles of oriented crystals [14] as well as by MD simulations [15, 16], that eq. (11) does in fact provide a reasonably good estimate of the correlation between the relevant diffusivities. Still better agreement may be attained if possible correlations between subsequent shifts along the channel seqments are - at least partially- taken into account in a "two-step" model [ 17]. The first unequivocal evidence of diffusion anisotropy in zeolite ZSM-5 has been provided by PFG NMR studies with macroscopic ensembles of oriented crystals [ 18] as well with powder samples [ 19]. The limited accuracy of these measurements, however, did not allow the separate determination of all three principal tensor elements. In the measurements with macroscopic ensembles of oriented crystals [18] the separate determination of D~ and (Dx + Dy)/2 has been possible. The obtained values were in fact found to be compatible with the correlation rule provided by eq. (11). In a powder sample of zeolite crystallites, the PFG NMR spin echo attenuation results as a superposition of exponentials of the type of eq. (2), with the respective orientation-dependent diffusivities. For isotropically distributed orientations one thus obtains 1
~(fig,t) = ~
2~r
f o
!
fexp(-g2fi2g2t[DxcoS 2 O+ DySin20COS2~ffq- Dzsin2/gsin2 g/])dq~(cosO). --1
(12) In principle, the three principal values of the diffusion tensor should be accessible by a fitting procedure of eq. (12) to the experimental data ~(Sg, t) of echo attenuation. In reality, the accuracy of the data is not high enough to allow the determination of three different parameters. Implying the validity of eq. (11), however, such a fitting procedure becomes possible. The thus obtained data were in fact found to be in satisfactory agreement with the diffusivities observed in the measurements with oriented samples [18, 19]. Diffusion anisotropy may substantially affect the permeation properties of membranes with oriented zeolite crystallites [20-22], making them totally different from those with random orientation [23, 24].
101
3.2. Single-File Diffusion Zeolites consisting of parallel channels A1PO:5, -8, -11, L, Omega, EU-1 and anisotropy: two principal elements of the PFG NMR spin echo attenuation, eq. (12),
with impenetrable walls - like ZSM-12, -22, -23, -48, VPI-5 - give rise to an extreme case of diffusion diffusion tensor degenerate to zero. In this case, the simplifies to
1 1
~(6g, t) = ~ ~exp(- y262g2Dtx2)dx
(13)
-1
with D denoting the diffusivity in channel direction. If the permeate molecules are too large to pass each other within one channel (i.e., roughly speaking, if the molecular diameters are larger than the channel radii), molecular transportation does not follow the laws of ordinary diffusion. This means in particular that eqs. (3), (7) and (9) are not valid, anymore. Due to the fact that like with a file of strung pearls, one molecule (or pearl) can only move if the adjacent one has been shifted into the same direction, molecular motion is highly correlated. Molecular motion under such conditions has been termed single-file diffusion [3, 25, 26]. It can be shown [27] that also under single-file conditions the propagator is still a Gaussian. In contrast to normal diffusion, however, the molecular mean square displacement
(r2(t))=2F4~
(14)
increases in proportion to the square root of the observation time rather than to the observation time itself. F is the mobility factor of single-file diffusion which had been introduced in analogy to the diffusivity in Einstein's law, eq. (3) [26]. The fact that under single-file conditions the molecular mean square displacement increases less than linearly with the observation time is a consequence of the correlation between subsequent displacements: Under the conditions of ordinary diffusion it is always possible to choose a time interval large enough so that the displacements during two subsequent time intervals are independent from each other. Hence, the mean square displacement over a period of time t is equal to the sum of the mean square displacements over the individual time intervals At, with t = ~ A t. Proportionality between the mean square displacement and the observation time is a consequence of this fact. Under singlefile confinement, however, displacements in one particular direction are more likely followed by displacements in the opposite direction, leading to a less than linear increase of the mean square displacement with the observation time. Being exclusively a subject of theoretical consideration over many years [25-30] it was not before the successful application of PFG NMR [31-34] that eq. (14) as the key equation of single-file diffusion could be confirmed experimentally. Experimental verification of eq. (14) is complicated by the influence of the boundary conditions on molecular displacements which is much more pronounced in the case of single-file diffusion than under the conditions of normal diffusion [35]. For practical use in catalysis or gas separation, it is the exchange with the surrounding gas phase rather than the time dependence of molecular displacement which is of immediate interest. Molecular exchange between an adsorbent and the surrounding atmosphere may be characterized
102 by the residence time distribution qffx). It is worthwhile to note that the residence time distribution is closely related to two other characteristic functions, viz. the tracer exchange curve Y(O by t
~o(r)dt
r(t)=
(15)
o
and the effectiveness factor rl(k) by oo
rl(k ) = ~e -*r ~o(r)dt ,
(I 6)
0
where k denotes the intrinsic reactivity in first order reactions [36, 37]. The mean residence or exchange time Xi,~a may be determined on the basis of the characteristic functions via the relations [37] oo
ri.tr a = f[1-7(t)]dt0
oo
frq~(~)dT.
(17)
0
For single-file systems and sufficiently large file lengths, the mean exchange time is found to obey the relation [38, 39]
"t'intra oCL3
(18)
with L denoting the file length. It is interesting to note that this dependence is in contrast with the expressions ,,.a.
"t'intr a o(2
L2
(19)
for normal diffusion [26, 40] as well as with the result of scaling arguments, "['intra oC
L4
(20)
which would be attained on the basis of eq. (19) by considering the equivalence of eqs. (3) and (14) [26]. Relation (18) may intuitively be understood by realizing that displacements, not negligibly small in comparison with the file length, are again controlled by a mechanism equivalent to ordinary diffusion with a diffusivity being proportional to L ~ [35, 38, 41 ]. Thus, by introducing a file-length-dependent diffusivity into eq. (19) one does in fact obtain the dependence as given by relation (18).
103 Membranes with zeolites of single-file type are subjected to two peculiarities. The influence of crystal orientation on the permeation properties is still more pronounced than considered in the previous section on structure-correlated diffusion anisotropy: Zeolite crystallites with channels parallel to the membrane surface would in no way contribute to the permeation flux. Moreover, as a consequence of the exclusion of mutual passages of the individual molecules, the molecules have to stick to their order within the channels, irrespective of their individual mobilities. In the literature, this phenomenon has been termed "constrained" single-file diffusion [42]. Under such conditions membranes would not be suitable for gas separation, even if the permeation rates of the individual components under the conditions of single-component adsorption were extremely different [20, 22]. Such a tendency may even be observed in systems which do not obey the single-file condition. ZSM-5 type membranes, e.g., at sufficiently high loadings, did not reveal any separation effect on mixtures of o- and p-xylene [43], while the p-xylene diffusivity at single-component adsorption is well-known to be by 3 orders of magnitude larger than that of o-xylene [44]. It is noteworthy that at sufficiently low concentrations - i.e. under conditions where mutual hindrance of the molecules is essentially excluded- both components are easily separated from each other in the same membranes [45].
4. M E M B R A N E DIFFUSION STUDIES BY PFG N M R
Diffusion measurement by PFG NMR clearly implies the existence of a measurable NMR signal. Therefore, the molecules under study must contain "NMR active" atoms, i.e. (cf. Section 1) nuclei with a non-vanishing gyromagnetic ratio, which have to occur at a sufficiently large concentration. With sample volumes of about 300 mm 2 for hydrogen, which offers the best measuring conditions with respect to both the minimum number of diffusants and minimum displacements, typical minimum concentrations are of the order of one hydrogen atom per 10 nm 3 which corresponds to about 0.1 moles per litre [3]. Hence, PFG NMR does not apply anymore if the averaged concentration of the diffusants under study within the sample volume is below this value. According to eq. (8), the permeation rate is maximum for maximum concentration gradients. This means that for a given concentration difference over the membrane, the membrane thickness should be chosen as small as possible, with values in the 10 ~tm range. Moreover, for guarenteeing mechanical stability, the membrane is generally produced as a small layer on a much bulkier support. The permeability of this support is unspecific and generally of minor interest. Since it would occupy by far the largest part of the sample volume, as a consequence of the above described limited sensitivity, PFG NMR studies have to be carried out with samples exclusively containing the microporous parts of the membranes at an utmost packing density. It is due to this reason that microporous membranes have not yet become a standard system for PFG NMR studies. In the following, a first example of PFG NMR diffusion studies with microporous materials suitable for membrane fabrication is given [46]. The particular materials used in this study were pieces of membranes that were fragmented during handling. From scanning electron micrographs, these pieces appeared to be crystallite
104
agglomerates with diameters of tens to hundreds of micrometers, where the crystallite diameters were of the order of micrometers. The membranes were prepared from homogeneous solution with a composition given by the molar ratio 5 SiO2 9A1203 " 55.12 Na20 91004.66 H20. An aluminate solution was prepared by dissolving small pieces of aluminium wire in aqueous NaOH over a 48 h period. A sodium silicate solution was prepared by dissolving NaOH pellets in distilled water then adding an aqueous silicate solution with vigorous stirring. Alter 15 min of stirring, the pre-heated aluminate solution was added, and the stiring continued. The resultant solution was transferred to a preheated container for membrane preparation. Free-standing samples of zeolite membrane were prepared by placing the above solution in a sealed Teflon container which was placed in an oven at 50 ~ for 48 h. The container was removed from the oven, drained and the zeolite film that lightly adhered to the container walls was thoroughly rinsed with distilled water. Samples of the membrane detached themselves during this procedure and were ion exchanged to the Ca-form by soaking it in 0.1 M Ca(NO3)2. Further details of membrane preparation may be found in [46]. For the preparation of the PFG NMR samples, the zeolite material was filled into glass tubes of 7.5 mm o.d. and activated by heating at a rate of 10 K h 1 under continuous pumping up to a fmal temperature of 400 ~ where it was kept for 1Oh. After cooling to room temperature the probe molecules were introduced by chilling from a calibrated gas volume with a set pressure. The diffusion measurements have been carried out by means of the home-built PFG NMR spectrometer FEGRIS 400 at a proton resonance frequency of 400 MHz with magnetic field gradient amplitudes up to 24 T m l [47]. The attenuation of the NMR signal (the 'spin echo') v e r s u s the squared gradient amplitude was essentially found to follow a monoexponential decay, as to be expected for normal diffusion in a quasi-homogeneous medium on the basis of eq. (2). The effective diffusivity was determined by comparing the signal decay with that of a standard [water, D = (2.04 + 0.08) x 10.9 m 2 sl at 20 ~ [48]. The fact that molecular transport in zeolite NaCaA is found to follow normal diffusion as described by eq. (3) deserves some further discussion. Zeolites of this type are well-known to be percolation systems [1, 3, 49], since molecular propagation from one cavity ("site") to an adjacent one is only possible if the connecting window ("bond") is permeable. This permeability may be significantly affected by the presence of cations. As a consequence of the blockage of a fraction of the windows, the mean square value of molecular displacements taken over the sample may substantially deviate from the behaviour described by eq. (3) [49]. The deviations are caused by the fact that certain fractions of the molecules experience strong confinement effects due to closed windows while other fractions are on pathways through open windows, thus being able to cover large distances. For the system under study, the blockage of the windows is known to be incomplete [50]. In PFG NMR studies, as a consequence of the limited spatial resolution, molecular displacements over distances of at least 100 nm, i.e. passages through thousands of cavities, are observed. The fmite permeability of the "closed" windows leads to the situation that over the observation time t of the PFG NMR experiment- at least in a statistic sense - all molecules experience the same history. As a consequence, over the relevant time scale, molecular transport can again be expected to obey the laws of ordinary diffusion [51 ].
105
(a)
(b)
D/m2s-1
- - u - - 173 K _ ) = - - ref. - - o - - 238 K - - x - - ref. _ & _ 294 K _ + - - ref. - - v - - 373 K - - e - - ref. 2 molecules per cavity
+T
v\
&~"& '~
1E-10
1E-10
;~
~ o
\
eL'~ u
1E-11
ref. O
5'0
~
_ = = _ 173 - - e - - 238 _ & _ 294 - - v - - 373 2 mol. per
K K K K cavity
jr
~I'~Y%--V--~_ V~V~rAr~v
e-._~_ A...a~a______a__a_Aa
m~ll-I...
'"~0%0_0
9
1(~0
1~0 " 2~0
2~0
3;0 t/ms
350 1E-11
......
~
. . . . . . .
1'o
1/2 / pm
Fig. 1 (a) Ethane diffusivity in a NaCaA membrane as a function of the observation time at different temperatures; ref." results of previous PFG NMR studies with crystalline zeolite NaCaA. (b) Ethane diffusivities in NaCaA membrane as a function of the root mean square displacement at different temperatures. [46]
Fig. 1(a) shows the dependence of the ethane diffusivity in the zeolite membrane at a loading of two molecules per cavity for different temperatures. For comparison, the diffusivity data of previous PFG NMR studies [52] with ethane in NaCaA zeolite crystallites are also included. It appears that these data are in reasonably good agreement with the results of the present study for sufficiently short observation times. The information provided by these studies becomes more obvious in the representation of the diffusivities v e r s u s the covered displacements [Fig. 1 (b)]. There is a pronounced decay for displacements around 1 rtm, which should be attributed to transport resistance, most likely situated at the interfaces between the individual crystallites. For shorter displacements, the majority of the diffusants do not interfer with these barriers. In this case one is able to trace the true intracrystalline diffusion. For larger displacements, the molecules repeatedly have to overcome these transport resistances. This leads to a slight reduction of the diffusivity. The enhancement observed in the high-temperature case for displacements > c a . 10 ~tm may be associated with the occurence of long-range diffusion, when more and more molecules are able to get out of the zeolite bulk phase, either through cracks in the material or through the outer surface of the membrane particles.
106 It should be pointed out that the range of apparently genuine intracrystalline self-diffusion is only observable at the lowest measuring temperature of 173 K (fig. 1b). Under these conditions, however, the measuring conditions are poorest and one cannot exclude that the diffusivity is further increasing. Such a behaviour could be explained by the fact that there are transport resistances within the individual crystallites with spacings of the order of or smaller than the minimum displacements. The existence of substantial intracrystalline transport resistances as a consequence of deviations from an ideal crystalline structure has been demonstrated in comparative permeation measurements with twinned and single crystals [9].
5. CONCLUSIONS The PFG NMR method has been shown to be able to monitor the time dependence of molecular propagation. In this way, in microporous materials a large variety of peculiarities of molecular transportation may become observable. Molecular mobility is in fact one of the rate determining features of membrane permeation. Application to diffusion studies with actual microporous membranes is limited by the relatively low sensitivity of PFG NMR with respect to the number of diffusants necessary for an appropriate signal generation. The potentials of such an application are illustrated by first PFG NMR measurements with A type zeolite membranes.
6. ACKNOWLEDGEMENT Financial support by the European Community (Joule JOE 3-CT95-0018; Brite-EuRam II; BE-97-4783) and the Deutsche Forschungsgemeinschaft (SFB 294) are gratefully acknowledged. We are grateful to Jiirgen Caro for giving ref. [9] to our knowledge before publication.
REFERENCES
1. J. Kfirger, D.M. Ruthven: Diffusion in Zeolites and Other Microporous Solids, Wiley & Sons, New York, 1992, 605 2. R. Kimmich, NMR Tomography, Diffusometry, Relaxometry, Springer, Berlin, 1997 3. J. Kfirger, G. Fleischer, U. Roland, PFG NMR Studies of Anomalous Diffusion, in: J. Kfirger, P. Heitjans, R. Haberlandt (Eds.), Diffusion in Condensed Matter, Vieweg, Braunschweig/ Wiesbaden, 1998, pp. 144 4. M.F.M. Post, Stud. Surf. Sci. Catal. Vol. 58 (1991) 391, Elsevier Science B.V., Amsterdam 5. K~ger, D.M. Ruthven, Self-Diffusion and Diffusive Transport in Zeolite Crystals, in: H. Chon, S.-K. Ihm and Y.S. Uh, (Eds.) Progress in Zeolite and Microporous Materials Stud. in Surf. Sci. and Catal., Vol. 105 (1997) 1843, Elsevier Science B.V., Amsterdam 6. J. K~ger, Molecular Transport in Zeolites - Miracles, Insights and Practical Issues, in Proc. 121nt. Zeol. Conf. (Eds.: Treacy, M.M.J; Marcus, B.K.; Bisher, M.E.; Higgins, J.B.), Mater. Res. Soc., Warrendale, 1999, 35 7. Krishna, Chem. Eng. Sci. 48 (1993) 845 8. E.R. Geus, H. van Bekkum, W.J.W. Bakker and J.A. Moulijn, Microporous Mat. 1 (1993) 131
107 9. J. Caro, M. Noack, P. K61sch and R. Sch/afer, Microporous and Mesoporous Mat., in press 10. J.C. Jansen and G.M. Rosmalen, J. Cryst. Growth 128 (1993) 1150 11. A. Gouzini and M. Tsapatsis, Chem. Mater. 10 (1998) 2497 12. J. Kfirger, J. Phys. Chem. 95 (1991) 5558 13. J. K/irger and H. Pfeifer, Zeolites, 12 (1992) 872 14. J. Caro, M. Noack, J. Richter-Mendau, F. Marlow, D. Petersohn, M. Giepentrog and J. Komatowski, J. Phys. Chem. 97 (1993) 13685 15. E.J. Maginn, A.T. Bell and D.N. Theodorou, J. Phys. Chem. 100 (1996) 7155 16. R.Q. Snurr, A.T. Bell and D.N. Theodorou, J. Phys. Chem. 98 (1994) 11948 17. J. K/arger, P. Demontis, G.B. Suffritti and A. Tilocca, J. Chem. Phys. 110 (1999) 1163 18. U. Hong, J. K/~rger, R. Kramer, H. Pfeifer, G. Seiffert, U. Mtiller, K.K. Unger, H.B. Ltick and T. Ito, Zeolites 11 (1991) 816 19. U. Hong, J. K~irger, H. Pfeifer, U. Mtiller and K.K.Unger, Z. Phys. Chem. 173 (1991) 225 20. M. Noack, P. K61sch, D. Venzke, P. Toussaint and J. Caro, Microp. Mat. 3 (1994) 201 21. P. K61sch, D. Venzke, M. Noack, P. Toussaint and J. Caro, J. Chem. Soc., Chem. Commun. (1994) 2491 22. I. Girnus, M.-M. Pohl, J. Richter-Mendau, M. Schneider, M.Noack, and J. Caro, Adv. Mat. 7 (1995) 711 23. M.C. Lovallo and M. Tsapatsis, AIChE-J. 42 (1996) 3020 24. M.C. Lovallo, A. Gouzinis and M. Tsapatsis, J. Cryst. Growth 128 (1993) 1150 25. L. Riekert, Adv. Catal. 21 (1970) 281 26. J. Kfirger, M. Petzold, H. Pfeifer, S. Ernst and J. Weitkamp, J. Catal. 136 (1992) 283 27. J. Kfirger, Phys. Rev. E, 47 (1993) 1427 28. J.L. Lebowitz and J.K. Percus, Phys. Rev. 155 (1967) 122 29. R. Kutner, Phys. Lett. 81A (1981) 239 30. H. van Bejeren, K.W. Kehr and R. Kutner, Phys. Rev. B 28 (1983) 5711 31. V. Gupta, S.S. Nivarthi, A.V. McCormick and H.T. Davis, Chem. Phys. Lett. 247 (1995) 596 32. V. Kukla, J. Komatowski, D. Demuth, I. Girnus, H. Pfeifer, L.V.C. Rees, S. Schunk, K.K. Unger and J. K~ger, Science 272 (1996) 702 33. K. Hahn, J. K~xger and V. Kukla, Phys. Rev. Lett. 76 (1996) 2762 34. M. Ylibautala, J. Jokisaari, E. Fischer and R. Kimmich, Phys. Rev. E 57 (1998) 6844 35. K. Hahn and J. K~ger, J. Phys. Chem. B 102 (1998) 5766 36. C. R6denbeck, J. K~rger and K. Hahn, Ber. Bunsenges. Phys. Chem. 102 (1998) 929 37. C. R6denbeck, J. K~ger, H. Schmidt, T. Rother and M. R6denbeck, Phys. Rev. E 60 (1999) 2737 38. C. R6denbeck and J. K~ger, J. Chem. Phys. 110 (1999) 3970 39. P.H. Nelson and S.M. Auerbach, J. Chem. Phys. 110 (1999) 9235 40. R.M. Barrer, Zeolites and Clay Minerals as Sorbents and Molecular Sieves, Academic Press, London, 1978 41. H. Rickert, Z. Phys. Chem. N.F. 43 (1964) 129 42. D.S. Sholl and K.A. Fichthorn, J. Chem. Phys. 107 (1997) 4384 43. C.D. Baertsch, H.H. Funke, J.L. Falconer and R.D. Noble, J. Phys. Chem. 10 (1996) 7676 44. D.H. Olson, G.T. Kokotailo, S.L. Lanton and W. Meier, J. Phys. Chem. 85 (1981) 2238 45. K. Keizer, A.J. Burggraaf, Z.A.E.P. Vroon and H. Verweij, J. Membr. Sci. 147 (1998) 159 46. W. Heink, J. Kfirger, T. Naylor and U. Winkler, Chem. Commun. (1999) 57
108 47. J. K~ger, N.K. B~, W. Heink, H. Pfeifer and G. Seiffert, Z. Naturforsch. 50 a (1995) 186 48. H. Weing/~tner, Z. Phys. Chem. N.F. 132 (1982) 129 49. A. Bunde and S. Havlin, Fractals and Disordered Systems, Springer, New York, 1996 50. D.M. Ruthven, Can. J. Chem. 52 (1974) 3523 51. S. Vasenkov, J. K~ger, D. Freude, R.A. Rakoczy and J. Weitkamp, J. Mol. Catal., in press 52. W. Heink, J. K~ger, H. Pfeifer, K. P. Datema and A. K. Nowak, J.C.S. Faraday Trans., 88 (1992) 3505
Recent Advances in Gas Separation by Microporous Ceramic Membranes N.K. Kanellopoulos (Editor) 2000 Elsevier Science B.V. All rights reserved.
109
Diffusion studies using quasi-elastic neutron scattering H. Jobic Institut de Recherches sur la Catalyse, CNRS, 2 Avenue Albert Einstein, 69626 Villeurbanne, France Quasi-elastic neutron scattering allows to study molecular diffusion in condensed or adsorbed phases. Diffusion coefficients can be derived, without a model, over space scales where molecular motion follows Fick's law. Furthermore, using jump diffusion models, one can determine characteristic times and distances for the elementary jumps. For isotropic diffusion, the existing jump models are discussed and a new model, which takes into account the delocalisation of the molecule on its site, is proposed. The cases of normal one-dimensional diffusion and of single-file diffusion are examined. Applications of the technique reviewed here concern mainly molecules adsorbed in zeolites, some results obtained in microporous silica are also presented.
1. INTRODUCTION Neutron scattering is one of the many physical techniques used to characterize solid materials and adsorbed species. There are in fact several neutron-based techniques: neutron diffraction yields structural information [1], textural studies can be performed by small-angle neutron scattering [2], vibrational modes can be measured by inelastic neutron scattering [3], and translational and rotational motions of adsorbed molecules can be characterized by quasi-elastic neutron scattering (QENS). We will limit ourselves here to QENS, which is now regarded as a useful method to determine diffusivities in porous materials. This technique has also been used to study the diffusion of hydrogen in metals [4] and of ions in oxides or solid electrolytes.
2. THEORY 2.1. Interaction of neutrons with matter
Neutrons are electrically neutral particles with a spin of 1/2, a mass mn of 1.675• -24 g, and a magnetic moment/J = -1.913 nuclear magnetons. Neutrons can also be considered as plane waves, with a wave vector k of magnitude 2~X. The neutron wavelength is given by the de Broglie's relationship ~, = h/mnV, where h is Plank's constant and v the neutron velocity. For a wavelength of 1 A, this corresponds to a neutron speed of 3956 m/s. Because of its mass, the neutron has a sizable momentum p = mnV = h k. The neutron energy is given by its kinetic energy, E = 89mnV2 = h k2/2mn. Since this energy can be varied in a wide range, this means that both the structure and the dynamics of a sample can be studied.
110
Neutrons interact with the atomic nuclei on a very short range, = 10 14 m, (we leave aside magnetic scattering). It is useful to split the total scattering cross-section into two parts, a coherent and an incoherent one. Coherent scattering corresponds to an average of the potential over the nuclei and gives rise to interference effects. Incoherent scattering depends on deviations from the mean potential, due to isotopic or spin effects. Values are given in Table 1 for some elements. A cross-section, which has the dimension of a surface, is measured in barns (1 barn = 10 .28 m2). This shows that the interaction of neutrons with matter is relatively weak. Neutron adsorption is small for most elements, except for a few nuclei like boron. It appears from Table 1 that the scattering cross-sections vary irregularly from one atom to another, even from one isotope to another, unlike with X-rays. For an assembly of nuclei containing only one isotope, with zero spin, the scattering is totally coherent (e.g. 12C). For each natural element, an average over all stable isotopes must be performed. In the case of diffraction experiments, it is usually desirable to use deuterated compounds, since incoherent scattering from 1H would increase the background. For quasi-elastic or inelastic studies concerning adsorbed molecules, the best contrast will be obtained with hydrogenated species. Table 1 Coherent, incoherent, and absorption cross-sections in barns for some elements (1 barn = 10 .28 m 2, the absorption cross-section is proportional to k, here ~, = 1 A) Element
Atomic Number
H
1
Li Be B C
3 4 5 6
N O Na AI Si P Ni Pt
7 8 11 13 14 15 28 78
Mass number 1 2= D
12 13 23 27 31
~coh 1.7586 1.7599 5.597 0.454 7.63 3.54 5.554 5.563 4.81 11.01 4.235 1.66 1.495 2.163 3.307 13.3 11.65
O'inc 79.9 79.91 2.04 0.91 0.005 1.7 0.001 0. 0.034 0.49 0. 1.62 0.009 0.015 0.006 5.2 0.13
(~abs 0.185 0.185 0. 39.2 0. 426. 0. 0. 0. 1.06 0. 0.3 0.13 0.1 0.1 2.5 5.72
The unit most used in neutron scattering is the meV. Some useful conversion relationships are 91 meV = 8.065 cm 1 = 0.24 THz = 11.6 K = 23.06 cal.
]]l
2.2. Molecular dynamics
The two important quantities in a neutron scattering experiment are the energy transfer h(o and the scattering vector Q defined as h(_O - E 0 - E 1 = ( h 2 / 2 m n
)(k ~)- k 12)
(1)
Q=ko-k 1 (2) where ko and k1 are, respectively, the incident and final wave vectors (the momentum transfer is hQ). Elastic scattering corresponds to k] = k 0 (hco = 0), so that only momentum is transferred. Quasi-elastic scattering occurs at very small energy transfers, + 2 meV, around the elastic peak. Experimentally, one measures the double-differential cross-section which represents the number of neutrons scattered into the solid angle dD with energy in the range dE (or h dco). This cross-section can be split into incoherent and coherent contributions [5,6]
d2t7
dD dE
k1
N
k o 4re h
[GincSinc(Q,o))+GcohScoh(Q,(o)]
(3)
Because of the large scattering cross-section of the hydrogen atom, orinc, it is essentially the diffusion of hydrogenated molecules which has been studied by QENS. The scattering functions, S(Q, ar), are Fourier transforms of correlation functions which describe the motions of the scattering particles in space and time. The incoherent scattering function is defined as ]
Sinc(Q,(o)=-~dr dt exp{i(Q.r-(ot)} Gs(r,t) system (ksT>> ho~), Gs(r,t) corresponds to
(4)
For a classical the probability to find a particle at position r at time t, if the same particle was at the origin at time zero (the subscript s stands for self) a s (r, t) = ~-
S [r + r i ( 0 ) - ri(t)]
(5)
Therefore, one follows the motion of one individual proton or of one given molecule, and the self-diffusion coefficient can be obtained, like in PFG NMR. In principle, Gs(r,t) can be derived from the measured intensities by inverse Fourier transform. However, the range of Q and co covered by a neutron spectrometer is too limited to obtain the self-correlation function with sufficient accuracy. What is clone in practice is to use a theoretical or model expression for Gs(r,t) and compare the calculated scattering function with the measured intensities. Even if one is only interested by the long-range diffusion, the other molecular motions of rotation and vibration have also to be taken into account. The position vector of a scattering nucleus in a molecule can be decomposed into three components: r=c+b+u (6) where c describes the position of the center of mass of the molecule, b the mean distance of the nucleus from the center of mass, and u the displacement of the nucleus from its equilibrium position under the effect of vibrations. A key
112 approximation is to consider that the translational, rotational, and vibrational motions are not coupled. Indeed for most systems, these motions are observed on different time scales. The total incoherent scattering function can then be written as a convolution product in to (symbolised by | of the different scattering functions : S inc (Q,
to) = ~'inc ~ trans (Q, to)|
.~ rot (Q,to)|
.~ vib (Q, co) ~.mc
(7)
- The energy transfers involved in QENS experiments, + 2 meV, are too small to excite intramolecular vibrations so that the vibrational term in Eq. (7) consists only of a Debye-Waller factor, exp(-Q2 2), where 2 is the mean-square amplitude. The effect of this factor is to decrease the intensity of the QENS spectra, for increasing Q values (the intensity goes into the inelastic domain). For a rotational motion, the incoherent scattering function can be separated into an elastic component and a quasi-elastic contribution : sr~ Ao(Q) &(co)+ ~ Ae (Q) L(to,Fe ) (8) e An elastic component occurs because the self-correlation function has a finite value at long times (or co~0). This happens for example if an atom is rotating around a fixed position. The factor Ao(Q), which governs the intensity of the function is called the elastic incoherent structure factor (EISF). This factor can be shown to correspond to the space Fourier transform of the proton trajectory averaged over a long time ('long' depending on the time scale of the experiment). The variation of the EISF with Q gives information on the geometry of rotation. The experimental EISF can be compared with various models, e.g. rotational diffusion on a sphere, diffusion within a sphere, uniaxial rotation, and fluctuations around equilibrium positions. Characteristic times of the rotational motions can be obtained from the quasi-elastic component in Eq. 8, which usually consists of a sum of Lorentzians Le(to,Fe) whose number e and width F e depend on the model. - The most interesting molecular motion in this review is the translation, it will be described in more detail in section 4. -
The scattering from adsorbed non-hydrogenated molecules can also be studied by QENS, although it requires a high-flux spectrometer. In this case, the scattering will be partially coherent. The coherent scattering function corresponds to l
Scoh(Q,to)=-~dr dt exp{i(Q.r- tot)} G(r,t)
(9)
where G(r,t) gives the probability to find a particle at position r at time t, if any particle was at the origin at time zero
N N (t)] \/ (10) ~t~ [r +ri(O)-rj N \i=lj=l Here, collective motions are probed and the transport diffusivity, which measures the evolution of local concentration gradients, can be derived. These experiments are more difficult because the coherent and incoherent contributions must be separated [7,8]. A characteristic of coherent scattering is that the intensity depends strongly on Q, whereas the incoherent intensity has a relatively smooth Q dependence, being
G(r,t)=l[~,
113
only influenced by the Debye-Waller factor. The coherent structure factor is defined as
S(Q) = ~S ( Q , o ) dco (11) In a liquid, or for identical molecules adsorbed in a cubic zeolite, S(Q) is related through Fourier transform to a pair-distribution function, g(r), reflecting short-range order. 3. EXPERIMENTAL Neutrons are produced either from the fission of uranium or from the bombardment of a target by protons. The first possibility leads to steady-state reactors (e.g. the Institut Laue-Langevin, ILL, in Grenoble, France), the second to pulsed sources (e.g. the spallation source ISIS, Didcot, UK). For QENS experiments, the ILL is at the time being the best place in the world because there are several types of spectrometers:time-of-flight, back-scattering and spin-echo instruments, which are able to cover a wide range of energy and momentum transfers. The instrumental resolution is an essential parameter:for a resolution width Ao~, the time scale over which an average of G(r,t) will be performed is of the order of 1/Aco. By reducing A o , one can follow slower motions (the energy transfer range will accordingly be restricted). With a back-scattering spectrometer, the resolution is of = 1 peV so that l/Aco is = 1 ns. With neutron spin-echo instruments, the resolution can be as high as 1 neV giving access to characteristic times of = 1 ps. The Q resolution is less critical although one must be able to measure in between the Bragg peaks of the zeolite. The neutron cells can be cylindrical or slab-shaped, and they are usually made of aluminum. Sample quantities for QENS measurements are typically of a few grams, the exact amount depending on the scattering power of the adsorbate. Special care must be taken in order to avoid pollution of the substrate after activation, especially by water. It must be transferred into the neutron cell in a glovebox or under vacuum. 4. ISOTROPIC DIFFUSION Theories describing transport phenomena in liquids are based on the assumption that the medium is continuous. In fact, different experiments and computer simulations show that a liquid has a short-range order, leading to a diffusive and oscillatory behaviour. The interest of QENS is that continuous diffusion can be measured at small Q values and that jump diffusion can be characterised at larger Q values. 4.1. Continuous diffusion In a liquid, it is well known that a Gaussian approximation for Gs(r,t) is valid as soon as the diffusion is followed over a distance of a few tens of molecular diameters (Qd << 1, where d is the molecular diameter)
114
1
r
2
(12)
Gs(r't)= (4JrD t)3/2 exp(- 4--~t )
where D is the self-diffusion coefficient. Since the self-correlation function can be related to a particle density and since Gs(r,0)=&(r), Eq. (12) is an appropriate solution of the diffusion equation or Fick's second law
3Gs(r,t) =DV2Gs(r,t) 3t
(13)
The QENS intensities can then be calculated from Eq. (4). First, the space Fourier transform gives the intermediate scattering function
I S (Q,/) - j"exp(iQ.r) GS (r,t) dr = exp(-D Q2 t)
(14) This function can be measured with neutron spin-echo, for a given Q value. In traditional QENS, one measures energy spectra simultaneously at different Q values. The scattering function is obtained after a second Fourier transform, in time
Sinc(Q, oo)= j'exp(-i(.o t) Is(Q,t ) dt=
]
DQ 2
n" 092 + ( D Q 2
)2
(15)
The shape of the energy spectra is a Lorentzian, with a half-width at halfmaximum (HWHM) DQ 2. By plotting the width as a function of Q2, one may check that Fick's law applies if a straight line is obtained. The slope gives directly the selfdiffusion coefficient. While a linear variation of the broadening is often found at small Q values, it is usually observed that the width deviates from a straight line at larger Q values. This indicates that the continuous diffusion model is no more valid at small distances and that the details of the elementary diffusive steps have to be taken into account. Fick's phenomenological equations were demonstrated by Einstein from statistical considerations [9], showing the relationship between transport phenomena and Brownian or random motions. The concept of random walk for a particle diffusing by successive jumps on a cubic lattice can be applied to a hydrogen atom in a metal or to a molecule in a zeolitic network. In this model, the jump length g is a constant as well as the jump rate, ~:-1, where ~: is the residence time on a given site. Provided that the jumps are uncorrelated, the following relation is derived g2 O(16) 6"r The self-diffusion coefficient is independent of the number of jumps. This can be compared with the mean-square displacement calculated from Eq. (8) 4~
do
r2
-~r2Gs(r,t)dr=(4zrOt)3/2 ~r 4 exp()dr=6Ot 0 4Dt
(17)
This shows that a macroscopic diffusion coefficient can be related to jumps on an atomic scale. Provided that the interactions between the particles are negligible, the s a m e diffusivities should be obtained.
115
I
I
/
5I
4-3 2 ,,.
i
0.0
I
I
I
I
.2
.4
.6
.8
Q2
(A-2)
1.0
Fig. 1. Broadenings calculated as a function of Q2 for different models" ChudleyElliott (solid line), Singwi-Sj61ander (dotted line), Hall-Ross (dashed line) and Fick (dotted-dashed line). The HWHM are calculated for the same values of < r 2 > = 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_<2x10 -3
(50)
The resulting function is narrower than for normal 1D diffusion. This is illustrated in Figure 8(b) where the single-file scattering function, Eq. (48), has been computed for typical values of the parameters F and Q (solid line). In contrast to the case of normal 1D diffusion, the more waisted peak shape cannot be fitted with an isotropic diffusion (dotted line). 6. APPLICATIONS
Experimentally, the techniques that are used to measure the diffusion of molecules in microporous materials can be divided into two groups. Several methods such as chromatography, frequency response or permeability measure diffusion under the influence of a concentration gradient. The diffusivities which are obtained from these macroscopic techniques are usually referred to as transport diffusivities. There are only two methods which measure diffusion under equilibrium conditions : PFG NMR and QENS. With zeolites, these two methods are complementary in that molecular migration is followed over a few unit cells with QENS (time scale = l n s ) and over the whole crystal with PFG NMR (time scale = 1ms). It is generally the selfdiffusivity which is obtained from the 'microscopic' methods, although the transport diffusivity can be derived from coherent QENS (section 6.3). 6.1. Linear and branched alkanes in the MFI structure (ZSM-5 or silicalite) The structure type code MFI refers to ZSM-5 and to its microporous silica polymorph, silicalite. The Si/AI ratio ranges typically between 12 and 100 for ZSM-5 and it must be larger than 1000 for silicalite. Zeolite membranes are most often based on the MFI structure. Silicalite, which has no compensating cations, is also an ideal system for molecular simulation studies. The MFI structure is relatively complex:the unit cell contains 96 tetrahedral (SiO2) units which give rise to 4 straight channel sections and 4 zigzag channels, with 4 channel intersections. Both channels consist of 10-membered oxygen rings and their free apertures are about 5.5 A in diameter (Figure 9). In fact, the channel diameters are based on an arbitrary value of 1.35 ,~, for the oxygen radius, and deformations of the channel windows may occur due to changes in the structure. Indeed, a phase transition has been found for these materials between room temperature and 360 K (the exact temperature depends on the Si/AI ratio and on the presence of adsorbates). The low temperature phase is monoclinic and the high temperature form is of orthorhombic symmetry. ZSM-5 has found several applications in shape-selective catalysis, in the field of refining, and in adsorption processes. Considering the pore size of this zeolite, a straightforward application of MFI membranes would be the kinetic separation of alkane isomers. This explains the large number of papers devoted to diffusion measurements in this structure. Because there will be a strong dependence on the
128
Fig. 9. Schematic representation of the channels in the MFI structure size and shape of the molecule with respect to the zeolite pores, no quantitative theory is able at the present time to predict the diffusivities of linear and branched alkanes. Experimental or simulation methods have to be used. However there are still puzzling differences between the values of the diffusion coefficients obtained by various experimental and theoretical techniques. In the MFI structure the diffusion is anisotropic, diffusion in the ~- direction can only be achieved via alternating migration in the two other directions. The influence of this anisotropy on the QENS profiles has been studied [34,35]. The anisotropy of diffusion appears to be larger for the long alkanes : for C8, essentially 1D diffusion was found by 2H NMR and QENS techniques [35,36]. The diffusion coefficients determined by QENS, and which are plotted in Figure 10, are orientationally averaged. They are compared with the diffusivities obtained from techniques which are able to study a wide series of n-alkanes. For example, PFG NMR data which were obtained for short alkanes (up to C6) are not included (they are in good agreement with QENS). It appears from Figure 10 that the diffusivities seem to converge for the short chains, but large discrepancies can be noticed for the long alkanes. The very large and almost constant diffusivities predicted by MD simulations [37] are not observed by QENS. The reason of these large theoretical diffusivities is that the simulations are performed at infinite dilution in a rigid framework so that thermalisation is not effective [41]. MD simulations performed at higher Ioadings are in much better agreement with the QENS data [41]. The trend found by the hierarchical simulation approach [38] is in better agreement with the QENS values, although the two sets of data start diverging for C6. The comparison with the single-crystal membrane results is surprising : a good agreement is observed for short chains and for C8, but a large gap is noticeable in between. Even if the membrane configuration only measures diffusivity in one direction, it is difficult to understand this variation. The ZLC diffusivities are systematically 2 or 3 orders of magnitude lower than the QENS values. The activation energies for diffusion were compared in ref. 35: most
129
experimental and theoretical methods indicate small activation energies for short alkanes, = 5 kJ/mol up to C6. They increase progressively when the number of carbon atoms increases, the value for C14 is = 12 kJ/mol.
1 0 -4
10 -s O
""e
10 .6
..........
10-7 10 .8 10 .9 '
0
I
I
I
I
I
I
I
I
2
4
6
8
10
12
14
16
18
Number of carbon atoms
Fig. 10. Averaged diffusion coefficients obtained at 300 K by different techniques, for small concentrations of n-alkanes in the MFI structure: ( 9 MD simulations [37], (o) hierarchical simulation [38], (+) QENS [35], (V) single-crystal membrane [39], and (A) ZLC [40]. The diffusivities of branched alkanes in the MFI structure was found to be much lower than the corresponding linear alkanes. A QENS spectrum obtained for isobutane at 570 K is shown in Figure 11(a). It is clear that the broadening of the elastic peak, which is related to the long-range mobility, is very small for isobutane compared to n-octane at an even lower temperature, Figure 1 l(b). The self-diffusion coefficient obtained by QENS for a loading of 3 isobutane per u.c. is 5.5 x 10 .8 cm2/s at 570 K [42]. Extrapolation to room temperature indicates that the diffusivity of isobutane is more than 3 orders of magnitude lower compared to n-butane. The diffusivities obtained for branched alkanes with the supported membrane technique are in reasonable agreement with the QENS values [42].
130
500 -'~
v
+
(b)
400
"~ 300 200 .,_+. + _ . . , ~
o
5
+
-
.
+ +-,~_+
.... :,".
-10 400]
-5
+
.....
0
5
10
~>, 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).
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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.
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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 <10 -3 Pa and 623 K over night by rotary and turbo molecular drag pumps (6). The temperature was raised to 623 K at 2Kmin~ using a programmable tube furnace. A dose of purified sorbate is brought into sorption equilibriurn with the sorbent in the sorption chamber (8) at the chosen pressure and temperature. A square-wave modulation of + 1% was then applied to the gas phase equilibrium volume, Ve. The modulation was affected by applying a current to each of the two electromagnets (3) in turn, which moves the disc (4) between the electromagnets rapidly (<10 ms) and periodically. The brass bellows (5) attached to the disc, which is part of the sorption gas phase volume, was expanded and compressed to produce the • 1% change in volume. A frequency range of 0.001 to 10 Hz was scanned over some 30 increments. The range of d ~ i v i t i e s that can be covered by such a FR apparatus depends on the size and the shape of the adsorbent crystals, as is demonstrated in Figure 2. The pressure response to the volume perturbation was recorded with a high-accuracy differential Baratron pressure transducer (MKS 698A11TRC) (10) at each step over three to five square-wave cycles (256 reading points per cycle) after the periodic steady-state had been established. The volume, Ve, is 80 cm3 in the FR system. The isotherm describing the equilibrium sorption conditions can be linear or curved. However, the horizontal region of a rectangular isotherm cannot be used as there is no sorption/desorption following the square-wave modulation of the equilibrium volume. The frequency was controlled by an on-line computer (7), which was also used for the acquisition of the pressure data from the Baratron transducer. The conversion rate of the analogue-to-digital converter in the interface unit must be fast enough to cope with the 1 to 4 ms response time of the pressure transducer. The pressure response to the volume change over the whole frequency range was measured in the absence (blank experiment) and presence of sorbent samples to eliminate time constants associated with the apparatus. The FR spectra were derived from the equivalent fundamental sine-wave perturbation by a Fourier transfommtion of the volume and pressure square-wave forms. In the single-step FR experiments, the gas phase equilibritma volume, V,, is only subjected to a one-cycle square wave perturbation of • 1% at a certain frequency (0.01-1 Hz). Up to 2048 pressure readings can be recorded by the on-line computer during one adsorption or desorption
141
/-1 Sorbate Inlet
Rotaryand TurboDragPumps
TYPE270 I conditioner
signal
Fig. 1. Schematic diagram of the FR apparatus. 1: Sorbate Inlet; 2: Valve; 3: Electromagnets; 4: Moving Disc; 5: Bellows; 6: Rotary and Turbo Drag Pumps; 7: Computer with A/D and D/A Cards; 8:Adsorption Vessel with Zeolite in Glass-wool; 9: Vacuum Connectors; 10: Differential Baratron; 11: Signal Conditioner; 12: Reference Pressure Side half-cycle. The experiments were also carried out in the absence and presence of sorbents to subtract the dead-time of the apparatus. The adsorption and desorption uptake rate curves for each half-cycle were obtained from the difference in the pressure readings of the blank experiment and when the sorbent was present. 2.2. Analysis of the FR Experimental Data Figure 3 shows a flow chart for the sunm3m~ of the evaluation of the FR parameters. The fiJll FR experimental parameters (phase lag and amplitude) can be obtained from the Fourier transformation of a square-wave perturbation of the volume, F(t), and the frequency response signals of pressure in the gas-zeolite system, g(t). As any periodic waveform can be described by a set of sinusoidal components [ 11], the Fourier series ofF(t) can be expressed as [12] 4 F(t)---
1 5-',-sin(na~)
;g" n=1,3,5,-../7
(1)
142
10-5
i
10-9 "7 .~
10-11 10-13 10-15 10-17
O.1
1
10
1O0
1000
Partical radius / ~tm Fig. 2. The relationship of diffusion coefficients, D; frequency, f; and spherical crystal radius, r. where t is time and cois the relevant frequency. For a linear system the steady-state response signals, g(t), is
g(t) = n(t) +
X
,=1.3.5.--.
an sin(nrot + O . )
(2)
where a. is the proportionality coefficient for the nth frequency, ~ . is the phase angle at the nth frequency, and n(t) the stochastic noise signal. By rearranging Equation (2), one can obtain g(t)=
n(t)+ X (ct. cos..)sin(nag) .=1,3,5r
+
X
(a. sin..)cos(nag)
n=1,3,5,.-.
(3)
Comparing Equation (3) with the definition of a Fourier series or Fourier expansion [12] of the function g(t), e.g. ao T +
E•. COS(nO.~')+ Zbn sirl(n(/~) ,=1.3.5r n=1.3.5.---
where the Fourier coefficients, a. and b., are given by
(4)
143 ,11
Input square-wave perturbation on volume, F(t)i
Sorbate gas/zeolite system Theoretical model Noise n(t) Output pressure response to the volume perturbation, g(t) i
d,
,111
Fourier transformation r _
i
Theor'etical Phase lag, ] amplitude and ]
1 Experimental phase lag Oz.B,
characteristic functions ] ~-
amplitude ratio PB/Pzand characteristic functions 6;,__andt~out i
I" 'Comparisonof results to ] [ evaluate diffusion coefficients "1 [ and other parameters [
Fig. 3 The flow chart of fi'equencyresponse data analysis
144
(-1) ~r,/to
an = -
I g(t)cos(na~t)dt
(5)
and x/oJ
b. = o9 I g(t)sin(ncot)dt
(6t
-u/o~
it is evident that a. = a. sinO.
(7)
and b. = a. cosO.
(8)
From Equations (5) and (6), the frequency response parameters phase lag, O., and amplitude ratio, Pr,., at the nth frequency can be calculated by
O n = tan-l (afro-)
(9)
and P~.. =--~-an =--~-., . + b . )
(10)
In practice, the integration of the Fourier coefficients, a. and b., is carried out by a computer over a number of cycles to reduce the effect of noise and to improve the accuracy of the FR parameters [ 13], i.e. 2 S'2
a,, :~_~2g(x)cos(2~'nx/S )
(11)
and 2 s~2 g(x)sin(2 moo/S)
bn = --S-s/2
(12)
where S is the number of points per square wave, co = 2x/S and x is the position along the S points per period square-wave, x -=t. Generally, the FR parameters can be derived from the equivalent fundamental sine-wave
145
perturbation by the first harmonic (n=l) Fourier transformation of the input signal and the pressure response signal. The higher harmonic (n>l, where n is an odd number) can be, nevertheless, used to extended the experimental frequency range by a factor of n when high quality response data can be obtained [9]. 3. THEORY 3.1. Full FR Method The theoretical solutions of the frequency-response technique have been comprehensively developed over the past decade for microporous systems and for bidispersed porous systems. The full FR parameters (phase lag and amplitude) are experimentally derived from a Fourier transformation of the volume and pressure square-waves. The phase lag Oz.s= O z - OB is obtained, where Oz and OB are the phase lags determined in the presence and the absence of zeolites, respectively. The amplitude is embodied in the ratio PJPz, where Ps and Pz are the pressures response to the +1% volume perturbations in the absence and presence of sorbents, respectively. From the solution of Fick's second law for the diffusion of a single diffusant in a solid subjected to a periodic, sinusoidal surface concentration modulation, the following equations
in-phase: (PB / Pz )cos ~z_s - 1 = K6i,, + S
(13)
out-of-phase: (PB / Pz)sin ~z_B = KSout
(14)
can be obtained [1,14,15]. K is a constant related to the gradient of the adsorption isotherm, S is a constant that represents a very rapid adsorption/desorption process, which may co-exist with the diffusion process being measured, 6~nand &ut are the overall in-phase and out-of-phase characteristic functions, respectively, which depend on the theoretical models describing the overall kinetic processes of a system. The following models are avaLlable. 3.1.1. Single diffusion process model When only a single intracrystalline diffusion process occurs in a system, the characteristic functions are [1,2]
in-phase: K~,~ RTVsKe
(15)
RTV, K? out-of-phase: KSo~ = - - - - - - - ~
v,
(16)
where R is the gas constant, T is the isotherm temperature, V~ is volume occupied by the sorbent, V, the mean volume of sorbate outside the sorbent and Kp is the equilibrium constant based on pressure. For crystals of slab shape, & and 6~ are given by [1]
146
1 sinh r/+ sin r/) 8c = ~ (cosh 7/+ cos r/
(17)
1 sinhr/- sinq) 6~ = -~ (cosh r/+ cos r/
(18)
For diffusion in spherical crystals, & and t$ are given by [ 1]
8c
3 sinh r / - sin q
(19)
)
3 sinhr/+si n q 2 6s = -~ (cosh r/ cos r] - -~)
(20)
Where r/= (2col2/D) v2 , co is the angular frequency, f = co/ 2x = frequency, 1 is the half thickness of the slab or the radius of the sphere, and D the transport intracrystalline diffusion coefficient. 1.0 K~I
0.8
0.6
0.4
0.2
1
0.01
0.1
1
10
Frequency / Hz Fig. 4. The ideal shape of the phase lag O z_ B and amplitude ratio P J P z curves vs. frequency.
0.0 0.01
0.1
1
10
100
Frequency / Hz Fig. 5. Theoretical characteristic functions, K&, and KSo,t, for a single diffusion process when 1 = 101am (sphere), K=I, and D=10llm2s "1.
147
The diffusion coefficient is obtained by a least-squares curve-fitting of the experimental characteristic functions versus frequency data, with the diffusion coefficient being the only adjustable parameter. Solutions similar to Equations (17) - (20) have now been carried out for parallelepiped crystals and anisotropic diffusion [ 16]. The ideal shape of the phase lag Oz.B and amplitude ratio P J P z curves versus frequency should be as shown in Figure 4. Such ideally shaped curves lead to characteristic functions versus frequency curves, as shown in Figure 5. 3.1.2. Two independent diffusion processes model When two diffusion processes occur simultaneously, provided they are independent of each other, the theoretical treatment can be expanded to give [1,17]
in-phase: K6i, = K16r 1 + K28c, 2
(21)
out-of-phase: K6o~ t
(22)
=
KiSs, 1 + K 2 8 s , 2
where subscripts 1 and 2 indicate the two separate kinetic processes. The characteristic functions 6~ and ~ are also generated by Equations (17) - (20).
1.2
IiII
1.0
1.0
0.8
0.8' 0.6
0.6 0.4
0.4 "...... II
0.2
0"8.01
I+II
0.2
O.1
1
10
Frequency / Hz Fig. 6. Theoretical characteristic functions, K&, and g~out, for two diffusion processes (I+II) when Kt=Kzt=0.5 , l I = 111 =20~trn, and Dt=5XDll=5x 10"1~
"1.
1O0
0.0 0.01
0.1
1
l0
100
Frequency / Hz Fig. 7. Theoretical characteristic functions, K&, and K ~ t , for two diffusion processes (I+II) when Kr=0.6, Kzr=0.3, li=/tl=20~tm, and Dr=10 -9, Dzr=l 0q lm2s-~"
148
When two such processes exist then K/~n and K~ut characteristic functions as given in Figure 6, respectively, are obtained. Such curves can be deconvoluted into their respective separate components I and II with diffusion coefficients that differ by a factor of five, but with K constants that are the same for both dif~sion processes. In Figure 7 the corresponding characteristic curves for two diffusion processes are seen, where the diffusion coefficients differ by a factor of 100 and when the constant K is twice as large for the faster process than for the slower process. In this latter case the flux associated with the faster process is thus twice that of the slower process. 3.1.3. Non-isothermal diffusion model Periodic adsorption and desorption inside adsorbent particles, induced by the volume modulation, may lead to a heat of sorption effect which is dissipated through a heat exchange between the sorbent and the surroundings. When the heat exchange rate is comparable with the diffusion rate, a bimodal form for the frequency response characteristic curves is found [18-20]. The overall characteristic functions ~, and (2~outfor this model are given by
in-phase: K S ,
RTV~Ke (de(1 +ro2t~)+?'(82 +82)ro2t~)
=---V--e
out-of-phase: K~5o~
rs,
(23)
+ (1 +
RTVsKp ( 8s (1 + 092t~ + y(t~) + 82 )oXh
(24)
where th is the time constant for heat exchange between the sorbent and its surroundings, and
r = K~ I ~ / c,
(25)
is a measure of the non-isothermalicity of the system. AH is the heat of adsorption, Cs is the volumetric heat capacity of the sorbent and Kr is derived from the adsorption isotherm with respect to temperature and defined by Kr -
PAH K? RT 2
(26)
and 6 are also given by Equations (17) and (18) respectively for slab-shaped crystals and Equations (19) and (20) respectively for spherical crystals. 3.1.4. Diffusion-rearrangement model When Fickian difl~ion occurs in transport channels, for example, the straight channels of silicalite-1 framework structure, and sorbate is immobilised in storage channels, e.g. the sinusoidal channels of silicalite-1, and a finite-rate mass exchange between these two kinds of channels exists [21 ] the overall characteristic functions derived by Sun et al.[18] are
149
in-phase: 4. = 6c + K n
~c -- ~ s m t R
(27)
1 + to2tzR
out-of-phase: 8o~t = 8~ + K n
8 s + (~cOgl R
(28)
1 + CO2t~
For diffusion in slab geometry, 8c and 6~ are given by 2 c sinh 22 c + 2~ sin 22s 6c =(2r
(29)
+ #Xcosh22c +cos22s) 2~ sinh 22 c - 2 c sin 22~
+
(30)
+ cos2 ,)
For diffusion in spherical geometry, 8~ and 6~ are given by 3 ( 2 c sinh22 c - 2 s sin22 s 6c = g + 2 z cosh 22 c - cos 22~
g+g
(31)
3 (2~ sinh 22 C + 2 Csin 22 s 4 = 2~ + 22 cosh 22 c - cos 22~
#+g
(32)
with
-[(v, +,Vc)O,,,'-/o]"'
(33)
and Kn
v c = 1 + 1+ o)2t------~R
K~ox R 1 +co2t2R
v, = ~
(34)
(35)
tR is the time constant of mass exchange between the transport and storage channels and K a is the ratio of mass hold-up in the storage and transport channels. 3.1.5. Diffusion with surface-resistance or surface-barrier model
When surface-barriers or surface-resistance to sorbate gases or 'skin' effect occurs, the overall characteristic ftmctions can be indicated by [2,22,23]
150
in-phase: ~n = (ak-A out-of-phase:
/o9)2(a + c6~ )/(9
(36)
6o,# = (ak_A /co~l - (ak_.4 ;'co){(ak_A .,"co)+cgs }/6)]
(37)
where k_ A is the rate constant for the resistance, & and 6~ are as same as those in Equations (17) - (20) for slab and spherical crystals respectively, and (38) (39)
C ~" (dC d e ) e / { d ( 2~ + C) de}e = 1 - a
Here A is the adspecies on the external surface, C is the adspecies within the porous adsorbent and P the equilibrium pressure, a ~. 10-2 and c = 1 for most zeolites. The surface resistance can be demonstrated by the area of the intersection between the inphase and the out-of-phase characteristic function curves as presented in Figure 8, which depends on the ratio of ~: defined by
~=ak_,t/(D
12)
(40) 0.18
suggesting that the 'skin' effects depend not only on the ratio of the rate constants between the surface resistance and diffusion processes, but also on the size of crystals. A large value of ~: means small 'skin' effects [23,24]. The limiting values of the in-phase component as cJj--~0 can be experimentally used to determined the equilibrium constants [25] since
0.15
0.12 o
0.09
0.06 K~,,I
o.,= o = K =
RTV,V~Kp
(41)
If the experimental range of frequency is wide enough to cover all the rate processes occurring in a system, the asymptotes of the in-phase and out-of-phase characteristic curves should satisfy the following two relations[2] linaoo(PB/Pz)c~
- 1= 0
._
9
....... ~=1 .............~=10 ~=100
/if
0.03
0.00 0.001
0.01
0.1
1
10
1()0
Frequency / Hz Fig. 8. Theoretical FR spectra for diffusion with surface resistance with g as parameter for spherical crystal geometry when K=0.15 and D/r 2 = 0.1 s~.
151
(42)
and lirn(PB/Pz) sin * Z-B : 0 RTVsKp
lim(PB/Pz)cOs~z_ co---~0
~
-1= K = ~
and lim(PB / Pz )sin (I) Z-B = 0
Ve
(43)
(.o--~0
3.1.6. Mass transport in zeolite pellets or membranes
For practical useful sorbents or catalysts, zeolite crystals must be formed into pellets of suitable dimensions, porosity and mechanical strength, or be formed into a membrane on the surface of support materials. Such composite pellets or membranes offer a bidispersed porous structure, with macro- or meso-pores between the crystals and micropores inside the crystals. The overall rate of such a system depends on the interplay of various processes occurring within the particles. Jordi and Do [10,26] have developed a general theoretical model and seven relevant degenerate models to analyse the frequency response spectra of a system containing microporous solids exhibiting a bimodal pore size distribution for slab, cylindrical and spherical macroparticle and microparticle geometry. Sun et al. [20] also reported the theoretical models of the FR for non-isothermal adsorption in biporous sorbents. The overall characteristic functions ~, and 8out for the system involving biporous materials are given as below [ 10].
in-phase: 6,n = 6c: M O.1 d- 1 + 2
'
out-of-phase: 6out = 6s,~M O'l + 1 + 2 6 c : .
"
1+ 2
(44)
'
+ 6c:M 1+ 2
'
(45)
where 6c,sM and 6s,,M, are the in-phase and out-of-phase characteristic functions for macroparticle shape factor s M , and 8c,~. and 8~.~ are the in-phase and out-of-phase characteristic fimctions for microparticle shape factor s u , o.l and 0-2 are the fractional adsorption capacities in the macropore void and the microparticles, respectively. For most commercial sorbents, o.1 is close to zero and o-2 is close to unity. The parameter 2 is a measure of the approach to saturation of the Langmuir isotherm and is defined by
ka - -~d CBe
(46)
where CBe is a bulk sorbate concentration under equilibrium conditions, k a and k d are the rate constants for adsorption and desorption. Small values of 2 indicate an equilibrium state in the linear region of the Langmuir isotherm, while saturation is approached as 2 increases. The ratio of the macropore diffusion rate to the micropore diffusion rate is defined by
152
R2 7'- 1 D~,
(47)
2
o'! R u D p
where Dp and D u are the macro- and micropore diffusivities, respectively, R and R u are the radii of the macro- and microparticles, respectively. If 7' is small (<<1), micropore diffusion controls, while maeropore resistance dominates when 7' >> 1. When the macropore diffusion rate for a system involving biporous sorbents is far faster than the micropore diffusion rate, i.e. 7' <<1, the overall kinetic processes for the system can, then, be simply described by the models given in sections (3.1.1), (3.1.2) and (3.1.5). Three different degenerate models incorporating macropore diffusion for spherical macroparticle and microparticle geometry reported by Jordi and Do [ 10] (isothermal systems) are presented as follows. Model 1. Macropore-mieropore diffusion
When the macro- and micropore diffusion rates are compatible and control the overall dynamic processes of the system, the macro- and micropore characteristic functions are given
by cos(0 2)sinh[2,ff cos(0 2)1- sin(0 2)sin[2~-sin(0/2)] 8~,sM
=3
~r {cosh[24~-cos(0 2)1 - cos[2~tr- sin(0 2)]}
6s.m = 3(cos(O 2) sin[2,~-sin(0 2)] + sin(O 2) sinh[2,ffcos(0, 2)] ~r {cosh[2qr7 cos(0 2)] - cos~2,ff sin(O2)]}
3[sinh(r/u) - sin(r/l')] 3[sinh(qu)+ sin(r/u)] ~ ~"~ ,~[cos~(,~) ~o~,~)]-.~
cos(0) / r
(48)
sit~t
(49)
(50) (51)
where r and 0 can be calculated by re '~
= r/M
(52)
153
+ ico
R'/Dp i3~
(53)
+.(1+ .>[cosh(,~)-co~,~)]
and
~7~,=i2coR2/Dl,
(54)
where co is the angular frequency. By fitting experimental data with the theoretical model, both macropore diffusivity, Dp, and micropore diffusivity, D~,, can be derived. It should be noted that when both diffusivities are significant, macropore diffusion retards micropore dif~ison and thus the FR spectra behave like diffusion with a surface barrier as shown in Figure 8 [ 10,20]. When attempting to measure intracrystalline diffusivity in the presence of a surface barrier, therefore, it is essential that all interparticle diffusion resistances must be eliminated. Model 2. Maeropore diffusion and external film mass transfer
This model incorporates only film mass transfer and macropore diffusion mechanisms (y >> 1) for the system. The macro- and micropore characteristic functions are given by
3Bi2.M[Sinh(.M) - sin(r/M)]
8~.~ =
~cosh(r/M )[r/~/~2+(Be-1)2]+ cos(r/M)[r/~/2-(Bi-I) 2]]
r/2 ][+ JTM(Bi - 1)[sinh(r/M) + sin(r/M)]
(55)
f
3BilCosh(r/M )[ r / ~ - 2 ( B i - I ) ] + Cos(r/M)[r/~+ 2(Bi - I)]}
5...1~ =
[ + rlu(Bi- 2)[sinh(r/u )+ sin(r/u )] icosh(rlu )[~72M/2 + (Bi _ l)~_] + cos(~?u )[J72M/2 _ (Bi _ l)2 ])
(56)
7?2[ + J7M(Bi - 1)[sinh(r/M) + sin(~TM)] a~.,, = 1
(57)
8,,.~ =0
(58)
where
,- = li,o~'/(-.~.)}[-.
+o./0 + ;>]
(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<
t?M= DpcriO+--2)(1+ q2) +ic~ or' + (1 + )L)(cr21+ r/2 and
(61)
flu - 3BD It Micropore characteristic functions can be obtained by 1 (~c s u
'
--
6ss,,_ '
(62)
2
l+r/u
qu
(63)
l+r/~
The parameter B is the ratio of the adsorption rate to the micropore diffusion rate. When B is larger, equilibrium at the pore opening of the micropores is rapidly attained and the overall kinetic process is, then, simplified to only macropore diffusion control. The effect of the adsorption rate to the macropore diffusion rate is similar to the case of micropore diffusion control as presented in Figure 8, i.e. a large value of B (~ in latter case) means small adsorption effects. 3.1.7. Characterisation of acid sites
The FR technique is also capable of determining the different strengths and concentrations of acid sites of catalysts under equilibrium pressure. In these cases, the experimental FR data, the FR spectra, can be described by [3,27]
in-phase: (PB/Pz )COSOz-B -- 1= X
k2 j + coz
(64)
out-of-phase:
kj[ k_jco]
(PB/Pz)sinOz_B = ~ ~ j
155
(65)
k2 j +092
where
kj /k_j = (dN~ j)/dP)e
(66)
RT/Ve
is an intensity parameter of the FR spectrum, which is related to a gradient of the adsorption isotherm arising from N~J) , the amount of adspecies on the j sorption site; k_j is the time constant of the adsorption/desorption process for adsorbate on site j and co is the angular velocity of the square-wave generator. The FR parameters k j / k j and k_j can be derived from the fitting of the experimental characteristic functions by an appropriate numerical method. Whether or not the frequency range is wide enough to investigate all detectable surface species can also be decided from the asymptotes of the in-phase and out-of-phase characteristic curves. The in-phase components tend to kj/k_j in the lower frequency region, but to zero in the higher region as shown in Figure 10. 1.2 .......
in-phase ....... out-of-phase
Bi=0.1
............. B i = l
,, ',
..
"..:
,
-
:~
,.,
.......
Bi=10
~
Bi=500
1.0 L
_~_
\
0.8 el)
g~ o
y' "~
0.4
: ,,
,
0.0 0.001
0.5
..,, ,.~[ -9 -... X\:,,. 'i - ".. ., ': ....- ,,./~ .. -... \..,., .';
-;'[ 0o0
0.01
0.1
1
10
100
-'"
0.01
1
10
-:: . . . . 100
Frequency
Frequency / Hz Fig. 9. Theoretical FR spectra for macropore d i ~ s i o n with film transfer resistance as rate-controlling processes with Bi as parameter for spherical crystal geometry when K=I, 2=1.0, and tr 1=0.01.
0.1
Fig. 10. Theoretical FR spectra stemming from the j surface species. Each curve is characterised by a pair of parameters, kj
and kj /k j .
156
If the Langmuir model is valid, the rate constants for adsorption, k(a J) , a n d desorption,
ktdJ) , on sitej can be obtained from the FR parameters kj/k_j and k_j using k_, = k~') Pe + k{J )
(67)
and the number of sites available for adsorption ofj species, NJ J) , relationship between kj /k j and k y, i.e.
be calculated from the
can
(68) The validity of the model can be verified by the linear relationship of the plot of k j against equilibrium pressure, Pe, and of the plot of log(kj/k_j ) against log(k_j) with a slope equal to -2. The non-isothermal adsorption model has been also reported by Yasuda [2]. 3.2. Single-step FR Method The pressure response of the system following the fast (a) expansion and (b) compression of the volume in the absence (blank experiment ) and in the presence of the microporous solid sample was recorded, as shown in Figure 11. There is a delay time of ca. 10 ms before the pressure transducer starts to record a pressure change. The pressure recordings in the absence and presence of sorbent samples were time dependent until, finally the pressure reached a
(a) o [..,
r~
I
0
.
I
10
9
I
20
,
L
0
I
I
10
9
J
20
Time / Sec. Fig. 11. Pressure changes of benzene response to a volume increase (a) and decrease (b) in the absence (narrow line ) and in the presence (bold line) ofsilicalite-1 sample.
157
constant value, as can be seen in Figure 11. In the analysis of the pressure data obtained by the SSFR technique, the dead1.0 time is first subtracted from the time scales of the blank experiment and when sample is present. The subsequent difference in the pressure of the blank and in the presence of sorbent can be considered as the amount 0.5 sorbed by the solid crystals as a function of time. If Mt denotes the amount of sorbate sorbed at time t and M. the corresponding amount atter infinite time, e.g. at sorption 0.0 equilibrium, then the adsorption and 0.0 0.2 0.4 0.6 0.8 desorption uptake rate curves can be obtained by plotting M t ~Moo against the square root oftime, as shown in Figure 12. As the pressure in the gas phase is not Fig. 12. Sorption uptake-rate curves of constant during the rate measurements the benzene in 50 mg of NaX at 440K and changing boundary conditions have to be taken into account. Two different 2.0Torr. E5 and * denote adsorption and representative treatments of the Mt ~Moo desorption processes, respectively. Line is fitted by equation (69) with fractional data are given below. uptake of 0.6 and D=4.9x 10-1~ -1. (i) The solution of diffusion controlled uptake from a well stirred solution of limited volume [28] was employed to fit the sorption uptake rate curves. The solution to diffusion equation for a sphere with radius r is given by
s
- 1 - 6 ~ a(cr + 1)exp(- D q 2
MOO
n=l
2
9 + 9 a + q. a
t//r 2 )
2
(69)
where the values of q. are the non-zero roots of 3qn tanq, =--------23+aq,
(70)
and a is the ratio of the amount of sorbate in the gas phase to the amount in the sorbent atter infinite time, i.e. when equilibrium is established. The corresponding solutions for diffusion in cylindrical and slab crystals can also be obtained [28]. (ii) From the early time linear plots of sorption uptake against x/t, the xft law [29] for the simultaneous volume and gas-phase concentration changes can be used. The slope, S(0), of a plot of M t - M o against 4~ is given by [29]
158
t/2
s(o)=
where
Cg
Vg(0) Cg (oo) 1 + aMoo _ Mo KVg (oO) ( M| _ Mo ) 1 + -Vg-(-O-)- C g (oo) 1 + aM|
(71)
is the concentration of diffusate in the gas phase and M 0 the concentration of
sorbate in the sorbent at time, t = 0.
Vg denotes the volume of the
gas phase, A the total area
normal to the direction of the diffusion flux, '0' and 'oo' refer to t = 0 and oo, respectively.
k = KMoo =
M t/Cg
.
In the SSFR method, the volume change of the gas phase is only +1% of the total volume, therefore, Vg(oO)/Vg(O).~l. When sorption/desorption follows Henry's law, then Equation (71) becomes
S(O) =-~
[Moo - Mo ~1 + 1/a)
(72)
When the experiment is carried out in the near-saturation region of the sorption isotherm, a becomes large and Equation (71) approaches that for the infinite volume case
2A(D) 1/2 S(O) = - ~
[M~ - M0]
(73)
When the diffusion is measured at an equilibrium pressure, Pe, which is outside Henry's law range, the diffusivity, D, obtained from the both FR methods has to be corrected, by using the Darken Equation (74), to obtain the so-called corrected diffusion coefficient which is taken to be the self-diffusion coefficient Do: Do = D(dlnq~81n p~) r
(74)
where q is the amount absorbed at the equilibrium pressure, Pe.
4. RESULTS AND DICUSSION 4.1. Diffusivity Measurements in Microporous Crystals The FR method has been widely used over the past ten years to measure diffusivities of many different sorbates in various zeolites, e.g. Kr-mordenite [1], Kr-, Xe-, ethane-, and propane-5A [ 13,30], n-alkanes-silicalite- 1[5,6,25,31-34], Xe-silicalite- 1[35], aromatics-MFI [36-40] and -NaX [36], n-alkanes-NaX [41], and CO2-theta-1 [24], etc.. The dynamics of various smface phenomena have recently been reviewed by Yasuda [2] who was the first to use the method. Earlier studies on the diffusivities of hydrocarbons in silicalite-1 [5,6,25,42,43] indicated
159 0.3 (c-l) T=348K P=l.0Torr 0.2
1.2 0.9
(a-l) T=303K P=1.0Torr
(b-l) T-303K P=l.0Torr
0.6
O0~'uno~omu'ID~
.o~ooo~ 0.1
0.3 0.0
0.4
(a-2) T=303K P=4.0Torr
(b-2) T=303K P=4.0Torr
0.0 (c-2) T=348K P=3.0Torr 0.2
O~
0.1
0.2
0.0
~ (a-3) ~ T = 3 2 3 K
~
(c-3) T=363K
0.0
0.2
0.0
(b-3) T=323K
' 0.0 (c-4) T=363K P=6.0Torr 0.2
oooo,~,~
(a-4) ~ T=323K ,.N%oo Torr . _ _ _ _ ~ ~ .
.
.
.
.
(b-4) T=323K P=4.0Torr
9. ~ , ~
0.1
. . . . . .~
0.1
-,.. 0"~.01.... I)i1 .......i ..... "i"O" "'()'i01
% 0.1
1
10
0.01~.1
1
10
108"0
Frequency / Hz Fig. 13. Fits of the experimental in-phase K6m (r-I) and out-of-phase K6o~ (O) characteristic functions for propane diffusion in silicalite-1 by (a) non-isothermal diffusion model, (b) two independent diffusion processes model, and (c) single-diffusion model with the parameters in Tables 1 and 2.
Table 1
FR parameters of propane in silicalite-1 derived by two different models Non-isothermal diffusion model
T
P
Kuo
K
DoXlO'
(K) (Tom) 303
323
(rn's-')
td
(s)
th
h
(s) (W/m*K)
Y
Two diffusion processes model
-AH
Ki
K2
K
DoiXlO' D o z ~ l O ' ~t d i
K2
Id2
~
(kJ/mol)
Kl
+
K2
(m2s-'> (rn2s-'>
(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 <0.01 "Diffusion coefficients related to "one diffusion process or to the faster diffusion process; bDiffusion coefficients related to the slower diffusion process. . . . . . .
,
. ,,
.
t
.
,
|
,
,
ii
,.
'
"
i
predicting that molecules can readily overcome conformational energy barriers and this enables them to explore the entire zeolite channel system As temperature decreases, it is difficult for the molecules with longer chain-length to lose their conformational 'memory' quickly, meaning that molecules aligned along a particular channel will tend to move along that channel at lower loadings. The FR data, therefore, developed bimodal behaviour. When the loading increases the interactions between molecules increase, which increases the interference between the two flux in the two channels, suggesting that a firfite-rate mass exchange between the two channels could be observed. The FR data, therefore, showed a more complicated behaviour which cannot be well fitted by the models above [see (a,3), (b,3) and (c,3)]. When the loading was even higher, however, a simple FR spectrum returned representing diffusion only in the straight channels. The very slow diffusion (or even stationary) molecules in the sinusoidal channels of silicalite-1 due to the greater pore wall-adsorbate molecule and adsorbate-adsorbate interactions are not observed in this spectrum because the response is outside the frequency window. An increase in the intrusion between the two fluxes in the straight and the sinusoidal channels, respectively, must be present. K values derived from the FR data fits would then become much smaller than those calculated from the isotherms, K~o, at high loadings as illustrated in Figure 24 since only the part of the total sorbate loading resulting from the diffusion in the straight channels is observed. The arguments above are in good agreement with the results derived from simulation calculations [48,55].
170
0.6
, ~~0 4 "
\ \ .~
(a) P=O.5rorr o T=423K ~
"t3 E
o. \
o.2---
0.10E~ .................~ 1 9 -30.01 0.1
,1.2
(b) | P=O.5rorr} T=398K 10 8
~'0
......................... --'P,~-~-,~ n0 0.1 1 10 100"
1E-30.01
Frequency / Hz Fig. 22. Experimental FR spectra of cyclohexane (a) and cis-l,4-dimethylcyclohexane (b) in silicalite-1 of cubic shape crystals (4• lam3. Symbols (r'i,O) present in-phase and out-of-phase characteristic function data, respectively. The gap between the in-phase and out-of-phase characteristic functions shown in some cases in Figure 23 [see (a.4), (b,4) and (c,2) for examples] may be associated with a rapid adsorption/desorption process taking place in these systems. The chain-length dependence of the corrected diffusion coefficients measured by the FR method is illustrated in Figure 25 accompanied with the results obtained from other methods [44,48,56-58]. A good agreement has been found, indicating the validity of the FR technique. The diffusion coefficients of molecules in the sinusoidal channels where two independent diffusion processes apply are about one order of magnitude smaller than those in the straight channels. The activation energies for the diffusion of propane to n-hexane in silicalite-1 (related to the straight channels for anisotropic diffusivities) have been calculated from the Arrhenius plot of the diffusion coefficients measured by the FR method and are listed in Table 7. It is noted that these values are nearly a factor of two or three larger than those obtained from the PFG NMR technique. The discrepancies may be ascribed to the fact that the activation energies obtained from the latter method are based on the average values of the diffusivities of d~t molecules in the three crystalline directions, while the results derived from the FR technique is only associated with the diffusion coetticiems in the transport channels (in the straight channels for anisotropic diffusivities). The increase in E, with chain length as found by the FR technique is in agreement with the corresponding increase in the heat of adsorption with chain length. It is difficult to accept the very small constant E, values found by the NMR method independent of chain length. The experimental results [38,40,59,60] of p-xylene/silicalite-1 system also show deviations of the sorption kinetics from Fiekian behaviour. These results have been interpreted using the diffusion-rearrangemem model discussed above [59,60] but it is difficult to imagine that the long and rigid p-xylene molecules can rotate at eharmel intersection (as discussed above). The findings and conclusions of the above p-xylene/silicalite-1 FR studies can, however, easily be explained by the two diffusion processes model. If the p-xylene molecules diffuse as two "independent" fluxes in the straight and sinusoidal channel networks of silicalite-1 and the diff~sivity and fraction of molecules diffusing in the straight channels is greater than those in the sinusoidal channels at high loadings the molecules in the sinusoidal channels will, then, tend
171 0.4
0.3:
(a,1)
T=398K P'-1.0Torr
0.3
---
(b,1) T=450K P=1.0Torr
0.2;
(c,1) T=473K 0.2 P=1.0Torr
=-
.
0.2
nt:j 0.1
0.1 0.0 1
.
2
~
0.8
T=__314gKorr
~q=l.0m/uc
0.0 (c,2) T=423K P=4.0Torr 0.3 q=0.38m/uc 0.2
(b,2) T=423K P=l.0Torr q=0.25m/u(
9 f
"o t--
~
(a,3)
% 2.0 ~
T=323K e=l.0morr
1.5
~
. ~ " ~
~
.
,
, .~l
0.1 .
.
.
" i;;;~ i T=373K P=l.0Torr
="
.
.
.
.
.
.
.
.
.,
":
--
~c,a~ o.o T=373K P=l.0Torr 0.6
L
1.0
0.4
~
0.5
0.2
0.0 ................................. (a,4) T=323K o. 15 ~ P=8.0Torr '= . 0.10
.
T=273K P=l.0Torr 0.06 q=8.51m/uc 0.04
0.05
~
0.02
~176
o.1
1
~o
~oo
9 []
ol
(b,4)
]
.......................
T=303K P=l.5Torr q=7.75m/uc.
o.1 ....... i ..... l b ' t i i 0 1
o.1
1
0.0
(c,4)t
lo
1
.oo
Frequency / Hz
Fig. 23. Fits of experimental in-phase KSin (r'l) and out-of-phase KSout (O) characteristic functions of n-butane (a), n-pentane (b) and n-hexane (c) in silicalite-1 by the single diffusion process mode for (a,1), (b,1), (c,1) and (c,4), the non-isothermal diffusion model for (a,2), (a,3) and (b,2), the two independent diffusion processes model for (b,3), (c,2) and (c,3), and the diffusion-rearrangement model for (a,4) and (b,4).
172
0.4
10 -7
0.3
10-8
oo
%
0.2I0
10 -9
o
0.1
oo
10 -10
oo 9
0.0
.,,
.
. , , ~
.
8
10-11
.
1
nm/m(u.c.) l
,
2
,
,
3
.
~
4
.
.
.
5
.
.
6
Nmflaer of Carbon Atorm Fig. 24. Concentration dependence of the deviations of K values derived from the fits of the FR spectra of n-butane in silicalite-1 from those calculated from the isotherms, K,,o to be trapped waiting for the traffic light to change to green i.e. awaiting a vacancy in the channel intersection to
Fig. 25. Chain-length dependence of the self-diffusion coefficients of the n-alkane in silicalite-1 at 303K at ca. seven molecules per unit cell derived from the FR [32-34] technique ( - - O ~ ) compared with the results measured by PFG NMR [44] at 298K and four molecules per unit cell ( - - O - - ) , QENS [56-58] (--A--) and molecular dynamic calculation [48]
(---+-).
occur.
Table 7 Activation energies derived from the FR method compared with those obtained from PFG M R [44] Sorbates Propane n-Butane n-Pentane n-Hexane
E. (FR) (kJ/mol) . . . . 15.g:k-O.7 18.6~0.7 21.0~:1.0 21.?+2.1
E~ (NMR) (kJ/mol) 7.1 7.5 8.3 8.5
,
In Figure 26 the intracrystaUine self-diffusivities of benzene and p-xylene in silicalite-1 and 2 are plotted as a function of temperature. The activation energy for p-xylene diffusing in the straight channels of silicalite-1 and in the channels of silicalite-2 is 20.3 kJ/mol. This agreement is further confirmation of the assmnption that the faster p-xylene diffusion process in silicalite-1 represents diffusion down the straight channels of this zeolite. The diffusion of p-xylene in the sinusoidal channels of silicalite-1 involves a much larger activation energy of 35.1 kJ/mol. The
173
(a)
10 -1~ Ea--20.3 kJ/mol 10-11
0.2'
~
",~
Ea=35.1 kJ/mol 0.1
10 "12
~o
~ 7 . l k J / m o 10" 1
1
Ea=26.2 kJ/mol
O A |0 -l 0 V [] 10-15 . . . . 2.2 2.3
p-xylene/silicalite- 1(s) p-xylene/silicalite- 1(z) p-xylene/silicalite-2 benzene/silicalite-2 benzene/silicalite-1 ~ .... , .. , . , 2.4 2.5 2.6 2.7 2.8 2.9
1000K/T
Fig. 26. Temperature dependence of selfdiffusion coefficients of benzene and pxylene in silicalites 1 and 2 at a low coverage of N1 m/u.c.. (s) and (z) represent the straight and the sinusoidal channels respectively.
0.0
~ ' " N 2 ~
.
.
.
.
.
.
..................
.
.
.
.
.
.
.
.
.
.
]
I
(b) S~ 0.2
0.1
sz~ 0.0
0.01
0.1
1
10
100
Frequency / Hz Fig. 27. FR response curves of CO2 dit~sion in silicalite-1 at 273K and 2.0Torr. (a) The fundamental frequency response data; (b) the first (l,El), third (O,O), fifth (~,0), seventh (V,V) and ninth (&,A) harmonic frequency data fitted by the theoretical model (lines) with D=2.5x 10-9m2s-1 and K=0.27.
activation energy for benzene diffusion in silicalite-1 and 2 are the same within the experimental error, at 26-27 kJ/mol, which supports the suggestion that benzene tends to diffuse in both the straight and the sinusoidal channels of silicalite-1 with a identical di~sivity. The faster diffusion and lower activation energy of p-xylene compared with benzene in silicalite-2 suggests that the methyl groups in p-xylene (i) reduce the height of the barrier that the molecule has to overcome in a diffusion step compared to the barrier encountered by benzene and (ii) decrease the rotational freedom of p-xylene so that the jump step involves a smaller entropic factor in the case of p-xylene compared with benzene. The FR measurements of fast rate kinetic processes require very large crystals or high frequencies. As mentioned in the data analysis section (2.2) the higher harmonic (n> 1, where n is an odd number) Fourier transformation, however, can be used to extended the experimental frequency range by a factor of n when high quality response data can be obtained. Figure 27 (a) shows the fundamental frequency response curves of CO2 diffusion in silicalite-1 at 273 K and 2 Torr equilibrium pressure. It can be seen that the frequency range scanned for this fast diffusion process was not wide enough to cover the full range of the response curves. Only the left hand side of the response curves was obtained. Higher harmonic Fourier transforms are therefore necessary to derived data points above the highest experimental frequency of 10Hz. Figure 27 (b) presents the third, fifth, seventh and ninth
174
harmonic frequency response spectra of the same raw data superimposed on the fundamental points. It can be seen that these higher harmonic data repeat well the fundamental data at frequencies below 10Hz and the full range of response curves can now be covered. An excellent agreement between these higher harmonic data points and the theoretical lines fitted using a single diffuison model can be observed. These higher harmonic Fourier transforms widen the dynamic timescales that can be followed by the FR method from 0.1-1000s to 0.011000s. The diffusivities of N2, CO and CO2 in theta-1 zeolite have been studied using the FR technique [24]. A single-file diffusion mechanism [61,62] has been used to described the mass transfer in these system. Intersections of the in-phase characteristic function over the out-ofphase characteristic function were observed as illustrated in Figure 28. The FR experimental data can be well fitted by the diffusion with surface-resistance model discussed in section 3.1.5 with the parameters given in Table 8. The intersections indicate the presence of a surface resistance on the external surfaces of theta-1 associated with the diffusion process. The intersected area depends on the ratio of the rate constants between surface resistance and diffusion processes, which is defined by the parameter ~ in Equation (40). A large value Table 8 FR parameters of N2, CO, and CO2 diffusion in theta-1 ii
Sorbate N2 CO CO2
a K, so is
i i ii
ii
T/K
P/Torr
245 195 273 298 323 348
5 2 2 2 2 2
Dox
101~ 4.9 1.5 1.5 2.4 2.9 4.0
,,.
"l
"'
"
k-A/s "1
K
K / K , so
'471 45 60 150 450 626
0'155 0.56 0.87 0.44 0.22 0.11
--1.03 1.33 1.3 --
the c0nstant calculated from the isotherms of C()2.
1.0
o.s
=
~,
0.0
.
.
.
(r
0.5
tO.3 0.2 0.1
.
(d)
!o.o
o.,
o.,o
0.1
o.o5
0.01
O.C
.
0.1 .
.
i
.
0.01 .
0.1
11.8 3.8 5.0 7.5 19.2 18.9
10.4
~
.
-
.....
. . . . . .
(a) ( b . ~ )
., 0 . 6 ~ ~ , , ~ _ o = 0.4 0.2
a
1
10
.
Froquency / I-Iz
Fig. 28. FR experimental data (I-I,O) of CO2 diffusion in 0.4g theta-1 at 2.0Torr and temperatures of 273 (a), 298 (b), 323 (c) and 348K (d) fitted by Equations (17), (18), (36) and (37) (lines) with the parameters in Table 8 [24].
175
I
O.4
{a) | t
O.3
0.2- "r'a aa 0.1 0.0
d
+,9~
................
(a)
O2
0.0
,0 . . . . . . . . . . . . . . . . . . . . .
0.3
(c)
0-2f "aaaaa * 0"11
0.0"0.01
ooO*~176176176 o. +..._., O9OOOOll q 0.1
1
1o
Frequency / I-Iz
corresponds to small 'skin' effects. The decrease of ~:from ca. 19 to 5 with decreasing temperature from 348 to 273K implies a strong external surface resistance to intracrystalline diffusion at low temperatures, i.e. the 'skin' effect has a strong temperature dependence. The behaviour of a binary gas mixture in a microporous adsorbent represents an important field of work with respect to both its theoretical foundations and its possibilities of practical application in separation and conversion processes. The FR technique can also be used to investigate the adsorption and diffusion properties for such a system. Some measurements, e.g. N2+O2 mixture adsorbed in 4A zeolite [63] and p-xylene + benzene vaporous gas mixture in silicalite-1 [39], have shown that the FR method can provide some additional interesting results.
4.2. Diffusivity Measurements in Bidispersed Porous Pellets Studies on the mass transport of sorbates in bidispersed porous solid materials, exhibiting macro- or meso-pores between crystals and micropores inside the crystals, is essential and practical in obtaining a better understanding of the separation and catalytic processes involved in such systems. Such systems have not, however, been studied in depth. As discussed in section 3.1.6, the frequency response technique provides a realistic way to investigate the dynamics processes taking place in such biporous systems. Like the situation for the systems including only microporous crystals (see 4.1.), the major difficulty in the application of the FR method is that the rate spectra or the FR spectra are not always uniquely defined and there are generally several combination of parameters, i.e. several theoretical models, which could produce virtually the same amplitude ratio / frequency or phase lag / frequency relationships. This difficulty can be, nevertheless, tackled by investigating the systems over a range of reasonable or possible parameter values, e.g. variation of particle size or temperatures. Several sorbates such as carbon dioxide, isobutane, propane and ammonia have been used to study the dynamics processes occurring in commercial pellets or pellets pressed from crystal powder using the FR technique [64-66]. Figure 29 [64] shows the significant difference in response behaviour for isobutane in 13X crystal powder and pellet. The diffusion of isobutane in X zeolites is expected to be very fast and this is clearly demonstrated by the response signals at high frequencies as presented in Figure 29 (a) and (b). A simple micropore diffusion model (see 3.1.1) can be used to fit the response curves in Figure 29 (a) which were obtained using larger laboratory-synthesised NaX crystals of 50 ~tm in diameter. The diffusivity of isobutane in
Fig. 29. FR Characteristic functions KSin (!'-I) and K6out ( O ) of isobutane diffusion in (a) 54mg laboratorysynthesised NaX, (b) 52mg Lancaster 13X and (c) 57mg Lancaster 13X pellets (R=0.30mm) at 423K.
176
this X zeolite sample at 423K and 1 Torr derived from the FR data is 6.9x 109m2s"1 which is in reasonable agreement with the PFG NMR value. While it is difficult to 0.3 deduce the diffusivity of isobutane in the commercial 13X crystal powder from the 0.2 FR spectrum shown in Figure 29 (b) because the crystal size of 1.2~tm is too 0.1 small to develop the full response curves within the scanned frequency range of 0.0 0.00 0.20 0.05 0.10 0.15 0.01-10Hz. R2/mm ~' The response data for the diffusion of Fig. 30. Pellet size dependence of macropore isobutane in the commercial 13X pellet diffusion time constant for isobutane diffusion under the same conditions as those for in 13X pellets (121) and CO2 diffusion in 5A pure crystals are presented in Figure 29 pellets (O) at 423K obtained using model 3 in (c). The response peak of the out-ofsection 3.1.6 phase characteristic function for this system appears at a frequency more than three orders of magnitude lower than that in the commercial 13X crystals and the spectra reflects a diffusion process, which has been attributed to macropore diffusion between crystals, with a very small surface resistance. The m a c r o - d ~ i v i t y of 2.2x 10-7m2s "l w a s derived from the theoretical fitting to the experimental data using model 3 in section 3.1.6. The pellet size dependence of the diffusion time constants of isobutane within the 13X pellets illustrated in Figure 30 exhibits further evidence that the response curves for the 13X pellet system result '
i
I
,,
i
1.0
0.8
(b)
(c)
(el
(f)
0.6 cT M .~9
0.2
~ o . o i..................
,~
(a)
0.4' 0.3'
0.2.
0.1, 0.0 0.01 0.1
1
100.01 0.1
1
100.01 0.1
I
10
Frequency / Hz Fig. 31. FR characteristic functions K~Si,(1"1) and K~5o=(O) ofisobutane (a,b,c) and CO2 (d,e,f) in 55mg of Lancaster (a,d), Ajka (b,e) and Linde (c,f) industrial 13X pellets (R=0.3mm) at 373K. Lines are fits using model 3 in section 3.1.6.
177 0.6 (a,2) 0.6 0.4 0.4 0.2
0.2
0.0
~
.
0
.
2 g
0 (b,2) t0.6
0.4 0.4 -
0.2
0.2
0.0
0.0 (c,3) 0.6
(a,3) i 0.4
0.4 0.2 84 0.0 0.01 0.1
0.2
1
10 0.01 0.1
1
10
0.0 100
Frequency / Hz Fig. 32. FR characteristic functions K6,, (UI) and K6o~ (O) for CO2 (1) and propane (2) at 373K and 4Torr in 4A (a), 5A (b) and 13X (c) zeolite pellets (ca. 100mg for COz and 200mg for propane) fitted using model 3 in section 3.1.6.
from macropore diffusion rather than micropore diffusion. The intercrystalline diffusion coefficient, Dp, Can be calculated from the slope of the linear plot to be ca. 5x 10.7 m2s~ for the isobutane/13X pellet system. The diffusion in the mesopore to macropore range is generally considered as Knudsen diffusion which can be estimated by [67]
Dx = 9 7 . 0 r ~
(76)
where DK is the Knudsen diff~ivity, r is the pore radius, T the temperature and M is the molecular weight of the sorbate. The Knudsen dii~sivity has to be corrected by an empirical tortuosity factor, r, and the porosity, ep, to get the diffusivity in a random ,pore network [67].
Dp = •pD K/r
(77)
The diffusion coefficient of isobutane in the mesopores of 13X pellets calculated from Equations (76) and (77) at 423K is 3.9x10 7 m2s~ which is very close to the value determined by the FR method. The difference in the response behaviour for isobutane and CO2 in 13X pellets from different manufacturers can be clearly seen in Figure 31. No intersection of the two characteristic functions for Linde 13X pellets but a significant intersection for the Lancaster 13X pellets can be observed, which may be ascribed to the effect of the different preparation processes or binder materials used for producing the pellets. These studies are quite useful in assessing catalysts and sorbents for reaction and separation processes. The FR studies on the mass transport behaviour of carbon dioxide, propane and ammonia in 4A, 5A and 13X commercial pellets [66] (see Figure 32 and 33) showed similar results to those for isobutane/13X pellet system, i.e. macropore diffusion with a surface resistance is the rate-controlling step for these systems, with an exception that the FR signals of propane in 4A
178
1.2 (a,1)
(a,2)
%
'
0 . 6 % Rh/TIO 2
0.8 s9 ~
t
0.4
"~o "--a,
- ' " "r
1% Rh/SIO
c
0.0 ~
#
\
C
-~-
o
.,
e
o
I
u
-1
I
_
I
I
I
I I
C
(b,2)
(b,1)
q. . . . 2
= I&. o.s
'\\
=
t: =. o m
'~-~y
1
0.4 " ~1
.t . -~
.
.
.
\ ~~
(c,1)
-
.
o.o
~ "~
I
Rh - u/'no 2
I
I
(c,2) 0.8 ~
~
. . . . .
._-"
. . . . .
I
..
...
I
....
. ._...._
I
I
I I
0.4
\ 0
0.01
'
0.1
..
1
"~
10
0.01
........................
0.1
1
0.0
10
100
Frequency / Hz Fig. 33. FR characteristic functions K6m (El) and K6o= (O) for ammonia at 373K and 1Torr in ca. 30mg well-dispersed crystal powder (1) and pellets (2) of4A (a), 5A (b) and 13X (c). Lines are fits of the theoretical models.
9
10-=
" 9' " I
,
10-~
9.-,-i
10 ~
" " "'"r
...... I
101
10 =
Frequency (rad./sec.)
Fig. 34. FR spectra containing outof-phase characteristic function for the chemisorption of H2 on supported rhodium at 533K and 0.5Torr.
pellets were too small to be detected. This very small latter signal arises from the lack of sorption of propane in the micropores of zeolite 4A. Propane cannot diffuse through the 8-ring windows which contain N d cations in the 4A form and reduce the free diameter of the window to ~ 4 A which is too small to allow the ingress of propane molecules. The isotherms for propane in 4A pellets show only very small sorption of propane in the micropores and, thus, the FR signal is too small to be detected. The ditfusion time constants via the square of the pellet size all presented linear relationship analogous to the plot in Figure 30. Ammonia, which possesses a large dipole moment, has been used extensively as a probe molecule for the characterisation of both Lewis and Bronsted acidic sites. Figure 33 shows the significant difference in the FR data between ammonia in zeolite crystals and in pellets. The FR spectra of ammonia in zeolite crystals demonstrated that the ammonia adsorption on different acidic sites in the crystals eomrols the overall dynamics processes occurring in the systems,
179
373K
1.0
A
0'
F
t
0.0 ~
j
8Z~
1.0
t
" - ~ - - - : - - : : - : ~ 0.0 773K 1.0
1.0-
E 0.5
0.5 .....
ODOr, ~
On
....
OOC~DC~D-!
0.0 723K 1.0
0.0 1.0[]
n
0.5
0.5
.....
........
........
.....
~
Fmqte~ / I-Iz
Fig. 35. FR spectra of ammonia in ca. 50mg H-ZSM-5 zeolite with Si/A1 ratio of 34 at 1Torr and temperatures shown above fitted using the adsorption model described in Equations (64) and (65). while in the case of pellets, the rate-controlling step was found to be macropore dit~sion with (Figure 33 (a,2) and (b,2)) or without (Figure 33 (c,2)) surface resistances. It has been found that micropore di~sion dominates the overall kinetic processes for the system with charcoal pellets as sorbent. More detailed investigations of these systems are being carried out. The FR spectra when both micro- and macropore diffusion processes are rate-controlling in systems involving dispersed biporous structure solid materials has not been observed as yet. But it should be possible to do so by adjusting crystal and pellet sizes, i.e. y value in Equation (47). 4.3. Characterisation of Acid Sites
Naphtali and Polinski [68,69] first demonstrated the utility of the FR method on the studies of chemisorption for a H2/supported-Ni system. Yasuda [2,3,27] further developed the technique. Marcelin et al. and Li et al. [70-72] applied this method to study hydrogen chemisorption on supported rhodium catalysts. Some FR spectra involving several kinetically distinct chemisorption sites are presented in Figure 34. Onyestyak and Rees et al. [73-77]
180
,
l"i
/O
,\
15D B 2"3ZX ~ -
:=,"1
O
340C
ZX
57vD_
o
U 9" ~ . v " v
' ',~ []
Tom~mture / K Fig. 36. Temperature dependence of the FR intensities at 1Torr for ammonia in 50mg H-ZSM-5 zeolites with Si/A1 ratios of (A)15 (Z15), (B) 23 (Z23), (C) 34 (Z34) and (D) 57 (Z57). Solid symbols (O) represent the value obtained as 5 times the gradient ( in units of mmols-lTorr' ) of the isotherms of sample C at the same pressure.
extended the FR technique to the studies on characterisation of acid sites existing in different kinds of zeolites by using ammonia as a probe molecule. Figure 35 [77] shows the FR characteristic functions of ammonia adsorption/desorption in H-ZSM-5 with a Si/Al ratio of 34, Z34 (see Figure 36), at the equilibrium pressure of 1 Torr and various temperatures. That adsorption is rate-controlling for these systems can be verified by the following features of the spectra; (a) the in-phase characteristic function intersects with the out-of-phase function and (b) the points of intersection locate at the maximum of the out-ofphase curves and at half of the maximum values of the step-like in-phase curves (see Figure 10). The integrated intensities of the out-of-phase function,
~(kj/k_j
), which are associated with
the gradient of the ammonia adsorption isotherms according to Equation (66), decrease with increasing temperature. When the temperature is higher than 600 K, however, an additional peak with lower frequency appears (Figure 35 C-E). The intensity of the lower frequency peak and, as a consequence, also the total intensity of the response signals increases with increasing temperature in the range of 600-700 K. If temperature is elevated further, the intensity starts to drop again. Temperature dependencies of the integrated FR intensities are presented in Figure 36 for H-ZSM-5 samples with different Si/AI ratios. Similar dependencies can be observed for all the samples and the intensities become smaller as the Si/AI ratio increases, suggesting that the total intensity corresponds to the aluminium content, which, on Table 9 FR parameters derived from the fits of the FR curves of ammonia in H-ZSM-5 zeolites presented in Figure 37 [77] ' '
Si/A1 '
/~' / Torr
k/k.j
ak.j / s
Z k/k_j
j-1
/-2
/-1
/--2
1 2 1 4 1 12 0.4 5 57 1 12 0.4 0.6 a Sorption time constant of speciesj.
40 85 72 21 75 14 i
0.40 0.05 0.28 0.70 0.16 0.22
1.15 0.65 0.35 0.73 0.18 0.31
15 23 34
1.55 0.70 0.63 1.43 0.34 0.53
181
.
.
.
81
.
k 1 _= 0 0
~
c '~~
.................... ; 0.0
0.5.
0.5
o:o.
o.o
~.0.
o.8,)I
~
o\
0.4ro.~ [---%_
0.4ro~~
10-5
0:I ....... ~ ...... 1b .... Oib~ ..... 0:~ ....... 1 ....... I'o .... i6B ~
FrequencyI Hz
Fig. 37. FR curves of ammonia in 50mg H-ZSM-5 zeolites with Si/A1 ratios of (A) 15 (Z15), (B) 23 (Z23), (C, c) 34 (Z34), and (D, d) 57 (Z57) at 723 K and an equilibrium NH3 pressure of (A-D) 1.0 and (c, d) 0.4 Torr. the other hand, is closely related to the number of acidic sites. The findings in Figures 35 and 36 are in good agreement with the results obtained from the NH3 TPD measurements for HZSM-5 zeolite [78]. At about 400 K a TPD peak associated with physical or weak chemical adsorption was observed, while the desorption maximum was seen above 600 K which was supposed to be due to the process of decomposition (Nt-I4+ r NH3 + I-V) [78]. The FR results can be, therefore, ascribed to the interactions of ammonia molecules with the strong Bronsted acid hydroxyl groups and the weak Lewis acid site NH4+ ions. In Figure 37 the FR curves of ammonia in H-ZSM-5 zeolites with different Si/A1 ratios at 723K are presented and the parameters derived from the adsorption model theoretical fitting are listed in Table 9. As expected from the discussions above for Figures 35 and 36, two response peaks in the out-of-phase curves were detected. In general, the intensity of each peak increases with increasing the A1 content. The high-frequency peak (/=2) for Z23 sample is, however, a remarkable exception which has been attributed to the higher concentration of the extraframework aluminium (EFAI) in this sample. The comparison of Figure 37 B and C implies that the acidic sorption site associated with the low-frequency FR peak is present in a larger concentration in sample Z34 than that in Z23. As mentioned above, a larger fraction of the lattice A1 is charge-compensated by positively charged extraframework aluminium (EFA1) species in sample Z23 than that in Z34, indicating that the low-frequency FR peak stems from the interaction of the sorbate ammonia with the Bronsted acidic protons of the H-ZSM zeolites. In sample Z23 only a few Bronsted protons are available for ammonia adsorption as some of the sites were removed by dealumination and some were neutralised by the
182
2
.
0
a
1.5
H-ZSM-5
A
t 2~
~~
11.5
1.0
~
o.o
I
.
.
.
.
.
.
.
.
.
.
41.0
.
.
.
.
.
.
b INa-ZSM~5
o.o ~ ' . . - : - - - - ~
c
o
.
~
o.o
B
........
....... ~ o . o
Cu-ZI~-5
C
1.5
1.5 --~1:~ 3
1.0
1.o
.
0.5 oo__ 0.1
1
1'0
0.01 011 Frequency/ Hz
~,~.~.~_0.5.~+ 1
1'0
o0
100"
Fig. 38. Ammonia responses curves for ZSM-5 samples of different cationic forms. About 50 mg of sample Z15 was studied in (a,A) H-; (b,B) Na- and (c,C) Cu-form at 1 Torr NH3 pressure at temperatures 473 K (a,b,c) and 573 K (A,B,C).
extraframework aluminium species. Figures 38 [77] and 39 [76] clearly demonstrate the effect of cations on the ammonia adsorption behaviour in zeolites Y and ZSM-5, indicating that the FR technique is a powerful one for distinguishing the different acidic sites present in microporous materials. The comparison between the results from FR and FTIR shows a good agreement on the characterisation of the acidic sites in zeolites [75-77]. By measuring the FR spectra at several equih'brium pressures, the plots of the time constant of adsorption/desorption process for adsorbate on site j, k_j, vs. pressure and ky/kj vs. k_j as presented in Figure 40 can be obtained. From the linear regression of Equations (67) and (68) all the other kinetic parameters, i.e. the rate constants for adsorption, k~j), and desorption, kdtj) , on site j and the number of sites available for adsorption o f j species, N~j) , can be derived.
183
A 4
B
o
Do
I
2
1t0 o.............................................. . . I Na-Y]~
0
.................
0
,
..............
...............................................
! ................... 0
1
1
0 .................................... c~.~..~, 0.1 1 10 0.01 0.1 I
0.01
10
.~0100
Frequency / Hz Fig. 39. FR in-phase (r'l) and out-of-phase (O) characteristic functions for ammonia adsorption/desorption in ca. 50mg of various cationic Y, FAU zeolites at 0.75Torr and temperatures (A) 523 and (B) 723K. Lines represent the theoretical fits. In addition to the measurements with ammonia, some other probe molecules such as NO, CO, CO2 and 02 were also used in FR studies of the characterisation of acid-, base- and redox-type sites in zeolites [75]. The results presented above clearly indicate that FR method has much to offer in the studies of diffusion of sorbate molecules and the characterisation of acid sites in zeolite channel networks especially when the sorbate molecule is a reasonably close fit to the channel dimensions and when the channels have interesting characteristics as those found in the silicalite framework.
184
150 100
"T, 3"
50 0
0.0
I0 -I
'
ols
'
1.'o
'
'
Pe/Torr
21o
El
O~1~ ~ - - . vo
3"
(B)
.
10-2
10-3
,
20
,
,
K_ 1 IS-1
,
,
,
,
|
100
Fig. 40. FR parameters for ammonia in H-ZSM-5 (CAZ 36) using the Langmuir model, Equations (67) (A) and (68) (B), with a slope of-2 at 373 (n), 423 (O), 473 (A), 523 (V), 573 (0) and 623K (o).
REFERENCES 1. Y. Yasuda, J. Phys. Chem., 86 (1982) 1913. 2. Y. Yasuda, Heterog. Chem. Rev., 1 (1994) 103. 3. Y. Yasuda, J. Phys. Chem., 80 (1976) 1867 4. Y. Yasuda, J. Phys. Chem., 82 (1978) 74. 5. N . G . Ven-Den-begin and L. V. C. Rees, Zeolites: Facts, Figures, Future, Studies in Surface Science and Catalysis, Eds. P. A. Jacobs and R. A. yen Santen, Elsevier, Amsterdam, 1989, Vol.49B, p.915. 6. M. Bulow, H. Schlodder, L. V. C. Rees and R. E. Richards, New Developments in Zeolites Science and Technology: Proc. of the 7th International Conference on Zeolites, Eds. Y. Murakami, A. Iijima, J. W. Ward, Elsevier, Kodansha, 1986, p.579. 7. L.V.C. Rees, Structure and Reactivity of Modified Zeolites, Studies in Surface Science and Catalysis, Eds. P. A. Jacobs, N. I. Jaeger, P. Jirfi, V. B. Kazansky and G. Schulz-Ekloff, Elsevier, Amsterdam, 1984, vol. 18, p. 1. 8. L.V.C. Rees and D. Shen, Gas Sep. & Purif., 7 (1993) 83. 9. D. Shen and L.V.C. Rees, J. Chem. Sot., Faraday Trans., 90 (1994) 3011. 10. R.G. Jordi and D. D. Do, Chem. Eng. Sci., 48 (1993) 1103.
185 11. C. C. Goodyear, Signals and Information, Butterworths, Guildford, 1971. 12. M. R. Spiegel, Fourier Analysis, McGrew-Hill, New York, 1974. 13. Y. Yasuda and G. Sugasawa, J. Catal., 88 (1984) 530. 14. R. E. Richards, Ph.D. Thesis, University of London, 1986. 15. D. Shen, Ph.D. Thesis, University of London, 1991. 16. D. Oprescu, L. V. C. Rees and D. Shen, J. Chem. Soc., Faraday Trans., 88 (1992) 2955. 17. Y. Yasuda, Y. Yamda and I. Matsuura, New Development in Zeolite Science and Technology, Proc. of the 7th International Conference on Zeolites, Eds. Y. Murakami, A. Iijima, J. W. Ward, Elsevier, Kodansha, 1986, p.587. 18. L.M. Sun and V. Bourdin, Chem. Eng. Sci., 48 (1993) 3783. 19. L.M. Sun and F. Meunier, Chem. Eng. Sci., 48 (1993) 715. 20. L.M.F. Meunier, Ph. Grenier and D. M. Ruthven, Chem. Eng. Sci., 49 (1994) 373. 21. R.G. Jordi and D. D. Do, J. Chem. Soc., Faraday Trans., 88 (1992) 2411. 22. Y. Yasuda, Y. Suztdd and H. Fukada, J. Phys. Chem., 95 (1991) 2486. 23. Y. Yasuda, Bull. Chem. Soc. Jpn., 64 (1991) 954. 24. D. Shen and L. V. C. Rees, J. Chem. Soc., Faraday Trans., 90 (1994) 3017. 25. D. Shen and L. V. C. Rees, Zeolites, 11 (1991) 684. 26. D.D. Do, Chem. Eng. Sci., 45 (1990) 1373. 27. Y. Yasuda, J. Phys. Chem., 80 (1976) 1870. 28. J. Crank, The Mathematics of Diffusion, Oxford University Press, Oxford, 1975, p.94. 29. R.M. Barrer and J. B. Craven, J. Chem. Soc., Faraday Trans. 1, 86 (1990) 545. 30. Y. Yasuda and A. Yamamoto, J. Catal., 93 (1985) 176. 31. N.G. Van-Den-Begin, L. V. C. Rees, J. Caro and M. Billow, Zeolites, 9 (1989) 287. 32. L. Song and L. V. C. Rees, Micro. Mater., 6 (1996) 363. 33. L. Song and L. V. C. Rees, J. Chem. Soc., Faraday Trans., 93 (1997) 649. 34. L. Song and L.V.C. Rees, Proc. of the 12th International Zeolite Conference, Baltimore 1998, Eds. M. M. J. Treaty, B. K. Marcus, M. E. Bisher and J. B. Higgins, Materials Research Society, Warrendale, Pennsylvania, 1999, p.67. 35. L.V.C. Rees and D. Shen, J. Chem. Soc., Faraday Trans., 86 (1990) 3687. 36. D. Shen and L. V. C. Rees, Zeolites, 11 (1991) 666. 37. D. Shen and L. V. C. Rees, J. Chem. Soc., Faraday Trans., 89 (1993) 1063. 38. D. Shen and L. V. C. Rees, J. CherrL Soc., Faraday Tram., 91 (1995) 2027. 39. D. Shen and L. V. C. Rees, Proc. of the 9th International Zeolite Conference, Montreal 1992, Eds. R. von Ballmoos, J. B. Higgins and M. M. J. Treaty, Butterw~ Boston, USA, 1993, Vol.II, p.45. 40. L. Song and L. V. C. Rees, Micro. and Meso. Mater., in press. 41. J. Giermanska-Kahn, J. Cartigny, E. C. De Lara and L. M. Sun, Zeolites, 17 (1996) 365. 42. L . V . C . Rees and D. Shen, Characterisation of Porous Solids III, Studies in Surface Science and Catalysis, Eds. J. Rouquerol, F. Rodriguez, IC S. W. Sing and K. K. Unger, Elsevier, Amsterdam, 1994, Vol. 87, p.563. 43. R.E. Richards and L. V. C. Rees, Langmuir, 3 (1987) 335. 44. W. Heink, J. Karger, H. Pfeifer, K. P. Datema and A. K. Nowak, J. Chem. Sot., Faraday Trans., 88 (1992) 3505. 45. L.V.C. Rees, P. Brilckner and J. A. Hampson, Gas Sep. Purif., 5 (1991) 67. 46. J.A. Hampson and L.V.C. Rees, J. Chem. Sot., Faraday Trans., 89 (1993) 3169. 47. E. Hernandez and C. R. A. Catlow, Proc. R. Soc. Lond. A., 448 (1995) 143.
186 48. R.C. Runnebaum and E. J. Maginn, J. Phys. Chem. B, 101 (1997) 6394. 49. J. Caro, H. Jobic, M. Bulow, J. Karger and B. Zibrowius, Ad. Catal., 39 (1993) 351. 50. R . L . Portsmouth, M. J. Duer and L. F. Gladdey, J. Cham. Soc., Faraday Trans., 91 (1995) 559. 51. H. Thamm, J. Phys. Chem., 91 (1987) 8. 52. B. Smit and T. L. M. Maesen, Nature, 734 (1995) 42. 53. A. Micke, M. Bulow, M. Kocirik and P. Struve, J. Phys. Chem., 98 (1994) 12337. 54. D.D. Do and R. G. Jordi, J. Chem. Soc., Faraday Trans., 88 (1992) 121. 55. E.J. Maginn, A. T. Bell and D. N. Theodorou, J. Phys. Chem., 100 (1996) 7155. 56. H. Jobic, M. Bee and G. J. Kearley, Zeolites, 9 (1989) 312. 57. H. Jobic, M. Bee and G. J. Kearley, Zeolites, 12 (1992) 146. 58. H. Jobic, M. Bee and G. J. Kearley, J. Phys. Chem., 98 (1994) 4660. 59. A. Micke and M. Bulow, Chem. Eng. Sci., 48 (1993) 2777. 60. M. Kocirik and A. Micke, Langmuir, 11 (1995) 3042. 61. J. Karger and D. M. Ruthven, Diffuison in Zeolites, Wiley, New York, 1992, pp.23-70, 110-116. 62. J. Karger, M. Petzold, H. Pfeifer, S. Ernst and J. Weitkamp, J. Catal., 136 (1992) 283. 63. Y. Yasuda and K. Matsumoto, J. Phys. Chem., 93 (1989) 3195. 64. G. Onyestyak, D. Shen and L . V . C . Rees, J. Chem. Soc., Faraday Trans., 91 (1995) 1399. 65. G. Onyestyak, D. Shen and L.V.C. Rees, Micro. Mater., 5 (1996) 279. 66. G. Onyestyak and L.V.C. Rees, J. Phys. Chem., in press. 67. J. Karger and D. M. Ruthven, Diffusion in Zeolites and Other Microporous Solids, Wiley, New York, 1992. 68. L.M. Naphtali and L. M. Polinski, J. Phys. Chem., 67 (1963) 369. 69. L.M. Polinski and L. M. Naphtali, Adv. Catal., 19 (1969) 241. 70. G. Marcelin and J. E. Lester, React. Kinet. Catal. Lett., 28 (1985) 281. 71. G. Marcelin, J. E. Lester and S. F. Mitchell, J. Catal., 102 (1986) 240. 72. Y. Li, D. Willcox and R. D. Gonzalez, AIChE Journal, 35 (1989) 423. 73. G. Onyestyak, D. Shen and L.V.C. Rees, Catalysis by Microporous Materials, Studies in Surface Science and Catalysis, Eds. H. K. Beyer, H. G. Karger and J. B. Nagy, Elsevier Science B. V., Amsterdam, 1995, Vol.94, p. 116. 74. G. Onyestyak, D. Shen and L.V.C. Rees, J. Chem. Soc., Faraday Trans., 92 (1996) 307. 75. G. Onyestyak, J. Valyon and L.V.C. Rees, Proc. of the 1l th International Zeolite Conference (Seoul 1997), Studies in Surface Science and Catalysis, Eds. H. Chon, S.-K. Ihm and Y. S. Uh, Elsevier, Amsterdam, 1994, Vol. 105A, p.703. 76. L.V.C. Rees and G. Onyestyak, Micro. and Meso. Mater., 28 (1999) 293. 77. J. Valyon, G. Onyestyak and L.V.C. Rees, J. Phys. Chem. B, 102 (1998) 8994. 78. B.M. Lok, B. K. Marcus and C. L. Angell, Zeolites, 6 (1986) 185.
RecentAdvances in Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) e 2000 ElsevierScienceB.V. All rightsreserved.
187
M e a s u r e m e n t o f Diffusion in Porous Solids by Zero L e n g t h C o l u m n (ZLC) Methods D o u g l a s M. R u t h v e n (a) and Stefano B r a n d a n i (b) (a) Department
of Chemical Engineering, University of Maine, Jenness Hall, Orono, ME
04469-5737 (b)
Department of Chemical Engineering, University College London, Torrington Place London WC 1E 7JE, UK
The measurement of diffusion in zeolite crystals and pellets by the Zero Length Column (ZLC) method is reviewed, including the extension of this technique to selfdiffusion, counter-diffusion and liquid phase measurements. 1. INTRODUCTION Measurement of diffusion in microporous solids has proved to be a much more challenging task than might have been anticipated. Many of the microporous materials of interest, such as zeolites, are available only as rather small (micron sized) crystals and this precludes the application of Wicke-Kallenbach and most other quasi-steady-state methods. Transient measurement of adsorption/desorption rates under carefully controlled conditions provides the most obvious approach to the measurement of intracrystalline (or intraparticle) diffusion but, except for slow systems, such measurements are prone to the intrusion of thermal effects and external resistances to mass transfer. The "Zero Length Column" (ZLC) method, which can be considered either as the limiting case of a chromatographic experiment for a very short column or as the limiting case of a desorption rate measurement in a flow system, was developed in order to minimize such problems. In the basic ZLC experiment a small sample of the adsorbent (typically - 1 mg) is equilibrated with an inert carrier gas stream containing a small concentration of an adsorbable component. At time zero the flow is switched to a pure carrier stream and the effluent concentration of the adsorbable component is monitored using an appropriate detector. The diffusivity (or more correctly the diffusional time constant R2/D) is determined by matching the experimental response curve to the dimensionless theoretical curve derived from the appropriate solution of the Fickian diffusion equation. The basic experiment measures the limiting transport diffusivity at low loading (see section 2). Simple variants of this experiment allow the technique to be extended to the measurement of (tracer) self-diffusion and counter-diffusion in a binary system. Although, for a linear system, adsorption and desorption are symmetric processes,
188
following the desorption response offers the important practical advantage that, since the baseline concentration is zero, the tail of the desorption curve can be measured accurately over several orders of magnitude. This is not true for adsorption where the final steady state concentration is finite. 2. DEFINITIONS OF DIFFUSIVITY The distinction between "Transport" and "self-" diffusion is important since these processes are physically different and the corresponding diffusivities, although related, are generally not the same. The physical situation is shown schematically in figure 1. In transport diffusion there is a concentration gradient and the diffusivity (D) is defined in accordance with Fick's first equation:
J =-D Oq
(1)
Oz For self-diffusion we consider situation in which there is no net gradient of concentration, only a gradient in the proportion of (isotopically) marked species. The (tracer) self-diffusivity is then defined by:
Oq,
J. = - D ~ [ q
(2)
az I
I
L"'o' ' 4- 4- 4-
4-
Fo §
+
4-
§
4.0+
J" ,0., q
F~ "
!
9
,
,
? I
§
§
+
§
4-
,0,
Figure 1
9+ g o 1-
i O ~
!
. ~ § 2 4 7
'"
!
..,
Microscopic situation corresponding to measurement of (a) transport diffusion (Eq. 1); (b) tracer diffusion (Eq. 2); (c) self-diffusion (Eq. 3). From K/irger and Ruthven 0).
189 The self diffusivity may also be defined in an alternative but equivalent way based on the Einstein representation of a diffusive process as a random walk: 2,2 D . . . . (3) 2nr 2nt where n is the dimensionality (1, 2 or 3) and r 2 is the mean square displacement during time t. Since the driving force for diffusive transport is the gradient of chemical potential, rather than the concentration gradient, the basic expression for the flux (Eq. 1) should more properly be written on the basis of chemical potential as the driving force:
J = - B q -~z
(4)
where ~t = ~t~ + RT In p. Combining with the definition of diffusivity (Eq. 1) yields" d In p d In p D = BRT~ = Do d In q d In q
(5)
The quantity Do is known as the "corrected" or "limiting" diffusivity since this is the value approached by the transport diffusivity in the low concentration limit where Henry's Law is obeyed and d In p/d In q ~ 1.0. As a result of the factor d In p/d In q the transport diffusivity will generally be strongly concentration dependent. Do is also, in principle, a function of concentration but the concentration dependence is generally much less pronounced. In the low concentration limit Do should approach the self-diffusivity ( D ) . However this equivalence does not necessarily hold at higher concentrations (1). 3. THE BASIC ZLC E X P E R I M E N T : M A T H E M A T I C A L M O D E L (2)
In modelling a ZLC system we assume that the "column" is sufficiently short that there is no overall gradient of sorbate concentration through the cell. This should always be a valid approximation for a sufficiently short column since the Peclet number approaches infinity. As a result the "zero length column" can be accurately modelled as a perfectly mixed cell, greatly simplifying the mathematical representation. For an isothermal system of uniform spherical particles with a linear equilibrium isotherm the dynamic behavior of the system is described by the following set of equations(Z):
Oq=D(O2q 2c3qI -~
[,,~r 2 + rc3r )
aq (0,t)= 0; q(R,t)= Kc(t); q(r, O)= qo = Kco
-g;r
(6)
(7)
190
D Oq (R,t)+ 1 FR q(R,t)= 0 & -3~K
(8)
Equation (3) is the boundary condition at the particle surface resulting from a mass balance over the cell. The basic assumptions are equilibrium at the particle surface, perfect mixing through the cell and neglect of hold-up in the fluid phase in comparison with the adsorbed phase hold-up. The solution is readily obtained by separation of variables or directly from known solutions (Crank, 1956). The resulting expression for the desorption curve is:
expc = 2 L y ,~ Co
where
R2 )
+ L(L-1)]
..,
(9)
~n is given by the roots of:
13. cot 13. + L - 1 = 0
(1 O)
and 1 FR 2 3 XV.D
L= - ~
(11)
The corresponding expressions for a parallel sided adsorbent slab (half-thickness 1) are: ~, exp - 12 c = 2L~--'~ Co .=, [f12 + L(L + 1)] where
(12)
[~n is given by: Ft 2
fl. tan fl. = L = ~ KVsD
(13)
In the long time region Eqs. (9) and (12) reduce to simple exponential decay curves since only the first term of the summation is significant:
c__
2L
(/3~Dt)
7 7 - [f12 + L(L- 1)]exp - R 2
(14)
191
~
_
2
I
"':,. 9
. . . .
I
"
I
-
-
""'-, -.,....L=3
(a)
C/C. 0.1 "'.
9 ..o
"'--o
L- 10
9 *..
o. ~
-o.. 9...
-Oo ~
""'.... 9 9.
..o -% ".
%. oo
:
0.01
J
o
"-.,
_
~
,
0.4 . . . .
0.2
.." .... :....
o,s
0.6
T
o
,,.j,
,I
-I.5
' "
I~ ],
/~nI
'
,'1
,,i'
,41[ . . . . , I
I.,
4 -'"-,
I'1'
' '1
'
[,i
t~ I"t
,
I'
[
'
'1 I
I ~ 1'' r,l'~
,I
~ ~,' .t ~ t
~'
,
t
,
I
'1
lll!,
,
~, ~ ~ I,I
,i
~'
I
'1 I ,t . . . . ,'
I
I
..........
..t~ ' ,
~-['
,,,
,
I '
,
'
I
[,,'~111',
'!'I
i
'
I'
' i ....
"""
'
,,', 0
II
0.2
-o.~
,
0.4
I'
,
~t
,~, " ~
1
0.6
0.8
'
, [-'i,
1.2
~) ..
,
i .6
4
! .8
,I
2
,
~il
~!!f
ill
[11~tl ,I,,
1.4
!
t
.... . .... 1!'
!
: !i,. . .',ltl~,t, . -i etlt,-! -: I~ ~t , . . . . . I It' I':"~:l !I!~i!!i '~'I;:' ~:~1 tl,,;}ii,l:;'~r~-lt! '" I ~;i,,',~t '-~t
"
::
'~ ' ;I]:]: .~i: I ' : ~',, ~ ,..?~ 1 ~=' i ' ' ', I ,~,~~,,,i,~1:!
, , I t, ~. I , II' ,,:l,l
,
,
I ~ ' ~" ' I I' I' I [ ;! l~''~!,itl:i'~N~
2.2
,
2.4
i1!
2.6
2.11
3
3.2
:3.4
~ I
I
3.6
I
,l
} ,1
(c)
dnI
'., -,.,
t,lt t~,, t._
~il i~ii! ~i!!1
]il}ii!il)iiiiiiLi!l!ii?il
0
10
20
30
410
50
60
70
80
90
100
..
I I0
;It 120
t,[ 130
140
L Fig. 2. (a) Theoretical ZLC response curves calculated from Eq. 12 (b) and (c) Variation of intercept (I) of the long time asymptote with parameters 13~and L (Eq. 10 and 12).
192 with a corresponding expression for the parallel sided slab. A plot of in In (C/Co) vs. t should therefore yield a linear asymptote, in the long time region, from the slope and intercept of which the parameters D and L can be found. This is the basic model which is generally used to extract the diffusional time constant from the ZLC response. Representative theoretical curves showing the variation of C/Cowith dimensionless time for various values of L are shown in figure 2a while the relationship between the intercept of the asymptote (I) and the values of L and 131 is shown in figure 2b. It is in principle possible to extract both the kinetic and equilibrium parameters (D/R 2 and KVs) from analysis of a single ZLC response curve provided that the value of L is large enough (L > 5) to render the fit unambiguous. However, to ensure validity of the model replicate measurements performed at at least two different purge flow rates, as well as a blank run and some other experimental checks discussed below, are desirable. 3.1 External Mass Transfer Resistance The model represented by Eqns. 6-8 assumes instantaneous equilibration at the external surface of the adsorbent particle, i.e. no external resistance to mass transfer. It is however a straightforward matter to extend the analysis to allow for external mass transfer resistance (3). The final expressions for the desorption curve remain the same but with a modified value for the parameter L given by:
I=KDI3V ~ 2 ] -[ L FR ~ + Sh-D.
(15)
where the Sherwood Number is defined by:
Sh = kc2R Dm 3.2 Short Time Analysis (2) The initial portion of the ZLC response curve is less sensitive than region to errors that may arise from baseline drift, particle size distribution rate of heat dissipation. Rather than relying entirely on the long time therefore sometimes desirable also to extract parameters from the initial response curve. A detailed analysis shows that the simple expression:
c = 1 - 2 L J . Dt Co ~l rcR2
(16)
the long time and the finite analysis it is region of the
(17)
provides a good approximation to the initial region of the response curve. This equation suggests the use of a plot of (1-c/Co)VSx[t as a way to extract the diffusional time constant. However, such a plot is quite sensitive to error in the zero time. A more useful
193
approach is a plot of (1- c / c o )/~/-tvs x/-[ which is practically linear and may therefore be easily extrapolated to determine the time zero intercept (2L~/D/zcR 2 ) from which the time constant (R2/D) is found directly (see fig. 3). In the intermediate time region the response curve varies with 1/~-"
Spherical particle:
One-Dimensional Model:
z
co
-1
L
c--lIl2_ Co
L
(18)
zcDt
A plot of C/Co vs 1/xft- therefore passes through the origin for the one-dimensional case but yields a finite intercept for a spherical particle. This approach has been used by Cavalcante et al. (4) to identify the main diffusion path in various intergrowths of erionite and offretite.
3.3 Equilibrium Control Convergence to the linear asymptote represented by Eqs. 12 or 14 occurs at a measurable concentration level only when the parameter L is relatively large. For small values of L the system becomes controlled by adsorption equilibrium and the response curve contains no kinetic information. For L --> 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 <
Z~ / Ryco
(24)
For a helium carrier at atmospheric pressure
Zg/Rc o ~_4.4(T/300)lS(cm2" s -1) so
the
criterion becomes" 2
KoD<4.4( T ~15 y \-~)
(cm2"s-1)
(25)
It is evident that whether or not heat effects are significant depends mainly on the basic system properties (K, D, AH). Variables such as crystal size, purge flow rate, sample volume etc. affect both heat transfer and diffusion equally, so they have no influence on the relative importance of heat and mass transfer resistances. The only significant variables that can be selected arbitrarily are temperature and sorbate mole fraction (y). Varying the sorbate concentration level in the feed gas thus provides a convenient experimental way to confirm the absence of a significant heat effect in a ZLC experiment. The criterion for isothermolity is normally easily satisfied for weakly adsorbed species (eg N2-5A) but may be violated for strongly adsorbed species at low temperature and for macropore controlled systems for which high values of K.D are possible.
200 Table 1 Validity of Isothermal Criterion in ZLC Experiments System
T(K)
(KoD)max Ko
D
KD
Benzene-NaX
350 400 500
0.81 1.3 2.9
1.2xl 08 5x10 6 5.2x104
1.5x10 -8 4x10 -8 2x10 "7
1.8 0.20 0.01
p-Xylene-NaX
350 400 500
0.63 1.0 2.2
1.2x10 l~ 2.5x108 1.1xl06
8 x 1 0 "10
2.2x10 9 1.1xl0 8
9.6 0.55 0.012
300 300
5.2 5.2
35 22
10-6 6x10 4
3.5xl 0-5 0.013
N2-5A (crystals) N2-5A (pellets)
K values are dimensionless; D is in cm2.s "l (KD)max is estimated from the right hand side of Eq. 25 assuming y = 0.01.
4.2 Equilibration Time t2) In the analysis of ZLC response curves it is implicitly assumed that the adsorbent is initially fully equilibrated with the feed gas. For a linear system the approach of the effluent gas to equilibrium during the pre-equilibration step will be governed by the same expression as governs the desorption curve (Eq. 9). However, the approach of the adsorbed phase concentration to equilibrium is governed by a slightly different expression:
q =~-] 6L2 qo
exp(-fl:Dt/R 2)
.=, f12[f12 +L(L-1)]
(26)
If diffusion is slow, the time required for the adsorbed phase concentration to approach equilibrium will be very much longer than the time at which the effluent gas approaches the fixed steady concentration. To ensure proper initial equilibration the equilibration time should be at least equal to R2/D which, for a slow diffusing system, can amount to several hours.
4.3 Partial Saturation (2) The nature of the controlling resistance to mass transfer is not immediately obvious from the form of the ZLC response. For example the curves for a surface resistance controlled system will be of the same general form as the curves for a diffusion controlled system. However a partial loading experiment provides, in principle, a practical way to distinguish between diffusion and surface controlled systems. In a surface resistance controlled system the distribution of sorbate through a particle is
201
always uniform, even when not fully equilibrated. For such a system the dimensionless desorption curve will therefore be unaffected under conditions of partial saturation. In contrast, in a diffusion controlled system, if the adsorbent sample is equilibrated for a time that is short compared with the time required to establish equilibrium, the sorbate will initially be concentrated near the surface of the particle, leading to further initial desorption and a ZLC that lies below the response for a fully equilibrated sample but with the same asymptotic slope. This type of behavior is illustrated in figure 9 confirming diffusion control. 4.4 Macroporous Particles tl~ The ZLC method has been used mainly to measure intracrystalline diffusion in zeolites. However the system can also be applied to measurement of the effective pore diffusivity in a macropore controlled system. For such a system R becomes the particle radius and D is the effective macropore diffusivity given by:
D=
oep D p
(27)
where co is the volume fraction of crystals in the solid and particle ep is the porosity. This approach has been used to study the diffusion of N2 and 02 in 5A zeolite pellets. A representative set of ZLC response curves showing clearly the dependence on particle size, and thus confirming macro control is shown in figure 10. The solution for the ZLC response of a biporous adsorbent including both micropore and macropore diffusional resistances has been derived by Brandani 01) and by Silva and Rodrigues (12). However, by adjustment of the experimental conditions it is generally possible to approach either the macro control or micro control cases. Thus while the dual resistance model is useful for understanding the response obtained under intermediate conditions in the application of the ZLC approach to diffusion measurements, to avoid ambiguity in the results, it is normally desirable to work under conditions that approach one or other of the limiting cases.
202
1 m
0.01
0.001
0.0001
0
s
+0
+5
t(s)
20
~
30
35
(a)
0.1
0.01
0.001
o
s
10
1's
t(s)
~
~s
(b)
Figure 9. Experimental response curves for propane-NaX (50 btm) at 85~ under full and partial equilibration conditions. The curves clearly show diffusion control rather than surface resistance control. (a) represents a transport (NZLC) experiment and (b) is a tracer exchange experiment carried out under comparable conditions. From Brandani and Ruthven C2).
203 (a)
0.1
o o
~176
o o
0 0
0
0
0
0
0
k. O.OO01
I
I lO0
0
I
20o
,
3oo t
0
I
400
.,I
5oo
(s)
(b)
I0.1
IO eeeO000o 0000000
o.o~ ~
0000
.
0.0001'
A
I 100
0
I 2OO
.,
I 3OO
t (s)
Figure 10. ZLC response curves for N2 at (a) 174K and (b) 193K in 5A zeolite beads (O I, Rp = 1.03 mm; (@), Rp = 0.42 ram; (A), Rp = 0.42 mm. He purge at 20 cm/min STP. From Ruthven and Xu 0~
5.
EXTENSIONS
OF THE ZLC TECHNIQUE
5.1 S e l f D i f f u s i o n M e a s u r e m e n t s (is'
14)
A simple variant of the ZLC experiment (tracer ZLC or TZLC) can extend the technique to the measurement of self-diffusion. The sample is pre-equilibrated with sorbate at a specified partial pressure and, at time zero, the flow is switched to a stream containing the same sorbate at the same concentration but in an isotopically different form. The desorption of the pre-equilibrated isotopic species is followed with the aid of a species sensitive detector such as an on-line mass spectrometer. The mathematical model is the same as that for a normal ZLC experiment except that the equilibrium constant (K) is replaced by the equilibrium concentration ratio (q*/c). By varying the sorbate partial pressure such measurements can be made over a range of sorbate concentrations thus
204
Methanol
in 13X 1 O0 C
Tbath -20 C(7.8 Torr, 8 molecules/cage) Theoretical D = 2.06 E-7 cm/k
9 50.4 cc/min
KVs = 4.4 ml
26.9 cc/min
o
0.9. 0.1
0
~~.7 0.01
lO
6
2o
3b
4b
sb
60
t Is)
Figure 11. Comparison of theoretical and experimental tracer ZLC curves for methanol in NaX crystals (R = 50 ~tm) at 100~ 7.8 Torr methanol pressure. The response curves at two different purge rates yield consistent values for both parameters (KVs and ,,~/R2). From Brandani, Ruthven and K~ger (14).
3•
-11 0
0
[] O/
1• -11
o
f5"
% o
,~ ZLC o Tracer
ZLC
[] PF@ NMR 1X10-12
,
O
I
2
,
I
4
L
I
6
i
1
8
i
i
lO
,
12
q (molecules / cage)
Figure 12. Variation of self-diff-usivity with loading for the methanol-NaX system at 100~ showing the comparison between TZLC data (O) and PFG NMR selfdiffusivities (O). The limiting value of Do obtained in a NZLC experiment is also shown (A). From Brandani, Ruthven and K~ger 04).
205 yielding the concentration dependence of the self-diffusivity. Such experiments involve an equimolar counter-exchange between the two labeled forms of sorbate so the isothermal model is always valid for this type of experiment. Figure 11 shows a representative example of TZLC response curves for methanolNaX at 100~ together with the theoretical response curves. The effect of changing the flow rate is evidently well captured by the model. The variation of tracer diffusivity with loading for this system is rather unusual as it passes through a maximum. This behavior has been confirmed by both tracer ZLC and PFG NMR measurements which show excellent agreement (see figure 12). Note that at the tracer diffusivity at zero loading appears to approach the transport diffusivity derived from a regular transport ZLC experiment. 5.2 Counter-Diffusion Measurements (15)
In an obvious further extension the ZLC technique can also be used to study counter-diffusion. The sample is pre-equilibrated with a certain partial pressure of component A and then at time zero the flow is switched to a carrier stream containing component B. Depending on the equilibrium constants and partial pressures such an experiment can be made under conditions of net adsorption, net desorption or equimolar counter-diffusion (no net flux as in a tracer exchange experiment). In this way it is possible to investigate hindrance effects by comparing counter exchange, NZLC and TZLC response curves under comparable conditions. Such a comparison, for benzene (desorbing) and either p-xylene or o-xylene adsorbing, in large silicalite crystals, is shown in figure 13. The response curves for the NZLC, TZLC and CCZLC experiments with p-xylene have the same asymptotic slope showing no significant hindrance effect under counter-diffusion conditions. However, the asymptotic slopes of the CCZLC response curves for OX which diffuses much more slowly, are substantially smaller, indicating significant hindrance of the diffusion of benzene, especially at high benzene loading. 5.3 Liquid Phase Measurements (s)
The ZLC technique is in principle equally applicable to liquid phase systems. This can be regarded as a special case of a CCZLC system since the solvent is adsorbed while the sorbate is desorbed. However there are two main practical difficulties: (i) Detector sensitivity (ii) Fluid phase hold-up Detector sensitivity is not a problem for aromatic sorbates since a liquid chromatography uv detector has excellent sensitivity for such species. The sensitivity of refractive index detector is however lower and, depending on the system, may not be sufficiently high to provide sensitivity over a wide enough concentration range. A detector with very low hold-up is essential for these measurements. Fluid phase hold-up is a problem because, as a result of the higher molecular density, the extracrystalline hold-up in a liquid system is comparable with the hold-up in the adsorbed phase and must, therefore, be accounted for in the analysis of the response curves. In the mathematical model Eq. 1 is replaced by:
v -3i-+v+ ~dt+ F c = 0
(28)
206
t (sec.) 100
200
300
I
t
I
400
500 t-1
'1
Theoretical C u r v e s f o r B z / P X ~ Theoretical C u r v e s f o r B z / O X D o x / D e x = 0. I . . . . . Dox/Dvx = 0.01 . . . .
0.1
(=) Bz = 6 T o r r
c/co
0.01 CCZLC OX (5 Ton') C C Z L C -o~ PX (5 Tort)
(b) Bz ~ 58 T o r r
9
t
t
t
NZL(" TZi,(' ('CZLC (PX) (5 Torr)
.
.
t
0.001
C C Z L C ((IX) (5 Torr)
Figure 13. ZLC curves for benzene-silicalite at 130~ Sample is pre-equilibrated with benzene at (a) 6 Torr and (b) 58 Torr. The corresponding NZLC and TZLC curves and the CCZLC curves corresponding to 5 Torr p-xylene or o-xylene are shown. The asymptotic slopes of the NZLC, TZLC and CCZLC curves for PX are the same showing no significant hindrance effect. However the asymptotic slopes for OX are curves showing substantial hindrance by the slow diffusing ox,;'nolecules especially at high benzene purge.
207 which leads to a theoretical response curve defined by Eqs. 20 and 21. For a liquid system the effect of the fluid phase hold-up is considerable since 7 is typically of order 0.2-0.5. The response curve has approximately the form of a two time constant response, the faster response corresponding to the washout (purging of the cell) and the slower response to desorption from the adsorbed phase. Clearly the desorption rate will be measurable only if it is substantially slower than the washout. This requires the minimization of liquid volume in the experimental system and limits the applicability of the liquid ZLC approach to relatively slowly diffusing systems. A schematic of the experimental system for liquid ZLC measurements is shown in figure 14. The limitation on detector sensitivity necessitates the use of a somewhat larger
~URE HEXANE
4SORBATE
DETECTOR
--I~
ACOUISmON UMP :
k
2 WAY VALVE
CONSTANT
TEMPERATURE
BATH
~ n . . . . . . -"- " ~~. . . . . . . . .
*....
D - 4.4
Figure 14. Experimental set-up for liquid ZLC measurements.
quantity of adsorbent than in a vapor phase system (typically several mg/and the ZLC cell should be designed to minimize liquid hold-up. The steady liquid flows can conveniently be achieved with liquid chromatography metering pumps. In a liquid system it is essential to measure the blank response since a relatively small deadwater region can easily give the appearance of a kineticaUy controlled ZLC response.
208 An example of the experimental response curves measured under liquid phase conditions for benzene-n-hexene in large crystals of NaX is shown in figure 15(5). The experimental curves conform well to the theory and the curves for different crystal sizes yield consistent diffusivity values which agree well with the liquid chromatographic measurements of Awum et al. (16) for the same system. Somewhat surprisingly the diffusivities for this system, measured at close to ambient temperature under liquid phase conditions, lie very close to the extrapolation of higher temperature vapor phase ZLC data for the same system at low sorbate loading (see fig. 16). The diffusivity values are, however, significantly smaller than the self-diffusivities measured by the PFG NMR technique (17). We can, as yet, offer no fully satisfactory explanation for this discrepancy 9 j(18) although a number of plausible hypotheses have been exammea . Liquid ZLC measurements have been used by Rodrigues et al. (19) to study the kinetics of cation exchange. However, since the blank response is not shown it is difficult to assess the validity of the kinetic data. Diffusion of several differently branched hydrocarbons in silicalite, under liquid phase conditions, has also been studied by both HPLC and liquid ZLC methods (21). Surprisingly the diffusivities obtained for the liquid phase systems are substantially larger than for the corresponding vapor phase systems, at the same temperature, and show much smaller differences in diffusivity between different isomers. This difference has been tentatively attributed to swelling of the silicalite lattice when saturated with n-hexane (the carrier liquid). 6. CONCLUDING REMARKS ZLC techniques provide a simple and relatively inexpensive approach to the measurement of intracrystalline and intraparticle diffusion in porous and microporous adsorbents. This technique is now used on a routine basis in several industrial and academic laboratories ~21' 22). Variants of the ZLC approach have been successfully developed for measuring both self-diffusion and counter-diffusion in a binary adsorbed phase and for the measurement of diffusion in liquid systems. To date there have, however, been only a few published reports of ZLC counter-diffusion and liquid phase measurements and, in view of their practical importance, these may be the areas in which greatest future development of the ZLC technique may be expected.
209
~cul~ed 31 micron
o.1
o.ol
o
~
lb
~
z~
t (=)
~"
Figure 15. Experimental liquid phase ZLC response curves for benzene-n-hexene in crystals of NaX (13 ~tm and 31 ~m) at 273 K, 3 ml/min hexane flow showing conformity with the theoretical curves calculated for Eqns. 18 and 19 with D = 1.75 x 10 "9cm2.s "]. From Brandani and Ruthven (5).
"'""'".......
1E-06
"7
r/3
1E-07
IE-08 Awum
IE-09
1.8
i
2:2
2',
2'e
:,:8
(LC)
* A~,,~
s
s'.:,
3:4
s:e
lo3rr (K~)
Figure 16. Arrhenius plot for benzene-NaX showing conformity between vapor phase and liquid phase diffusivity data. From Brandani and Ruthven (5).
210
NOTATION a
B C Co
D Dm
D F h -AH J K
Ko l L n
P q qo r R R t
T Vs Vf Y z
~t T
external surface area per unit particle volume mobility (Eq. 4) fluid phase concentration of sorbate value of c corresponding to feed diffusivity molecular diffusivity (in fluid phase) self-diffusivity purge flow rate overall heat transfer coefficient (particle to gas) enthalpy of adsorption diffusive flux dimensionless Henry constant value of K at temperature To half-thickness of slab parameter defined by Eq. 11 dimensionality (Eq. 3) partial pressure of sorbate adsorbed phase concentration value of q at equilibrium with Co radical coordinate particle radius gas constant time temperature (K) volume of solid in cell volume of fluid in cell mole fraction in vapor phase distance coordinate roots of Eq. 10 or 13 non-linearity parameter (= qo/qs) average jump distance (in Eq. 3) chemical potential Vf/3KVs time interval between molecular jumps
REFERENCES
1. J. K~ger and D.M. Ruthven, Diffusion in Zeolites and other Microporous Solids, John Wiley, New York (1992). 2. S. Brandani and D.M. Ruthven, "Analysis of ZLC Desorption Curves for Gaseous Systems", Adsorption 2, 133-143 (1996)
211 3. D.M. Ruthven and M. Eic, "Intracrystalline Diffusion of Linear Paraffins and Benzene in Silicalite" in Zeolites: Facts, Figures, Future. P.A. Jacobs and R.A. van Santen eds., pp 897-905, Vol. 49B, Studies in Surface Science and Catalysis, Elsevier, Amsterdam (1989). 4. C.L. Cavalcante, S. Brandani and D.M. Ruthven, "Evaluation of the Main diffusion Path in Zeolites from ZLC Desorption Curves", Zeolites 18, 282-285 (1993). 5. S. Brandani and D.M. Ruthven, "Analysis of ZLC Desorption Curves for Liquid Systems", Chem. Eng. Sci. 50, 2055-2059 (1995). 6. S. Brandani, "Effects of Non-Linear Equilibrium on ZLC Experiments", Chem. Eng. Sci. 53, 2791-2798 (1998). 7. S. Brandani, Z. Xu and D.M. Ruthven, "Transport Diffusion and Self-Diffusion of Benzene in NaX and CaX Zeolite Crystals Studied by ZLC and Tracer ZLC Methods", Microporous Materials 7, 323-331 (1996). 8. D.M. Ruthven and M. Eic, "Intracrystalline Diffusion in Zeolites", Perspectives in Molecular Sieve Science, W.H. Flank and T.W. Whyte (eds.), Am. Chem. Soc. Symp. Ser. 368, 361-375 (1988). 9. S. Brandani, C. Cavalcante, A. Guinmares and D.M. Ruthven, "Heat Effects in ZLC Experiments", Adsorption 4, 275-285 (1998). 10. D.M. Ruthven and Z. Xu, "Diffusion of Oxygen and nitrogen in 5A Zeolite Crystals and Commercial 5A Pellets", Chem. Eng. Sci. 48, 3307-3312 (1993). 11. S. Brandani, "Analytic Solution for ZLC Desorption Curves with Bi-Porous Adsorbents", Chem. Eng. Sci. 53, 2791-2798 (1996). 12. J.A.C. Silva and A.E. Rodrigues, "Analysis of ZLC Technique for Diffusivity Measurements in Bidisperse Porous Adsorbents", Gas Sep. Purif 10, 207-224 (1996). 13. S. Brandani, J. Hufton and D.M. Ruthven, "Self-Diffusion of Propane and Propylene Studied by the Tracer ZLC Method", Zeolites 15, 624-631 (1995). 14. S. Brandani, D.M. Ruthven and J. Karger, "Concentration Dependence of SelfDiffusivity of Methanol in NaX Zeolite Crystals", Zeolites 15, 494-495 (1995). 15. S. Brandani, Mo Jama and D.M. Ruthven, "Counter-Diffusion of Benzene-p-Xylene and Benzene-o-xylene in Silicalite Crystals", Microporous Materials, submitted for publication. 16. F. Awum, S. Narayan and D.M. Ruthven, "Measurement of Intracrystalline Diffusion in NaX Zeolite by Liquid Chromatography", Ind. Eng. Chem. Res. 27, 1510-1515 (1988). 17. A. Germanus, J. K~rger, H. Pfeifer and N.N. Samulevich, Intracrystalline SelfDiffusion of Aromatic Hydrocarbons in NaX Zeolite", Zeolites 5, 91-95 (1984). 18. J. K~ger and D.M. Ruthven, "On the Comparison between Macroscopic and NMR Diffusion Measurements of Intracrystalline Diffusion in Zeolites", Zeolites 9, 267-281 (1989). 19. J.F. Rodriguez, J.L. Valverde and A.E. Rodrigues, "Measurement of Effective SelfDiffusion Coefficients in a Gel-Type Cation Exchanger by the ZLC Method", Ind. Eng. Chem. Res. 37, 2020-2028 (1998). 20. L. Boulicaut, S. Brandani and D.M. Ruthven, "Liquid Phase Sorption and Diffusion of Branched and Cyclic Hydrocarbons in Silicalite", Microporous Materials 25, 81-93 (1998).
212 21. D. Shavit, P. Voogd and H.W. Kouwenhoven, "Time Dependent Non-Steady State Diffusivities of C6 Paraffins in Silicalite by the ZLC Method", Coll. Czech. Chem. Commun. 57, 698-709 (1992). 22. P. Voogd, H. van Bekkum, D. Shavit and H.W. Kouwenhoven, "Effect of Zeolite Structure and Morphology on Intracrystalline Diffusion of n-hexane in Pentasil Zeolites Studied by the ZLC Method". J. Chem. Soc. Faraday Trans I87, 3575-3580 (1991).
Recent Advances in Gas Separation by Microporous Ceramic Membranes N.K. Kanellopoulos (Editor) 2000 Elsevier Science B.V. All rights reserved.
213
Characterisation of microporous materials by adsorption microcalorimetry Philip Llewellyn Centre of Thermodynamics and Microcalorimetry- CNRS, 26 rue du 1416meRIA, 13331 Marseille cedex 3, France Calorimetry, or the study of heat, traces its origins back to Lavoisier and Laplace in 1783. Although the use of calorimetry for the study of adsorption phenomena dates back to around Favre in 1854, it remains a rarely used technique. This is mainly due to the strict experimental conditions required to obtain good results. Under these conditions, adsorption microcalorimetry is both a powerful and sensitive tool for the study of adsorption phenomena. The energetic information thus obtained provides supplementary resolution with respect to adsorption manometry and is complementary to other structural and/or diffusion studies. The present chapter aims to give an introduction to current calorimetric methods available for the study of adsorption phenomena. This is followed by a hypothetical breakdown of the adsorbate - adsorbent interactions, which is the basis of a classification of different calorimetric curves. Finally, several experimental results are highlighted for various microporous adsorbents. 1. DIFFERENT CALORIMETRIC METHODS AVAILABLE FOR THE STUDY OF
ADSORPTION PHENOMENA There are a number of conditions under which calorimetric measurements can be carried out [1]. Adiabatic calorimetry, that is when the surrounding temperature is made to follow that of the sample, is quite interesting for the determination of the heat capacity of a system. Isoperibol calorimeters, where no special connection is made between the sample temperature and that of the surroundings were the first to be used to measure adsorption phenomena. However, there are a number of drawbacks which make gas adsorption studies uncertain. Finally, diathermal calorimetry, where the sample temperature follows that of the surroundings is that most suited to the following of gas adsorption phenomena. Thus the isothermal conditions of adsorption manometry can be reproduced to be able to measure the actual heat effects that occur during adsorption. The examples given later in this chapter are obtained under these diathermal or quasi-isothermal conditions. An example of a diathermal calorimeter used for adsorption studies is given in Figure 1. This apparatus is formed of three main parts : the dosing apparatus, the sample cell and the calorimeter. The dosing apparatus, consisting of a reference volume (A), pressure gauge (B) as well a vacuum line (C) and gas inlet (D) is connected to the sample cell (E). This cell is placed in the calorimeter. A detailed explanation of this Tian-Calvet calorimeter are elsewhere [2, 3]. The calorimeter itself is placed in a liquid nitrogen (or agron) cryostat (F). Two thermopiles (G) are mounted in electrical opposition. A resistance (H) is placed into the reference thermopile allowing calibration via the Joule effect. ~t
email, [email protected], fr
214
A
C
0
H
0
~-"G 0
J Figure 1 : Schematic representation of a calorimetric set-up used for adsorption experiments. There are however, two different methods of adsorbate introduction. The first, and most common, is to inject discrete quantities of adsorptive to the adsorbent. A peak in the curve of energy with time is obtained which has to be integrated to give an integral molar enthalpy of adsorption for each dose. This method is explained in section 1.2. Alternatively, it is possible to introduce the adsorptive to the adsorbent in a continuous manner whilst ensuring that the adsorbate - adsorbent equilibrium is maintained. This leads to a high-resolution curve that is necessary for the observation of subtle adsorption phenomena such as phase transitions. This second method is described in section 2.2. However, beforehand, it is worth describing an indirect manner to obtain energetic information directly from two or more adsorption isotherms using the isosteric method. 1.1 The isosteric method
If one has the possibility to carry out two or more isotherms at various different temperatures, it is possible to calculate the differential enthalpy of adsorption using the isosteric method. From these isotherms, a plot of log pressure, In p, for a given amount adsorbed n a as a function of reciprocal temperature, 1/T, can thus be drawn. It is then possible to make use of the Claussius-Clapeyron equation for a single gas-liquid system. One has to assume that there is no variation of enthalpy or entropy with temperature. The equation used is thus : '] A aa,/~,o : R 0(l/r) ),,o
/aln~]
{Eq. 1}
Where Aaa~/~ is the differential enthalpy of adsorption and R the gas constant. Often however, one can measure two isotherms measured at around 1OK apart; for example in liquid
215 nitrogen (77 K) and liquid argon (87 K). It is thus possible to relate the equilibrium pressures
pl and p2 at corresponding temperatures T1 and T2 for a given quantity adsorbed: A,d~/~= - RT~T2 In P__L
{Eq. 2}
It can be seen that the precision of this calculation depends greatly on the measurement of the pressure. This can be a problem at low pressures. Not due to the precision of the pressure reading itself, as modem pressure gauges are more than sufficient, but to the exactness of the adsorbate-adsorbent equilibrium itself. This is especially the case for micropore filling in poor conducting materials, such as silica. A small deviation from this equilibrium, due to molecular diffusion or thermal transfer, can lead to a relatively large variation in pressure. This would explain some of the disparity in results obtained using the isosteric method and direct calorimetric measurements. However, as we shall see later, the calculation of the enthalpy of adsorption using the direct calorimetric procedure becomes less precise at higher pressures. This makes both methods quite complementary.
1.2 Discontinuous procedure of adsorptive introduction The discontinuous (or point by point) procedure of adsorptive introduction is the one most widely used for the determination of adsorption isotherms via manometry experiments. The same procedure can be used for the determination of differential enthalpies of adsorption using an apparatus such as that shown in Figure 1. The introduction of each dose of adsorptive to the adsorbent gives rise to a thermal effect until equilibrium is attained. This results in a peak in the curve of heat flow with time. Integration of this peak gives the overall heat effect due to adsorption. The calorimetric cell (including the relevant amounts of adsorbent and adsorptive) is considered as an open system. In this procedure, as well as in the quasi-equilibrium procedure of adsorptive introduction (section 1.3) it is important to consider the adsorptive introduced reversibly. However, to calculate the differential enthalpy of adsorption via the discontinuous procedure, one must introduce quantities dn small enough for a given pressure increase dp. Under these conditions it is possible to determine the differential enthalpy of adsorption Aaa,/~, via the following expression :
Aads~ : l dQr;v~ .~ Vc( d~Pa~
{Eq. 3}
dn Jr t,.dn Jr Here, dQrev is the heat reversibly exchanged with the surroundings at temperature T, that is to say the heat measured by the calorimeter. 8n a is the amount adsorbed after introduction of the adsorptive dose, dp is the increase in pressure and Vc is the dead space volume of the sample cell within the calorimeter itself (thermopile). If the conditions of reversible adsorption and small doses are not fulfilled, then the quantity calculated using Eq. 3 should be more properly be termed "pseudo-differential enthalpies".
1.3 Quasi-equilibrium introduction of adsorptive For the observation of subtle adsorption phenomena such as phase changes, an increased resolution in both isotherm and differential enthalpy curves is requires. It would be possible to introduce very small doses of adsorptive to increase the number of points taken. This is both
216 time consuming and may lead to a number of errors. However, a continuous introduction of adsorptive leads to an infinite resolution in both curves.
Figure 2 9Comparison of the results obtained using either the discontinuous (rectangles) or continuous (full line) procedure of adsorptive introduction. Figure 2 highlights how this resolution can be interesting. The peak in the full line would be indicative of an adsorbate phase change which would go unnoticed using the discontinuous procedure of adsorptive introduction. In what has been termed the "continuous flow" procedure, the adsorbate is introduced to the system at a defined rate, slow enough that the adsorbate- adsorbent system can be considered to be essentially at equilibrium at all times [4,5]. As we shall see later, different tests easily allow verification as to whether the experiment indeed proceeds at quasiequilibrium. In this "quasi-equilibrium" state, the quantity of adsorbate admitted to the system An can be replaced in adsorption calculations by the rate of adsorptive flow dn/dt. The calorimeter, under these conditions, thus measures a heat flow, ~. Under certain experimental conditions, it is possible to render constant the adsorptive flow to the sample, f = dn/dt. A rate of adsorption, f~, can therefore be calculated using the following expression"
f<,
dn <' I ( V a Vc)dp : - - - - ~ : f - R ~,Ta --Tcc --~
{Eq. 4}
Here, Vd and Vc are the volumes of the dosing system and that "accessible" to the calorimeter at temperatures Td and To. The corresponding heat flow, ~b,can be given by 9
dQ,~,, dQ,e,, dna ~= dt - d n " at
= f<'fdQ-~r~ i
Can )~
{Eq. 5}
Introducing Eq. 4 into Eq. 5 leads to 9
an 9
+ Vc = +V tan ) 7 7 c at dn~
f--W ~b+Vc --~
{Eq. 67 {Eq. 7}
217 Blank experiments can lead to an estimation of Vc(dp/dt). This term is large at horizontal parts of the isotherm. The error in the estimation of the differential enthalpy thus becomes large. However, it is just in this region of the isotherm that the estimation of the differential enthalpy via the isosteric method is most exact. This highlights how both methods are complementary. In the present case however, where the adsorption on microporous materials is under examination, the term Vc(dp/dt) is minimal. Effectively, the increase in pressure with time is small during micropore filling. Furthermore, during micropore filling, all of the flow of adsorptive to the sample is adsorbed making f = f . In such cases, Eq. 7 can be simplified to :
A ~,,a.h ,~ s f
{Eq. 8}
Thus if the rate of adsorptive flow, f is constant, a direct measurement of A,d,/;~ with the amount adsorbed is recorded. An example of the results that can be obtained using combined adsorption manometry / calorimetry is given in Figure 3. This figure represents the direct signals of pressure and heat flow as a function of time, recorded during the adsorption of nitrogen onto a well-organised graphite sample [6].
Figure 3 : Plot of the signals of heat flow and pressure obtained during the adsorption of nitrogen on graphite at 77. 4 K. (adapted from [6]). This diagram highlights several points relative to the measurement of differential enthalpies of adsorption using the continuous procedure of adsorptive introduction. It can be seen that the initial introduction of gas, up to 1.5 hours, leads to only a slight increase in the pressure signal. This corresponds to a relatively strong signal in the heat flow curve that is the result of monolayer adsorption on a highly organised homogeneous surface. The point "P" corresponds to a small step in the pressure signal and a large peak in the heat flow signal. This phase transition corresponds to the completion of the monolayer in epitaxy with the highly organised substrate [6]. At point "s" however, the flow of adsorptive is stopped in order to check equilibrium. It can be seen that the pressure signal does not change and the heat flow
218 signal decreases to the baseline within the response time of the calorimeter. These two points allow the conclusion of a quasi-equilibrium state. At point "s'", the vacuum line is opened to desorb the nitrogen and check the reversibility of the system. Note that this is one of the requirements for the above-mentioned calculations. It can be seen that at "P'", an effect similar to that produced on adsorption occurs. This and the fact that the two hatched areas are equivalent show the reversibility of this system. 2. CLASSIFICATION OF CALORIMETRIC CURVES As shown above, the differential enthalpy curves obtained using such adsorption microcalorimetric experiments is a global effect that includes both adsorbate- adsorbent as well as adsorbate- adsorbate interactions. Various adsorbate filling mechanisms and phase transitions can be highlighted as well as any structural changes of the adsorbent. Interaction Energy
Relative Coverage 0
Figure 4 9Hypothetical breakdown of calorimetric curves due to various interactions in play during the adsorption of simple gases at low temperature 9(a) adsorbate- adsorbate interaction, (b) interactions of an adsorbate with an energetically h_omogeneous adsorbent, (c) interactions of an adsorbate with an energetically heterogeneous adsorbent In general though, the calorimetric curve highlights three different types of behaviour as schematised in Figure 4. As the amount of adsorbate increases on a sample, then the interactions between the adsorbate molecules increase (a). Concerning the a d s o r b a t e adsorbent interactions themselves. The interaction of an adsorbate molecule with an energetically homogeneous surface will give rise to a constant signal (b). Finally, in most cases, the adsorbent is energetically heterogeneous due to a pore size distribution and/or a varying surface chemistry (defects, cations ..). One would expect relatively strong interactions between the adsorbing molecules and the surface initially which decrease as these specific sites are occupied. Thus, for energetically heterogeneous adsorbents, a gradual decrease in the calorimetric signal is observed (c). However, each differential enthalpy curve varies and is a composite of varying percentages of each type of interaction. Both Kiselev [7] and Sing [8] have put forward classifications of differential enthalpy curves. Figure 5 shows hypothetical differential enthalpy of adsorption curves which would correspond to the IUPAC [4] classification of adsorption isotherms. For non-porous and macrporous (dp > 50 nm) solids which give rise to Type II isotherms, the differential enthalpy curve invariably decreases rapidly to the enthalpy of vaporisation (AvapH) of the adsorptive. In several cases where there exist many specific sites on these
219 materials, this decrease in the curve is less marked. These differences would seem to correspond to different C values derived from the BET equation. Mesoporous materials (2 < dp < 50 nm) which normally give rise to Type IV isotherms also give rise to differential enthalpy curves which decrease to the enthalpy of vaporisation (AvapH) of the adsorptive under investigation. For solids with a very narrow pore size distribution (MCM-41 type materials, for example) a slight increase in calorimetric signal of around 2 kJ-mol "l is observed during the capillary condensation step [8]. II high CBET
I
l
B
f
~O=WCBET %~
aads ~1
,AvapH
III
IV
AvapH i
VI ~Av_ae.l-I "
..f
_._."'_..
,
J B <-
na/m s
J
IV
III
v
_s f
vl
j
: p/pO
Figure 5 : Hypothetical differential enthalpy of adsorption curves (7eft) corresponding to the IUPAC classification [4] of adsorption isotherms (righO. Systems that give rise to Type III or Type IV isotherms are indicative of very weak adsorbate - adsorbent interactions. For these systems, the differential enthalpy of adsorption is initially below that of the enthalpy of vaporisation of the adsorptive. In such cases, it would seem that entropy effects drive the adsorption process. Type VI isotherms are typical for very homogeneous two-dimensional solids such as graphite. Each step corresponds to the edification of a different adsorbate layer. The differential enthalpy curve is relatively constant for the initial monolayer coverage. The completion of this monolayer results in a distinct peak in the differential enthalpy curve which corresponds to the epitaxal formation (see above, Figure 3). It is noteworthy that this 2dimensional disorder - order transition was first observed by microcalorimetry [5] before being characterised by neutron diffraction methods. Finally, the filling of micropores (dp < 2 nm) is characterised by Type I isotherms. The initial uptake is characterised by a very small increase in pressure and is the result of enhanced interactions. Such cases are ideal for microcalorimetric studies as the technique is at its most sensitive. The differential enthalpy of adsorption curves are typically elevated
220
throughout the pore filling process. The examples given later in this chapter all give rise to primary micropore filling process [10]. The secondary micropore filling process gives rise to a slightly weaker signal. 3. VARIOUS RESULTS OBTAINED WITH MICROPOROUS ADSORBENTS 3.1 Carbons Carbons are one of the most widely used industrial adsorbents. They can be prepared with surprising high surface areas and in certain cases, with a relatively narrow pore size distribution. Their hydrophobic properties make them quite interesting for the separation of organics from water. However, their applications are far wider. The adsorption of simple gases onto microporous active carbons generally lead to calorimetric curves containing three different regions during the filling of the micropores. An example is given in Figure 6 for the adsorption of nitrogen and argon onto an activated carbon at 77.4 K. The three regions are clearly shown : the first region, AB, decreases before a second, more horizontal region, BC. The third region, CD, again shows a marked decrease towards the enthalpy of liquefaction of the gas under consideration.
~ 0
o
10
E E
a
t-
6
E
--j
15
r 13
9
IA,~pH~I _
0
005
0.1
p / pO
0.15
02
0
_ IAvapHN,I,
0.'2
04
,
- -
016
0.'8
i
Relative Coverage (0)
Figure 6 9Isotherms (left) and corresponding differential enthalpies (right) at 77. 4 K for nitrogen and argon adsorbed onto an activated carbon [11].
A number of authors have noted and discussed such phenomena with varying interpretations [1, 12]. It would seem that the following conclusions are generally given : 9 Region AB is characteristic of interactions between the adsorbate and an energetically heterogeneous adsorbent (Figure 4). If one considers that the 2-dimensional graphite surface is energetically homogeneous, as explanation of the observed heterogeneity has to be found. Such heterogeneity can arise from defect, impurities as well as from a large distribution in micropore size. Although the first two solutions can be eliminated in some cases, the nature of the preparation and activation of such materials make a certain pore size distribution inevitable. One can therefore assume the filling of the smallest micropores (or ultramicropores) in this initial region AB. 9Region BC however, corresponds to a more homogeneous phenomenon than the latter. It is also noteworthy to remark that this region corresponds to an enthalpy of adsorption not far
221 from that for the adsorption on a perfect 2-dimensional surface (~ 14 kJ'moll). Furthermore, simulation studies [ 13] have shown that for the adsorption of nitrogen in larger micropores (or supermicropores), above 0.7 nm in diameter, a two step process may occur. The first step would seem to correspond to the coverage of the pore walls whereas the second to the filling of the void space. It would thus seem possible that the region BC corresponds to the coverage of the pore walls. The fact that this step is not completely horizontal in comparison to the adsorption on a 2-dimensional graphite surface may be due to curvature effects within the micropores. 9 Taking into account the above-mentioned hypothesis, it would seem that the region CD corresponds to the completion of the filling of the larger micropores. The adsorption of simple gases onto carbon nanotubes leads to slightly different results. An example here is given in Figure 7 [14]. Here, two main regions can be distinguished. It is well known that such nanotubes are closed at each end so blocking any inherent microporosity. Moreover, these nanotubes arrange themselves into bundles with a porosity of around 0.3 nm between the fibres. This latter porosity should thus be inaccessible. 2119
S... o E --, v'
A
B
08
17
06
15
r-
13
<] '
11
%. 0.4 t:).
c
D 02
9 7
o o
1
2
3
4
5
n a / m m o l . g "~
Figure 7 : Enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for methane on carbon nanotubes [14]. The first step (AB, Figure 7) may be explained by the filling of a small percentage of unblocked nanotubes. According to the preparation mode, the quantity of unblocked pores can be in the region of 20%. The second region, BC, would thus seem to be the formation of a monolayer on the external surface of these nanotubes.
3.2 Clays Clay materials form a vast family of inexpensive and readily available adsorbents. They can be used for their intra-sec properties as well as binders for other active materials such as zeolites. Due to the sheet-like nature of the majority of clays, no microporous properties are observed. Nevertheless, it is worth dwelling on the example of the adsorption of nitrogen and argon on kaolinite (Figure 8). This example shows a possibility, via microcalorimetry, to estimate the ratio of different mineral facets.
222 Kaolinite has a 1:1 sheet structure with a layer repeat distance of 0.72 nm. This is approximately the distance of the sheets themselves which means hat there is insufficient space to accommodate intercalated molecules such as water. The isotherms obtained for such materials are of Type-II which are typical for non-porous or macroporous materials. 25-
o E
--j "" .,c:
Ar 15
IAv,~H,,I 5
0
0~2
IAvapHN, I 9-
o', o~8 o18 Relative Coverage (0)
;
1.2
Figure 8 9Enthalpies of adsorption with respect to relative coverage at 77. 4 K for nitrogen and argon on kaolinite. (after [15]).
The differential enthalpy curve for argon and nitrogen (Figure 8) [15] shows two main regions. The first, AB, corresponds to the adsorption on defect sites and the adsorption on lateral facets of the materials. These high energy domains provoke an enhanced interaction with the nitrogen quadrupole. The second region, CD, corresponds to the adsorption on more energetically homogeneous basal planes. Such calorimetric measurements are thus a simple means to estimate the proportion of lateral and basal planes of such materials as well as the effect of grinding. It is possible to create microporosity in these layered clays materials via the replacement of exchangeable ions with more bulky ions. The more bulky ions can then be stabilised by an appropriate thermal treatment. However, some clays do have intra-sec micropores. The palygorskites are fibrous clay minerals. Attapulgite and sepiolite are two members of this family which both contain structural micropores. Their structures comprise of talc-like layers arranged quincuncially, forming microporous channels of rectangular cross-section parallel to the longitudinal axis of the crystals [15]. Whilst attapulgite has a pore section of 0.37 x 0.64 nm 2, the section of sepiolite is of 0.67 x 1.34 nm 2. The pores contain Mg(OH2)2 groups situated in the structural micropore walls. The differential enthalpy curves obtained for the adsorption of nitrogen on sepiolite and attapulgite at 77.4 K are shown in Figure 9 [17, 18]. Two separate domains can be observed for each of these curves. The first, domain, AB (Figure 9), is quasi-horizontal which is characteristic of adsorption in highly homogeneous regions. This would seem to correspond to the adsorption within the intrafibrous micropores containing the Mg(OH2)2 groups.
223
ca)
- (4)
--5 a~
15
t-
<,
IAvapHN21 o
o12
oi~
oi~
o~
relative coverage (0)
Figure 9 "Enthalpies of adsorption with respect to relative coverage at 77. 4 K for nitrogen on attapulgite (a) and sepiolite (b). The second domain in corresponds to the end of any micropore filling in the adsorption isotherms. The differential enthalpy curves in this region, CD (Figure 9), correspond to a decrease towards the enthalpy of liquefaction. This is characteristic of more energetically heterogeneous regions. It would seem that such regions are found between the fibres. Thus this would seem to correspond to adsorption in these interfibrous micropores. 3.3 A m o r p h o u s
Silica's
There are three main classes of amorphous silica's 9pyrogenic silica' s, precipitated silica's and silica gels. Pyrogrenic silica's and precipitated silica's are essentially not microporous. An exception is made for those silica's prepared by the St6ber process. These silica's would seem to be ultramicroporous with pores too small to allow nitrogen molecules to penetrate the porosity. However, the pores are large enough to allow the adsorption of water within the porosity at ambient temperatures. Silica gels can be prepared to contain micropores. A large number of physisorption studies have been carried out on silica gels. A certain number of these are described in Ref. [1]. Although initial synthesis of silica gels resulted in relatively ill-defined samples, it is currently possible to control both the synthesis and drying to form microporous Aerogels and Xerogels.
224 N2
Ar
10,
o E E
%
,.
. ,
'-N2
?
a.
6,
<4,
. . . . .
[AvapHArl
o;
o os
0"4 p /
pO
,
,,
9
o is
,|,
o2
5
o
,
03
0"4
,
o'6
IAvapHN=[ 0"8
Relative Coverage (0)
Figure 10 9Isotherms (left) and corresponding differential enthalpies (right) at 77. 4 K for nitrogen and argon adsorbed onto a microporous amorphous silica gel (Davison 950) [11]. An example of the adsorption behaviour on microporous silica gels is given in Figure 10. This figure shows the isotherms and differential enthalpy curves for the adsorption argon and nitrogen on a microporous silica gel (Davison 950). Both the differential enthalpy curves obtained with argon and nitrogen decrease continually with relative coverage. This is characteristic of large electrical homogeneity. This is probably due to both the surface chemistry and pore size distribution. Often the comparison between the results obtained with argon and nitrogen can give an idea of the relative importance of the inhomogeneity due to the pore size distribution and surface chemistry. Indeed, argon being a spherical and non-polar molecule interacts only weakly with surface chemical species such as hydroxyls. The behaviour thus observed is essentially due to the textural properties (pore geometry, pore size distribution ...). Nitrogen however, has a permanent quadrupole which is able to interact with any specific surface groups. The behaviour thus observed corresponds to any specific interactions with the surface as well as any interaction due to the textural nature of the sample. The difference in differential enthalpies of argon and nitrogen can be taken as an indication of the extent of the interactions due to the surface chemistry of the adsorbent under investigation. This for silica' s and other adsorbents. 3.4 Zeolites
From the applications point of view, particularly in membrane science, zeolites and related materials (aluminophosphates, gallophosphates ...) are interesting materials. ~1he synthesis of such materials can be adjusted to give a wide range of crystal structures and an almost infinite variety of chemical compositions giving the possibility to tailor-make samples for specific applications. From a fundamental point of view, the regular pore systems can be indexed by X-ray diffraction and the structure can be elucidated using Riedvield refinement-type methods for example. The zeolite family of materials are thus ideal for the understanding of adsorption phenomena. It is the knowledge gained by such studies, using thermodynamic methods (manometry, calorimetry ...) complemented by structural methods (neutron diffraction, X-ray
225
scattering ...) which permit, by analogy, the interpretation of adsorption phenomena in more disordered systems. Simulation studies are essential to complete the fundamental understanding. Three of the most widely used zeolites today are silicalite, Linde A and faujasite. Probably the most widely studied aluminophosphate is A1PO4-5. All four of these structures give rise to unusual adsorption phenomena during micropore filling. Several examples are highlighted in the following section. 3.4.1. Silicalite Silicalite is the pure silica end analogue of ZSM-5 (structure type MFI [19]). The pore network consists of straight elliptical pores of 0.51 x 0.57 nm 2 in section which intersect (0.8 nm in diameter) with sinusoidal, quasi-circular pores of 0.54 x 0.56 nm 2 in section. As the framework is purely silicic, there are no compensation cations. Figure 11, Figure 12 and Figure 13 highlight the three types of adsorption behaviour that can be observed with silicalite at 77 K for various adsorptives. The adsorption of methane (Figure 11) gives rise to a type I isotherm and a differential enthalpy of adsorption curve which is strictly horizontal during micropore filling. The adsorption of argon (Figure 12) and krypton both give rise to isotherms with a second step (or sub-step), noted [~ in Figure 12. This step in the isotherm corresponds to a distinct variation in the differential enthalpy curve. Finally, for gases such as nitrogen (Figure 13) and carbon monoxide two steps (ct and 13) in the isotherm can be observed. These steps also correspond to distinct variations in the differential enthalpy curve.
r
0,025
..-b, 0,02 16 0
E
0,015
14
12 10
6,, 0
%
0,01
IAv.~HcH,,I
0,005
i
__/ 1
na / mmol.g 1
Figure 11 " Enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for methane on silicalite-I [20].
The behaviour shown during the adsorption methane on silicalite at 77.4 K (Figure 11) can be considered almost model. The quasi-horizontal calorimetric signal, corresponding to the entire micropore filling region would seem to be purely the result of adsorbent - adsorbate interactions. One would expect a certain contribution due to a d s o r b e n t - adsorbent interactions, however this would seem to be minimal.
226
17
0,002 9
0,2
17 ,1,
,i,l
15
o
T._ 0
13
%.
11
0,16
13 0,12
E
0,0012
E ..~
15
0,0016 9
.-j
o
r
t,--
,0,08
0,0008
~,
~,
9
9 ,0,04
0,0004
7
f
5 0
1
2
3
4
5
6
n" / mmol.g -1
Figure 12 : Differential enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for argon on Silicalite [20].
0
1
: .
2
3
4
.... ,5
6
0
na / mol.uc 1
Figure 13 : Differential enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for nitrogen on Silicalite [21].
The adsorption of argon on silicalite at 77 K (Figure 12) shows similar behaviour to that of methane during the initial micropore filling process. This would seem to indicate the interaction of the adsorbate with an energetically homogeneous surface. However, the sudden substep at around p/p0 = 0.0002 corresponds to a distinct change in the differential enthalpy curve. Note that the substep in the isotherm was searched for after the change in the calorimetric curve was first observed. This substep, 13, was then characterised by neutron diffraction [20] giving rise to an explanation of a phase change in the adsorbed phase from a fluid state to a more dense "solid-like" state. The picture is certainly more complex with a probable transition of the silicalite structure itself. The adsorption of nitrogen on silicalite at 77 K (Figure 13) gives rise to an isotherm with two substeps ot and 13. It is interesting to note however, that the initial pore filling results in a differential curve which is not completely horizontal. An initial decrease would seem to indicate an enhanced interaction, maybe with defect site. This curve then increases again which would seem to be characteristic of increasing adsorbate- adsorbate interactions. The substeps in the isotherm correspond to marked differences in the differential enthalpy curves. Although this second substep 13, was observed in the isotherm prior to any microcalorimetic measurements [22, 23], the first substep a, was initially observed in the calorimetric curve [21 ]. Again, a complementary study by neutron diffraction was carded out on this system. This study [21 ] concluded that the first substep a, is due to an ordering of the adsorbate from a fluid phase to a network fluid. The second substep 13, would seem to correspond to an adsorbate phase transition similar to that observed for argon (Figure 12), that is to say from a network fluid to a "solid-like" adsorbate phase. These particularities in the behaviour of the adsorbate phase are influenced by the quality of the substrate. The introduction of compensation cations with the introduction of aluminium into the framework (ZSM-5) influences the marked nature of these variations in behaviour of the adsorpbate. Indeed these variations become less marked. This is especially the case for the substep ct which disappears from the isotherm as soon as the quality of the pore network
227 degrades due to the presence of compensation cations, preadsorbed species or even after grinding. These examples however, show the interest of such microcalorimetric measurements with the high resolution, continuous procedure of adsorptive introduction. Such subtle adsorption phenomena allow, not only the quality of crystals to be verified, but also an increased understanding of the influence of the substrate on the adsorption of simple probe molecules. 3.4.2. 5,4 and 13X The study of relatively simple solid / gas systems such as those in sections 3.4.1 and 3.4.3, allow a better understanding of more complex systems such as industrially prepared zeolites with cationic sites. The two most widely used zeolites are 5A and 13X. The 5A zeolites, with LTA structure [19] consist of regularly spaced spherical cages of 1.14 nm in diameter. These cages are linked to each other by six circular windows of around 0.42 nm in diameter. The negatively charged silico-aluminate framework requires compensation cations. In the case of zeolite 5A, these exchangeable cations are generally a mixture of calcium and sodium. The 13X zeolite, or faujasite of FAU structure [19] has very similar primary building blocks to the 5A zeolites. For 13X however, the spherical cages are of 1.4 nm in diameter, which are linked to each other by four circular windows of around 0.74 nm in diameter. The exchangeable cations are generally sodium (NaX). 25-
5A 20 ,1_ o E ,-j
13 X
15
10
IAvapHN, I 5
o
;
i
~
8
n a / m m o l . g -~
Figure 14 9Differential enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for nitrogen on 5A and 13X [24].
A prior study of the adsorption of nitrogen at 77 K on 5A and 13X zeolites using quasiequilibrium, isothermal, adsorption microcalorimetry experiments at 77K [24] detected a step in the differential enthalpies of adsorption, towards the end of micropore filling (Figure 14). At the time, this was interpreted as a consequence of specific adsorbate - adsorbate interactions. Recently however, in the light of other microcalorimetry studies this change in signal has been interpreted as a possible phase change within the cavities [25]. This latter study detected the same phenomenon for a number of other probe molecules including, argon and methane as well as for carbon monoxide. An independent study showed that this latter
228 step corresponds to the delocalised adsorption of mobile molecules as the main cages (or orcages) become almost full [26]. 3.4.3. AIPOr Recently, much research has been made into the synthesis of zeolite-like materials with framework species other than silica and alumina. The first family of materials that resulted from this research were the aluminophosphate molecular sieves. Thus A1PO4-5 [27] with an AFI-type structure [19] has a unidirectional pore system consisting of parallel circular channels of 0.73 nm in diameter. AIPO4-5 has a framework which, like silicalite-I, theoretically is globally electrically neutral, although the pore openings is slightly larger than those of the MFI-type zeolites. These characteristics make AIPO4-5 a fine structure for fundamental adsorption studies. For ALP04-5 the adsorption isotherms of argon and nitrogen traced up to a relative pressure of 0.2 are indistinguishable (Figure 15). This is not the case for methane which adsorbs significantly less, suggesting a different pore filling mechanism. The differential enthaply curves for argon and nitrogen vary. For argon, a slight increase in the differential enthalpy curve occurs due to the increase in adsorbate- adsorbate interactions during the filling of the micropores. For the adsorption of nitrogen, the differential enthalpy curve initially decreases as a result of decreasing adsorbate - adsorbent interactions. The curve then increases due to the adsorbate- adsorbate interactions that increase as the micropore filling process procedes. 3
~
N2
CH4
2.5
14
Ar, N 2
2 .=,: O [::15
E
o E
13
-~9
12
e-
11
1
10 0.5
0
0 05
0.1
p/p0
0.15
0
0.2
0.4
0.6
0 8
Relative Coverage (0)
Figure 15 9Isotherms (left) and corresponding differential enthalpies (right) at 77. 4 K for nitrogen, argon and methane adsorbed on ALP04-5 [28]. For the adsorption of methane however, an exothermic peak (noted ~ in Figure 15) is observed in the differential enthalpy curve for methane, which would seem to correspond to an energetic term ~ RT. This would seem to indicate both a variation of mobility and a variation of the adsorbed methane phase. A complementary neutron diffraction study [29] indicates that an unusual behaviour of the methane adsorbed phase occurs. It would seem that the methane undergoes a transition between two solid-like phases. The first "solid-like" phase
229 corresponds to the adsorption of 4 molecules per unit cell whilst the second phase corresponds to a jump in the quantity adsorbed to 6 molecules per unit cell. This would seem to be a result of a favourable dimensional compatibility between the methane molecule and A1PO4-5 micropore, permitting, from a volumic point of view, the apparition of two relatively dense phases. This hypothesis is supported by simulation studies [30]. 4. CONCLUDING REMARKS The aim of this chapter is to highlight the interest of adsorption microcalorimetry, not only to characterise various adsorption phenomena on well defined adsorbents but also for the characterisation of less well defined microporous adsorbents. Indeed, it is the information gained from fundamental studies on these energetically homogeneous adsorbents that allow, by analogy, the pinpoint of different phenomena that arise in more heterogeneous adsorbents. Microcalorimetric measurements allow the easy detection of adsorption phenomena that are difficult to observe in the adsorption isotherm alone. Direct calorimetric measurements are quite complementary to calculations via the isosteric method. However, direct measurements are far more sensitive for the adsorption of molecules within micropores. Such calorimetric measurements can be completed by structural studies (e.g. neutron diffraction) and finally by computer simulation. 5. LIST OF SYMBOLS C BET constant
Qrevheat reversibly exchanged with the
dp pore diameter
surroundings R gas constant T absolute temperature Vvolume (Vc volume of sample cell "accessible" to the calorimeter) AvapHenthalpy of vapourisation
frate of gas flow f ' rate of adsorption n amount of substance n a amount adsorbed nammonolayer capacity p pressure p0 saturation pressure p/pO relative pressure
Aads/~ differential enthalpy of adsorption r heat flow 0relative coverage (i.e. na/nam)
6. REFERENCES
1. 2. 3. 4. 5. 6. 7.
F. Rouquerol, J. Rouquerol and K. Sing, "Adsorption by Powders and Porous Solids", Acad. Press, London, 1999. J. Rouquerol, In "Thermochimie", Colloques Intemationaux du CNRS, No.201, CNRS Ed., Paris 1972, p.537. Y. Grillet, J. Rouqu6rol and F. Rouqu~rol, J. Chim. Phys., 2 (1977) 179. K . S . W . Sing, D. H. Everett, R. A. W. Haul, L. Moscou, R. A. Pierotti, J. Rouquerol and T. Siemieniewska, Pure Appl. Chem., 57 (1985) 603. C. Letoquart, F. Rouquerol & J. Rouquerol, J. Chim. Phys. 70(3) (1973) 559. J. Rouquerol, S. Partyka and F. Roquerol, J. Chem. Soc. Faraday Trans. 1, 73 (1977) 306. A.V. Kiselev, Doklady Nauk USSR, 233 (1977) 1122.
230 8. 9. 10. 11. 12.
13.
14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
26. 27. 28. 29. 30.
K . S . W . Sing, In "Thermochimie", Colloques Intemationaux du CNRS, No.201, CNRS Ed., Paris 1972, p.537. P.L. Llewellyn, Y. Grillet, J. Rouquerol, C. Martin, J-P. Coulomb, Surf Sci., 352-354 (1996) 468. S. J. Gregg and K. S. W. Sing, "Adsorption, Surface Area and Porosity", 2nd Edn., Academic Press, London, 1982. M. Salameh, Ph.D. Thesis, Universit6 d'Aix-Marseille I, 1978. D. Atkinson, P. J. M. Carrott, Y. Grillet, J. Rouquerol and K. S. W. Sing, In "Proc. 2 nd Int. Conf. On Fundamentals of Adsorption" (A. I. Liapis ed.), Eng. Foundation, New York, 1987, p.89. P. Brauer, H._R. Poosch, M. V. Szombathely, M. Heuchel, and M. Jarioniec, In "Proc. 4th Int. Conf. On Fundamentals of Adsorption" (M. Suzuki ed.), Kodansha, Tokyo, 1993, p.67. M. Muds, N. Dufau, M. Bienfait, N. Dupont-Pavlovsky, Y. Grillet and J. P. Palmary, Langmuir, in print, 2000. J. M. Cases, P. Cunin, Y. Grillet, C. Poinsignon and J. Yvon, Clay Minerals, 21 (1986) 55. K. Brauner and A. Preisinger, Tschermarks Miner. Petr. Mitt,. fi (1956) 120. Y. Grillet, J. M. Cases, M. Frangois, J. Rouquerol and J. E. Poirier, Clays and Clay Minerals, 36(3) (1988) 233 J. M. Cases, Y. Grillet, M. Frangois, L. Michot, F. Villieras and J. Yvon, Clays and Clay Minerals, 39(2) (1991) 191 Meier W. M. & Olson D. H., "Atlas of Zeolite Structure Types", Butterworth-Heinemann, London, 1992. P. L. Llewellyn, J.-P. Coulomb, Y. Grillet, J. Patarin, H. Lauter, H. Reichert and J. Rouquerol, Langmuir, 9 (1993) 1846. P. L. Llewellyn, J.-P. Coulomb, Y. Grillet, J. Patarin, G. Andr6 and J. Rouquerol, Langmuir, 9 (1993) 1852. P. J. M. Carrott and K. S. W. Sing, Chem. & Ind., (1986) 786. U. Mtiller and K. K. Unger, Fortschr. Mineral., 64 (1986) 128. F. Rouqurrol, S. Partyka & J. Rouqurrol, in "Thermochimie", CNRS Ed., Paris (1972) p.547. N. Dufau, N. Floquet, J. P. Coulomb, G. Andrr, R. Kahn, P. Llewellyn and Y. Grillet, In "Proc. 5th Int. Conf. on Characterisation of Porous Solids" K.K. Unger, G. Kreysa, J.P. Baselt eds., Elsevier, Amsterdam, 2000. D. Amad, J. M. Lopez Cuesta, N. P. Nguyen, R. Jerrentrup & J. L. Ginoux, J. Therm. Analysis, 38 (1992) 1005. S. T. Wilson, B. M. Lok, C. A. Messina, T. R. Cannan and E. M. Flanigen, J. Amer. Chem. Soc., 104 (1982) 1146. Y. Grillet, P. L. Llewellyn, N. Tosi-Pellenq et J. Rouquerol, In "Proc. 4 th Int. Conf. On Fundamentals of Adsorption ", (M. Suzuki ed.), Kodansha, Tokyo, 1993, p.235. J-P. Coulomb,C. Martin, P. L. Llewellyn, Y. Grillet, In "Progress in Zeolites and Microporous Materials" (H. Chon et al. eds.), Elsevier, Amsterdam, 1997, p.2355. V. Lachet, A. Boutin, R. J. M. Pellenq, D. Nicholson and A. H. Fuchs, J. Phys. Chem., 100 (1996) 9006.
Recent Advancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) o 2000 ElsevierScienceB.V. All rightsreserved.
231
Simulation of Adsorption in Micropores David Nicholson 1 Thanos S t u b o s 2 1. Department of Chemistry, Imperial College of Science Technology and Medicine, London SW7 2AY 2. Institute of Physical Chemistry National Center for Scientific Research, Demokritos, Athens, Greece GR- 153 10 1. INTRODUCTION With the rapid increase in computer power and availability in recent years, simulation studies of adsorption have come to play an ever increasing role in the understanding and interpretation of experimental data. In membrane materials designed for gas separation, the pore structure of the separating layer must contain a predominance of pores with widths fairly close to the size of the molecules in the gas mixture to be separated. This is one reason for the keen interest in adsorption studies of adsorbent pores in the micropore size range. The original IUPAC classification [ 1] of pores into micro-, meso- and macro- groups was based on observations from a large number of experimental data for adsorption of nitrogen at 77K. The essential feature that distinguishes mesopores is that nitrogen isotherms exhibit a steep adsorption curve and a broad hysteresis loop (type IV adsorption). Pore filling in mesopores is associated with a two stage process. In the first stage a monolayer or more of nitrogen covers the pore wall, this is followed by a second stage, at higher relative pressure, in which capillary condensation occurs into the central core [2]. Below a pore width of-~2nm, the distinction between these two stages becomes increasingly blurred, the hysteresis loop is absent, and isotherm shapes move from type IV to type I, typefied by the monotonic Langmuir isotherm. In fact, as will become apparent from the discussion below, computer simulation studies have shown that this picture is rather oversimplified. Nevertheless, it highlights an important distinction between two types of pore filling mechanism, and serves to emphasise that, whilst thermodynamic models - based on the Kelvin condensation mechanism - can be of use in describing mesopore adsorption, this mechanism is not applicable in the micropore size range. One major contribution from the theoretical and simulation studies of the past 15 years is to delineate more clearly the limitations of the Kelvin mechanism, even for describing mesopore adsorption [3]. In the micropore size range, the specific nature of the adsorption potential field is increasingly important compared to the adsorbate intermolecular interactions, since most adsorbed molecules are within two molecular diameters of the adsorbate surface, and dispersion forces from a planar wall are relatively long ranged, decreasing approximately as the inverse cube of distance from the walL In micropores the adsorbent field is further intensified due to overlap of fields from opposite parts of the wall. Thus local variations in pore width may be reflected in adsorption properties. To
232
a first approximation at least, the response of adsorption to variation in pore width can be expressed as a pore size distribution and regarded as being a property characteristic of the adsorbent. For mesopores the Kelvin mechanism, at least in principle, offers a route for the rreasurement of pore size distn'bution, since according to the Kelvin equation the pressure at which capillary condensation occurs is inversely proportional to pore radius, if the pores are taken to be cylindrical. A more careful examination of the problem reveals that, even within the context of a thermodynamic analysis, the pore size distribution problem in mesopores is more complicated [2, 4, 5,6]. In micropores, this route to pore size analysis is not available. An alternative route which has been developed over the last 20 years uses theoretical models such as lattice theories [7, 8], density functional theories [9,10,11], or simulation [12,13]. In these methods, the adsorption properties of single pores is used to build a database which, as explained below, may then be used as a starting point for pore size distribution analysis. As well as the specific effects of pore width variations, adsorption may be influenced by local heterogeneities in the adsorbent. An important example in adsorption technology is the extra-framework cations in zeolites that compensate for the excess negative charge resulting from T-atom substitution of Si by AI or other trivalent species. Another example occurs in activated carbons where graphite edge sites are terminated by oxygen or larger organic groups. Clearly heterogeneities of this type can be expected to interact more strongly with more polar adsorbate species than with less polar species. In principle this offers a means of distinguishing pore size from electrostatic effects [ 14], but further work is needed to clarify these effects. In this chapter we concentrate on the role that simulation in particular, has played in helping to understand micropore adsorption. In the next section we review briefly the relevant simulation methodology, and discuss some basic theoretical aspects of the problem. We then discuss some of the results for single components and for mixtures in simple model microporous systems. The determination of micropore size distribution is of critical importance in many practical systems, and we review some recent advances in this field in section 4. The final section reviews the factors affecting selectivity in mixtures of simple molecules in model pores. 2. SIMULATION AND EXPERIMENT 2.1 Simulation methods Several standard texts describing simulation methods and the underlying theory are available [7,15,16]There are two basic techniques that can be used in simulation. In molecular dynamics (MD) the Newtonian equations of motion are set up for the system of interest, and solved numerically by advancing in small time steps. In the Monte Carlo (MC) method the configuration of the system is randomly changed in such a way as to ensure that its properties are properly averaged within a given statistical ensemble. Grand canonical Monte Carlo simulation (GCMC) in the ~ , V, T) ensemble offers a direct method for the study of adsorption. In this method, three types ofrnove are used: (i) Phase moves, in which molecules (usually one at a time) are moved to a new position and orientation. (ii) Creation moves, in which an attempt is made to insert a new particle at a random position in the system. (iii) Destruction moves, in which an attempt is made to delete a particle from the system. These moves are steps in a Markov chain and are subject to microscopic revers~flity. The criterion for acceptance is determined by the Boltzmann factor of the energy change between the trial state of the system and the original state. In GCMC, this factor involves g, the chemical potential, which is chosen as an input to the simulation. Its conjugate, the mean number of particles in the system , is determined as an average over several million configurations. Usually it is convenient to choose the absolute activity, z for each species in the simulation, where z is given by:
233
z
exp(flp)
:
O)
A AI
where fl=l/kT, and the thermal wavelengths A~, and A~ may be expressed in terms of the molecular mass, m, and moments of inertia, I~.
A t _-
h3 0 ~1/2(8~.2Ix kT)u2 (8g2iykT)1/2
h2
:
(871;2/zkT)1/2
non linear molecules
linear molecules
(2)
8on2IkT A] h3 (2 nmkT) 3r~
In practice it is rarely necessary to use these equations since it is readily shown that z is directly related to the fugacityfofthe adsorptive by: z
: #f
(3)
A plot of against f or p, at a fixed temperature, is the adsorption isotherm. Heats of adsorption are also readily calculated in this type of simulation; for example the differential enthalpy of adsorption (isosteric heat) qst which is the is given by the fluctuation equation, qst =
f ( N , U N) f ( N , N ) - Ng
+ kT
(4)
where UN is the total potential energy of the adsorbate, and the fluctuations are defined by
f(X, IO = <XY> - <X>
(5)
Numerous modifications and variations of the MC technique have been discussed in the literature. One major difficulty in GCMC is to achieve a statistically significant number of creations and destructions. This problem is exacerbated at low temperature and high density. To date no standard solution has emerged, and it is necessary to be cautious in accepting results from GCMC simulations close to complete pore filling. A similar difficulty occurs with certain types of model. For example hydrogen bonding in water, and its large multipole moments, are often represented by placing fractional point charges at suitable locations in the molecular model. If a creation step is attempted with an orientation that places like-charges too close to one another, creation will be rejected due to the high repulsive energy. To ensure that a sufficient number of creations occur, a suitable orientation can be chosen for the molecule and statistical compensation introduced to
234 counteract the bias [ 16,17]. A similar problem occurs in creating long chain molecules with several conformational isomers. In this case the molecule can be created by adding new elements to the chain in orientations that avoid overlap with adsorbent walls [ 18 ]. Again statistical correction must be included in the calculation to compensate for bias. 2.2 Surface excess and absolute adsorption As interest in adsorption at high pressures and temperatures has increased, and as simulations have approached more closely to reality, the relation between absolute and surface excess adsorption has attracted more attention [ 19,20,21,22]. All adsorption experiments measure surface excess, whilst simulation calculates absolute adsorption. The difference between surface excess and absolute adsorption is usually negligible at low temperature. However, membrane separations are often carried out in microporous adsorbents at ambient temperature. Under these conditions, deviation between excess and absolute adsorption can be considerable. This is dramatically highlighted for ambient terr~rature studies, where the excess isotherm passes through a maximum because adsorptive density can increase with pressure in the external phase when pores are full of dense fluid. Formally, adsorption excess is defined by,
N r' : N - N
g
= f(p(r)
(6)
- p~) dr
V
where lag is the density ofthe external gas phase, and Ng = p j d r , is the number of molecules in the volume V in the absence of adsorption forces. The volume can be written as: V = V + Vf
(7)
where V~is the volume of the solid and VI the volume occupied by the adsorbate phase. V~, Vfare separated by a Gibbs dividing surface [2, 7]. In experiments, the volume V includes the 'dead space' volume surrounding the adsorbent as well as any pore volume and there is no way of distinguishing these two volumes experimentally. The Ng gas phase molecules only occupy the volume up to the Gibbs dividing surface and Ng is therefore given by,
N . : p.fa
: p.v,
,
v
Thus in the ideal pycnometry experiment, carried out with He for example, the number of molecules admitted to the system is N~ e = p~eVf
(9)
235
where pgHeis the density of He at the chosen pressure and temperature. The excess number of He molecules in the ideal pycnometry experiment is given by equation (6) as
fGo-o(,) - ,o"O) d,.
0o)
v
where pile(r)
=
p?e Vf/V
=0
r c
Vf
r~
giving, N~S- 0. In reality helium (or indeed any other calibrating gas) is adsorbed. At high temperatures, and for a weakly interacting species such as helium, it is reasonable to assume that the low density Henry's law limit is valid for heliunh and to write,
pne(r ) = pye exp[_~ul(r)]
(11)
where Ul is the He-adsorbent potential energy. The surface excess for the calibrating gas is then given by N~,ne = pile f[exp(_13u 1(r)) - 1 ]dr
(12)
To determine Vy, it is assumed that N ~'He '-0, whence
=
fexp[-~l (r)]dr
(13)
v
Clearly V/determined in this way depends upon the temperature, and a 'true' value does not exist strictly speaking. Therefore all experimental data depend upon the calibrating procedure used in their determination. Steele [ 19] has suggested that calibration should be carried out at the Boyle temperature defined by exp(-flul)=l. Experimentally this would require several determinations at a series of temperatures, since Ul is not an experimental quantity. For the purpose of comparison between experiment and simulation (or theory) the optimum procedure (as suggested by Neimark and Ravikovitch [21]) is to calibrate the simulation using the same method as that used experimentally. The differential enthalpy of adsorption, as customarily defined [2,7], is not subject to this problem, although it should be noted that it is usually plotted against adsorbate density so that experimental isosteric heat curves would differ from those obtained from simulation without a correction to convert absolute to excess adsorption.
2.3 Adsorption thermodynamics The thermodynamic description ofmicropore fluid differs from that of a bulk system (that is one without a boundary phase), since the fluid is non-uniform. It also differs from that of an adsorbate at a plane surface since it is confined. As a consequence a confusing array of pressures and tensions
236 can be defined. To minimise the confusion we restrict the discussion to an illustrative example of the slit pore, [23, 24]. A re-examination of adsorption thermodynamics applied specifically to adsorption in pores, has led to the conclusion that an important modification to IAS theory, as normally used, is necessary - namely that absolute rather than excess adsorption should be employed in the calculation [25,26]. The themaodynamic system comprises a parallel sided slit of uniform material and total internal sta'face area a immersed in a bath of fluid having a vottmae V[23]. The pore walls have no volume, and there are no edge effects between the fluid in the pore, and the external bulk phase of the same fluid. At e q t f i h ~ the chemical potentials of the internal phase and external phase of component are equal. Inside the pore, the pressure tensor has diagonal components p s (x,y) normal to the pore walls (= 89 and pr(z) parallel to the walls. For a slit of width H, an infinitesimal change in the internal energy, U, of an open multi-component system is given by: z d U = TdS - p B d V - d a f
[pr(z)
- PB ]dz
o
-
ff
(14)
-p ]dxdy+ F..=dN=
a
Mean values of the tangential and normal components of the pressure tensor can be defined by averaging over the pore width, and over the area of the pore surface, H
-
1
(16)
Pr = - ~ f Pr(z) dz 0
-
1
pN = -a
f f p (x,y)a ay
(15)
171
The expression for the change in the internal energy then simplifies to dU = TdS - pBdV
- [fir - PB] H d a
- [PN - PB] a d H
+ ~-, luadN~
(17)
The disjoining pressure,//is defined by the expression,
// .
l.( a ~ ) .
. s,v,a,N,
. 1 (dd_~AH) . . a
LV, a,N a
.
l(a~H ) . a
- - PB PN
0s)
Lg, a,~q
in which A is the Helmholtz free energy (U-TS'), and f~ is the grand free energy (U-TS-~2 p,,N,~). The surface tension may be defined by
237
-
HE~r
-
PB]
(19)
and analogous derivatives of the Helmholtz and grand free energies to those given in equation (18). The spreading pressure [19, 27] is defined by = (/~r - P--N) H
(20)
Comparison with equation (19) shows that this is not, in general the negative of the surface tension, except in the limiting case of a single adsorbing surface, when pB=ffN [23]. Finally, the solvation force, f~ is given by,
f~ :/~N a
(21)
A virtual change in pore volume, Vpcan be written as, (22)
d Vp : a d H + H d a
and with a little straightforward manipulation, equation (17) can be written, using the definitions in equations (18) and (20) as, d U : T d S - p , d V + PB dVp - ~ d a - fiN dVp + ~_./z, dN.
(23)
If the Gibbs dividing surface is now defined such that V,=V [24], equation (23) reduces to dU = TdS-
nda
-PNdVp
+ ~
g~dN~
(24)
From equation (24) we obtain the Gibbs-Duhem equation, 0 : SdT - ad~
- Vpd~ N + ~ N,~d,u,~
(25)
and at constant temperature, this reduces to a thermodynamic expression for an adsorption isotherm equation, analogous to the Gibbs isotherm,
1: Equation (26) may be written as:
(26)
238
add
= ~_~ N~dlz~
(27)
where the thermodynamic variable 9 is defined by [24] a e~ -
a ~
+ Vpp u
(28)
Clearly if 9 is constant then ~ V ~ , = 0 at constant temperature. A major goal in the theory of mixture adsorption is to be able to predict mixture isotherms from single component isotherms. An established routte is through the ideal adsorption theory (IAS) [28] or the non-ideal modification of this theory. For an ideal adsorbed solution theory, we can write the chemical potential in the adsorbed phase as
kt~T,d#,x~ .... ) = l ~ (T) + RTln[p~ (~) ] + RTlnx~
(29)
where x~ is the mole fraction of component tt in the adsorbate phase, and p~'(~) is the pressure in a single-component, pure bulk phase that would give rise to ~. In a gas phase, at total pressure p, the chemical potential for component ~, at mole fraction y~, is
p,~(T, ~,y,~ .... ) = p~ (I) + RTlny~p
(30)
and it follows from equations (29) and (30) that
py~, - p2( ~) x~,
(31)
This expression differs from the original IAS theory [28] in that p~* is determined at a particular value of 9 and not at a specified spreading pressure, n. Equation (27) shows that absolute, rather than excess, amounts adsorbed must be used to determine this pressure [24]. In an application to a model system, the adsorption of methane and ethane in slit pores of width 0.95 nm, was calculated from simulation at 296K, and compared with the alternative interpretations of the theory. IAS proved very successful when absolute adsorption was used to calculate p~" at constant ~, but failed badly when the excess adsorption was employed [24] (see figure 9). The wide divergence between the "excess" and "absolute" versions oflAS observed in these calculations are expected to be much smaller, or even non-existent, in low temperature adsorption and to diminish as the pore width is increased. Simulations and IAS calculations on a model adsorbent of silica microspheres have confirmed that absolute adsorption should be used in IAS [29]. In this work, an IAS theory for isosteric heats of mixtures in pores was also derived, again absolute rather than excess adsorption should be used in the calculations in order to achieve satisfactory agreement between theory and simulation.
239
3. SINGLE COMPONENT ADSORPTION IN SINGLE MICROPORES 3.1 Adsorption potential energy in mieropores Simple geometric models highlight the effect of overlap of potential energy from opposite parts of the pore wall. In many cases the dispersive and repulsive parts of the interaction are the only contributions to the physical adsorption energy. When the adsorbate is polar, electrostatic and induced interactions may also contribute. The latter are usually a very small fraction of the total, but cannot be obtained additively. To a good approximation the remaining terms are additive, and their contribution to the adsorbate adsorbent potential energy for a molecule at position ri may be written,
(32)
ul(ri) = I2 u2(ri,rj) J
where u2 is the potential energy for interaction between the adsorbate atom and an atom of the adsorbent at position ~. When only dispersive interactions are included, the attractive part of u2 varies approximately as ro6. For a probe at distance z, from a plane surface, the attractive part of the wall potential varies approximately as z, 3. The potential is reinforced if there is a second wall parallel to the first, and the effect intensifies as the walls are brought closer together, as illustrated in figure 1. As the separation between the walls is decreased, repulsive interactions begin to take over until eventually the probe is excluded, that is to say it is too large to fit into the pore space [11 ]. In cylindrical pores, the same principles apply, but generally the field at a given pore diameter is enhanced more than in the slit pore because curvature augments the overlap effect.
-2000 L/
0.0
~
......
,'~-~ 0.1
//
o/linder ~lit pore
~
---
.........
i
i
i
0.2
0.3
0.4
0.5
d s l a ' ~ frcxnpwe ce'tre' rrn Figure 1 Adsorbate adsorbent potential energy in silts and cylinders having the widths (diameters) indicated on the plots.
240 Many simulation studies have used slit or cylindrical pore models. Frequently the former are modelled as parallel graphite planes since the slit pore model with adsorbing planes extending to infinity is widely regarded as a plausible representation of the graphitic pores, and these are believed to be predominant in activated carbons. The interaction potential between an atom and the surface may expanded as a Fourier series [27] and expressed in the form (33)
u(r) = no(Z ) + Ul(Z) f ( x ~ y ) + ...
where r is the position of the adsorbate atom, and z is normal to the graphite basal plane. The fimction u~(z) attenuates, approximately exponentially with z, whilstf(x,y) is periodic in the plane of the adsorbent surface and commensurate with the graphite hexagons. Higher order terms in the expansion make a negligible contribution to the potential, and it is adequate at high temperature to model the surface as a solid continuum, represented by the so-called 10-4-3 potential which is dependent only on z,
u(z) = 2~p~%fos~A
~
_
~
_
o~f 3A(0.61A + z) 3
(34)
where Ps is the number density of the carbon, esl and o,f are the solid-fluid Lennard-Jones parameters and A is the spacing between graphitic planes. The Fourier expansion technique can be adapted equally well to substrates of other symmetry [27], and to various potential models [7], and has proved valuable as a means of rapid calculation for the adsorbate-adsorbent interaction. Cylindrical pore spaces occur in nanotubes [30,31] and in the MCM silicas [32,33]. An important difference between silts and cylinders is that confinement is in one or two dimensions respectively. Truly one-dimensional confinenmat is unlikely to be found in real materials, and some studies of other geometries such as square or rectangular cross sections have been reported [34, 35] that attempt to take this into account. The most important parameters influencing adsorption in micropores are pore width (relative to adsorbate molecular size), temperature and the relative strength of the adsorbate-adsorbent interactions. Other effects include the atomic structure of the surface and molecular shape of the adsorbate species. Surface structure, giving rise to potential corrugation or to more random heterogeneity, is often neglected in modelling, but may be important at low temperature.
3.2 Adsorption isotherms It is convenient to consider single component adsorption as being divided into low temperature and high temperature categories. The former implies studies at sub-critical temperatures, usually at 77K, where many routine characterisation amasurements are performed. High temperature refers predominantly to ambient temperattL~S which are relevant to many separation processes, and which are gaining popularity for characterisation purposes (see section 4 below). An important difference between high and low temperature adsorption is that the balance between kinetic and potential contr1%utions to the total energy moves towards the potential energy contribution as temperature is lowered. Low temperature adsorption is therefore more sensitive to structural details of the adsorbent, and can exhibit transitions, such as capillary condensation in mesopores, that may not be seen at ambient temperature if this is above the relevant critical temperature [36]. A survey of slit pore adsorption that illustrates these points was made by Balbuena and Gubbins [37], who used density functional theory as a basis for interpreting adsorption behaviour. Their
241
1.5
1.0
0.5
0.0 o.oool
o.ool
o.ol
-
o l
p/po
Figure 2. Simulated adsorption isotherms for nitrogen, modelled as a two centre molecule with quadrupole, in MgO slits at 77K. N/N,, gives the filling in monolayer units. Numbers on the plots are physical pore widths in nm.
discussion is based on the IUPAC classification of isotherms [1 ]. All six types of isotherm were found. At a reduced temperature of 0.8, type V isotherms occur in all but the smallest pores for weak adsorbents, but are replaced by type IV or type VI mesopore isotherms as the adsorbent strength increases. Type VI isotherms, in which layering transitions are manifested as isotherm steps, were found in pores with widths above 5 molecular diameters. In micropores, having widths smaller than 3 molecular diameters, which are the main focus of this chapter, the isotherms were classified as type I for all adsorbent strengths. An interesting feature that emerges when there are strong adsorption forces, is that 0~ 1 layering transitions are seen for both type I and type VI adsorption. These transitions only occur in pores within a rather narrow size range, where a very sharp change from nearly zero to monolayer coverage of the pore walls takes place over a very small pressure range. A simulation study [38] ofdiatomic nitrogen in MgO slit pores at 77K shows a similar transition at a pore width of 1.06nm (figure 2). At lower and higher pore widths, the 0-~ 1 transition is absent, and type IV behaviour starts to emerge when H is > 1.48nm. A similar pattern of behaviour was found in a density functional study of spherical nitrogen in graphitic slit pores [11]. Thomson and Gubbins have recently drawn attention to the existence of capillary condensation in 1.4nm width graphitic pores [39] in a model activated carbon. There is evidence to suggest that the location of transitions at low temperature, in pores of this size, may also be influenced by the existence of surface corrugation in the wall potential [40]. Several studies have appeared recently of adsorption in single pores at ambient temperature. For the adsorbates of interest this implies supercritical, or near supercritical adsorption. Because potential overlap can appreciably lower the adsorption potential energy in the micropore size range, pore filling can be achieved at pressures of a few bar, which is below the operating pressure of some industrial processes, and within the range of many contemporary adsorption rigs. Above the critical temperature, micropore isotherms have a classical type I shape, but when collected for a set of pore sizes it is clear that isotherm crossing occurs in all geometries [13,35,41,42]. This phenomenon is primarily due to packing restrictions which are most readily appreciated by plotting the data as isosteres [35,13]. An example, for methane in graphitic slits, is illustrated in figure 3. It is seen that at low pressures there is a favourable pore width at about 0.7nm. As pressure is
242
12 113bar 8 6
..~
9
7.5bar '--"----------, , . |
.
-
. . . . . .
, = = ,
i,
.
.
.
.
.
.
.
.
.
.
.
|
!
i
|
!
!
0.8
1.0
1.2
1.4
1.6
1.8
.
.
.
.
.
2.0
H/nm
Figure 3. Adsorption isobars for spherical methane (e/k-=-148K, 0=0.38 lnm) adsorbed in graphitic slit pores at 298K. increased, central regions of the pore begin to fill, and a second packing transition develops in pores of slightly above lnm in width, which moves to smaller pore sizes with increasing pressure. It is interesting to note that in closed cross sections, packing transitions are more clearly defined, and that higher order maxima appear [35]. Similar transitions are found for isosteric heat curves [13]. At higher pressure, the adsorption excess isotherms measured experimentally, pass through a a maximum, since it becomes easier to add molecules into the external gas phase than into the tightly packed adsorbate. This effect is also reflected in the isosteric heat curves [43]. A great deal ofrnodelling of pore adsorption, especially that using density functional theory, is perfonmd using spherical models for the molecules. In a simulation study of nitrogen adsorption into graphitic slit pores at 298K, it was found [20] that two centre and spherical models produced very similar results for wide (H=l.7 nm) pores, but that significant deviations between the two models occur at pressures above about 10 bar in pores of width 1.0nm. Clearly this effect will become more important as the aspect ratio of linear molecules increases.
3.3 Heats of adsorption The isosteric heat of adsorption (or isosteric enthalpy of adsorption), qs. is a differential heat, defined as the negative differential of the excess enthalpy of adsorption with respect to the excess adsorption [2,27]; qs, is a positive quantity. Experimentally, q~, can be calculated from a set of isotherms measured at close but different temperatures, or obtained directly by calorimetry [2]. Isosteric heat curves for microporous materials, plotted against adsorbate density, usually, though not always, have a steeply descending initial section at low density, pass through a minimum, and then through a maximum close to completion of the pore filling. If the experimental isotherm has a transition, such as the sub-monolayer steps that can appear at low temperatures, the q~, curve typically shows a cusp-like minimum followed by a sharp maximmn. The initial steep decline in qs, is conventionally attributed to heterogeneity in the adsorbent, and conversely if this feature is absent, the adsorbent is sometimes claimed to be homogeneous.
243
20 "T,
~__ 16
20
O
E
O
E
18
~-o
---o
~
0"
16
12 "7, E
qw
15 ~
8
"7 =o 10
4
5
f
,
,
r.J
....
,
,
5 p/nm -3
,
,
,
----o___ o-_
~
qw
~-~-%
0
10
0
2
4 p/nm -3
6
8
Figure 4. Isosteric heat curves for methane at 150K on a weakly adsorbing surface (left hand graph) and carbon dioxide at 298K on a strongly adsorbing surface (right hand graph) in model slit pores. The broken lines are for surfaces that are highly disordered, the full lines for an ordered surface. The upper graphs show qsr In the lower graphs, q,t has been split into molecule-wall (qw) and molecule-molecule (q~) parts [44].
A simulation study has been made of methane and carbon dioxide adsorbed in slit pores with walls formed from discrete atoms, interacting with the adsorbate atoms through a Lennard-Jones potential [44]. Severe thermal roughening of the surfaces did not significantly modify the qst curves in either low temperature, or high temperature, adsorption and could not account for the observed steep negative gradient in qa at either low or high temperature. Two examples are shown in figure 4. The figure also shows the separate contributions to qst from the adsorbate-adsorbent part of qst (qw) and from the adsorbate-adsorbate part of q,t (q,,,). These quantities are not available from experiment, but can be easily calculated in a simulation. In figure 4 it can be seen that the horizontal part of the q,t graph for methane at-150K can be attributed to the balance between the negative slope ofqw and the positive slope ofqm. The decrease in q~ occurs because the pore is wide enough to have a potential minimum at the wall but a higher adsorption potential energy at the centre (compare the curve labelled 1.0nm in figure 1). The first molecules adsorbed (i.e. at low adsorbate density) occupy positions in the potential minima at the walls, but at higher densities molecules tend to be adsorbed closer to the pore centre, and consequently qw decreases. On the other hand qm increases with density because there is an increase in the number and proximity of the neighbouring adsorbate molecules. This kind of compensation is not uncommon, and generally accounts for the horizontal q,t curves sometimes seen in experiments. It is clear that this feature in qst is not atm'butable to a homogeneous adsorbing surface, in the sense that all adsorbent sites have identical energies, since such an interpretation fails to account for the increase in adsorbate interaction energy. Similarly, it is hazardous to estimate the adsorbate interaction energy from the slope of q,, curves.
244 30
25
25
20
0.8nm
15
O.9nm
L. 0
E 20
~
0.7nm
E
~ 10 5 ~ 0
i i
3.Onto ~ 2
4
6
8
_
1.1nm
10 5
0
I 1.4nm
0
2
4
6
8
p/nm -3
p/nm"3 Figure 5. Isosteric heat curves (left hand graph) for methane adsorbed in a series of graphitic slit pores at 273K for the slit widths indicated. In the right hand graph, the top set of curves is for the corresponding adsorbate-adsorbent part of q,, (qw) ranging from the smallest pore width at the top to the largest at the bottom. The lines through the origin are the adsorbate-adsorbate part of qst (qm)" The lowest curves are for the smallest pore widths, qm curves are not resolved on this scale for the larger pores. Figure 5 shows a set of q,, curves calculated for methane adsorbed in graphitic slit pores at 273K [13]. In the narrowest pores qs, is very high, but rapidly decreases as H increases. The adsorbateadsorbent part of qst shows that these high isosteric heats are entirely attributable to strong molecule-wall interactions, and are expected when pore width is such as to maximise the well depth for adsorption. By contrast, the adsorbate-adsorbate part ofq~, shows little variation over the whole range of pore widths. There is a slight reduction in slope in the smallest pores (where the number of molecular neighbours is sterically reduced by the pore walls) and also maxima in these small pores; which can be attributed to adsorbate repulsions at high adsorptive pressure. When q,, is calculated for a suitable distribution of pore sizes, it is found that a steep initial decrease in qst call be created [13,44]. This occurs when there is a small numbe" of very narrow pores in the distribution (i.e. the distribution is skewed towards the large pore widths). Under these circumstances the relatively few high energy pores are filled at low pressure (low adsorbate concentration) and q,, falls when these sites have been used up. Grooves, crevices, and other molecular sized features of the adsorbent topology, could give rise to this effect (for example, certain orientations of the TiO 2 surface would possess very deep energy minima for some adsorbates). In some cases it may be a matter of nomenclature as to whether or not a particular feature is regarded as being a "pore". 4. THE DETERMINATION OF PORE SIZE DISTRIBUTION IN MICROPORES 4.1 Micropore
size distribution
The assessment ofmicroporosity (pores of sizes less than 2 nm) remains problematic despite the increasing interest in microporous materials like zeolites, activated carbons and clay minerals [45]. Indeed, while a number of more or less established characterization methods are currently in use for mesopores and macropores providing information on the pore size distribution (PSD), pore network connectivity and other structural parameters of the material [45], the determination of
245 micropore size distribution is an issue of active debate. The commonly employed DubininRadushkevich (DR) method [2] is based on nitrogen adsorption and the thermodynamic approach of Dubinin [46]. Although nitrogen isotherms may be routinely obtained at 77 K to high precision, the subsequent extraction of PSD using the DR approach has been subject to criticism, mainly because the mechanism of molecular adsorption in micropores is still under discussion [40,47]. Here we examine the application of GCMC simulations similar to those described above for single pores in determining the micropore size distribution. As conventional macroscopic descriptions of states of matter are generally invalid in micropores, improved approaches to the problem have been developed recently, based on molecular level theories and statistical simulations. In particular, density functional theory (DFT) has been used to provide an accurate description of simple (in practice atomic) fluids in geometrically simple confined spaces [48, 49]. Spherical nitrogen models have been employed in this context to develop practical methods for the evaluation of the pore structure over a wide range of pore sizes [ 11,50, 51 ]. Other applications of DFT to the determination ofPSD's have also been reported. [52,53,54]. Monte Carlo simulations have likewise been used to determine micropore size distribution and pore network connectivity from adsorption data [55,56]. Percolation theory has been used to extract an estimate of the connectivity of the pore network [56], and the possibility of using isosteric heat data as well as isotherm data has been proposed [57,58]. 4.2 Determination of micropore size distribution from CO 2 adsorption Contemporary computing power makes it feasible to construct a database from grand ensemble Monte Carlo (GCMC) in a reasonable time, and offers the advantages over DFT that no statistical mechanical approximations need to be made, and that multi-atom models of molecules can be employed. An example is the use of GCMC, in combination with CO2 experimental isotherm data, to characterize microporous carbons and obtain the corresponding pore size distribution [42]. The adsorptive gas and the temperature were selected on the grounds that it is relatively easy to obtain experimental isotherms at dry ice conditions (i.e. 195.5K) with realistic equilibration times, and the molecule is known for its ability to enter narrow micropores. The method was originally applied at low temperature (195.5K), and has recently been extended to high temperature isotherm data (at 298K and 308K, i.e. slightly below and above the CO 2 critical temperature, respectively). The mean CO2 density inside a set of single slit shaped graphitic pores of given widths, H, was found, using GCMC simulations, for a given temperature and a series of relative pressures. The carbon dioxide molecule was modelled as Lennard-Jones interaction sites on the atoms plus point charges to account for the quadrupole [59]. The graphitic surface was represented by the 10-4-3 potential (see section 3.1). The solid-fluid Lennard-Jones parameters acand er were calculated by combining the graphite parameters with the appropriate fluid parameters according to the Lorentz-Berthelot rules. The validation of the adsorbate-adsorbent potential functions used in this study was made by comparing measured and calculated isosteric heats of adsorption at zero coverage as well as experimental and simulated isotherms on non-porous surfaces [42]. In the simulations, H is defined as the distance between the nuclei of carbon atoms in opposite pore walls. This differs from the pore width probed in experiment. For comparison between computed and measured isotherms, the simulation results were corrected using the effective pore width H' (which is determined by the experiments) is given by:
H' = H -
A
(35)
where A=0.335 nrrL Alternatively, it has been proposed [20,60] to use an estimation of the effective
246
pore width based on the reduction in accessible pore volume by the adsorbate, caused by the physical size of the carbon atoms. Taking the distance of closest possible approach of adsorbate to adsorbent to be Zo, the position where the potential function for a plane wall passes through zero, the corrected pore width is, H' = H -
(36)
2z o - Og
where ag is the hard sphere diameter of an adsorbate atom. If equation (36) is applied in the CO2graphite system, it is found that about 0.24 nm should be subtracted from H to define H'. As pointed out in section 2.2 above, the pore width H' can only be precisely defined with respect to the method used for calibration. To create the dataNtse, CO2 density profiles across the slit pore have been computed (at 308K and 298K) for a range ofmicropore widths from 0.65 nm to 1.95 nm, in steps of 0.1 nm. From this information, the average density in the micropores was used to construct the isotherms shown in figure 6. The CO: isotherms (at 195.5, 298 and 308 K) were used as a basis for the PSD analysis of two different microporous carbons (A and B). Carbon A (BP Chemicals J1011H) was made from phenolic resin [61 ], and has a highly microporous structure with an estimated most probable pore size of the order of 0.7-0.9 nm. Carbon B (Norit RB4) is a commercially available activated carbon possessing pores in the high micropore range, close to 2 nrnThe determination of the optimal PSD requires the solution of a numerical minimization problem under certain constraints. The function to be minimized can be written, k Q, = E j=l
(37)
PoVJ
at different pressure values p,. In equation (37), Q, is the experimentally found sorbed amount at pressure p,, p,j the calculated fluid density in a pore of width//j at the same pressure p,, and Vj represents the volume of the pores with size//1 ( O<j
12
10
10
p8 i 6
P6
8
4
4
2
2
0
0
20
p/bar
40
60
0
298K
0
20
40
p/bar
60
Figure 6. Adsorption isotherms in graphitic slit pores from GCMC simulations for CO2 at two different temperatures for a series of slit widths from 0.65 to 1.95nm in steps of 0.1nm. The initial slope decreases as pore size increases.
247
1.5
e-
195K-~ B //5 2 9 8 K
.195K
A 1.0
Eo
.'r "o 0.5 v
/ //"-
7/1
K
/
0.0
'
0.8
"
,' ' - /
1.0 H/nm
..
,..
_x__ . . . . . .
1.2
~-,-~>~'--
1.4
--
0
0.8
1.0
1.2
1.4
1.6
1.8
H/nm
Figure 7. Pore size distributions in two carbon samples, A and B (see text) determined by CO2 adsorption at 3 temperatures.
their sum should be equal to the measured total pore volume. A FORTRAN routine solving linearly constrained linear least-squares problems, based on a two-phase (primal) quadratic programming method (E04NCF routine, NAG library), was implemented, and the resulting PSD's (from the isotherms at 195.5,298 and 308 K) are shown in figure 7 for each carbon sample tested. The PSD's ofcarbon A ( ~ e 7)exhibit a broad band of pore sizes between 0.65 and 1.15 nm in good accord with previous estimates [61 ]. However, there is a significant difference between the low (195.5 K) and the high (298 and 308 K) temperature PSD's. Indeed, the pore volume associated with the high temperature - high pressure PSD's is about 73% of the corresponding pore volume of the PSD at 195K. It is unlikely that molecular sieving is the cause of this discrepancy, since the gas employed is the same at the three temperatures. The most plausible explanation is that, in the experiments, the interaction of the carbon dioxide quadrupole with polar sites on the pore surfaces becomes a more dominant part of the total energy at low temperatures [61], and this is not accounted for in the model. The enhanced adsorption of CO 2 at low temperature/pressure is attributed, in the PSD analysis, to extra micropore volume and when used to predict CO2 uptake for the same material at high temperatures, systematically overpredicts the amount adsorbed. On the other hand, the 298K PSD satisfactorily predicts the 308K isotherm and vice versa. The presence of polar defects in the carbon structure appears to impose a significant limitation on the use of low terr~rature CO2 adsorption for the determination of pore structure and caution should be exercised in this respect. Similar results have been found previously using low temperature nitrogen and high temperature methane adsorption data [61 ]. In the The Norit sample 03) the main part ofthe pore volume is concentrated in the range 1.551.65 nm. In this material the production process eliminates most of the polar sites and the pore volumes and the PSD's are quite similar for all three temperatures; the use of each PSD to predict adsorption at other temperatures here gives good results. Similar results have been obtained when the method is applied again on the same samples using nitrogen adsorption [62]. For example, in sample A, polar sites lead to overestimation of the high temperature isotherms when using the PSD found from the N 2 data, but for sample B the PSD obtained from nitrogen adsorption gives a satisfactory prediction of the CO2 isotherms as shown in figure 8. It may be concluded that the method of micropore size distribution determination based on GCMC simulations shows great promise. However, caution should be exercised when interpreting the results, especially if the probe molecule is polar and the existence of polar sites in the sample is suspected. Conversely the
248
7 r =~ 5
,
0.5
t
f 7I/
~ 4 ~i
t.m
o~
B
0.4
l----l-
-- ~
. . . .
_~,--=-~m-o-------,~----~
0.3
/
i
t~
0.1 0
~
10-,=
lO-a
10-2
10-1
0.0
9
10 ~
10 4
p/bar
lO-a
10 2
10-1
p/bar
Figure 8. Experimental low temperature adsorption isotherms for CO2 adsorption on carbon samples A and B (open points). Isotherms recalculated from PSD obtained from nitrogen (77K) adsorption (filled circles) and from carbon dioxide adsorption at 298K (filled squares). See text for details. possibility exists to exploit differences between the results for polar and non-polar species as a means of probing polar sites [ 14]. Currently cylindrical pore geometries and the use of argon are being investigated. .
5. MIXTURE ADSORPTION IN SINGLE MICROPORES
The equilibrium binary selectivity, sometimes known as the equilibrium separation factor, is a useful guide to the separative potential of an adsorbent. It is defined by the equation, s~,~ -
xAYB xBYA
(38)
where x~, y, are mole fractions of component a in the adsorbate phase, and in the gas phase respectively. Recent simulation results [63] suggest that SA/Bcould be a good guide to the general trends in dynamic separation factors. Here we concentrate on adsorption equilibrium. The selectivity is dependent on many variables, including temperature, pore size (and pore size distribution and network structure), gas phase mole fraction, and the total pressure in the adsorptive phase, as well as the specific geometry and molecular properties of the components in the mixture, and the adsorbent surface energy. Tan and Gubbins [48] used density functional theory to study a mixture of spherical LennardJones molecules in graphitic slit pores. They were able to establish a classification scheme and to identify the salient features of temperature and pressure dependence. They showed that total pressure was a far more important variable than y , in determining SA/Bat a constant temperature. Selectivity isotherms in this study typically showed a maximum at low pressure and at temperatures substantially above the capillary critical temperature for the mixture. At lower temperatures, SA/B versusp isotherms exhl%ited transitions related to phase transition phenomena. These general trends are observed when GCMC is used to model mixtures of spherical molecules in pores. Although DFT has been invaluable in establishing the patterns of selectivity behaviour, agreement with GCMC is not always good [64] as we illustrate below. Moreover, multi-atom models in which the
249 molecular model has an aspect ratio > 1 can differ significantly from spherical models [65 ]. When spherical models are used, the kinetic diameter that best represents bulk phase gas or liquid state properties is greater than the axial diameter of the molecule. For example, a suitable choice of kinetic diameter for CO2 is 0.40 nm, but in the three-centre model, described in section 4.2, the diameter of the oxygen atom (the larger atom) is 0.3026nrn. Thus the minimum pore size accessible to a three-centre model is smaller than that accessible to the one-centre model. A second factor is that there is interplay between entropic and energetic effects for linear molecules confined in narrow pores. The end atoms of a linear molecule in a narrow slit pore can interact favourably with the same wall, or with opposite walls by spanning the pore. However, restriction of rotational freedom imposed by the pore walls can limit this advantage. In a simulation of methane-ethane mixtures, in which ethane was modelled as a two centre molecule [65], it was shown that SuB decreased when the ethane was artificially elongated without altering any other parameters. In the low density limit, when both species obey Henry' s law, it is not difficult to demonstrate how this effect operates. In this limit Sus between a long (L) molecule, and a spherical (S) molecule is given by the expression 1
Sus =
(39)
fexp(-flUs) dr
in which o is the orientational coordinate normalised by ,(2 (4g for a linear species), and uL, Us are the interaction energies of L and S with the pore wall. As the pore is narrowed, or the molecule lengthened, the integration limits on ~ are restricted to a smaller range of angles, and consequently SL/s decreases. Some of the above points are illustrated in figure 9 which shows selectivity at 296K, from approximately equimolar mixtures, for different adsorbate models in a graphitic 10-4-3 slit pore of
3o
l
IAS excess adsorption -
. / / /
---'~
IAS absolute adsorption
20~1~
- - ~
10 ~_~-----o__~_/e2 ~
0
DFT~ ~ .
. . . .
~_____-
.G---
5
10 15 20 p/bar Figure 9. Methane/ethaneselectivityfrom a 50/50 gas phase in a graphitic slit pore of width 0.925nmat 296K. The full line is from DFT calculations [48]. Openpoints are from GCMC simulations using the spherical ethane model [64], filled points are from GCMC simulations using the two centre ethane model [65]. The broken lines show the corresponding IAS calculations (see section 2.3).
250 width 0.953nm (H=-2.5am,,ha,e). The selectivity isotherms all have a maximum in the low pressure region, before ethane adsorption reaches the "knee" of the isotherm, which may be attributed to favourable cooperative interaction between the ethane molecules. Density functional [48] theory typically overpredicts the selectivity as calculated by GCMC for the same spherical models ( e m ~ 1 4 8 K , e~cqc~243K; a,~,=0.381nm, a~th~,,=0.395nm). Similar results were found for wider pores, although the agreement between between DFT and GCMC is improved. Later versions [49] of the DFT theory show closer agreement with simulation [66]. The two centre model has much higher ethane selectivity over the whole pressure range. In this model, the ethane molecules are modelled as two Lennard-Jones pseudo-atoms with e/k=-139K, tr =0.3512nm and a bond length of 0.235nrn. The increased selectivity, compared to the spherical models, is attributed to the ability of both atom centres on the ethane to interact with the wall. If the bond length is increased from 0.235nm to 0.4ran, selectivity falls to the same level as for the spherical model because of the effect oforientational restrictions discussed above [64]. The IAS theory discussed in section 2.3 agrees rather well with GCMC calculations from both models. The accuracy of the theory, as is well known, depends rather crucially on the accuracy of the single component isotherm fit at very low pressure [65]. Again it should be stressed that all the calculations here refer to absolute, rather than excess, adsorption. The generally good agreement between GCMC and IAS has been confirmed independently for ethane-methane mixtures in graphitic pores [12], and more recently for these mixtures in a silica sphere model [29]. Simulations of mixture adsorption with multi-atom models have revealed selectivity isotherms outside the original Tan and Gubbins classification [48]. Propane-ethane mixtures, for example show a monotonic increase of S~v8in narrow pores as total pressure is decreased [67]. This type ofbehaviour is quite common in e ~ n t a l systems. Conversely, mixtures of carbon dioxide with methane or nitrogen, in graphitic slit pores, typically show an increase of S,vBwith pressure that exhibit no maximum, or only a very weak maximum at pressures up to 50bar [60,68]. This may be explained by the rather weaker interactions between CO2 molecules compared to ethane or propane. The less dense packing in the CO2 systems means that there is less inhibition of reorientation by neighbouring molecules which, combined with the energetic advantage of the larger molecules, favours the longer molecule of the pair. The effect is analogous to that discussed above for the Henry law limit, and expressed in equation (39). When several selectivity isotherms are plotted on a single graph, it is apparent that, like the single component adsorption isotherms (c.f. figures 3 and 4), there is generally a complex series of crossings, implying that different pore sizes are effective for separation at different total pressures. As an example, figure 10 shows the selectivity in a multi-atom propane/ethane mixture in a graphitic slit pore at 296K [67] at a pressure of 12.8bar. The various minima and maxima appearing in this plot can be interpreted from detailed analysis of the single particle density and orientational distributions across the pore [47,67]. The propane has 3 united atoms and the ethane two, and selectivity always favours propane for energetic reasons. The first minimum (H=0.762) occurs when both the ethane and the propane are constrained to lie fiat. The entropic disadvantage is greater for the bent propane molecule for which to in equation (39) has three degrees of freedom than it is for the linear ethane with only two. The highest maximum (H=0.857) occurs at a pore width where propane atoms can lie in the energy minima at both walls; for most propanes this occurs in such a way that two atoms are at one wall and the third at the opposite wall. The implication is that the pore is now just wide enough to permit free re-orientation of the propane, but still sufficiently narrow that propane is strongly favoured energetically. The energy advantage is lost as the pore width increases. When the pore width is 0.991nm, the adsorbate can pack into two layers each fiat against the pore walls, and orientational freedom is inhibited by other molecules. As before propane loses more orientational advantage than ethane in this situation. At
251 i
/~/=0.857nm
1
i
,.- 6 -~"'
, ~ j H= 1.24nm
e 0. co 4
2
0.8
1.0
1.2
Hlnm
1.4
1.6
Figure 10. Selectivity at 296K and a pressure of 12.8 bar, for propane/ethane mixtures in graphitic slit pores.
the next maximum, most propane molecules are found to orient with two atoms in a minimum at the wall, but the ethane is strongly constrained to the wall layers. The general picture remains the same over a wide range of pressures, although small shifts in the maxima and minima can occur, since packing is also dependent on pressure. It can be seen that the effect of pore size on selectivity can be rather subtle, because the balance between energetic and orientational effects is different for each species in a mixture. Two other pore properties can also influence selectivity; the surface energy of the adsorbent, and the geometry of the pore. In a study of CO2-methane mixture adsorption [68] it was found that a changeover could take place from selectivity in favour of carbon dioxide to selectivity in favour of methane as these factors were altered. Thus it is possible, in principle, to tailor pores to favour the selection of either of the components in the binary mixture. Experimentally it has been observed that activated carbon pores (usually considered to be slit-like in geometry) favour carbon dioxide adsorption from this mixture [60], but methane adsorption was favoured in A1PO4-5 [69] which has unconnected pores of approximately cylindrical cross section. Simulations were carded out using the three-atom carbon dioxide model described in section 4, and a spherical methane model. The adsorbent was represented as a "pseudo-atom" model, in which smooth-walled pores of different geometry (e.g. slit or cylinder) and different adsorbent energy could be constructed. The adsorbent atoms were characterised by the Lennard-Jones parameters, { eJk, ass}, and eJk was chosen to represent either an oxide surface eJk=270K or a graphite surface ejk=600K (cf figure 1). Both slit and cylinder geometries were examined. It was found that selectivity as high as 5 in favour of methane could occur in narrow cylindrical "oxide" pores, and that methane selectivity was slightly favoured in these pores at sufficiently low pressure, even in much larger pores; in general agreement with experimental results. However, slit pores with oxide-like surfaces also showed some preference for methane at very low pressures. The graphs in figure 11 of the selectivity, S~bo, ~oxid~/meth~,e,against pore size for the two different pore geometries and two different surface energies summarise the main points. The general shape of the
252
4-~
[
e=~k=6OOK
~3-
/
I
/\ I\
/ \ / \
~-
~ss/k=6OOK
\ /
/
/
\ \
/
~ 2-
/ / / /
1-
~ ~;ss/k=270K 0 ~
0.6
0.8
I
~
I
I
I
I
1
1.0
1.2
1.4
0.8
1.0
1.2
1.4
Cylinder diameterlnm
1.6
Slit width/rim
Figure 11. Selectivity isotherms at 298K from 50/50 mixtures of methane and carbon dioxide into pseudo-atom pores of cylindrical and slit shaped cross section at a total pressure of 2.5 bar (open points) and 25 bar (filled points). The adsorbent energy is determined by the parameter ess/k [68]. selectivity versus H plot for the graphitic adsorbents is similar to that found earlier for 10-4-3 graphite slit pores. Initially there is a very high selectivity for carbon dioxide, corresponding to molecular sieving at pore sizes too small to accommodate methane. This is then followed by a minimum and then by a strong maximum at a pore width slightly less than l nm. The minimum corresponds to the pore width at which the methane molecule (with o=0.3812 nm) experiences a strong adsorption well in the pore centre, corresponding to maximum potential overlap for this molecule. By contrast the carbon dioxide, with smaller atomic sizes is not so strongly favoured energetically, and at the same time is constrained from re-orienting freely by the pore wall repulsions (c.f. equation (39)). In pores with H=0.95nm, CO2 can rotate without inhibition, whilst methane can no longer pack optimally, since the molecule is too large to form a bilayer. The high selectivity (-5) for methane in the cylindrical pores, compared to the highest value of Smm~na~o, 9oxm of only 1.2 that occurs in the slit pores, can also be explained according to these principles. In the most favourable cylindrical pore, methane experiences a stronger adsorption potential than in the corresponding slit pore because the overlap effects - enhancing the potential - occur in all directions. At the same time, the freedom of carbon dioxide to reorient is even more restricted than it was in the slit pores. The effect of temperature on selectivity has not been very widely studied but may have very substantial significance, since the relative Boltzmann factors of the species in the mixture are involved. For example in an ethane-methane-graphite pore study, it was observed that selectivity increased exponentially as temperature decreased, with doubling every 50K [65]. The variation of selectivity with surface energy observed in the study discussed above [68], suggests that temperature changes over a sufficiently wide range, may also cause an inversion from selectivity for one species to selectivity for the other species in a binary mixture. This was indeed found to be the case in a study of a binary Lennard-Jones mixture in single walled nanotubes [31 ]. The mixtures studied included spherical models for cyclohexane and octamethylcyclotetrasiloxane (OMCTS) for
253 which eJk=324K and 343K respectively and 0=0.54 nm and 0.77 nm respectively. In small diameter tubes, (D=1.36 nm) there is a sharp transition at about 220 K from complete exclusion of OMCTS to a high selectivity in favour of OMCTS. In larger tubes, the transition becomes more gradual, but inversion of the selectivity still occurs. 6. S U M M A R Y AND CONCLUSIONS
Computer simulation can be a powerful adjunct to the experimental investigation of physical adsorption in microporous materials. The problem is particularly well suited to this method of investigation for at least two reasons: Firstly, since there is a solid boundary phase, the number of molecules in the system is limited, and the number of particles in the model system can be similar to the number in a representative section of the real material. Secondly, the properties of matter in highly confined spaces are often quite different from those of bulk matter under similar conditions. In comparing simulation results with experiment, or using simulation as a basis for screening or prediction, it is necessary to keep in mind that isotherm measurements relate to excess amounts adsorbed, and that in micropores- especially at ambient temperatures - there can be large differences between excess and absolute adsorption. Conversely it turns out that it is the absolute, and not the excess adsorption, that is needed in applying IAS theory to microporous adsorption. Many of the properties of adsorbate fluids in microporous spaces derive from the high degree of confinement which leads to the phenomenon referred to as "potential overlap", illustrated in figure 1. The studies discussed in this Chapter mainly make use of simple potential models, however it must be mentioned that the adsorbent-adsorbate potential, since it is a major part of the total potential energy, can be crucially important in simulations of well-defined materials such as zeolites when the adsorbate species is close to the channel size [70]. Even in more amorphous materials the potential models employed in simulation may be highly significant, for example the difference between spherical and multi-centre molecular models can radically alter predictions of packing and selectivity in confined spaces. A problem central to all the above points is that of being able to characterise accurately the pore structure of an amorphous microporous material. Here, computer simulation has led to valuable advances, but it is clear that the problem is not yet satisfactorily resolved. In future work it will be necessary to develop methods with alternative probes and under alternative conditions, as well as to seek methods of interpretation which can reconcile observed differences. One problem that has not yet received much attention is that of the role of electrostatic sites. Evidence suggests that these can make substantial differences in the adsorption properties of polar species, particularly at low temperatures. Conversely, electrostatic sites are thought to be of paramount importance in determining selectivity in mixture adsorption into zeolites containing extra-framework ions. Single pore simulation studies have made it possible to lay down some basic principles underlying effective equilibrium selectivity in micropores. One important requirement is that the potential energy should be optimum for the retained species, which depends both on the adsorbent material, (e.g. carbon or oxide adsorbent) and on the shape and size of the pore spaces. Secondly larger molecules gain an entropic advantage when the pores are large enough to easily permit reorientation. Packing with other species at high densities also limits this ability. Membranes run under non-equilibrium conditions and usually contain complex interconnected pore structures. Therefore equilibrium selectivity in single pores cannot be expected to reveal a complete picture. Nevertheless there is evidence that simple models along these lines should be a useful guide to the kind of structures that should be targeted in attempting to tailor porous materials, and to expected performance.
254 REFERENCES
1. K. S.W. Sing, D. H. Everett, R. A. W. Haul, L. Moscou, R. A. Pierrotti, J Rouquerol, and T. Siemienieswska, Pure and Applied Chem., 57 (1985) 603. 2. F. Rouquerol J. Rouquerol and K S. W. Sing, Adsorption by Powders and Porous Solids, Academic Press, 1999. 3. R. F. Cracknell, K. E. Gubbins, M. W. Maddox and D. Nicholson, Acct. Chem. Res, 28 (1995) 281. 4. J. C. P. Broekhoffand J. H. de Boer, J. Catalysis, 9 (1967) 8, 15; J. Catalysis, l0 (1968) 368, 377. 5. D. Nicholson, Trans. Far. Soc. 64 (1968) 3416. 6. W. F. Saam and M. W. Cole, Phys. Rev. B, 11 (1975) 1086. 7.D. Nicholson and N. G. Parsonage, Computer Simulation and the Statistical Mechanics of Adsorption, Academic Press, 1982. 8. E. V. Votyakov, Y. K. Tovbin, J. M. D. MacEkoy, A. Roche, Langmuir, 15 (1999) 5713. 9. N. A. Seaton, J. P. R. B. Walton and N. Quirke, Carbon, 27 (1989) 16. 10. P. N. Aukett, N. Quirke, S. Riddiford, and S. R. Tennison, Carbon, 30 (1992) 913. 11. C. Lastoskie, ICE. Gubbins, and N. Quirke, J. Phys. Chero_, 97 (1993) 4786. 12. V. I. Gusev, J. A. O'Brien and N. A. Seaton, Langmuir, 13 (1997) 2815. 13. D. Nicholson and N. Quirke, Characterisation of Porous Solids (COPS) VI, in press, 1999. 14. S. G. Chen and R. T. Yang, Langmuir, 9 (1993) 3259. 15. M. Allen and D. J. Tildesley, Simulation of Liquids, Oxford University Press, 1986. 16. B. Smit and D. Frenkel, Understanding Molecular Simulation, Academic Press, San Diego, 1996. 17. R. F. CrackneU, D. Nicholson, N. G. Parsonage and H. Evans, Mol. Phys., 71 (1990) 931. 18. B. Smit and J. I. Siepmmm, J. Phys. Chem., 98 (1994) 8442. 19. W. A. Steele in The Solid Gas Interface, vol. 1, Ed. E. A. Flood, Marcel-Dekker, New York (1967). 20. K. Kaneko, R. F. Cracknell and D. Nicholson, Langmuir, 10 (1994) 4606. 21. A. V. Neimark and P. I. Ravikovitch, Langmuir, 13 (1997) 5148. 22. A. L. Myers, J. A. Calles and G. Calleja, Adsorption, 3 (1997) 107. 23. J. J. Magda, M. TirreU and H. T. Davis, J. CherrL Phys., 83 (1985) 1888. 24. R. F. Cracknell and D. Nicholson, Adsorption, 1 (1995) 7. 25. D. J. Diestler, M. Schoen, J. E. Curry and J. H. Cushman, J. CherrL Phys., 100 (1994) 9140. 26. P. Bordarier, M. Schoen and A. H. Fuchs, Phys Rev. E., 57 (1998) 1621. 27.W.A. Steele, The Interaction of Gases with Solid Surfaces, Pergamon Press, Oxford, (1974). 28. A. L. Myers and J. M. Prausnitz, AIChEJ, 11 (1965) 121. 29. T. Vuong and P. A. Monson, Adsorption, 5 (1999) 295. 30. S. Iijima, Nature, 354 (1991) 56. 31. K. G. Ayappa, Langmuir, 14 (1999) 880. 32. J. S. Beck, J. C. Vartuli, W. J. Roth, M. E. Leonowicz, C. T. Kresge, K. D. Schmitt, C. T.-W. Chu, D. H. Olson, E. W. Sheppard, S. B. McCallen, J. B. Higgins and J. L. Schlenker,, J. Amer Cheli~ Soc., 114 (1992) 10834. 33. M. W. Maddox, S. L. Sowers and K. E. Gubbins, Adsorption, 2 (1996) 23.
255 34. M. J. Bojan and W. A. Steele, Langmuir, 5 (1989) 625; Carbon, 36 (1998) 1417. 35. G. M. Davies and N. A. Seaton, Carbon, 36 (1998) 1473. 36. L. D. Gelb, K. E. Gubbins, R. Radhakrishnan and M. Sliwinska-Bartkowiak, Rep. on Prog. in Phys., 62 (1999) 1. 37. P. B. Balbuena and K. E. Gubbins, Langmuir, 9 (1993) 1801. 38. D. Nicholson, N. A. Freeman, and M. A. Day, Royal Society of Chemistry Special Publication No. 213, (1997) 549. 39. K. Thomson and K. E. Gubbins, 2 nd Pacific Basin Conference on Adsorption Engineering and Technology, in press. 40. D. Nicholson, J. Chem. Soc. Faraday Trans., 90 (1994) 181. 41. D. Keffer, H. T. Davis and A. V. McCormick, Adsorption, 2 (1996) 9. 42. S. Samios, S., A. K. Stubos, N. K. KaneUopoulos, R. F. CrackneU, G. K. Papadopoulos and D. Nicholson, Langmuir, 13 (1997) 2795. 43. D. Nicholson, R. W. Adams, R. F. Cracknell, and G. K. Papadopoulos, Royal Society of Chemistry Special Publication No. 213, eds. B. McEnany, et al. (1997) 57. 44. D. Nicholson, Langmuir, 15 (1999) 2508. 45. K. Kaneko, J. Membrane Sci. 96 (1994) 59. 46. M.M. Dubinin, Chem. Rev., 60 (1960) 235. 47. D. Nicholson, J. Chem. Soc., Faraday Trans., 92 (1996) 1. 48. Z. Tan and K.E. Gubbins, J. Phys. Chem., 96 (1992) 845. 49. E. Kierlik and M. L. Rosinberg, Phys. Rev. A, 44 (1991) 5025. 50. N. A. Seaton, J. P. R. B. Walton and N. Quirke, Carbon, 27 (1989) 853. 51. P. N. Aukett, N. Quirke, S. Riddiford and S. R. Tennison, Carbon, 30 (1992) 913. 52. J. P. Olivier, Carbon, 36 (1998) 1469. 53. P. I. Ravikovitch, S. C. O. DomhnaiU, A. V. Neimark, F. Schtith and K. K. Unger, Langmuir, 11 (1995) 4765. 54. K. A. Sosin and D. F. Quinn, J. Porous Mater., 1 (1995) 111. 55. V.I. Gusev, J. A. O'Brien and N.A. Seaton, Langmuir, 13 (1997) 2815. 56. M. V. Lopez-Ramon, J. JagieUo, T. J. Bandosz and N. A. Seaton, Langmuir, 13 (1997) 4435. 57. D. Nicholson, Langmuir, (1999) 2508. 58. D. Nicholson and N. Quirke, COPS V, Heidelberg, 1999 (in press). 59. C.S. Murthy, S.F.O'Shea and I.R. McDonald, Mol. Phys., 50 (1983) 531; K. D. Hammonds, I. R. McDonald and D.J. Tildesley, Mol. Phys., 70 (1990) 175. 60. R. F. Cracknell, D. Nicholson, S. R. Tennison and J. Bromhead, Adsorption, 2 (1996) 193. 61. N. Quirke, and S.R. Tennison, Carbon, 34 (1996) 1281. 62. T. Stubos et al, in press. 63. L. Xu, M. G. Sedigh, M. Sahimi and T. T. Tsotsis, Phys Rev. Letts., 80 (1998) 3511; L. Xu, T. Tsotsis and M. Sahimi, J. Chem. Phys., 111 (1999) 3252; K. P. Travis and K. E. Gubbins, J. Chem. Phys., Submitted (2000). 64. R. F. Cracknell, D. Nicholson and N. Quirke, Mol. Phys., 80 (1993) 885. 65. R. F. Cracknell, D. Nicholson and N. Quirke, Molecular Simulation, 13 (1994) 161. 66. S. L. Sowers and K. E. Gubbins, Langmuir, 11 (1995) 4758. 67. R. F. Cracknell and D. Nicholson, J. Chem. Soc. Faraday Trans., 90 (1994) 1487. 68. D. Nicholson and K. E. Gubbins, J. Chem. Phys., 104 (1996) 8126.
256 69. C. A. Koh, R. L. Nooney, S. Tahir, C. C. Tang and G. Georgiou, Fundamentals of Adsorption V, ed D. LeVan, Kluwer, Dordrecht, (1996) 473. 70. R. J.-M. Pellenq and D. Nicholson, J. Phys. Chem., 98 (1994) 13339; D. Nicholson and R. J.-M. Pellenq, Adv. in Coll. and Interf. Sci., 76-77 (1998) 179.
Recent Advancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) 92000 ElsevierScienceB.V.All rightsreserved.
257
M o l e c u l a r S i m u l a t i o n of Transport in a Single Micropore David Nicholson and Karl Travis Department of Chemistry, Imperial College of Science, Technology and Medicine, London SW7 2AY United Kingdom I. INTRODUCTION
1.1 Flow of adsorbate through porous materials The interpretation of experimental transport data for real porous materials is complicated by their underlying structural complexity [ 1,2]. This is apparent for compacts made from primary porous or non-porous particles, but is also true for crystalline microporous solids such as zeolites, where small variations in channel geometry, and the consequent variation in the potential field experienced by the transported molecules, may result in quite significant alterations to diffusion coefficients [3]. Attempts to prepare model systems in the laboratory whose geometry can be understood in simple terms tend to be frustrated by artefacts such as macroscopic density inhomogeneity due to compacting or to unquantifiable skin effects where symmetry is broken at the solid boundary [ 1,4]. These difficulties are particularly pronounced for materials with pores in the sub-nanometre size range, that are believed to be the most effective for the separation of small molecules [5]. Microscopic experimental probes, such as NMR and neutron scattering [ 1,6], offer the possibility of accessing detailed molecular motion, but are still reliant on an understanding of the movement of molecules in complex force fields. Computer simulation is well suited to achieving insights into the molecular processes occurring in highly confined environments. The application of molecular modelling techniques is now sufficiently advanced that realistic representations of matter at the molecular level are commonplace, and by using simplified models for boundary surfaces, it is possible to work with a relatively small number of particles. One approach to modelling porous solids is to represent (more or less) disordered materials as collections of particles (see Chapter 2.1). An example where such models have been used to study transport phenomena is the modelling of porous silica by micro-spheres [7]. This type of approach dates back to the so-called Lorentz gas [8]; a mixture of normal and massive gas particles, later developed as the dusty gas model [9]. Although these types of model have the advantage that they capture the essentially random nature of many pore spaces, they suffer from the disadvantage that specific geometrical effects cannot be easily understood. For example molecular sized crevices between micro-spheres where strong adsorbent fields can exist, may have the effect of strongly localising molecules which would be more mobile in the larger inter-particle voids. Moreover, the scale of system required to achieve a statistical representation places heavy demands, even on
258 contemporary computing resources. An alternative program is to study systems of simple geometry with a view to constructing networks that are statistically representative of real porous materials (see Chapter 2.3). Clearly there are also disadvantages to this approach. For example it is difficult to handle pore junctions and geometric variations that are local on the atomic scale. Nevertheless single pore studies are useful for focussing attention on fundamental molecular processes, otten they can be of practical importance in cases where the behaviour of real materials tends to be dominated by a narrow range of pore sizes as in some microporous carbons.
1.2 Gas flow in single capillaries A simple view of flow in confined spaces can be achieved by ignoring intermolecular interactions. The assumption that only molecular kinetic energy contributes to the total energy of the flowing particles leads, of course to the ideal gas equation of state and to the corresponding kinetic theory equations for diffusion, thermal conductivity and viscosity [8,10]. The steady state flow of a single gas under a pressure gradient 8p(x, t)/ax can be expressed as the flux dx (molecules per unit time per unit area) in Fick' s law form, by
where D~), the ditfusion coefficient at the mean number density p = p/kT, is in general dependent on the density of the gas and on the capillary geometry. The first studies of gas flow in glass capillaries were carried out ninety years ago by Knudsen [ 11 ], who made measurements of the flux of rarefied gases through bundles of capillaries. In a cylindrical capillary of radius r, at very low pressure where the mean free path is much larger than the capillary radius, D(p) has the (density independent) limit
DK
Totald
D(p)~ c ) s~<~'iJ " o~
~ scorrelationdiffusion~ " ~ Poiseuilleterm i!
Figure 1. Gas phase diffusion coefficient as a function of the gas phase density in a single cylindrical capillary, illustrating the minimum in the total diffusion. D(p) is calculated as the sum of the self diffusion, cross correlation diffusion and Poiseuille (viscous terms). See equations (44) and (73) below.
259 D~: = D (p) - 2
,~0
r(v)/3
(Z)
where (v) is the mean speed of the gas molecules. At higher pressures, D(p) passes through a minimum and eventually reaches a viscous flow limit, where it increases linearly with pressure. A schematic plot is shown in figure 1. Similar experiments carried out on porous materials containing large pores, for example certain ceramics, do not generally exhibit this so-called Knudsen minimum. In the context of kinetic theory this has been attributed to curtailment of long free paths due to the tortuosity of the pore structure. More detailed accounts of kinetic theory models for gas phase flow may be found in references [ 1, 12]. One problem, that first arose in the nineteenth century, was the nature of the interaction between the gas and the solid. Since there can be no adsorption potential energy in a kinetic theory model, reflection at the wall should be entirely specular (as in the reflection of light from a mirror). However, this would lead to infinite flux at the low pressure limit where there is no scattering by intermolecular collisions. In fact one of the assumptions in deriving equation (1) is that surface reflection obeys a cosine law [ 10], where the probability of reflection in a direction O, measured from a normal through the surface, is proportional to cos(0). Although cosine law reflection was originally attributed to surface roughness, the precise mechanism has remained obscure. A contemporary view is that it could arise from exchange of momentum between fluid phase molecules and vibrating atoms in the adsorbent. The computer simulation studies discussed in Chapter 2.1 clearly demonstrate that for most, if not all the systems of interest for gas separation processes in micropores, the kinetic theory view does not furnish a complete picture. Even at quite high temperatures, adsorption potential energy can play an important role in densifying the fluid inside micropores, thereby creating gradients in local mean density in directions normal to the solid surface, as well as smaller variations that reflect the local structure of the solid. It follows that even where kinetic theory is perfectly adequate to describe the external gas phase, theoretical models based on kinetic theory, such as the dusty gas model, or Knudsen diffusion, will not be able to account correctly for the effects on flow of the interaction between molecules in the densified adsorbate, nor for the effects of the adsorbent field. 1.3 S u r f a c e f l o w
That adsorption forces could significantly enhance flux through porous solids has been recognised and studied experimentally for several decades. Comparison between the flow of helium at ambient temperature and other species led to the elaboration of the concept of surface flow on the assumption that helium was not affected by adsorbent fields at these temperatures and could therefore be taken as an ideal (kinetic theory) reference [12,10]. However, both experimental and theoretical work [ 13] have cast doubt on this assumption, particularly in the augmented adsorption fields present in micropores. Theoretical elaborations of the surface flow concept tend to rely on models involving single (or in some cases multiple) distinct adsorbed layers in equilibrium with less dense (usually gas phase) fluid inside the pore. In wide pores at low temperatures and below the capillary condensation phase transition, such models may indeed correspond to physical reality to some extent. However it is clear from simulation studies of equilibrium adsorption that this type of model bears little resemblance to molecular behaviour in microporous systems of importance for gas separation, since the adsorbate phase is dense and is distributed non-uniformly over the pore
260
space. The more neutral term "extra flow" that denotes the phenomenon without implying any specific mechanism is therefore to be preferred. Some recent discussions of the surface flow model have been given in [ 1,14]. Most gas separation processes of practical interest involve pores of near molecular dimensions, typically at ambient temperatures and under gas phase pressure ranging from a few bar to over 100 bar, depending on the process. Simulation studies of equilibrium adsorption show that molecular densities inside the pore are high under these conditions and that intermolecular potential energy is a significant fraction of the total energy. Moreover, the adsorbent field can promote substantial non-uniformity in the mean adsorbate density. Under these conditions it seems likely that neither kinetic theory, nor a combination of this with a surface flow model, will be adequate to describe correctly the molecular processes involved. Thus although phenomenological expressions constructed on this basis may be useful for correlating observed data, they lack the predictive content which would enable any a priori assessment of optimum pore structure. In the next section we review the phenomenological theory that underlies transport processes in single pores and identify the coefficients that characterise these processes, showing how they can be related to molecular properties obtainable from simulation. We then review the simulation techniques that can be used to study transport properties. The final two sections discuss examples of simulations in model systems for single components and mixtures. 2.0 THEORY 2.1 Stefan-Maxwell equations for diffusion The earliest theoretical description of diffusion flux was developed by Stefan and Maxwell in the context of the kinetic theory of gases. The original Stefan-Maxwell equations were applied specifically to a mixture of two or more ideal gases where each component has a partial pressure gradient in a system with spatially uniform total pressure [1,10]. However, a more general derivation, given here, places no constraint on the density of the fluid. Other discussions of the Stefan-Maxwell equations may be found in references [ 15, 16,17,18]. Here we focus on a system where the fluid is an adsorbate mixture confined by boundary surfaces of simple geometry, such as a slit or cylinder. To simplify the development, and to emphasise its applicability to a simple single pore model, we consider the system shown in figure 2, where M is a solid wall consisting of atoms
.f ~ \
'~_/', . / / ~ - ~
,/~
~.~
Figure 2. Schematic diagram showing two adsorbate species in a slit pore.
261 vibrating about fixed positions, and the confined fluid comprises k components of type n. Each fluid component has a local number density p.(r, t) at position r, and time t. Its chemical potential #. varies in the direction of flow, but is uniform at a cross section through x. The local chemical potential is
:
~ + k T l n ( f ~ / p ~)
(3)
where f . ( x ) is the partial fugacity of an external gas phase that would be in equilibrium with the dense adsorbate at x at the same temperature. The standard chemical potential can be expressed in molecular terms as 3 /~. = kT In (tip oA ,,r A.t) ,~
(4)
where Anr and Ant a r e the rotational and translational thermal wavelengths and p~ is the standard pressure (1 bar). In simulation studies, it is convenient to choose the absolute activity, z,, for species n as input in the calculations (see Chapter 2.1), where, exp(fl/~ .)
z
:
3
A,,r Ant
(s)
The work done on a particle i of type n in transferring it from (x+Ax) to x at a chemical potential
#(x) is
where f= is the frictional drag force in the x-direction and the Taylor expansion has been truncated at the first derivative. Frictional forces between particles occur as a consequence of their different velocities. Thus the frictional force in the x-direction on particle i of type n due to particlej of type m is fjx-
/'/m
~,j' (V,x - vx)
(7)
where v~ is the x-component of the molecular velocity of i at time t, within [x,x+ Ax] and ~,f,m is a frictional coefficient for the pair ij. To simplify the equations at this stage we consider only two fluid species in the system, labelled m and n. The mean frictional force on particle i at time t from all other atoms in the system is
262 N.
N~
n m
n,n
jcm
(8)
jlcn
jcM
wherej'excludes i. The first term on the right hand side is due to the friction between particles of type n and those of type m; the second term is a self term, and the third term arises from the interaction of type n with the solid walt (M). In the steady state, and after a long time, a statistically representative set of particles of type n pass through Ax, and the mean force on N,, particles of this species is N.N
N N.
S.x-EE ,;
n m
N.N u
_
n,n
1En j c m
~n,M
tcn jl~n
(9)
1~n j c M
The streaming velocity, u, D for species n is given by N. 1 ~v
D_
N
llnx
t=l
(lO)
tx
A mean frictional coefficient ~,.m, on particle i of type n from all particles j of type m may be defined by N
~7,m D _ lgmx
1 Nm
(11)
~,j" v jx
and the mean frictional coefficient between species n and species m is defined by N _
(m.
N
N
n
:
N.N~ n,m
_
N
N N m U , . Dx
~'
E
E
1=1 1~ 1
(12)
~lj ' V jx
where N is the total number of molecules, and is included in the definition in order to ensure that the equations are consistent with the Stefan-MaxweU gas phase equations. Clearly ~v=~j, (equivalent to the Onsager reciprocal relations), and therefore the second (self) term in equation (9) vanishes. Inserting equation (12) into equation (9), gives
-N
[ .Or)
N
N
The solid M contains atoms vibrating about their mean positions, so it is natural to choose the laboratory frame, in which the average streaming velocity of M is zero, as the reference flame.
263 Since the solid is, by definition, uniform in the x-direction, we also have 3,itM/Ox=O.It is more usual to write the friction coefficients as (Stefan-Maxwell) diffusion coefficients through the Einstein relation
kT On m
--
(14)
~nm
For k fluid species equation (13) then yields a set ofk equations: _
~c
kT
Ox)
m : 1
ND
nm
OhM
(15)
where N~,M/N has been replaced by kT/D~. The set of equations represented by equation (15) is essentially the Stefan-Maxwell equation for diffusion adapted for what is frequently known as the dusty gas model [9], but specific reference to gaseous species has been avoided, and the geometry of the adsorbent can be clearly defined. The equation expresses the fact that the mean frictional forces, due to the relative streaming velocities of the different species, are associated with the pair diffusion coefficients in the system. Equation (15) differs from the Stefan-Maxwell equations in that one species (whose atoms form the solid pore) has been accorded the privileged status of the reference flame against which other streaming velocities are measured. The more usual procedure, in considering a mixture of fluid components, is to choose some average velocity (usually the barycentric average) as the reference velocity [19,20]. Regardless of the choice of reference frame, equation (15) is incomplete since it fails to account for any viscous stresses that may be present in the fluid. Viscous stress occurs whenever streaming velocity gradients are set up in the fluid giving rise to momentum exchange between regions of fluid moving with different velocities. In some circumstances it may be justifiable to neglect viscous flow; in a highly confined space in particular, streaming velocity gradients may be negligible on a molecular scale (see w below ). Similarly in a large sea of fluid components, the boundaries may be so distant that their existence can be neglected, and since no particular species is accorded the privilege of having a zero streaming velocity, the fixed reference flame is chosen as the "laboratory". Diffusion velocities are measured relative to this flame and equation (15) is then:
kT
Ox )
= N
Dnm
(16)
Multiplying both sides of (16) by iV,, summing over all species, and invoking the Onsager reciprocal relations D,,,,,=D,,,,, gives
264
(17) n--1
Equation (17) may be compared with the Gibbs-Duhem equation which leads to the expression
.:iT where N,/V is the mean number density, p, of the adsorbate species n. Equation (17) therefore implies that no pressure gradient can exist in a system described by equation (16). On the other hand, when equation (15) is multiplied through by N, and summed, one obtains Y'.N,V~/~, ~'0, implying that a pressure gradient can exist as a consequence of the condition U~ Since there is a pressure gradient in the system that can drive viscous flow, equation (15) no longer furnishes a complete description of isothermal transport, as would be the ease for a uniform fluid mixture (in which case the final term of (15) would not be present). Mason and Viehland [ 16], basing their discussion on the earlier statistical mechanical treatment of Bearman and Kirkwood [ 19], were the first to point out that the conventional Stefan-MaxweU equations, when applied to membranes, omitted a viscous flow term. In reality any extended fluid will have some contact with a solid boundary; certainly the boundary phase is expected to be important for fluids in a pore or membrane, and the pore wall will exert frictional drag on the molecules of the fluid. Since these forces decay with distance from the wall, streaming velocity gradients will be established in confined fluids. In many eases, as mentioned above, the omission of a viscous term may be justified [ 1], but conversely, viscous flow is often regarded as being the only significant contribution to transport of dense fluids. Adsorbates in micropores are frequently approximated as dense (albeit non-uniform) fluids, whilst at the same time, their transport behaviour is treated exclusively as a diffusion phenomenon. The work of Mason et al [ 16, 17, 20] pointed the way to the resolution of this apparent paradox, but a detailed understanding of which mechanisms apply under given conditions remains to be worked out. An early discussion of the particular eases of transport phenomena in bounded spaces can be found in Hanley [21 ]. 2.2 Navier-Stokes equations and viscous flow
Statistical mechanical equations for transport were derived by Kirkwood and co-workers [ 19], from the starting point of the Liouville equation. They express the rate of change of mass flux in terms of a partial stress tensor and partial shear, (r/,) and bulk ((~) viscosities, of component n, such that ~ r/,=r/. (It should be noted that these partial viscosities do not correspond to component viscosities in a mixture which have a different combining rule [22]). For component n in an isothermal mixture of fluid components, the equations of Bearman and Kirkwood are a (~/~nP n U n)
Ot
1 : r/" V2u + (-~q,, + (,,) VV.u - p.(Vla. - X
- F.)
V.(M,p, uu)
(19)
265 where M, is the molecular mass of component n, p, its mean number density (= N/V), u is the barycentric streaming velocity of the fluid, and X~ is the external force acting on a molecule of species n. The frictional force terms are F,, : - ~
Pm ~,,,,,(u
-
11 m
)
(20)
m
As before (equation (14)), the frictional coefficients can be related to the reciprocal of the diffusion coefficients. In the absence of external forces, equation (19) can be re-arranged [ 16] to read pnV/an : - B
(21)
+p F
where B, contains the "partial" constitutive terms [19]. Summation of the set of equations represented by equation (21), leads to the momentum conservation equation expressing the relation between the time derivative of the barycentric velocity of the fluid and the gradient of the stress tensor, II. The summed equations can be written in the form: M p ( r , t ) d(u(r,t)) + V - I I ( r , t ) : 0
(22)
dt
II f~(r,t) = t~ flp(r,t) - rI
au~(r,O
Ouf~ (r't) ) + 6ep12-3 rl - (" ) V" u(r,t) ar~
(23)
where M is an averaged mass, given by F.A4,,o,/~p,. Equation (23) may be recognised as the Newton constitutive relation for the whole fluid expressing the stress tensor components II~p in terms of the shear (r/) and bulk ( 0 viscosity coefficients (which should be distinguished from the friction coefficients, (,m) and the spatial gradients of the streaming velocity components [21,23 ]. The Navier-Stokes equation for momentum flow is obtained by substituting equation (23) into the equation (22), the equation for momentum conservation in the fluid. As a specific example, we consider steady state flow of an adsorbate in the x-direction through slit pore with z normal to the pore walls. The assumption of steady state flow sets the time derivative in equation (22) to zero; moreover the term involving the bulk viscosity vanishes at low Reynolds number for weak flow of this type, and the derivative ~ / c ~ - 0 . However, the adsorbate density may vary strongly with distance from the wall, and consequently q would also be zdependent. The equation for viscous flow of adsorbate in a slit pore is therefore written [24]:
ap ax
3__ az
- -:-r/(z)
aUx(Z)
- 0
(24)
az
where the gradient of II in equation (22) can now be replaced by -qb/dx, and the symbol ux(z) refers to the x-component of the mass average streaming velocity of the whole fluid at position z in the cross section,
266 k
k
.x(~) : ~ ~p~(z),,x(~)/~ ~p~(z) n:l
(2s)
n:l
The shear viscosity in equation (24) is the viscosity of the mixture and varies with the mole fraction, x n of component n. In equation (24), p refers to the hydrostatic pressure inside the adsorbate fluid. The pressure difference across the interface between the adsorbate and the adsorptive gas phase will not necessarily be zero. Classically, it is given by the form of the Laplace equation that is appropriate for the geometry of the pore [25]. In other words, although the fugacity can often be reasonably approximated by the gas phase pressure, pg, w e would not expect pg to be equal to p. The GibbsDuhem equation (c.f. equation (18)) is applied to the adsorbate phase. The chemical potential is, of course, uniform throughout adsorptive and adsorbate phases in equilibrium at a uniform temperature. Equation (24), integrated once between the limits z'=0 and z, gives,
eu (z)
ap z = r/(z)~ Ox
(26)
dz
where, by symmetry, (c~ux/oaz)=0 in the centre of the slit at z=0. If the shear viscosity is not a function of z, a solution for ux(z) can readily be found; in this case we can write, HI2
u x(H/2 )
(27) z
u~,(z)
where H is the width of the slit. The streaming velocity at the wall, U x ( • (the slip velocity) is usually taken to be zero for dense fluids. Integration of equation (27) then gives: J
Ux(Z) :
-
2 rI
-
z
(28)
revealing the characteristic parabolic dependence of the streaming velocity. It is consistent to assume that if r/has no z-dependence, then the number density is also independent ofz although, as already pointed out above, equilibrium studies show this to be manifestly untrue for adsorbates in capillary spaces. If the density is uniform over a cross section, the average streaming velocity over a cross section, ux is given by:
267
1
Hx
/-//2
(29)
= ~ f . (=)d= -H/2
Inserting equation (28), equation (29) results in: x
(30)
12r/
To generalise this result to spaces of other geometry, one can write: Ux=
---2-~
~7
For cylinders of radius R, for example, Bo = R2/8 (Poiseuille' s equation). Expressions for Bo for porous materials and for other geometries have also been deduced [ 18]. When the assumption that r/is independent of z is removed, it is convenient to retain the form of equation (31), however r/aquires a different meaning. In place of equation (28) we now have:
r/(z) Moreover the total number of molecules per unit volume at z having this streaming velocity is now p(z), so the mean streaming velocity from equation (29) is, HI2
f p(z)u(z)dz u
-
-14/2
(33)
H/2
f
p(z)dz
-H/2
With equation (32) this gives 14/2
1-1/2
dzz
f d=p(=)f ,7(=) -HI2 llx
z 1t/2
f dzp(z) -H/2
(34)
268 An effective viscosity can be obtained by comparing equation (34) with equation (30), H/2
H/2
12-./~ f dzp( ) fz H/2
rt(z) (35)
H ~ f dzp(z) -H/2
A similar expression was derived by Bitsanis et al [26] who used the Enskog model [8] to obtain an estimate of ri(z). In their equation, p(z) does not appear under the integrals. The streaming velocity of component M (the adsorbent) relative to the barycentric velocity was denoted by uDMxin equation (13) and set to zero in equation (15). When the whole fluid moves with a barycentric velocity Ux, U~ should be replaced by U~ -U~ where UMx is the velocity of component M in the barycentric frame. A similar shift applied to the x-components of the other species gives, D Hnx
=
Hnx
-
Hx
=
Hnx
+
~
(36) r/
Usually it is assumed that viscous flow is non-separative. However it is possible to imagine situations where this may not be the case. To allow for this possibility [ 18,20], equation (36) may be modified to read, u,,x :u,= + a,,--2~ q
(37)
where a, is a viscous separation factor. No theory exists for a,, but arguments have been given to suggest that this factor could take any value dependent on the specific system [ 18,20]. For example, distributions that favour one species occupying a central region of the pore, whilst the other occupies regions nearer to the adsorbent wall, could result in a, > 1 for the first species, and tr,
269
Pm
S
m=l P D . m ( U
- u
) + ~D ~
+ a,
q Do~
ap
08)
where Nm/N has been replaced by the ratio of mean number densities p,/p. This set of equations is applicable to isothermal flow in single capillaries. The diffusion coefficients are the relevant Stefan-Maxwell diffusion coefficients for the confined fluid and are phenomenological in this equation. The viscous separation factors are related to a ~ by [ 18,20] a'
= a
+ ~
n
~Pm
(a
- a )
m-~1 PDnm
m
(39)
When there are temperature gradients, the equation is supplemented by an additional term on the left hand side, T ,OnD nm Oln T 10Dn m
(40)
Ox
where Dr,, is the thermal diffusion coefficient. If there is only a single fluid species, the surviving equation from the set of equations (38) may be rearranged to read
dx - - P D~ -~xOkt ) - B~ P -~xOP )
(41)
where Do now signifies the value of D,M for a single pure species of mean density p. The molecular flux in the x-direction is Jx=p ux and subscripts denoting species have been dropped. With the aid of the Gibbs-Duhem equation(equation (18)), equation (41) may be rearranged to read:
Ix 9 =-
+
( Olnf
o- np
Op
(42)
from which the effective Fickian diffusion coefficient, D, for the single species can be identified as
D:
[
Do +
rl
/~ / O-~np
The term 01nf/0 lnp is known as the Darken factor [ 1] and can be obtained as the inverse slope of the logarithmic adsorption isotherm (/9 vsf). In the low coverage (Henry law) limit this becomes
270 unity. Equation (42) contains a diffusion component and a viscous component, the ratio of the viscous to the diffusion flux, is #kTBo/Dorl. According to the stokes equation, D or/is constant, and the viscous to diffusion flux ratio would then increase with density and with the square of the pore width (see equation (30)), implying that viscous flow would very quickly become the dominant mode of transport as pore width increased and would be increasingly important at higher adsorbate density. If the fluid is an ideal gas, then p - - f / k T (where the fugacityf is equal to the gas phase pressure in the ideal gas limit), and equation (42) reduces to, Op
which has the form of the classical slip flow equation [ 10]. At the low pressure limit, Do-.Dx, the Knudsen diffusion limit, where D x in a cylinder is given by equation (2). In the ideal gas limit, the self diffusion and cross correlation contributions to Do (see equation (73) below) can be specifically identified [ 12], and the total diffusion coefficient in an infinitely long slit or cylindrical can be shown to pass through a minimum, as illustrated in figure 1.
2.3 Mixtures The molecular flux (molecules per unit time per unit cross sectional area) of component n in a mixture is given by J,~ : ,on u,~
(45)
To obtain explicit expressions for the fluxes, we rewrite equation (38) in the form Gu=F
(46)
where the elements of the vector F are F - -
kv
-
r
,47,
u is a vector of the x-components of the streaming velocity for each species in the mixture, and the diagonal and off diagonal elements of the matrix G are Gnn = 1 +
P mD,~t ,,~,
Gm. = _ PmD,,u P Din,,
pD
(48)
271
A formal solution to these equations is
u - G-iF
(49)
When there are more than two components in the fluid mixture, the matrix inversion leads to expressions that are not easily simplified. For a two component mixture, a simple expression for the inverse matrix can be found,
G_ l =
1 (O12 +
( D'2 + x1D2M
XlD2avt + x2D1M) ~
Xl D2~t
x2D~
]
(so)
D12 + x2D1M)
where x, is a mole fraction (=p/p). The component fluxes may be written in irreversible thermodynamic format as, - Jlx = L l l gxltll + LxVx]'t2
+ a~Lo,V.P
(51)
J a = L xv* ~, + L==V ~= + a2Lo2Vxp
-
where, Vx stands for O/Ox and and a~ and a 2 have been defined in equation (37) as viscous separation factors and Lo,=Pfla/rl. Using (50) with (49) and (45) in equation (51), we can obtain expressions for the other phenomenological coefficients in terms of the Stefan-Maxwell diffusion coefficients [22,27]
kTLll =
kTL x
=
(P D1~ + t~
Pl D ~
(52)
PD12 + tOlD2a4 + 102D1M
Pl Pe D ~ D~t PD12 + plD2M + P2DIM
(53)
and the coefficient L= can be obtained by interchanging the subscripts in equation (52). It is of interest to note that these expressions imply that the condition Lx<
D~
L11L22 - L~
kT
piL22 - P2Lx
D12 kT
When p2<
LllL22 - L~ (Pl + Pe)Lx
(54)
272
kTLlz D~ 92/Pl -'0
(ss) D1
which is the expression for D0~, the collective diffusion coefficient for a pure single component of type 1. In principle, using equations (47) - (49), multi-component flux equations similar to (51) may be obtained in which all the phenomenological coefficients can be expressed as functions of the Stefan-Maxwell pair diffusion coefficients.
2.4 Permeability The permeability P, of component i in a mixture is often measured experimentally, and is of paramount practical importance for membrane transport. It is related to the flux by Pt
(56)
-
where Apg is the difference between the ingoing and outgoing gas phase pressures (approximately equal to the corresponding difference in fugacity), over a length 1. With equation (18), equation (51) can be rearranged as - J~x = (L~, + a~Lo, P ~ ) k T V l n f ~
+ (L x
+ a1Lo,P2)kTVxlnf 2
- dz~ = (L x + a 2 L o 2 P , ) k T V l n f ~
+ (L22 + a 2 L o 2 P 2 ) k T V ~ l n f 2
(57)
In order to integrate these equations it is necessary to obtain expressions for the phenomenological coefficients as functions of p, which can then be related to f through the component adsorption isotherms. Attempts to carry through these steps have necessitated quite severe approximations or questionable assumptions [22, 28]. Experimental measurements of permeability can exhibit a remarkable variety of concentration dependence according to the porous material and system studied [29] and the general problem must be regarded as being far from solved at the present time. It should be noted that in [22], equations (39), (62) and (63) apply only to the case where there is no overall density gradient and not to a more general situation as implied in [22].
2.5 External force fields When a liquid is placed in a vertical tube under gravity, flow occurs under the action of the gravitational field. In a simulation, an equivalent situation can be reproduced by applying a force field to the fluid particles. To ensure measurable flow, the field must of course be much greater than the gravitational force (see below). When there are no gradients V/~.:0 (and hence Vp=0), the total force Xx acting in the x-direction is related to the forces acting on each molecule of component n (X,x) by
n
273 where x, is a mole fraction. Summation of equation (19) over all components then leads to 0 II~z
a--Z: pX
(s9)
which with equation (23) forms a basis for the direct study of purely viscous flow [30]. 3. SIMULATION METHODS 3.1 Simulation models When simulating transport through porous materials on an atomistic scale, it is necessary to consider the fluid model, a model for the potential energy of interaction between adsorbate fluid and the adorbent pore, and the model for the reflection of molecules from the pore walls. 3.1.1 The fluid model The fluid is generally modelled as a collection of Lennard-Jones particles i.e. structureless spheres which interact via the following effective intermolecular pair potential
in which o,j is the separation corresponding to the energy zero and e0 is the depth of the potential well. An electrostatic term can be added to the Lennard-Jones term to account for interactions between charged particles, ,
q, qj
t • ct,r,j)o u t4~ze0r,j ,
(61)
where q, and qj are the charges on the sites and e 0 is the permittivity of a vacuum. Interactions between molecules with permanent electric moments can be modelled in the same way if the electric moment is represented by partial charges superimposed on the molecule. Molecules can be constructed by linking together a number of Lennard-Jones particles, which may represent individual atoms, or groups of atoms (united atom model). The molecules are then either modelled as rigid entities with fixed internal geometry, or as flexible units, in which intramolecular potentials govern internal motions such as bond vibrations, bond angle bending, torsional rotations, improper rotations etc. Typically, bond vibrations are not considered since they are of high frequency and therefore contribute little to thermodynamic properties. In practice holonomic constraints are employed to fix the nearest neighbour distances in molecules [31 ]. The Lennard-Jones potential is always truncated at some value of the pair separation, r,j, to facilitate computational speed. In work requiting accurate values of the thermodynamic quantities, it is becoming the standard practice to truncate the potential at 5 qp though in earlier work values of the truncation radius of 2.5~j are more common. The effect of the finite truncation upon the
274 thermodynamic properties can be estimated as long range corrections and can be quite large for quantities such as the pressure. In porous systems, such corrections are rarely made since the use of a longer truncation radius renders them unnecessary. The electrostatic interactions, being longranged, cannot be similarly truncated without risking unacceptable errors. In this case one must replace the usual electrostatic energy term by an Ewald summation which divides the interaction into a direct (electrostatic) part and a long-range part calculated in reciprocal space which converges rapidly [31,32]. There are several variations on the standard Lennard-Jones 12-6 potential, including an exp-6 form in which the repulsive r -~2 term is replaced by a Born-Mayer exponential term, but the 12-6 form has found widespread use because of its simplicity and computational advantages. 3.1.2 The adsorbent model
At the atomistic scale, the solid adsorbent can be modelled either by an explicit atom representation, or by a potential energy function (implicit atom) representation. The explicit atom representation involves a one to one mapping of the atomic nuclei of the solid by spherical centres of force. Most simulations involving transport through pores have employed a stationary wall particle approximation in which the wall particles remain fixed throughout the simulation and therefore have zero momentum. A more realistic model employs thermally agitated wall atoms; i.e. particles which vibrate around their lattice positions as a result of some constraining potential. If the wall atoms do not interact with each other, the model resembles an Einstein crystal and no lattice phonons are developed. If the atoms are thermally agitated, exchange of thermal energy between the adsorbent atoms and the fluid molecules can occur. In non-equilibrium molecular dynamics simulations, heat is produced irreversibly and must be removed in order to achieve a steady state. By using a thermally agitated atom model for the pore walls, the heat will be removed by conduction through the solid in much the same way as would occur in nature. For stationary atom models, artificial thermostats need to be applied to the fluid in order to remove the heat which may result in simulation artefacts in some systems [31]. Heat is removed from the thermally agitated atoms by application of a deterministic thermostat. The absence of lattice phonons in the Einstein crystal means that any local hot spots that develop in the pore cannot be effectively dissipated in this model. Thermostats applied in this case can lead to very high amplitudes of vibration and may even result in break down of the wall model. In an alternative model [33], atoms interact with each other through a 12-6 potential and vibrate around their equilibrium lattice sites with a simple harmonic restraining potential, but this has the disadvantage that the fluid molecules may penetrate into the adsorbent. Moreover this model cannot be used for covalent solids such as graphite, in which the carbon atom spacing is much less than the diameter of a carbon atom. More sophisticated models of graphite exist in which two and three body interactions are included [34] (to allow for lattice phonons) but the potential energy functions are so complex that they have found only limited use in atomistic simulations involving adsorbate phases. In the implicit atom-wall models, the atoms constituting the adsorbent are replaced by a smooth potential energy surface, creating a more coarse-grained solid. For example, microporous carbon is o~en represented as a single slit of parallel sheets of graphite. These graphite sheets may be modelled as collections of carbon atoms, or as a smoothly varying potential energy function. If the carbon atoms are taken to be 12-6 Lennard-Jones particles, integration of the total interaction potential arising from an infinite stack of parallel sheets (stacked along the z-axis) in the x and y directions yields the so-called 10-4-3 potential [3 5] (see Chapter 2.1). To simulate the effects of a more realistic, partially crystalline surface structure, MacElroy e t
275 al [36] developed the "randomly etched graphite" (REG) model. Here, the slit pore is modelled in the usual way, as a set of parallel sheets of graphite planes, but the innermost basal planes are represented by explicit atoms with a degree of random etching (carbon atoms are removed) and the remaining graphite planes by the 10-4-3 potential. The REG model was used successfully to obtain kinetic oxygen selectivities from mass transport of oxygen and nitrogen through a carbon slit-pore [3 7] see section 4.4 below.
3.1.3 Wall reflection One problem connected with the use of smooth wall potentials is that no momentum exchange takes place when a fluid particle encounters the wall. To overcome this problem, one can impose a set of artificial boundary conditions which have the effect of randomising the momentum of particles which have collided with the wall. Two different methods are currently in use: diffuse boundary conditions [38] and the cosine law condition [39,40]. In the diffuse scattering algorithm, the post-collisional components of velocity parallel to the wall (in slit pores) are randomised according to / vx = vxcos 2~:(
/
Vy = vsin 2~(
(62)
where ( here is a normalised random number. A particle is considered to have collided with the wall if: (a) the component of the molecular velocity normal to the wall is reversed, and (b) the molecule is closer to the wall than the minimum in the molecule-wall potential energy. In the cosine scattering boundary conditions, all three components of momenta are randomised. When an explicit atom model is used, it is customary to omit specific wall reflection conditions of the type discussed above. The extent to which molecules alter their momenta in response to the wall then becomes a function of the particular wall model employed. If the wall is modelled by an array of nuclei in fixed positions, then the potential function will in effect have some "corrugation" parallel to the surface, as well as variation normal to the surface, and this serves the purpose of introducing some randomisation in the velocities of the molecules reversing along a direction normal to the wall. Walls with vibrating atoms will have a similar effect, but clearly the amount of diffuse (in contrast to specular) reflection will vary. Simulations and theoretical calculations of single atom reflection at a surface indicate that neither the specular nor the diffuse model are correct in a general situation [41 ].
3.2 Equilibrium Molecular Dynamics (EMD) techniques. For bulk fluids, each of the thermal transport coefficients is related to equilibrium fluctuations by a Green-Kubo relation. These relations involve infinite time integrals of autocorrelation functions of dynamic quantities. The Green-Kubo equations for self diffusion, thermal conductivity, shear viscosity and bulk viscosity are given in Table 1, where the off-diagonal stress tensor components
276
Table 1 Green Kubo expressions
Self diffusion
N
1
O
~
o
x--
Thermal conductivity
V m(6(o.6(o)>
3k T 2Jo
V Shear viscosity o
co
1
Bulk viscosity
f d, <tp(ovo -O,v>3tp(o)vo) - 0
Hap may be expressed in terms of the molecular velocities, v, and the components of the force (fj) between particle i and particlej. For monatomic fluids, II ~ = ~
y~mv
v~ + -~
r j~
1
The heat flux vector components are given by: \
1
I
(66)
Corresponding expressions for molecules have been given elsewhere [42]. For fluids in confined geometries, evaluation of the transport properties is complicated by the presence of the solid, which removes the homogeneity of the fluid. The stress tensor for example, becomes dependent on position, giving rise to a position dependent shear viscosity and is written II(r,t) = --~
m v(t)v(t)
+ -~
rj (t) O j(t)f,j(t)l,,(t)= ,
277 and the heat flux vector for an inhomogeneous fluid is
1(
JQ (r,t) : ~
~ v (t) e (t) -
2,j
1
rj (t) v (t) . f,j(t) O,j(t)l~,
(68)
where Oij is the differential operator,
I O +... +l[_r... 0 ]n- 1+... O j - 1 ------r..--2! ~t dr n! ~t Or
(69)
and can be handled in simulations by techniques discussed in section 3.4 below. As an alternative to the Green-Kubo expressions, the thermal transport coefficients may be written in the form of generalized Einstein formulae, for example the self diffusion coefficient is
--~ t-.~ 6 N , :
[r~(o) - r~(t)]2
(70)
In slits or cylinders, 6 is replaced by either 4 or 2 respectively, and r has components in the direction of flow. In section 2 we showed that the theoretical treatment of fluid diffusion through porous solids must include the solid as a component in the fluid mixture. A single component fluid adsorbed in a porous membrane therefore has a mutual diffusion coefficient which describes the transfer of fluid through the immobile solid. Without the solid, this diffusion coefficient is meaningless and therefore can only be calculated or measured for the binary solid-fluid system. In the case of a single component fluid, the mutual diffusion coefficient is often given the symbol Do, and is referred to by some authors [ 1] as the corrected ditfusivity. Since the Darken factor is also referred to as a correction factor this terminology can be somewhat confusing and here, we refer to this transport coefficient as the collective diffusivity. The collective dit~sivity is related to fluctuations in the fluid streaming velocity via a Green-Kubo type formula [27,43] oo
(71) 0
where Nis the number of fluid molecules, d is a symmetry factor (2 for slit pores, 1 for cylindrical pores) and u is the streaming velocity of the fluid, whose components are defined by equation (10). For a bulk fluid at equilibrium, conservation of linear momentum (a direct consequence of Newton's law) implies that the zero wavector streaming velocity is zero, hence Do vanishes. Like the coefficient of self diffusion, the collective diffusivity can also be expressed in the equivalent Einstein mean square displacement form
d Lim N ((R(t) _R(0))2)
(72)
278 where R is the centre-of-mass of the fluid. The above definitions represent orientationally averaged diffusivities. There is no equivalent Einstein equation that can be used to calculate viscosity or thermal conductivity. The expression in earlier literature [44] has been shown to be incompatible with the periodic boundary conditions used in a simulation [45]. In a network of pores, the motion of fluid particles through the network may be anisotropic and the di~sion coefficients would be replaced by a tensor. The diagonal components, D~ Dyy and D= are readily calculated in a molecular dynamics simulation. In slit pores, D= will be zero since the limits in equations (70) and (72) do not exist when the system is finite or bounded. The equilibrium route to Do, like other collective transport properties, suffers from poor signal to noise ratio. The self diffiasivity is much easier to calculate since averages can be taken over the N molecules in the system. From equation (71) with equation (10) it can be seen that the collective diffusivity can be written as the sum of two parts: a self term, Ds, defined in Table 1, and a cross correlation term, D~ D O : D s + D~
(73)
where De comprises the sum of the off-diagonal terms in the array of molecular velocity products appearing in equation (71) [73 ]. Equations (71) and (72) may be generalised for application to mixture transport. In this case, it is more useful to calculate the phenomenological coefficients. These may be expressed as correlations of the fluctuating streaming velocities of the components in the form:
Zmn
[~c[
f (um(~
dt
(74)
and can be used with equations such as (51) or (54) to obtain Fickian or Stefan-Maxwell diffusion coefficients.
3.3 Non-Equilibrium Molecular Dynamics (NEMD) techniques. 3.3.1 Transient time correlation functions The Green-Kubo formulae refer to the linear response of the system to a perturbation and may only be used under equilibrium conditions. Non-equilibrium molecular dynamics (NEMD) provides the most efficient means of obtaining the non-linear response of the system. The major limitation of NEMD is that the signal to noise ratio goes to zero in the weak field limit. Transient Time Correlation Function (TTCF) formalism was developed to bridge the gap between the Green-Kubo formalism and NEMD, and is a non-linear generalization of the former [46]. TTCF has recently been extended to account for systems subject to time-periodic external fields [47] and has been used successfully [48] to calculate the non-linear response of a system of simple spheres to elongational flow. 3.3.2 Fictitious field NEMD In section 3 1 it was shown that the thermal transport coefficients for bulk fluids may be obtained from equilibrium simulations via the Green-Kubo relations or the equivalent generalized
279 Einstein formulae. With the exception of the coefficient of self-diffusion, which is a single particle property, such calculations are otten highly inefficient. A more useful approach is to conduct a nonequilibrium simulation of the transport process and calculate the transport coefficient from the appropriate linear constitutive relation. The shear viscosity for example, is obtained as the ratio of the shear stress to the shear rate in a simulation of planar Couette flow. A fictitious force ie one not occurring in nature, is invented which appears in the equations of motion for the fluid particles. This force mimics the effect of the linear thermal transport process. A general scheme for constructing fictitious field NEMD algorithms can be found in [49].
3.3.3 Dual Control Volume Grand Canonical Molecular Dynamics (DCV GCMD) DCV GCMD is a hybrid algorithm utilising both molecular dynamics and Monte Carlo techniques. Several implementations involving pore models have been reported [7,50] including a massively parallel code [51 ], recently modified [52] for the study of mass transport of flexible molecules including polymers. The basic idea is to simulate transport through a porous solid under a chemical potential gradient. The total dit~sivity can then be calculated from the ratio of the steady state flux to the chemical potential gradient. In practice, it proves easier to calculate the density gradient, and it is the total diffusion coefficient (see for example equation (43)), rather than the collective diffiasion coefficient, that is typically measured. Simulations can be of two types: Norton or Thrvenin ensembles. In Thrvenin ensemble methods, the thermodynamic force is the independent state variable, such as the strain rate or the chemical potential gradient. In Norton ensembles, the thermodynamic flux is the independent state variable. Thrvenin ensemble methods are the most common in which the properties of interest are the thermodynamic fluxes conjugate to the thermodynamic driving forces. In simulations of Poiseuille flow, the force is the uniform external force acting upon each molecule. The thermodynamic flux conjugate to this force is the pressure tensor. The DCV GCMD algorithm employs a Thrvenin ensemble in which a chemical potential gradient is created by establishing special end zones within the usual simulation box in which particles are created and destroyed according to the prescription of equilibrium grand canonical Monte Carlo. The two zones (source and sink) are maintained at different, constant chemical potentials by these means. The simulation proceeds by solving Newton's equations of motion for all particles in the system, including those in the control volumes i.e, standard molecular dynamics techniques are used to explore phase space. After each molecular dynamics step, a number of creations and destructions (and exchange moves if there is more than one component) are carried out in the control volumes. The local flux, density and streaming velocities are all calculated along the flow region between the control volumes. It is usual practice in DCV GCMD to place the control volumes witl-finthe pore space to remove any barriers to diffusion which might exist at the pore mouth. If the control volumes are outside the pore space, then it can be shown that there is a very low probability that molecules leaving the adsorbate space will enter the gas phase, which leads to statistical sampling problems [53]. Of course, there is considerable theoretical and practical interest in studying entrance effects. Little simulation work has appeared in the literature [54], mainly due to the difficulties described above; a theoretical study has been given [4,55]. Because DCV GCMD is a non-equilibrium method, it is essential to apply a thermostat to the system to remove the heat generated as a result of the irreversible work done on the system. If no thermostat is employed, steady state will never be attained and the postulate of local thermodynamic equilibrium breaks down. Linear irreversible thermodynamics shows that mass diffusion and thermal diffusion are coupled; thermal gradients can drive mass transport while chemical potential gradients
280 can drive thermal transport. To study di~sion alone, it is necessary to nullify any temperature gradients along the flow direction. Consequently, a spatially dependent thermostatting scheme must be employed in the DCV GCMD algorithm. Nose-Hoover thermostats applied to local regions along the flow direction can be used for this purpose [32,49] but the correct local streaming velocity must be subtracted from the total kinetic energy, and degrees of freedom correctly accounted for. For slit pores, the flow region is typically divided into 20 slabs of equal volume and a Nosr-Hoover thermostat is applied to the subset of particles in each of the slabs. The local streaming velocity can be obtained as the ratio of the running average of the local flux to the local density (the use of a running average rather than the instantaneous average is preferable because the latter may contain too much statistical noise, especially when the slabs contain only a few particles). 3.3.4 Pure viscous flow algorithms The main advantage ofDCV GCMD is that one can simulate mass transport in a manner which replicates processes occurring in nature. The diffusion coefficient is obtained with a much greater signal to noise than can be obtained from an equilibrium simulation. The price that is paid is that the DCV GCMD diffusivity is only an effective diffusivity, since in general, the total intrapore flux will contain a contribution from viscous flow. However, Travis and Gubbins [56] have recently demonstrated that the viscous flow component (in pores with simple geometry), can be calculated separately, and with high signal to noise, using a simulation of pure Poiseuille flow. The basic equations describing Poiseuille flow were discussed in section 2.2. In laboratory and industrial situations Poiseuille flow is often driven by a gradient in the hydrostatic pressure; in a molecular dynamics simulation, it is advantageous to use an external field rather than a pressure gradient to drive the flow (see section 2.5). Pressure gradients imply density gradients which can drive diffusion, thereby complicating the analysis. The external field is chosen to be large enough to achieve a significant flux, and the equations of motion for each particle are then supplemented with a constant force in the flow direction. With the usual periodic boundary conditions, a uniform density profile is created along the flow direction. The local flux can be measured during the simulation and averaged to give the total viscous flux which can then be subtracted from the total intrapore flux obtained from a DCV GCMD simulation to leave the diffusive contribution [56]. The fluid viscosity can be obtained, either from Poiseuille' s law, or by calculating the local stress and strain rates and then using Newton's law of viscosity. The thermal conductivity of the fluid can be calculated similarlyby using Fourier's law together with the calculated values of the local heat flux and local temperature gradient [57,58]. Simulation of planar Couette flow proceeds in a similar manner to Poiseuille flow but in this ease there is no external field; the flow is generated by translating the solid boundaries of a slit pore with velocities -- +TL in the flow direction. After a suitable settling time, an approximately linear velocity profile is established. The degree of linearity will depend on the slit width and the strain rate, y. Too high a value of), will introduce non-linearities in the response of the phase variables to the driving field leading to a non-linear velocity profile for example. As with all the NEMD methods, the external driving fields are typically several orders of magnitude greater than the values encountered in their equivalent experiments; although this may seem a severe limitation, in practice, as long as the system response is linear in the applied field, the transport properties obtained from the simulation can be equated with field free (equilibrium) values. This can be realised by ensuring that the field is weak enough to avoid any non-linear response, but large enough to maintain a good signal to noise ratio.
281 3.3.5 Coupled heat and mass flow According to the equations of irreversible thermodynamics, temperature gradients can drive both heat flow, and mass flow (diffusion). This effect is known as the thermal diffusion or Soret effect. The converse may also occur; i.e. chemical potential gradients can drive the flow of heat, known as the diffusion thermoeffect or Dufour effect. In real systems, in which temperature gradients and chemical potential gradients occur together, thermal diffusion may contribute significantly to the total flux. The transport coefficients describing these coupled phenomena may be calculated for bulk liquid mixtures using the Green-Kubo formalism described earlier [59], or may be calculated more efficiently using NEMD methods. The earliest NEMD method for calculating the Soret coefficient was applied to ideal mixtures [60] and later generalized to non-ideal mixtures [61 ]. A DCV GCMD method [62] has been applied to methane-n-decane mixtures and would seem to be the most appropriate method for coupled heat and mass flow in pores. 3.4 Properties obtained from simulations The properties of most interest in simulations are the transport coefficients. If bulk transport coeiticients are required, bulk simulations should be performed which, in principle, can yield all the transport coefficients. The non-linear behaviour of the transport coefficients may be probed with TTCF or fictitious field NEMD techniques (see section 3.3.1). Phenomena such as shear thinning and shear thickening for example, may be studied by subjecting a model fluid to planar Couette flow using the Sllod algorithm [63]. All fluids studied to date have shown a shear thinning regime. There has been much debate regarding the issue of string phases. Simulations of simple fluids have been reported in which the viscosity of the fluid drops dramatically at high strain-rate in tandem with a high degree of translational ordering of the constituent molecules [64]. Such behaviour is known to occur in real fluids but was not expected for simple fluids. It was pointed out in a series of papers that the string phases observed in the simulations were in fact an artefact stemming from the use of thermostats which are profile biased [65]. String phases were reported in Brownian Dynamics simulations which do not use explicit thermostats and this casts some doubt on the artefact explanation. However, some a priori assumptions about the thermostat are built into Brownian Dynamics and this argument therefore collapses. One should proceed with caution when interpreting the results of non-equilibrium simulations in the non-linear regime. The local values of temperature and density can be calculated by a histogram technique (bins method) or equivalently, the planes method for the calculation of kinetic properties (PKP method) [66]. Transport coefficients may then be calculated directly by using the localised versions of the linear constitutive relations such as Newton's law of viscosity, or Fourier's law. In the zero wave vector limit, the operator in equation (69) averaged over all spatial positions, becomes equal to unity and equations (67) and (68) reduce to the standard expressions given by equations (65) and (66). Fluids in pores are non-uniform normal to the pore wall and the operator expansion of equation (69) is difficult to calculate for such systems. A more direct alternative is to use the method of planes (MOP) [57,67]. This involves dividing the simulation box into a number of parallel planes of uniform area and calculating contributions to the momentum and intermolecular pair forces at each plane crossed by a particle. This technique removes the spurious oscillations in the normal component of the pressure tensor for a fluid subjected to planar Poiseuille flow. A weakness of MoP is that it is only applicable in cases with planar symmetry. Equations (67) and (68) represent exact expressions for the pressure tensor and heat flux vector of a flowing fluid; it is also possible to use the equations of hydrodynamics to arrive at the same quantities. The equation of continuity for example, may be integrated to yield the stress for a fluid undergoing
282 Poiseuille flow in a slit pore. Since this mesoscopic route to the thermodynamic fluxes is only useful in systems with planar symmetry, it does not appear to offer any advantages over MoP. However, in practice, the mesoscopic route can yield a higher signal to noise ratio compared with MoP [67]. 4.0 SIMULATION STUDIES OF TRANSPORT IN SINGLE PORES 4.1 Self diffusion in m i c r o p o r e s Self diffusion ofadsorbate fluids in confined spaces has been studied in both cylindrical [27,68] and slit pores [69, 70,71,72,73], as well as in more elaborate geometry [74]. Suh and MacElroy [39] made detailed studies of the flux of a tracer (1 *) in a fluid of type 1 particles. They examined specular and diffuse reflection limits for hard sphere fluids. For tracer diffusion with diffuse wall reflection, equation (52) can be rewritten as an expression for the Fickian diffusion coefficient of the tracer in the pore D~.p where, Pl ,Dl,p = kTL1,1 Pl. D1,M (PD1,1 + Pl,D1M)
(75)
9Dl.1 + Pl, DIM + Pl D1.M
and, since Pl, -.0 and p~/p-- 1 in tracer diffusion, equation (75) becomes 1
Dl.p
1 -
DI.U
1 +
Dl.1
(76)
With the aid of velocity autocorrelation representations (see for example Table 1 and equation (71)), the tracer diffusion coefficients in this equation can be expressed in terms of D~, Do, and the cross correlation coefficient, De(see equation (73)): ( N D s - D o ) / ( N - 1) D I.1 : Do(ND - D o)/ND~ D1 ,m = Do D1, p =
(77)
Substitution of these expressions into equation (76) results in equation (73). It is clear that in the limit N-.o% Dl..p can be identified with Ds and Dl..Z becomes Do DJDr When the molecules are specularly reflected, Do --0 and then D~..p-- Ds as N-.oo. The general trend is for the self diffusion coefficient to decrease with density at a given temperature approximately as the inverse of the mean pore density. In cylindrical pores with specular reflection at smooth walls [68], it was found, after correction for the inaccessible volume of the pore walls, that the density dependence of D, followed that of a bulk liquid and was of similar magnitude. With this wall model, it was also found that D, approaches the bulk phase diffusion coefficient more closely as pore size increases [27]. With diffuse wall scattering, D, still tends to decrease with density [72,73], but the magnitude of the diffusion coefficient is substantially lower than for specular reflection, especially at low density [27,73]. With diffuse reflection for hard
283 4 ,
!
i+ '
__/l_ llo,<. ii /!
O a - ~
,
10 -5
10 -4
,
p*
I ~3
10 -2
Figure 3. Self diffusion coefficients from EMD simulations for 12-6 methane at 298K in smooth cylinders with diffuse wall reflection. Circles: weakly adsorbing (oxide-like) surface with esJk=395K. Squares: strongly adsorbing (graphite-like) surface with cJk=650K. Broken lines: R=0.78nm Full lines: R=0.68nm. The arrows indicate the classical Knudsen diffusion coefficient for these cylinders.
spheres, or for 12-6 molecules in pores with atomically structured walls, Ds is below the bulk di~sion coefficient by as much as 2 orders of magnitude in narrow pores where single file diffusion begins to dominate the transport mechanism [27, 39]. A close examination of the mean density dependence of Ds in the very low density region, reveals that maxima occur in a variety of systems with narrow pores [27,72,75,76,77]. The earliest explanation for this phenomenon was that molecules immobilised in potential pockets of a complex potential surface at low density, could be dislodged by collisions with other molecules as the density increased. However, subsequent investigations revealed that low density maxima occurred in simulations of diffusion in smooth slit and cylindrical pore models. Figure 3 shows some examples for methane in cylindrical pores. A possible alternative explanation is that short, "hopping", molecular trajectories are lengthened, as the concentration increases, due to the mutual attraction between molecular pairs that can occur during close encounters [73]. More recently [77] an examination of trajectories occurring at densities close to the diffusion maximum, strongly suggests that the mechanism is essentially repulsive, and is brought about when a rare collision event between two diffusing molecules forces one of them deeply into the repulsive part of the wall potential. The reflected molecule thereby gains a high acceleration and executes relatively long trajectories between wall collisions. At higher densities intermolecular collisions between fluid molecules become more frequent, and consequently long trajectories are less frequent, causing D s to decrease. In figure 3 it is notable that the diffusion coefficient at zero density, is below the calculated Knudsen limit, given by equation (2) where the effective radius, r, is related to the pore diameter measured between the centres of adsorbent atoms, R, by r=g
- o ~g
(78)
284
The low value of the diffusion coefficient in this limit is expected from earlier experimental, theoretical and simulation results [ 13 ] for molecular flow with wall particle interactions, and may be attributed to the shortening of molecular trajectories under the influence of the adsorbent field compared to the longer linear trajectories that would occur if no field acted on the molecules. Simulations for hard sphere fluids in cylinders give excellent agreement with the Knudsen theory in the zero density limit [39]. From equations (43) and (73) it is seen that it is not D~, but the product of Ds and the Darken factor that contributes to the total adsorbate flux. This product is often referred to as the transport diffusion coefficient,
Dtrans
-
Ds
0 lnf ] 0 In P }
(79)
although it is clear from equation (43) that this term is only one contribution to the total flux. The Darken factor can be found from adsorption isotherms. In studies of ambient temperature diffusion it was found [71,72,73,78] that an excellent fit to the logarithmic plots for both methane and spherical ethane adsorbed in slit pores at ambient temperatures could be obtained with an empirical equation relating fugacity to the mean adsorbate number density of the form, 3
lnf - A o + lnp + ~
a2,,_lp2n -1
(80)
n:l
where the coefficients are found from the simulated (absolute) isotherms. Figure 4 shows D s and D~a,~ for spherical models of methane and ethane, with diffuse wall reflection, in slit pores of two different widths at 296K [73,78]. Several points may be noted. First it is clear that the Darken factor makes a major contribution to D,a ~ at high densities as a consequence of the flattening of the adsorption isotherm. At low densities on the other hand, when adsorption is governed by Henry's law (density is proportional to pressure at low pressure), the Darken factor becomes unity and D,.a~ and Ds are identical. A second point of interest is that the ratio of pore width to adsorbate molecular size plays a major role in determining diffusion properties. A similar observation was noted earlier [70,79] in studies of D s for 12-6 molecules in slit pores. When the bulk external phase density is kept constant, D~ oscillates with a gradual attenuation in amplitude, as the pore width increases [27,70,79,80]. In figure 4, the variation of D~ and D~,~ with pore width is particularly apparent for the methane model, but it is clear that any trend with pore width may also depend on other factors including the mean adsorbate density and the strength of the interaction between adsorbate and adsorbent. For example, D~,~,~ for methane at 296K passes through a shallow maximum in the wider pore, but no maximum occurs in the narrower pore. This is primarily a packing effect. The pore of width H = 1.144nm is able to accommodate almost exactly two parallel layers of methane, but in the wider pore a third central layer can partly form by filling interstitial spaces between the wall layers. As density increases, intermolecular repulsions increasingly frustrate transport, and D~ and Dt,.,,~ decrease. In the narrower pore collision scattering, due to repulsive effects, is delayed to higher densities because the adsorbent field tends to localise each layer. When pore width is reduced by a further half
285 1.0
//
1.0
/
/
o.8i
O o t--
.9 t/) :I= D
9
0.6
E :3
v .1-, E G)
J
o.8~
(/)
(!) O :3 -O
1
0.4 ~ ~ ~ ~ : /
-o -o
0.0
a) ,-
H=1.334nm 0.4
O O
E .9 (/)
0.2
-~ n
E
0.0
0.0
0.1
0.2
0.3
0.4
0.5
9
0.4
O
~ _ ~ _ ~
0.2 ~
H=I. 144nm
0.6
adsorbate density (reduced units)
0.2
0.0 / | 0.8,~ |
I
H=I 334nm "
i
9
0.6 0.4 0.2 0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
adsorbate density (reduced units)
Figure 4. Self diffusion of spherical methane (left hand panel) and ethane (fight hand panel) with diffuse reflection in smooth graphitic slits. Open points Ds, closed points Dtr,~, given by equation (79). molecule the maximum reappears, since the molecules in the two adsorbed layers now undergo frequent scattering collisions [71,73]. The effect of internal repulsions due to packing effects are seen also in a more rapid flattening of the adsorption isotherms for the wider slit close to saturation (since very high pressures are needed to force more molecules into the pore) and in the molecular part of the isosteric heat, which also passes through a maximum at this density [72]. The spherical ethane model differs from the methane model in that the molecules are larger (o=0.395nm compared to 0.38 lnm) and interact more strongly with the graphite walls (e/k=-243K compared to 148K). One consequence of this is that the adsorption isotherms, instead of showing a monotonic increase of density with pressure, as for methane, [72,73] are sigmoid on a linear scale [78] since ethane is below its bulk critical temperature at 298K. The Darken factor decreases in the region of rapid adsorption increase, and consequently D,~,,, passes through a minimum and falls below the self diffusion coefficient. At higher density, there are strong maxima for the ethane. 4.2 Self diffusion in highly constricted pores In cylindrical pores only the axial (z) component of the diffusion coefficient is non-zero at long times, and the term uni-axial diffusion is sometimes applied [81 ]. When the pore diameter is so small that molecules cannot pass each other, uniaxial diffusion changes over to single file diffusion [81,82], and the mean square displacement varies as t~ rather than t. In the limiting case of purely one-dimensional single file diffusion the mobility F, for a fluid of hard rods of diameter o, can be defined by the equation:
Lira (Az(t) 2) = EFt 1/2 t-.
oo
(81)
286 with
(82)
:
P where p is the 1-dimensional density, and DI~(0) is the diffusivity at infinite dilution [82]. In the transition regime it may become difficult to distinguish, from the mean square displacement plot, which type of diffusion is occurring. Long simulation times may help to resolve this problem, but it must be kept in mind that any simulation has a natural recurrence time approximating to the speed of sound divided by the box length, after which spurious correlations may be set up (see below). Single file diffusion has also been studied using DCV-GCMD (section 3.3.3) for hard sphere fluids with diffuse reflection in cylinders of finite length [83]. From this method it is possible to extract an effective total diffusion coefficient D. In the hard sphere system studied in [83], it was shown that the time dependent single file diffusion coefficient, found in single pores, correlated closely with the characteristic time 1/s, where I is the pore length and s is the speed of sound. This suggests that the effective total diffusion coefficient for transport through a single file pore can be found from EMD calculation of the mobility through an expression of the form: L i m D ~ F ( s / l ) 1'2 [
-.
~
(83)
Consequently, pore length may be an important, though largely neglected, parameter in determining the transport diffusion coefficient. An interesting situation arises when channel widths are large enough to permit occasional passing events or when these events can occur at channel intersections in networks [84]. In such cases, the system eventually undergoes a transition form single file to random walk diffusion. A very small increase in channel diameter above the critical value for single file diffusion can lead to a variation in the transition time of 10 orders of magnitude. In very narrow slit pores, molecules can always pass each other in the plane of the pore. Nevertheless, non-linear MSD-time plots have been found in slit pores having internal widths of about one monolayer [85]. In order to avoid any problems associated with recurrence times in finite systems, MSD's for very long times were generated from MC simulation, and a scaling factor relating 'time' in MC simulation was established by comparison with MD for simulation times less than the recurrence time for the system. In a similar manner to the near single file diameter cylindrical pores, two time regimes (in addition to an initial 'ballistic' regime) can be identified [5 7,61 ] according to the exponent d in the equation, (x2(t) ) = t d
(84)
In smooth walled pores with specular reflection, d has approximately its Brownian value of unity, but in pores with structured walls, where the molecules are caged by the corrugated potential energy surface, d was found to be much smaller than unity at short times.
287
4.3 Poiseuille flow of simple fluids in a slit pore The solution to the Navier-Stokes equations for flow driven by a pressure gradient, dp/dx, between two infinite parallel plates, width H apart, yields equation (28) for the streaming velocity profiles and an expression for the temperature profile 12~72
+ TO
(85)
where it is assumed that the density, shear viscosity and thermal conductivity are constant across the slit, and that no-slip (i.e. stick) boundary conditions apply. Recent computer simulation studies of planar Poiseuille flow [58,67] have revealed the realm of applicability of the Navier-Stokes equations and hence the validity of equations (28) and (85). In these simulations it was found that the streaming velocity is essentially quadratic for slits which are 10 molecular diameters wide. However for silts of width 5 molecular diameters or less, the profiles exhibit oscillations about the continuum solution [26,86,56]. The measured temperature profiles did not show these deviations. In all cases, the stress profile showed oscillations about an underlying linear variation in the confined coordinate. A non-linear strain rate profile (non-linear as a result of non-quadratic variations in the measured streaming velocity profile) and non-linear stress profile necessarily imply a viscosity which varies with position. Such a viscosity can be calculated by extending Newton' s law of viscosity (equation(23)), to define a local shear viscosity, r/(z) n(z)
:
-U(z)
Ou (z)) ~
is6)
However, Travis and Gubbins [97] found that the strain rate profile may contain zeroes which implies that even the local generalization above may be incorrect for highly confined fluids, since the shear viscosity cannot be infinite. By analogy with the treatment of viscoelastic behaviour, one might introduce a non-local generalization of Newton' s constitutive law,
' Oz
)
dz/
(87)
o
although the validity of this expression has not been verified. In very narrow channels, calculation of the heat flux profile reveals deviations from the Navier-Stokes solution [56,24]. A local generalization of Fourier' s law is then needed to calculate a local thermal conductivity,
JQz(Z) = - ~,(z) dT(z) dz
(s8)
In contrast to shear viscosity, there is no evidence to suggest that a non-local generalization of Fourier's law is required. However, recent work suggests that Fourier's law may need to be
288 modified for different reasons. Using a sinusoidal transverse force method, Baranyai et al [87] made the remarkable observation that a heat flux can arise in the absence of a temperature gradient. The thermodynamic force driving the flow of heat in this case is postulated to be the gradient in the square of the strain rate and Fourier's law may be modified to read JQ : - ~(z) VT - xV [Vu:(Vu) T]
(89)
where X is a phenomenological strain rate coupling coefficient. In planar Poiseuille flow heat flow can arise, not only from the temperature gradient, but also from the strain rate coupling. Strain rate coupling modifies the measured temperature profile, which introduces some quadratic character [88] into (85). The coupling effect is weak, and only shows up in wide channels. In these early studies it was assumed that the temperature appearing in equation (85) was the kinetic temperature (based upon the ideal gas thermometer). However, the kinetic temperature in Fourier' s law does not correctly account for the heat flux [89] and the normal temperature [90] should be used. The Navier-Stokes equations discussed up to now apply to structureless molecules. For multiatom molecular models, they must be modified to take account of rotational structure by including terms involving vortex and couple viscosities and the angular velocities of the molecules [91 ]. For planar Poiseuille flow at low Reynolds number, the modified equations have been solved analytically [92]. The solution for the streaming velocity turns out to be the classical Navier-Stokes expression with the addition of a hyperbolic term. The solution for the angular velocity involves a term linear in the confined coordinate plus a hyperbolic switch term. Computer simulations [93 ] of diatomic molecules undergoing planar PoiseuiUe flow are in general agreement with the profile predicted from the generalized Navier-Stokes theory except in regions close to the walls. The translational streaming velocity followed the classical quadratic Navier-Stokes behaviour in the regime studied. Inspection of the expression for entropy production for molecules which possess spin, and application of Curie's principle leads to the conclusion that the curl of the angular velocity field can couple with the mass flux, and hence drive diffusion. Though not yet investigated, this effect is expected to be negligibly weak in the flow of low density fluids through single pores. 4.4 Isothermal mass transport in slit pores
In DCV GCMD The mean density gradient is obtained by taking the slope of the measured density profile. For single component fluids, one can proceed easily to calculate a diffusion coefficient through use of Fick' s law. However, this diffusion coefficient must be regarded as an effective diffusion coefficient since the total flux measured in the laboratory flame contains an unknown contribution from viscous flow (cf equation (43)). The true diffusive flux can be calculated using the viscous subtraction method [56]. EMD calculations of collective and self diffusion coefficients have also been made for methane in graphitic slit pores [94]. An example is given in figure 5, for methane in a narrow slit pore. The cross correlation diffusion coefficient, D~ makes a substantial contribution to the total diffusion in this system with diffuse-scattering boundary conditions (see section 3.1.3), whilst the contribution from the mean viscosity, calculated from the equation in Table 1, is very small. The Darken factor correction, obtained from equation (80) by conducting separate equilibrium GCMC adsorption simulations, makes a substantial contribution [72,73] to the overall diffusion coefficient at higher densities where the adsorption isotherm becomes quite flat, but is of course unity at low densities in the Henry law region. In wider pores with H = 1.133nm, the mean viscous contribution was found to be about 10% of the total
289 0.6~,
! I
[]
D
4~
I
/
L
I
!
D*
o2I 0.0 r 0.0
1
o
o
/
I
q
oo
1t
0.2
0.4
0 0.0
,
0.2
0.4
]
Figure 5. Diffusion properties from simulation of methane in a graphite slit of (physical) width 0.959nm at 296K. The left hand panel shows the contributions to the mean Do (see equation (72)) as a function of the adsorbate density, calculated from EMD. In the left hand panel the squares are Do multiplied by the Darken factor (equation (78), filled circles are self diffusion coefficients multiplied by the Darken factor, the crosses include the mean viscosity term to give the total diffusion coefficient, according to equation (42). The circles represent the total diffusion coefficient calculated from DCV GCMD. All diffusion coefficients are given as reduced units of(e/m)V2o where e/k=-148.2K, o=0.3812nm and m is the molecular mass of methane. diffusion coefficient according to this type of calculation. In figure 5, the results from EMD and from DCV GCMD show similar trends, but there are quantitative differences outside the error bar limits as well as qualitative differences. In the NEMD calculations, there is a steep change in total D in the region of the "knee" in the adsorption isotherm which is also the density at which the effects of intermolecular repulsion are first seen in the compressibility and in the molecular component of the isosteric heat curve [5,73]. Differences between EMD and NEMD diffusion coefficients in highly restricted cylindrical pores have been noted in section 4.2 above, and may play some part in the slit pore system, even though molecules can pass freely parallel to the plane of the pore walls. Several mixture simulation studies using DCV GCMD have been reported recently, including methane/hydrogen [28] and oxygen/nitrogen mixtures in graphite slits [95], and carbon dioxide/methane separation in carbon nanopores [96]. For multicomponent mixtures, each component has an associated flux, which is typically measured in the laboratory (pore fixed) frame of reference. For binary mixtures there are four diffusion coefficients to consider; Dll, D22 and the cross coefficients, D12 and D2~. Unfortunately, these coefficients are not readily obtained from a binary mixture DCV GCMD simulation because the component fluxes contain contributions from the self and cross diffusivities, as well as a contribution from viscous flow arising from a pressure gradient in the system. In the case of molecular fluids, the situation is even more complicated since the component fluxes will contain a contribution due to coupling between the curl of the angular velocity field and the mass flux. In sufficiently narrow silts, the viscous contribution and the angular velocity coupling contribution, may be negligible. However there are no convincing grounds for neglecting the cross di~sivities. Few simulation results have been reported for the magnitudes of these coefficients in slit pores. In principle, they can be calculated from equilibrium simulations
290
1.6 o c,i z 0
1.2-
r
,^,
"~o -> 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.;
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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 <~2>, 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<~i2>/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<30 A the surface area values seem to converge to a constant value for each porosity (relative error on Sv going from le=30 A to
0o31
S v=0.00263+0.0673~(1 ~)
0021
A
001
x 1~=15A D /e=30A
t~=6oA
,,
ooo
0 10
9
0 '15
9
i
0 20
9
!
0 25
,
0;0
r(1-0
Fig. 9: Dependence of specific surface area, Sv, on porosity, e, in reconstructed Vycor.
311 le=15 ,~ ~-2%). For a Vycor bulk density of 1.58 g/cm 3, the surface area of the reconstructed Vycor porous glass with 28% porosity, is found as 103 m2/g, a value which is in very good agreement with independent experimental and computational measurements of this property [35, 50, 78-82]. 4.1.2 Simulation of Knudsen Diffusion in Reconstructed Vycor Computer simulations have been performed in 3-D images of reconstructed Vycor porous glass, with pixel size le=30 and sample size of 100xl00xl00. A total number of 2000 test molecules has been used in the majority of the simulations, while the total number of time steps was > 105 to 107 depending on the porosity of the sample. Note that additional simulations in 3-D images generated with higher resolution (le--15 2~) have shown overall very good agreement compared to the "coarser sample", with a relative error not exceeding 5% (see [27] for more details). The Knudsen permeability was found equal to 0.073• Since for He at 298 K the value of D~ is 0.0126 cm2/s (for le=3OA), it follows that the computed Knudsen permeability of He in Vycor porous glass is -9x10 "4 cm2/sec. This is in excellent agreement with the experimental result of-8.5x 10 "4 cmZ/sec obtained previously in our laboratory [83] as well as with experimental results from the literature [69] that report Knudsen permeability values of He in Vycor of the order of 1• 10.3 cm2/sec. Having validated the presently employed model, the effect of porosity on Knudsen permeability was examined next. From the results shown in Figure 10, it is evident that the Knudsen permeability shows a sharp decrease in the porosity region (0.15-0.2). An 101 100
Analytical Solu~on
10-~ ( ~ 10-2
)
10-3
10-4
10-~ 01
0~2
,,,
,
. . . . .
0~3
,
|
04
9
,
015
Fig. 10: Knudsen permeability vs. porosity in reconstructed Vycor. investigation of the percolation properties of the reconstructed material using standard algorithms [84] showed that the site percolation threshold of the reconstructed Vycor porous glass is ec--0.144. This is in agreement with the critical porosity value of 15%, which was first suggested in the seminal work of Cahn [42]. At this porosity, according to the theory of spinodal decomposition, there exists connectivity for the first time in the minor phase of
312
Vycor [42]. Note also that the Knudsen permeability curve of Figure 8 in the porosity region close to the percolation threshold, shows a power scaling law behavior with critical exponents around 1.9, in accordance with ordinary percolation theory [75]. For the case of Knudsen diffusion in a random medium, an elegant analytical solution based on the tortuosity model has been recently derived by Burganos [26]. According to this model the Knudsen permeability is given by the standard eq. (2) where the tortuosity factor is a function of the porosity and the percolation threshold of the material. The comparison between the analytical and the computational results as a function of porosity is also shown in Figure 10. Evidently, the agreement is very good for porosity values down to 0.2 and gets worse as the percolation threshold is approached. It is interesting to observe that the analytical solution predicts a zero permeability at the percolation threshold of the material albeit the wrong scaling in the vicinity of the percolation threshold. 4.2 Membranes made by Compaction of Microspheres The homogeneous model membranes formed by compaction of non-porous microspheres, are ideal for pore structure characterization and for Knudsen diffusion studies. Such model systems have been systematically investigated since the pioneering studies of Barrer and coworkers [70-72]. For this reason two types of well-defined mesoporous alumina pellets with porosities of 42% and 48%, respectively, have been fabricated in our lab [85]. The pellets were produced by uniaxial compaction of alumina powder consisting of non-porous spherical particles (Degussa Aluminium Oxide C of size 200 ~ in diameter, and specific surface area 100 m2/gr). The compaction pressures were selected appropriately so that no significant macroscopic porosity inhomogeneity would be produced. For the case of the higher porosity pellet (e=0.48) the compaction pressures were 80% of the corresponding ones used to develop the lower porosity membrane which corresponds to a loose random packing of spheres system (e=0.42). In both cases the resulting BET surface area values measured from nitrogen porosimetry were 96 and 97 m2/g, respectively, while the corresponding BET surface area for the powder was 99 m2/g. This agreement in the surface areas before and after compression supports the argument made that the porous compacts can be considered as random sphere packs of non-overlapping spheres. Since the dominant feature of sphere packs is the constrictions between the tetrahedral cavities formed by the alumina microspheres [86], a different reconstruction model is required, based on random packing of spheres [86-97]. Such models are obviously more complex. Conversely, they permit a more realistic representation of the pore space among the spheroidal particles. 4.2.1 Structure Generation and Characterization Random packing of hard spheres, discs, and spheroids of prolate or oblate geometry has been the subject of considerable attention for many years, mainly due to their role in understanding the structure of liquids [86,92] or in general amorphous, porous and random materials [92], and also due to their importance in powder technology [88,91]. Dodds and Lloyd [98] have considered the random packing of unequal spheres in connection with the interpretation of liquid capillary desaturation. The model consists of an assembly of tetrahedral, whose vertices lie at the centers of the spheres. A geometrically unrealistic feature of this model is the assumption of "gapless" packing; thus all the spheres forming the tetrahedron are assumed to be in contact. In order to compute capillary pressure curves, these
313 authors placed the cavities formed at the center of the tetrahedral on the nodes of a square two-dimensional network in a random manner. Each cavity communicated with four others via triangular windows, thus preserving the essential geometry of the original packing. However, the size of the windows was also assigned randomly. Thus, again, the requirements of geometry can be grossly violated. With reference to the random packing of equal spheres, Mason [90] has shown that the tetrahedral subunits can be constructed by taking edges at random from a tetrahedral edge length distribution function, which can be considered a characteristic property of the packing and has been obtained from experimental random packings of steel balls of porosity-~0.37. This approach was applied to the calculation of drainage of a liquid from a porous solid. Kanellopoulos et al., [99,100] proposed a model based on the dense random packing of equal spheres following Mason. The irregular tetrahedral constructed from the relevant edgelength distribution mentioned above is interconnected to form a two-dimensional network, akin to that of Dodds and Lloyd. The model is then applied to the simulation of adsorptiondesorption isotherms and of the gas relative permeability. A three-dimensional network model based on the structural characteristics of random packing of equal spheres has been developed for the simulation of sorption and diffusion processes in mesoporous sorbents composed by non-porous spheroidal primary particles [ 101]. The simulation provides satisfactory prediction of adsorption-desorption isotherms of carbon tetrachloride and pentane for different porosities, temperatures and adsorbates. In the present study, we will follow the random sequential deposition of non-overlapping spherical particles as in the pioneering work of Void [88]. In such a ballistic deposition, the packing rule differs from other methods in that the spheres position themselves under the influence of a unidirectional (vertical) force, rather toward a center of attraction, as can be seen from Figure 11. This type of random sphere pack is believed to be more representative of the compaction process, by which our pellets have been developed.
Figure 11: Examples of random sphere packs made from different processes: (a) ballistic deposition (b) central attraction
314
Several authors have proposed similar algorithms that generate random sphere packs under ballistic deposition. [88,91,93,94]. In this work we have followed the approach outlined in [91]. The basic idea of the algorithm is as follows: Balls are dropped sequentially from a random point well above the simulation box of length LxLxL. When a ball i, is dropped, it hits ball m, or the floor of the box, in which case it stops. If it has contacted with ball m, then it rolls down in a vertical plane on m until it is in contact with ball n. Then it rolls downwards in contact with both m and n until it hits ball p. If the contact with m,n and p is stable then ball i stops. If not, it rolls on the double contact that goes down most steeply, and so on. Such a procedure can be systematically followed through the use of a steepest-decent method followed by a conjugate gradient algorithm [94]. An alternative procedure which was pursued in the present study is based on a Monte Carlo method as follows: Each time we drop N "test" balls but allow only the one whose final position is lowest to remain and become a part of the stack. If N is large enough (N > 105) then we can recover random sphere packs with the same structural properties found by the more rigorous deposition algorithms. A dependence of the packing density on N is shown in Figure 12. From this figure it follows that we can generate porous media from a range of densities achieving porosities as high as --50% (above this value much simpler random sphere pack models exist). For the purposes of the present study a value of N = 105 was used to generate a random sphere pack of e=0.42 and a value of N=300 was used to generate a random sphere pack system of e=0.48. The number of spheres used ranged from 1000 to 2000 for different realizations. In order to study structural properties such as correlation function and chord length distribution in the developed random sphere packs, it was convenient to first digitize them and then work on the 2D and 3D digitized images. The simple algorithm proposed in [95], and 0 . 6
--~
0.4 + i 1
0.2 i 0
[
100
'
'
~
' ....
'
10000
'
'
~
' ....
J
1000000
Fig. 12: Effect of N on the porosity, e, of the random packing adopted by other researchers [96] has been employed in the present study. In Figure 13 we present typical 2D sections cut from the respective 3D images of each medium. It is evident that as the number of spheres in the pack increases the digitized images become rougher for the same number of pixels used to digitize the sphere pack. Grain packs resulting from a ballistic deposition process are expected to exhibit some anisotropy when comparing each of the horizontal directions x,y to the normal direction z. Nevertheless it was previously found [94] and also confirmed in the present work, that the
315
'IlIIIF v
am.
Fig. 13" 2D sections cut from different random packs.
auto-correlation functions R~y and Rz, set parallel and normal to the horizontal plane, respectively, do not show significant differences. This result reveals isotropy in the structure of the material although one could expect the opposite, as a result of a construction process anisotropic in character [94]. The auto-correlation function, Rz, shown in Figure 14 is in excellent agreement to the respective auto-correlation function obtained elsewhere [94], on a random sphere pack of
1 0.8 0.6 "
~=~ N
n,,
04 0.2 0 -0.2
0
1
2 fiR
3
4
Fig. 14: Auto-correlation function along the z-direction of a random sphere pack resulting from ballistic deposition
316 e-0.4, generated by the more rigorous ballistic deposition algorithm. Hence we observe first zero crossing in the R~ycurve around r/R=0.9 followed by an anti-correlation up to r/R=2. For r/R>3 R~y drops practically to zero indicating the absence of significant correlation at distance greater than 1.5 particle diameters. Note that Rz is identical for both packings examined, which means that the difference in porosity between the two materials is uniformly spread in their structure so that the basic features of the random pack are not altered. The surface area of the material can be determined from the slope of R, using the equation: Sg
=
-4 e R z(O) / p ,
(14)
For ps=3.28 g/cm 3 the value of Sg is around 99 m2/g for both materials. This value is in excellent agreement with the experimental measurements of surface area on the powder and the pellets of the alumina particles given above. The agreement between the theoretical and the experimental values of porosity and surface confirms the random packing of spheres consideration. In Figure 15 we present the pore chord length distribution functions determined in the two computer-generated sphere packs. It follows that the chord length distribution function in both cases follows an exponential distribution in agreement with previous studies on similar systems [93, 96]. Unfortunately no measurements have been obtained in the actual membranes due to the lack of appropriate experimental information (TEM images, valid SAS data, etc). When comparing the chord length distribution functions in Figure 15, between the two random sphere packs, we notice a small difference in the slopes of these curves indicating the existence of larger pores in the higher porosity pack.
0 ,--,
-2
e~
-4
.~.
-6
-
-8
"~-A.
c=0-48
-10 -12
I
,,
,
,,
0
2
4
6
8
r/2R Fig. 15: Chord length distribution function for sphere packs made by ballistic deposition
317 To further examine the above observation we have calculated the so-called interstice size distributions of these two systems based on the algorithm proposed elsewhere [97]. According to this algorithm one determines the distribution of non-overlapping spherical interstices that just touch each subset of four neighboring spheres in the pack. Such distributions can give a crude information on the pore size distribution of the sphere packs, a property which is often very difficult to be determined accurately, since it depends on additional assumptions regarding pore correlation and shape. The results of the interstice distributions for both sphere packs are presented in Figure 16. It is_evident that the two distributions have a similar shape with the one for the lower pack being shifted to lower interstice values. The average interstice radius is around 3.5 nm in the lower porosity pack and around 4 nm in the higher porosity pack. 4.2.2 Simulation of Knudsen Diffusion in the Random Sphere Packs Computer simulations have been performed in the generated sphere packs, by following the same approach to the one outlined above. Since in the present case the position of the spheres is known exactly in the three dimensional space, we have modified the approach followed for the case of random walk simulation in a digitized medium. Thus in the present case, at each time we determine the trajectory of the test molecule by solving the linear direction of motion with the surface of each sphere in the pack, keeping the smallest distance each time, and so on. In addition, since there is a speculation that the sphere packs made by
_
,
-
"
.
A
0.8
=0.42 ~
A
0.6 I,i,,,
0.4
~
0.2
~=0.48 .
0
0.2
0.4
0.6
.
.
.
.
.
.
.
i
0.8
1
dR Fig. 16: Cumulative Interstice distribution functions for the two sphere packs made by ballistic deposition ballistic deposition may exhibit anisotropy, the diffusivity component in the vertical, z, direction was also determined. The results on both, orientationally averaged and z-component, Knudsen permeability of He at 308 K, for each sphere pack are given in Table I, below. In the same Table the
318 corresponding experimental values are also presented. First of all, one can clearly observe a 10% increase in the diffusivity in the z-direction caused by the anisotropic character in the construction of the medium. Since the permeability experiments were performed in such way as to measure the z-component permeability, the latter simulation value is the one that should be compared to the experimental result. By comparing the simulation with the experimental Knudsen permeabilities we observe a very good agreement, as in the case of Vycor. Note that for the case of the sphere packs, Knudsen permeability is about an order of magnitude higher compared to the corresponding value for the case of Vycor. The reason for the difference in diffusivity is attributed, primarily, to the different porosity and structure between the two materials and, in addition, to small anisotropy effects appearing in the sphere packs. Furthermore, if we look at the results from Figure 10, we can obtain Knudsen permeabilities for porous glasses with the structure of Vycor but with porosity of 42% and 48%, respectively. The results are given in Table II together with the average permeability values of the sphere packs. Comparing the resulting Knudsen permeability values at both porosities reveals a consistently higher value for the permeabilities of the random sphere packs over the ones obtained on the controlled porous glass structure, by a factor of 1.8. Comparison between the structural and dynamic properties between the two model systems shows somewhat similar correlation functions but different chord length distributions. This result, together with the difference in Knudsen permeabilities, shows a more important effect of the chord length distribution over the two-point correlation function, in pursuing an accurate representation of the pore structure of a material. Nevertheless, when looking for order of magnitude estimations of Knudsen permeability, matching of porosity and correlation function seems to be quite enough.
Table I Comparison between experimental and simulation Knudsen permeabilities on the two sphere packs Membrane Random Sphere paci~ Random Sphere pack
e
6142 0.48
7.7x10 -3 cm2/s ' 1.13x10 2 cm2/s
Per~ 8.0x10 "3 cm2/s 1.23x10 -2 cm2/s
P e ~ exp 8.2x103'cm2/s 1.41x10 2 cm2/s
Table II Comparison of Knudsen permeabilities between random sphere packs and Vycor-like controlled porous glasses e 0.42 0.48
Random Sphere pack 7.7x10 3 cm2/s 1.13x10 -2 cm2/s
Controlled porous, glass 4.2X10 3 cm2/s 6.5x10 3 cm2/s
319
5. Conclusions
To summarize, in this section, we have demonstrated the ability of 3-D reconstruction methods to accurately represent the pore structure of porous membranes. Two model systems have been examined, Vycor porous glass and porous compacts made by pelletizing monosize spherical alumina particles. For the case of Vycor, a stochastic reconstruction process has been employed to generate 3D images which have the same basic statistical content with the actual material in terms of porosity, auto-correlation function and chord length distribution. Furthermore, the percolation threshold of 14.4% found for the stochastic process employed to generate the structure Vycor, is in close agreement with the value obtained based on the theory of spinodal decomposition, indicating that the developed reconstruction process mimics at some level the underlying process that takes place during the formation of the material. For the case of the porous pellets made by compaction of spherical monosize alumina particles, a ballistic deposition process of spherical particles has been employed, to accurately represent the pore structure the porous compact. Comparison between the computed and experimental permeability values obtained in the Knudsen regime shows a relative difference of less than 8% for both model membranes. This agreement has been obtained without resorting to any assumption or additional simplification in either the porous structure or the diffusion process. Small anisotropy is observed in the simulated sphere packs in agreement with the anisotropic character of the ballistic deposition process. Comparison between the structural and dynamic properties between the two model systems shows similar correlation functions but different chord length distributions and Knudsen permeabilities (not justifiable solely by the difference in porosity). This result shows that matching of the twopoint correlation function alone is not always adequate, when pursuing an accurate representation of the structure of a porous material. In such cases, higher order statistical properties of the material contained in the chord length distribution should be satisfied as well. Finally it is important to emphasize the fact that both reconstruction models seem to mimic at some level the underlying process that takes place during the formation of the actual porous material. This observation leads to the conclusion that proper account of the formation process in the reconstruction of a porous material leads to accurate representations of its structure.
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RecentAdvancesin Gas Separationby MicroporousCeramicMembranes N.K.Kanellopoulos(Editor) o 2000ElsevierScienceB.V.All rightsreserved.
323
Microporous carbon membranes Shigeharu Morooka a, Katsuki Kusakabe a, Yoshihiro Kusuki b and Nozomu Tanihara b aDepartment of Materials Physics and Chemistry, Graduate School of Engineering, Kyushu University, Fukuoka 812-8581, Japan bPolymer Laboratory, Corporate Research and Development, Ube Industries, Ichihara 290-0045, J a p a n This article surveys the production and permeation of carbon membranes in the field of gas separation. Carbon membranes, which are prepared under optimized conditions, show appreciable selectivities for gas mixtures such as H2/N 2, CO~/N2 and O2/N2. Separation between organic and inorganic gases, as well as alkane and alkene, is also possible using the carbon membranes. Permeances may be decreased by exposing the membranes to an oxidative or humidified atmosphere at temperatures below 100~ but can be recovered by heat-treating in an inert atmosphere.
1. INTRODUCTION The carbonization of polymeric membranes enhances both the permeation properties and thermal resistance of the precursor membranes, thus offering advantages for gas separation. Koresh and Sofer [1] reported the preparation of a carbon molecular sieve membrane. Since their initial report, carbonized membranes have been prepared from polyfurfuryl alcohol [2], polyvinylidene chloride-acrylate terpolymer [3], phenolic resin [4-6], acrylonitrile-methyl methacrylate copolymer [7], polyimides [8-17], polypyrrolone [18], polyetherimide [19], as well as polyaromatic resin [20]. Of these, the carbonization of polyimides has been the most intensively investigated, since the permeation properties of polyimide membranes are well known [21]. Because carbon membranes are not mechanically strong, they are typically formed on supports [2-4, 11, 15, 18-20, 22-28]. However, a support is not always necessary especially for the case of asymmetric carbon fibers [7, 8, 13, 14, 29-33]. McKelvey et
324 al. [34] surveyed techniques to produce polymeric hollow fibers. The flexibility of a polymeric hollow fiber can be maintained by controlling the carbonization parameters [8, 13]. The membrane used by Katsaros et al. [5] was prepared by coating a phenolic resin solution on an extruded tube, which consisted of partially cured phenolic resin particles and an extrusion agent. The composite fiber was carbonized in a flow of nitrogen and was then activated in a flow of carbon dioxide at 800~ 2. P R O D U C T I O N OF S U P P O R T E D CARBON M E M B R A N E S 2.1. H o l l o w fiber s u p p o r t s Supporting substrates for carbon membrane must be chemically and physically stable and possess a diffusion resistance lower than that of the carbon membrane itself. The contact between membrane and support should be maintained during repeated temperature changes. Tubular substrates are mechanically stronger than fiat substrates, and the m e m b r a n e area per unit module volume is increased by decreasing the diameter of the support. Figure 1 (a) outlines the procedure for the
Fig. 1. (a) Preparation of a-alumina hollow fiber supports. (b) Tube-in-orifice spinerret. (From Akiyama et al. [35])
325 preparation of porous a-alumina support tubes, which were provided by NOK Corporation, J a p a n [35]. A slip was prepared by dispersing sieved a-alumina particles in an organic solution of polymers. The solution was then continuously extruded into a poor solvent through a tube-in-orifice spinneret shown in Figure 1 (b). The poor solvent was also introduced into the inner tube of the spinneret. While the precursor moved in the bath, the solvent in the slip and the poor solvent in the bath diffused in opposite directions across the wall of the extruded hollow fiber. The slip was then separated into continuous and dispersed phases, resulting in an increase in the mechanical stability of the gel. The green hollow fiber was dried in air and calcinated at a t e m p e r a t u r e above 1300~
The average pore size, 50-200 nm, was
controlled by varying the size of the a-alumina particles and corresponded to 1641% of the particle size. The pore size distributions were narrow, and the porosity was in the range of 0.35-0.50. The fiber, whose porosity was 0.35, was ruptured at pressures in the range of 20-40 MPa, but was mechanically stable at pressures below this range. When carbon membranes are used in industrial processes, a technique to construct gas-tight bonding between a bundle of porous hollow fibers and a metal casing is required. The hollow fiber can be brazed to a metal socket. Leak tests show t h a t the brazed joint was gas-tight up to 500~
and t h a t the gas leakage
through the joint was 4 x 10 -15 mol s -1. This value is extremely low compared to the permeation rate through a molecular sieving carbon membrane which was formed on the support tube [35].
2.2. Supported carbon m e m b r a n e s Figure 2 shows chemical structures of (a) diandydrides and (b) dianilines, from which polyimides are synthesized. A typical experimental procedure is as follows [11, 24]: Powdered BPDA and pp'ODA are each suspended in distilled N,N'dimethyl-acetamide. The BPDA suspension is then added dropwise to the pp'ODA under an inert atmosphere. The suspended solution is stirred at 15~ for 1 h and at 25~ for 3 h, resulting in the formation of polyamic acid. The polyamic acid film is then coated on the outer surface of the support tube by dip-coating, and imidized in nitrogen at 300~ for 1 h. The coating-imidization cycle is repeated two or three times, a procedure which results in a pinhole-free BPDA-pp'ODA membrane. The membrane is then carbonized in a deoxygenated nitrogen stream at temperatures of 600-900~ Carbonization temperature strongly affects the permeation properties of carbon
326
membranes. In the case of the carbon membranes derived from BPDA-pp'ODA films [11, 24], hydrogen permeance reached a maximum, as the result of carbonization, at 700~
while nitrogen permeance decreased with increasing carbonization tem-
perature. Pores larger t h a n 0.5 nm, which are effective for nitrogen permeation, are minimized by carbonization at 800-900~ due to shrinkage of the carbon structure. The permeance and permselectivity are dependent on both pore volume and pore size distribution, which are determined by carbonization conditions. Excessive carbonization only decreases permeances. Hayashi et al. [24] also found that a carbonized membrane prepared with a BPDApp'ODA polyimide procedure gave higher C3H6/C3H8 and C2H4/C2H6 permselectivities t h a n those of the corresponding polyimide membrane. The C3He/C3H 8 selectivity was approximately 30 at a permeability coefficient of 70 B a r r e r (1 B a r r e r = 3.4 x
R1
(a) Dianhydride
N'-" R2
O Polyimide
R1 9
n
PMDA
BPDA
BTDA
6FDA
(b) Dianiline" R2
H 3 ~ 2,4-D A T
OoO
pp'-O D A
ICF3
H3 H3
CH3
CH3 H3 CH3 mTrMPD pTeMPD
mp'-O D A
MDA
CH~._
-O-c-O- -O-c-OCF3 BAHF
0"3
CH3 IPDA
OTD
OoO'cOoOQ0O, o CF3
CF3 BAPHF
CF i
CF3
CF3 BATPHF
CF3
Fig. 2. Chemical structures of dianhydride and dianiline.
327 10 -16 mol m -1 s -1 pa-1). This suggests t h a t the carbonized m e m b r a n e s possess a micropore structure, which is capable of differentiating between alkane and alkene molecules, based on size differences. The pore structure of the carbon membranes was further controlled by CVD of carbonaceous matter. The O ~ q 2 permselectivity at 35~
which was 10 for the as-prepared carbon membranes, was increased to 14
as a result of CVD t r e a t m e n t [25]. In typical procedures, polyimide films are carbonized in an inert atmosphere. However, heat-treatment in an oxidative atmosphere is effective in improving permeances [15, 26, 28]. Kusakabe et al. [28] carbonized BPDA-pp'ODA membranes in an inert atmosphere at 700~
followed by oxidization in a mixture of O2-N 2 (02
fraction = 0.1) at 300~ for 3 h. Carbonization at 700~ decreased the O/C ratio of the membrane without altering the H/C ratio. This suggests the thermal decomposition of oxygen-containing functionalities, such as carbonyl groups. Carbonization at temperatures higher than 700~ decreased both H/C and O/C ratios and altered the polymeric structure of the membrane toward a polycondensed aromatic structure. Oxidation at 300~ decreased the H/C ratio and increased the O/C ratio, suggesting the decomposition of peripheral alkyl groups and the incorporation of oxygen into the membrane. Figure 3 shows permeances for carbon membranes at permeation t e m p e r a t u r e s of 65 and 100~
[26]. The oxidation increased permeance
without greatly damaging the permselectivities. Thus, oxidation at 300~ for 3 h significantly increased the micropore volume while the pore size distribution remained relatively unchanged. However, treatment conditions in an oxidative atmosphere need more extensive study, since the results are often not reproducible. In order to determine long-term stability, Hayashi et al. [26] exposed BPDApp'ODA- based carbon membranes, which were carbonized at 700~
to air heated
at 100~ for one month. As shown in Figure 4, this exposure resulted in no change in the O/C ratio and a limited decrease in the H/C ratio, as a result of the decomposition of peripheral alkyl groups. The N/C and O/C ratios were not altered during the exposure. After the long-term oxidation, the m e m b r a n e was heat-treated in nitrogen at 600~ for 4 h. Figure 4 also shows that the mass of the membrane was decreased to 84% as a result of the long-term oxidation. After the heat-treatment, it was further decreased to 76%, while the H/C, O/C and N/C ratios remained unchanged within the experimental error. Figure 5 shows data on the permeance of the long-term oxidized and heat-treated carbon membrane to a single-component gas at permeation t e m p e r a t u r e s of 65~
The permeances of the m e m b r a n e were
decreased with increasing exposure time and were recovered after the heat-treat-
328
ment. The m e m b r a n e showed a CO2]CH 4 permselectivity of 80 at 65~
Thus oxida-
tion in air at 100~ does not a p p e a r to greatly alter the chemical s t r u c t u r e of the m e m b r a n e s . Oxides which are introduced by oxidation at 100~ m a y reduce the a p e r t u r e of the micropores and decrease permeances, and most of the surface oxides are decomposed by the post h e a t - t r e a t m e n t at 600~
3. P R O D U C T I O N O F S E L F - S U P P O R T I N G A S Y M M E T R I C C A R B O N M E M BRANES Yoshinaga et al. [8] and Kusuki et al. [13] produced a carbon hollow fiber membrane, for the first time, by continuously pyrolyzing an a s y m m e t r i c hollow fiber in an inert atmosphere. A schematic diagram of the experimental a p p a r a t u s is shown
'?4H;,SF6
Heat-treatment period (h) 100
~
I
9
,..
E o
v
80
I
2.4
-
~
2 . 2 -
10-7 t~
m
10-8
60
E
E 0 e-
I
~,,~..2_,,~c
"T, I:L
I
" :2.6 ~ 2.2
.>
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%<0.25 pm + 95%<1 ~tm) and (1.5%<0.27 ~tm + 89%<1 pm), respectively and a chemical purity of >99.99% as stated by the producer.
Figure 5:
AKP-30 tubes made by CC deposition: 1,3 with sinter warping and cracking defects ([APMA] = 417 kg/m3]) and 2,4 without visible processing defects ([APMA] = 167 kg/m3]).
350
To obtain tubes with 2 mm wall thickness and -~20 mm diameter, 120 gram of powder was mixed with different amounts of APMA (Ammonium PolyMethAcrylate aqueous solution, Darvan | C*) and distilled water. The mixture of water and APMA, 120 ml in total, was brought on pH = 9.5 by adding (-1.5 ml) concentrated ammonia t. The resulting suspension was ultrasonically treated for 15 minutes using a frequency of 20 kHz and a transducer output power of 100 W. With this suspension tubes were prepared with three different lengths: short, 6&10 cm, tubes in a home-built apparatus, using steel moulds and long tubes (16 cm) in a commercial centrifuge t using Delrin | moulds. The inner diameter of the tubes was -~20 mm. Before pouring the suspension into the moulds, the moulds were coated at the inside with a solution of Vaseline |
in petroleum ethertt (boiling range 40-60~
to obtain easy
mould release. The tubes were centrifuged for 20 minutes at 20.000 rpm and the remaining liquid was poured out of the moulds afterwards. The green tubes were horizontally dried inside the moulds in a climate chambertt for two days at 30~ and 60% RH. After drying the green tubes were removed from the moulds and sintered horizontally on a fiat support at 1150~ for 1 hour with a heating/cooling rate of 1~ To study the influence of the amount of APMA on the drying and sintering behaviour of the AKP-30 tubes a series with different APMA concentrations in the suspension was made.
R.T. VanderbiltCompany, Inc., Norwalk, USA. t E. Merck, Darmstadt, Germany. CEPA, GLE, Carl Padberg GmbH, Lahr, Germany. Du Pont de Nemours, Dordrecht, The Netherlands. **Elida Faberg6, Bodegraven,The Netherlands. tt E. Merck, Darmstadt, Germany. ~ Heraus V6tch, Ballingen,Germany
351
Results on the preparation of tubular supports Observations
[APMA]
The suspension mixtures of 120 gram powder and 120 ml stabilising liquid were sufficient for two
(kg/m 3) 0
No suspension possible
8
Low green strength; green tube difficult to re-
could be varied between 1 and 2 mm at least, de-
42
Better green strength; some surface roughness
pending on solid concentration. It was found that
83
Good green strength; some surface roughness
porous tubes, visually free of processing defects
loo
Ibid
tubes with a length of 16 cm (and a wall thickness of 2 mm). The wall thickness of the supports
lease
could be obtained only with a certain, optimum,
167
No visible processing defects
APMA concentration, [APMA], in the suspen-
250
Ibid
sion. With [APMA] below optimum drying
292
Reasonable quality; some sinter-cracking
cracks were observed after drying. At [APMA]
333
Some sinter-cracks; some surface roughness
417
Considerable cracks after sintering, warping
higher than optimum typical defects were ob-
and surface roughness
tained such as surface corrugation and excessive warping and cracking during sintering. Examples
Table 2:
Influence of liquid phase [APMA] on the quality of sintered porous AKP-30 tubes.
are given in Figure 5. Influence of binder concentration
The results of the study on the influence of the APMA concentration on the quality of AKP-30 tubes after sintering are summarised in Table 2. It was found that [APMA] = 167 kg/m 3 (addition of 20 ml APMA) gave optimal results. The AKP-30 results could be used to obtain rapidly the optimum [APMA] = 83 kg/m 3 (10 ml APMA) for tubes made from AKP-15 powders. Pore size dlstnbutlon tubular supports 140 -
i
120 100 o
E
8o
I
co
o-AKP-30
-~ 60 R
4o
g
a~ |
9AKP-151
LA 41'
v
20
40
60
80
100
20
140
radius (nrn)
Figure 6:
Pore-size distribution of AKP-30 and AKP-15 tubes made by CC at optimum conditions.
352
Properties ---...
The porosity of AKP-30 (AKP-15) tubes, made with optimum [APMA] was 42.5% (43.2%)* after firing at 500~
vL x
measured with the Archimedes
method by immersion in mercury. The sintered compacts had a porosity of 34.8% (34.5%). Their pore-size distributions, measured by mercury porosimetry t are given in Figure 6. The mean pore ra0.097mm dius was found to be 60(92)nm. The surface roughness ~ of the tubes was found to b e - 0 . 2 5 gm
Figure 7:
Roundnessdiagram of an AKP-30 centrifuged tube.
for the inside and -0.9 ~tm for the outside. The mean unroundness "~was --0.025 mm, based on a 100 point measurement; the unroundness diagram is shown in Figure 7. In this diagram the drawn line around the concentrical circles gives the deviation from a perfectly round object. Figure 7 shows a slight elliptic deformation, possibly caused by "gravitational stress" during sintering. For comparison: the unroundness of a typical" extruded ~-A1203 tube was measured to be 0.16 mm as shown Figure 8. The surface roughness of this tube was -~6 ~tm. Discussion and conclusions on the preparation of tubular supports With the CC technique excellent tubular membrane
vL
supports can be prepared with a very low surface
x
roughness (0.25 ~tm). The roundness of tubes was
/ /
//7I If;I~ ;tt',,, \
found to b e - 1 0 x better than that of a typical ex-
.d..,-~ ..
,
"\'~ \
,
,ss; i
truded tube. The roundness can possibly be im-
ifl
proved further if special attention is paid to mould roundness and drying and/or sintering is done ver0.1)97 mm
tically or in a rotating set-up. This roundness is Figure 8: very important for application in reactors. If the
Roundnessdiagram for a typical extruded ot-Al203 tube.
tubes are glass-soldered in ring-shaped machined flanges, a good roundness may result in a minimal and evenly filled solder space between the tube and
"The numbers between parentheses refer to AKP-15 tubes. t Series 200, Carlo Erba, Milan, Italy ~tMeasured with Mitutoyo Surftest III, Mitutoyo Mfg CO.,Ltd., Tokyo, Japan. wMeasured with MC 850, Carl Zeiss, Oberkochen, Germany. **
ECN (1990), Petten, The Netherlands.
353
the flange. This, in turn, will generally result in a better sealing process, quality and stability. If deformable (graphite) gaskets are used in a removable flange, a large unroundness will result in a radially inhomogeneous stress distribution in the tubes near the sealing, increasing the risk of brittle fracture. The wall-thickness of 2 mm provides the CC tubes with sufficient mechanical strength to withstand gas and liquid pressures that are common in membrane technology. The measured pore diameters of 120 and 184 nm are well in the range used for mesoporous membrane preparation and it is expected that 3t-alumina layers can be applied on the supports by conventional dip-coating and without the need of further intermediate layers [ 16]. The minimum membrane thickness that can be obtained defect-free can be expected to be of the order of the support roughness. This leads to the conclusion that membrane thickness' on CC tubes can be 50x less than those on extruded tubes. This, in turn, may result in a large flow increase for gasses and liquids. The best tube quality was obtained with an optimum APMA concentration that is proportional to the specific surface area of the powders. In the present experiments (with ot-A1203 powders) the optimum ratio between [APMA] and specific surface area was found to be -0.03 kg2/m5. An [APMA] of 8 kg/m 3 only, showed to be sufficient for electrosteric stabilisation and a rather stable suspension but also resulted in some drying cracks and roughness on the inside tube surface. This is likely to be caused by the fact that the suspension is partly flocked, leading to a poor particle packing that densities significantly during drying. In addition it was found that the green strength was insufficient at low [APMA]. This can be ascribed to poor particle packing too but it is more likely that APMA acts as a polymeric binder. At optimum [APMA] tubes can be prepared with sufficient handling strength and no surface roughness or cracking during drying or sintering. With higher [APMA], the condition of the green state looks all right but significant warping and cracking is obtained during sintering. This observation can be explained best by the presence of internal stresses in the green state caused by green state handling, or thermal processing. These stresses neither relax nor lead to cracks in the green state because of the combined effect of a particle packing, close to RCP and a significant amount of interparticle bonding. Perspectives for the use of the CC-technique It may be questioned whether the high degree of perfection of the CC tubes justifies possibly higher cost prices in mass-scale production and the limitation to circular shapes. Extrusion processes can be relatively cheap and easily continuous and enable more complex shapes such as multi-bore tubes. On the other hand the CC technique allows a radial variation of composition and particle morphology. The optimum support structure for a given application can be obtained using design rules that take into account the desired support shape, the material's strength and permeability [13]. This optimum is achieved at a certain thickness and spatial distribution of porosity and pore size. The use of a suspen-
354
sion that consists of largely different sizes of particles may naturally result in specific desired radial variations that can be predicted quantitatively on basis of the method described in [47]. In addition it is possible to inject small amounts of suspension layer-wise by using a tangential injection technique [37] so that all thinkable radial distributions can be realised.
Characterisation of membrane morphology
FE-SEM / TEM
Morphological membrane characterisation was done by Field-Emission Scanning Electron Microscopy (FE-SEM)" and Transmission Electron Microscopy (TEM)*. The FE-SEM recordings were made of a perpendicular fracture surface. TEM recordings were performed on a thin cross-section of the membrane, made as follows: One silica membrane was cut in halves and both parts were glued together with the silica top layers facing each other. From this "sandwich structure" a small slab was cut, which was abraded to a thickness of 200 lam. The specimen was further thinned by making dimples on both sides, in the middle down to 15 lam using a Dimple grinder. Finally the thickness of the centre of the specimen was reduced further by ion milling until a centre hole had just appeared. During the thinning procedure the specimen was carefully positioned so that the opposing silica layers formed the centre of the thinned area. The TEM recording was made near the centre hole, at the thinnest part of the sample. The FE-SEM an TEM recordings, given in Figure 9 and Figure 10 reveal a very thin silica layer of ~30 nm, obtained after 2 times dipping. This result is a little in contrast with earlier suggestions in the literature [ 16] in which a thickness of 100 nm is proposed.
*Hitachi, Type $800. tCM30 TWIN/(S)TEM,PhilipsAnalytical,Eindhoven,The Netherlands.
355
The TEM micrograph indicates that the silica layer is deposited on top of the 7-A1203 layer, as a distinct separation between the two layers is present. The y-AI203 layer is about 3 lain thick after 2 times dipping. The boundary between the first and second y-AI203 layer at approximately 250 nm from the surface is clearly visible in TEM. There is a clear "colour" difference between the two y-AI203 layers visible in the TEM micrograph. The second 7-alumina layer has a lighter appearance than the first layer that can be caused by two effects: 9
The first layer is calcined two times at 600~
9
The first layer is applied on the ~-A1203 support that has a much courser structure than the y-AI203 layer on which the second layer is applied. Since capillary forces play an important role in the layer formation this can result in a denser second ]t-A1203 layer.
The colour difference is not caused by a difference in pore size. This was checked by permporometry in which the one- and two-layer dipped membranes
Figure 10:
TEM Micrograph of Si(400) membrane cross section showing a part of the yalumina intermediate layers and the silica top-layer [48].
were found to have both a Kelvin radius of --2.5 nm. The permoporometry method is based on the measurement of permeation of a noncondensable gas while at the same time pores are blocked by a condensable gas. This makes that for multi-layer stacks of continuous defect-free membranes, pore radii are obtained that correspond to those of the layer with the smallest pores. Pore size characterisation of unsupported silica The unsupported Si(600) material shows a type II sorption isotherm, which is typical for nitrogendense materials. This result is in agreement with the pore size of the supported Si(600) membranes, estimated from the relation between permeance of various gases and their kinetic diameter.
356 180 160 140
~
120 100
o)
~
8o
~
6o 40 20 0
Figure 11"
N2 sorption isotherm at 77K of unsupported MeSi(400) and Si(400) material [1,15]
In Figure 11 the N2 physical sorption isotherms of Si(400) and MeSi(400) at 77K are presented. For both materials the sorption isotherms are type I, characteristic for microporous materials. From the figure it is clear that more N2 can be sorbed by the Si(400) material. This could be a result of a difference in pore structure of the silica materials, but also of the difference in amount of hydroxyl groups at the internal surface of these materials: N2 is expected to show particular interaction with the hydroxyl groups [50], so that more sorption of N2 is expected for Si(400). 180
MeSi(400)
160 140 1.
.
.
.
.
S~400)
120 100
~
8o
~
6o 40 20 0 0
Figure 12
1
Ar sorption isotherm at 77K of unsupported MeSi(400) and Si(400) material [1,15]
Figure 12 shows the Ar sorption behaviour of Si(400) and MeSi(400). Since the Ar molecule is spherical and more "inert" than the N2 molecule', it is assumed that the Ar sorption is determined by the structure of the pores and is less dependent on the concentration of hydroxyl groups [49]. A striking
Besides the hydroxyl interactions already mentioned, the interpretation of N2 adsorption data is further complicated by quadrupolar interactions.
357
observation is that the sorption behaviour of Si(400) is similar for Ar and N2, i.e. the amount of Ar that can be sorbed is only slightly higher, while for MeSi(400) material much more Ar can be adsorbed than N2. This may be explained from the molecular dimensions of the gas molecules: Ar has a kinetic diameter, dk, of 0.340 nm and covers a sorption area of 0.133 nm 2, while N2 has a dk of 0.365 nm and covers a sorption area of 0.166 nm 2 [22]. This suggests that MeSi(400) contains many small pores that are not available for the larger N2 molecules. The pore size distribution, calculated with the Horvfith-Kawazoe method [19] from the Ar sorption isotherms at 87K is given in Figure 13. This plot shows that the pore size distribution of the unsupported Si(400) material is narrow with a maximum at Deff~7A. The distribution in pore size of the MeSi(400) material is much broader, but has a maximum at approximately the same Deff. It should be kept in mind that the results for unsupported material can not be transferred quantita-
0.2 ~9
0.4
MeSi(400)
o.15
0.3
0.1
0.2
0.05
0.1
tively to the supported membrane situation. They can only be of use to show trends in changes in
o
pore structure with processing. It must be clear that
~;
the supported silica layer cannot be expected to
E u
have the same structure as similar processed unsupported silica material, since the forces present during the drying process of both materials are different.
;i(400 "'~-.
0 0
Figure 13
1 2 3 pore width (nm)
"a
.
~ E
0 4
Pore size distribution for unsupported MeSi(400) and Si(400) material, calculated according to the Horv~ith-Kawazoemethod [19] from Ar adsorption isotherms at 87K
Transport
[1,15]
The movement or rate of mass transport, of a species in a microporous material is generally determined by two parameters: the amount of a species present in the material and the mobility of the species. A proper description of mass transport in a microporous medium such as the amorphous silica layers studied here should consequently include a good understanding of the sorption properties of the system, as well as the diffusion mechanism by which transport occurs.
Diffusion The silica layer may be regarded as an interconnected network of voids with a concentration
qSat. It can
be assumed that during sorption each translational degree of freedom of a gas phase species is convetted to a vibrational one. Sorbed species vibrate around a minimum in the potential field inside a
358
void. Transport occurs when molecules jump from a minimum in one pore to a minimum in a neighbouring one. In such a system the species obey the statistics of a lattice gas. Irreversible thermodynamic description of single species permeation fluxes According to the theory of irreversible thermodynamics [51 ], the flux J of a single species i in the silica material is proportional to the gradient in its chemical potential
J, = -L.Vl.t,
(2)
The phenomenological (macroscopic) Equation (2) can be worked out further in terms of experimental quantities if the adsorption equilibrium and the mechanical mobility are studied in more detail including microscopic information. In the present paper we assume that the relevant adsorption data can be described with sufficient accuracy by the Langrnuir isotherm. This implies that the silica micropores can be either occupied by one molecule or empty and that the bonding energy of the molecules is independent of @. In that case a simple expression is obtained for the chemical potential of species i
(3)
where ~t,.0 is the concentration-independent part of ~t, and O, = q,/qSat is the fraction of occupied voids. In fact, this is the chemical potential of a so-called "building-unit" [52], which reflects the fact that species i the vacancies are conjugated. Combination of (3) and (2) results in
(4)
The direct coefficient Lii is the product of the mobility bi of the species and the concentration
qsat'0i.
When the mobility is expressed in terms of a component-diffusion coefficient, 1), = b~RT, the expression for the flux can be written as
ji=_q~at
D, VOi
1-0,
(5)
The component-diffusion coefficient is not necessarily constant. In fact, it seems plausible that it will decrease with rising occupancy of the voids, since a jump of a species to an adjacent occupied site will not take place. The mechanical mobility will be proportional to the probability that an adjacent void is empty, b, = b~(1- 0, ). In that case the flux obeys a, =
-13,vo,
(6)
359
where Di is the constant single component chemical diffusion coefficient and is related to the uncon-
ditional mechanical mobility, b~ , through /9, = b~ through/9i
=
(and to the component-diffusion coefficient,
Di )
Microscopic description of diffusion mobility In the derivation of equation (6) we already included some information about the system on a microscopic level. To obtain more information about the factors that influence diffusion mobility the flux expression must be derived with a less general but entirely microscopic molecular jump method [53]. When transport takes place by species jumping from void to void, the net flux of a species is determined by the overall number of successful jumps in the direction considered and the average jump distance a. The number of successful jumps is determined by: 9
a geometric factor g that is representative for the spatial arrangements of voids and their (percolative) connectivity,
9
the concentration of the species 0i,
9
the frequency at which a species attempts to jump v,(T)
9
and a Boltzmann factor that determines the fraction of species with sufficient energy Em., to cross the potential bridge between two adjacent voids.
In the case of single site occupancy a jump will only be successful if the adjacent site is unoccupied. The flux expression obtained from a microscopic approach is identical to (6), but the chemical diffusion coefficient contains information about the system on a microscopic level
Em ~)= ga2vA(T)e Rr
(7)
It is clear that also in this case it is found the chemical diffusion coefficient is not dependent on concentration, for the simple lattice model.
Sorption and permeance
In the derivation of the diffusion flux equation it is assumed that the sorption behaviour can be described with the well-known Langrnuir-isotherm
0,-
K,p 1 + Kip
For the T- and p-range used in this study the Langmuir isotherm reduces to the Henry isotherm
(8)
360
q, = K,p
(9)
If the rate of transport through the silica layer is limited by diffusion through the silica layer, thermodynamic equilibrium can be assumed at the interfaces, and the permeance is sat ~-~ r.,-
F, =
J----J-'-
Ap,
q u,t~,
(10)
L(l + K,p,,h)(l + K,p,,,)
where P,.h and p ,.1 are the high (h) and low (1) partial pressures of i at both sides respectively of the silica layer and L is the thickness. (In the derivation of (10) from (6) and (8) we made use of the fact that D, is independent of 0, so that for the case of stationary diffusion (6) can simply be integrated to J, =-/9, 01'' -Oh" ). In the Henry regime the denominator of (10) reduces to L and the permeance 8 becomes independent of pressure. The validity of Henry's law implies that the concentration of molecules absorbed in the microporous solid is small compared to the number of available voids.
Temperature dependence of permeance Diffusion in the silica layer is an activated process, since species have to pass a potential bridge between two adjacent voids. Furthermore, the attempt frequency v, depends on the vibrations of both the species in the voids, as well as their surrounding molecules in the solid and is thus also a function of temperature. Era.,
D, (T) = ~)~o(T)e RT
(I I)
For relevant temperatures it is safe to assume that the temperature dependence of the pre-exponential factor is negligible compared to the influence of the exponential factor. The temperature dependence of the sorption process is expressed in the Langmuir coefficient
Q~._.._~,
K, (T) = Kf ~( T)e Rr
(12)
where Qst., is the isosteric heat of sorption. The pre-exponential factor contains information such as the partition functions for the vibrational or rotational modes of a species and is thus slightly temperature dependent. It is again safe to assume that its influence on the temperature dependent behaviour is small compared to that of the exponential factor. In experiments an "effective" temperature dependence of the mass transport process will be observed. In the Henry regime this temperature dependence will be described by
361
sat ,-~
Qst,,-Em,,
F, = q--c-Df~
Rr
Ea,,
= jo e Rr
(13)
L
in which we define a new (nearly) temperature-independent proportionality constant J0 =/~r,,Kr,, and an effective activation energy for permeance:
Ea -- Em - P s t
(14)
Ea can have any sign; here a sign convention is used such that J increases with temperature if Ea is positive. Since Em and Qst can be expected to be about the same the value of Ea may well be close to zero so that slightly temperature-dependant factors in J0 must be taken into account to obtain a proper quantitative expression for the temperature dependence of J.
S u p p o r t resistance
The overall permeance of the membrane will be determined by the resistances for mass transport of all subsequent layers it consists of. These resistances are considered to be connected in series. 1
Foverall
1 - ~ 1+ ~ +1 ~ Fo~-layer F~-layer Fsilica
(15)
Due to the different structures of the layers, each layer will influence the motion of a species in a distinct manner, resulting in disparate mass transport behaviour in each layer. The mass transport all three layers is generally a function of pressure. In both the o~- and ~/-layer, a gas phase species has three degrees of translational freedom and transport will take place by a combination of viscous flow, Knudsen diffusion and, in the case of a multicomponent system, bulk diffusion [54]. Furthermore, for a strongly adsorbable gas diffusion over the pore surface may take place. A quantitative mathematical description of such mass transport involves solving a set of coupled non-linear partial differential equations, for which one needs to resort to numerical techniques [55]. Here a only a single gas is present, the contribution of viscous flow is only small and the temperature is sufficiently high for surface diffusion to be negligible. As a result the permeance F of the ix- and y-layer will only depend on the molecular weight of the permeating gas and the temperature, i.e. F-x/T-.xf-M can be expected constant. For reasons of simplicity the support will be treated as one effective layer. Since for most gasses the largest resistance for mass transport is situated in the silica layer this approach is justifiable.
362
Transport measurements Membrane gas permeance was measured in the pressure-controlled dead-end mode [56] in the temperature range of 50 to 300~
Prior to the permeance measurements the membranes were dried for
several hours at 200~ to remove adsorbed water from the micropores. The disk-shaped membranes were placed in stainless-steel permeance cells with the microporous top-layer at the feed side. The pressure difference over the membrane was adjusted by an electronic pressure controller.' The gas flow through the membrane was measured by mass flow meters with maximum flow ranges of 25 or 100 (cm3/min SPT). The pressure over the membrane was measured with an electronic pressure transducer.* A schematic representation of the permeance set-up is given in Figure 14.
...... j
Gas feed
i i = i '.
9
i
PC FI PI TC
~
= Pressure controller = Flow Indicator = Differential Pressure indicator = Temperature controller furnace ;
L.. . . . . . .
.J
Furnace and test cell
my
To atmosphere
"
;
,
=
Figure 14
~
.
"
Schematic diagram of the experimentalset-up for permeancemeasurements.
Supports The dead-end single gas permeance of the small gasses H2, CO2, 02, N2 and CI-I4 through the die pressed support was measured as a function of pressure and temperature. Data obtained from these measurements show that the permeance of the support is pressure-independent. The product F-x/-f.x/-M, (mol.K-kg)~
the so-called modified permeance, is for all gasses approximately 9.8-10 -5 and shows only little variation. From this it may be concluded that in the sup-
port diffusion takes predominately place by Knudsen diffusion. Only for CO2 the modified permeance is observed that is higher than that for other gasses while it increases slightly with pressure. This can be explained by the occurrence of diffusion over the pore surface of the support.
*Type5866, Brooks Instruments,USA. tValidine Inc., Northridge(CA), USA.
363
Si(400) Single gas permeance results for Si(400), corrected for support resistance, are independent of pressure. This was expected since the sorption occurs in the Henry regime. The highest permeance is observed for the smallest gas used in this study, i.e. F m = 4.4-10 -6 mol/m2-s-l.pa-1 at 200~ F,~
Si(400)
Si(600)
H2/CO 2
13
22
H2/O 2
1.6.102
43
H2/N 2
41
H2/CH 4
>>500
In Table 3 the permeance data of the other gasses compared to H2, at T=200~
are presented. Al-
though the kinetic diameters of 02 and N2 are quite similar, 3.46A and 3.65A respectively, our microporous membranes have an 02 permeance that is approximately 4 times higher than that of N2. The permselectivity F~ >>500 for H2/CH4 can not be determined more accurately, since the
Table 3:
Permselectivitiesat T=200 ~ and p=l bar
permeance of CH4 is very low and consequently difficult to measure. The fact that CH4, with a dk=3.8A has some detectable permeance and that SF6, with a kinetic diameter of 5.5A, does not permeate at all leads us to an estimate of the membrane pore size between 3.8
3.8 CH4
\
289H 2 \
\ Si(400)
3 46 02
82 \ "5 E
5000
-5000 2.5
\
\
\
\
\
//
/
O
3.64 N2
d //
\
/
\ ~ 3 3 CO2 3.0
35
40
ak [A]
Figure 15:
Apparent energyof activation(Ea)versus kinetic diameter(dk).
For all gasses, except for C02, the permeance increases with temperature, i.e. the apparent energy of activation (E,) is positive and hence the activation energy of mobility heat of sorption
(Era) is larger than the isosteric
(Qst). The CO2 permeance appears to decrease with T at higher temperatures. This
demonstrates that E, is not necessarily always positive. The apparent energy of activation for the different gasses is presented in Figure 15. The permselectivities for H2/CO2, H2]N2 and HJO2 increase with increasing temperature due to the fact that the apparent energy of activation Ea is largest for H2.
364
Due to the inaccuracies in the measurement of the low CH4 flow, no systematic temperature dependence of the permselectivity for H2/CH4 could be determined. Using the experimental data for E,, together with typical Q~, data, shown in Table 4~ values for Em are obtained by making use of equation (14). The results are given in Figure 16, from which it is clear that E,, increases with the kinetic diameter dk of the gas. As dk increases the molecule has more difficulty to jump from void to void. Due to the low accuracy of the CH4 permeance data, the absolute value of Em for CH4 will also be imprecise. It is clear however, that CH4 has the greatest difficulty moving through the pores and its mobility energy is much higher than that of the other gasses. Si(600) The Si(600) membranes show a permeance behaviour that is clearly different from that of Si(400). The permeance at 200~
Source
CH4
CO2
H2
De Lange [571
I0
22
6
Rees 1581
20.0
24.6
Golden [59]
18.6
24.0
Choudary 136]
28
20
Dunne 1601
20.9
27.2
Used in this study
20
24
N2
02
of H2 is lower,
2.4.10 -7 mol/mLs-~-Pa"I and at the same temperature the CO2 permeance is even much lower, i.e.
17.3 6.0
15.0
1.1.10 "8 mol/m2.sl-Pa -l, resulting in F~=22 for H2/CO2. The 02 permeance has reduced to 6.1.10 -9 mol/m2.s-l.Pa -~, at 200~
and the per-
meances of both N2 and CH4 were not sufficiently high to be determined with a reasonable accuracy. The observation that the supported Si(600) mate-
Table 4:
6
17.6
16.3
17
16
Microporous silica isosteric heats of adsorption, Qst (kJ/mol) at low coverage.
rial is not 'open' for N2 is consistent with results of the sorption behaviour of the unsupported Si(600) material described in the section "Pore size characterisation of unsupported silica" of this chapter. Using a very sensitive qualitative soap-solution test, some N2 flow was detected. Even with this very sensitive test, no permeance of CH4 was observed. Determination of the pore size by size exclusion by means of the permeance experiments thus results in a pore size 3.6<0<3.8 A which is significantly smaller than that of the Si(400) membranes.
365 35000
38 0
30000
"--'
%
25000
3.46 02 / 3.3 C02.I ;;~ ~ --0
E
Si(400)t 101 /
LLIE 20000
2.89 H2
Jl
15000
I0000
--
2
5
/
364 N2
J
o-/
/
CH 4
/
/
/
//Si(600)
3.0'
3'5-
40
d,, [A]
Figure 16:
Calculated energyof activationfor mobility(E,,) versuskinetic diameter(dk).
The decrease of the permeance is presumably a result of densification of the structure and a smaller pore size. The large increase of F~ for HJCO2 from 13 to about 22 can also be, partially, attributed to a decrease in the amount of terminal hydroxyl groups at the internal surface of the silica, since at higher calcination temperatures more hydroxyl groups are irreversibly removed [22]. It is recognised that the sorption behaviour of the silica material is strongly influenced by the concentration of hydroxyl groups due to gas molecule interactions with hydroxyls at the silica surface [49]. The lower (surface) occupation leads to a lower CO2 permeance. Due to the lower concentration of hydroxyls, the Si(600) material is also more hydrophobic compared to the Si(400) material. The apparent energy of activation E, for H2 and CO2 is lower than for the Si(400) membranes, while that of 02 is approximately the same. Since E,=E,,-Q~., the lower E,, may be explained by either a smaller E,, or a higher Q.~.,or a combination of both. For the time being it is not possible to confirm which of these hypotheses is valid. When taking into account the fact that the Si(600) is much denser than the Si(400) structure a larger Em and a smaller Q~t are both possible for Si(600). In Figure 16 values for E,, are presented, that have been obtained under the assumption that the Q.,., is the same for both the Si(400) and Si(600) materials. With increasing kinetic diameter of the gas molecule again an increase in Em is observed. The value of E,, is lower for Si(600) than for Si(400), suggesting that molecules are more mobile in this material. This is not sensible, taking into account the denser structure of the material and it is obvious that the lack of experimental data on Q~., is prohibits a proper understanding of the temperature dependence of the permeance behaviour of both silica materials discussed here. MeSi(400) Compared to the non-hydrophobic silica membranes the permeance data for MeSi(400) shows a remarkably different behaviour. The fluxes are quite high while the permselectivity is quite low. This
366
suggests that the membranes are either not microporous or contain many defects. Since the extremely low permeance of SF6 (dk=0.55 nm) and n-C4H10 (dk=0.5 nm) does not correspond to a large concentration of defects, it is expected that the MeSi(400) membranes have a larger average pore size or broader pore size distribution. This is in agreement with the Ar sorption measurements described in the section on characterisation of this chapter, where it was found that the unsupported Si(400) and MeSi(400) have approximately the same average pore size but a different pore size distribution. Comparison with open literature data The permeance and F~ values obtained compare favourable with literature results. De Lange et al. [57] previously reported values of Fro=7.4 - 10-6 (mol/mLs.Pa) and F~=3.9 and 24.7 for H2/CO2 and H2/CH4 respectively. Although the H2 permeance reported by the Lange is higher that that of our membranes, the selectivity is significantly lower. An F~ =235 for H2/CH4 at 150~ was published by Hassan et al. [46] for a silica hollow fiber membrane, but no single gas permeance values were specified. Commercially available CVI silica membranes* onpage1 are reported to have a F~ = 27 for H2/CO2 with a H2 permeance of 1.7x10 7 (mol/m2.s.Pa) at 400~ *.
*Measured in our lab on membranes deliveredby Media and Process TechnologyInc. (MPT), Pittsburgh, PA, USA.
367
le-5
S~(9
le-6
~
2
002
S" "7
13.. le-7 E 0 E ,,....._, LL le-8
q~ Si(600)
eSi(400)
E)
le-9
~3.8 CH 4
~,~so-C4H10
,
,
,
3
4
5
"o.5
SF 6
6
a k [A]
Figure 17:
Permeance of species with differentkinetic diameter, for Si(600), Si(4000 and MeSi(400).
Separation Experimental gas separation factors reported in [ 1] are of the same order of magnitude as permselectivities calculated from single-gas permeance experiments. This indicates that in transport of mixtures the molecules have only limited mutual influence, in agreement with the expected Henry sorption behaviour.
Conclusions
Homogeneous and clean TEOS-based sol-gel synthesis leads to reproducible high quality silica membranes with good separation characteristics. Si(400) membranes have a homogeneous 30 nm thick silica layer, which results in a permeance of Ha, corrected for the resistance of the support, Fm= 4.4.10 .6 mol/m2-s-l.pa1 at 200~
and F~(H2/CH4)>500. It is now possible to prepare intermediate layers at a
temperature as high as 1000~ with on top very thin high quality silica top layers fired at 400-800~ The membrane firing temperatures have an outspoken influence on the membrane properties. Increas-
368
ing the sintering temperature from 400 to 800~
results in a much denser membrane structure with
smaller pores. From the relation between kinetic diameter and permeance results, the Si(600) membranes are expected to have pores with 3.6<0<3.8 A and the Si(400) membranes to have pores with 3.8< O <5.5 A. These results are in agreement with physical adsorption experiments, performed on unsupported material, which reveal a pore size of~5A for Si(400) while the Si(600) samples were N2dense. All permeances are lower in the Si(600) membranes, e.g. H2 is 2.4-10 -7 (mol/m2.s.Pa), while permselectivities with respect to larger gasses are significantly higher. The best choice of the firing temperature depends on the envisaged application. In addition one should take into account that for high temperature applications the firing temperature of the membrane should be higher than the highest temperature during operation'. With the use of cleanroom conditions we were also able to reduce the number of layers for the intermediate as well as the top layer to just one layer each without any large defects. This reduces the preparation time for both layer types by a factor of two, which may save several days of processing time. By incorporation of methyl groups in the silica microstructure the surface and microstructural properties of the microporous silica membranes change significantly. 'MeSi(400) membranes' are 10• more hydrophobic and show much less water sorption than state-of-the-art silica 'Si(400) membranes'. MeSi(400) membranes have larger micropores with a wider pore size distribution than Si(400) membranes which influences their transport properties. Further development of hydrophobic silica membranes should focus on systematic optimisation of sol-gel and calcination procedures, studies of transport properties including water vapour and the introduction of hydrophobicity in the support structure. The separation characteristics of microporous silica membranes can be described very well for practical situations if accurate values of unconditional diffusion mobilities, b0, are available from single-gas permeation experiments. The effective activation energy, Ea, of membrane permeation is the result of counteracting thermal activation of diffusion mobility and sorption. This often results in relatively small values for Ea. This, in turn, makes that weak, non-Arrhenius-type temperature dependencies in the sorption equilibria can no longer be ignored. In addition it is difficult to quantify the diffusion mobility energy of gasses through the microporous structure if accurate Q,,-values are unavailable. Addressing these problems is the subject of future studies. A major problem that remains at this moment is the stability of silica membranes towards hot steam. Steam is used is many processes, in process industry (reforming, gasification, etc.) as well as in the medical and food industry (sterilisation). It would thus be very favourable if meso- and microporous membranes could be developed which are resistant towards hot steam environments. The steam-
This condition must be fulfilled if one has the objectiveof constantmembrane operationduring the complete lifetime of the process. The membrane can also be fired in-situ at the highest temperatureof the process. In any case the membrane properties can be expectedto change slowlywith time.
369
reforming conditions as used in our stability tests are among the harshest conditions one can think of. Hence if the membranes are stable under these conditions, they most probably can be used in any other steam-containing atmospheres as well. A large step forward has been made with solving the problem of the blistering of the y-alumina layer and the reduction of pore-growth and the formation of macroscopic defects in this layer during steam exposure. This result enables us now to test the stability of the silica layer proper against harsh steam-rich environments. The behaviour of the silica layer under steam-reforming conditions will therefore receive considerable attention in the near future. Improvements in high temperature resistance can possibly be achieved by doping with polyvalent metal ions or removal of silica surface hydroxyl groups. Additionally, the hydrophobic silica membranes that were developed recently may very well be more steam resistant than normal silica membranes since they have less affinity towards water molecules. The major part of H2 transport resistance in our state-of-the-art supported silica membranes is currently in the a-alumina support. This makes that more attention will have to be paid to the development of high-quality course porous membrane supports. The centrifugal casting technique equipped with an injection system might be very helpful to develop coarse porous multilayer supports with a very smooth inside surface on which highly selective membranes can be coated. The development of even thinner intermediate and top layers becomes worthwhile only when the transport resistance of the support is not limiting anymore. If membranes can be made with a thickness-1 nm, H2 permeances of > 10-4 (mol/ma.s.Pa) can be realised provided no support limitations or surface transfer rate limitations occur.
Upscaling of the present silica membrane technology into membrane modules is needed to increase the surface to volume ratio for practical applications. The processes of the silica membrane preparation by CVI techniques or by the wet-chemical methods presented here may very well be suitable for production scale manufacture of membranes on hollow fibre supports. The present results suggest that application of silica membranes in for instance natural gas purification, molecular air filtration, selective CO2 removal, industrial H2 purification and conversion enhancement in membrane reactors are feasible indeed.
Acknowledgement The authors are indebted to H. Kruidhof for technical support and supervision, C. Huiskes for technical assistance with the preparation of the tubular supports, prof. dr W.F. Maier and coworkers of the Max Planck Institut, Mtilheim an der Ruhr, Germany for infra-red and hydrophobicity measurements and dr R. Bredesen, SINTEF, Oslo for steam reforming treatments of the membranes.
370
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Recent Advancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) 2000 ElsevierScienceB.V. All rightsreserved.
ZEOLITE
373
MEMBRANES
J.D.F. Ramsay, S. Kallus Laboratoire des Matdriaux et des Procdd6s Membranaires, UMR CNRS 5635, Universitd Montpellier II, 2 place Eugene Bataillon, 34095 Montpellier, France
ABSTRACT Different routes for the preparation of zeolite membranes are described. These include (a) the incorporation of zeolite crystals in a matrix (polymer, metal), (b) in-situ hydrothermal synthesis in the presence of a substrate (e.g. porous ceramic) and (c) the application of twostage secondary growth methods either using colloidal zeolites, or by laser ablation techniques. The microstructures of these different types of membranes are discussed in the context of applications in gas separations. The different gas separations which have been performed with zeolite membranes are reviewed. Separations have been most efficient when one or more of the components in the gas mixture has been condensible. The mechanisms of these separations frequently involve selective sorption and pore blocking processes. Separations involving the size exclusion of non-condensable gases have been much more limited. The absence of defects in the membrane layer is a more critical requirement for efficient separation by this mechanism.
1. INTRODUCTION Zeolites are in general silicate or alumino-silicate crystalline materials which have a highly regular and open microporous (< 2 nm) structure (1-3). This structure is formed by a threedimensional network of SiO4 and A104 tetrahedra. The tetrahedra are linked to each other by shared oxygen atoms, to give cavities or cages, which are connected by ring or pore openings, with defined size and shape (Figure 1). Almost 100 different structural types of zeolite are known (4), each with its own distinct pore size, shape and interconnectivity (See Table 1). The size of these pore openings ranges from 0.3 nm to -1 nm (as illustrated in Figure 2). Furthermore the framework constitution (viz Si/A1 stoichometry) can give rise to hydrophilic, hydrophobic, acid, or basic properties within this pore structure.
374
Structural "Building Blocks" e.g. Sodalite cage (13 cage)
Crystalline zeolites
Structural type:
SOD (Sodalite)
LTA (Zeolite A)
FAU (Faujasite)
EMT
Figure 1. Oligomeric silicate and alumino-silicate species can form structural units or ~ building blocks ~, which subsequently organise to give different zeolite structures. For example, the sodalite cage is incorporated in the framework structures of Sodalite, Zeolite A, Faujasite and EMT zeolites as illustrated.
375
Table 1. Structural characteristics and properties of different zeolite types. Zeolite type Structural Formula [Si]/[A1] Window Dimension / A Silicalite 1 oo 5.2*5.7 Nan[Si96-nAlnO192]" 16 H20 ZSM-5 10 - 1000 4.1 Zeolite A Na12[Si12A112048]27H20 1 (1.2 3.7) Zeolite X 1 1.5 7.4 Na96-x[Si96+xA196.xO384]240 H20 9 > 2 . 5 Zeolite Y 7.4 Clathrasils e.g. Sodalite ; Dodecasil 1 - oo 2.2 2.8
Pore size / A
Size of Molecules (Kinetic diameter/A )
15 VPI-5
_..__.~(C4 F9).sa'N AIPO4-8
10-~
_.1
~/(C4Hg)3N
/dimethyl-butane
///benzene
Zeolite X ZSM-5 Zeolite A Sodalite
I/
54 -~
~ %'SobUatttteane
P P ~ l----methane
Figure 2. Comparison between the effective pore sizes of diffferent zeolites and crystalline oxides and the kinetic diameters of gas molecules. Due to this combination of properties, zeolites can interact very selectively with adsorbed molecules depending on their size, shape and chemical characteristics. These exceptional properties of zeolites have lead to numerous technical applications (e.g. size/shape - selective heterogeneous catalysis, gas separation, ion-exchange, dessication, and adsorption) following the industrial production of zeolite powders in the early 1960's. More recently however there has been a surge of interest in the preparation of thin films or membranes of zeolites (5-6). This interest has stemmed from very promising potential applications as highly selective separation membranes (7-9), sensors, conductors, and optoelectronic devices (10-15), which require thin layers of material to be effective. A variety of methods for the fabrication of zeolite thin films have recently been reported. These include dip coating, spin coating, sputtering and laser ablation (16). However the two most common methods used to produce membranes for gas separation have been (a) the
376 formation of a composite, by embedding zeolite crystals in a matrix, such as a polymer, and (b) in situ crystallization in the presence of a substrate, such as a porous ceramic, to give a supported zeolite membrane. In this short review some of these different methods will be described and the microstructural characteristics of the membranes so formed will be discussed. This will be followed by an overview of the extensive literature on gas permeation and separation using zeolite membranes. Finally an attempt will be made to rationalize these results in a qualitative way taking account of the microstructural properties of the membranes and the gas/zeolite adsorption interaction mechanisms.
2. ZEOLITE MEMBRANE SYNTHESIS AND CHARACTERISATION
2.1 General Aspects In general zeolites are synthesized hydrothermally using aluminosilicate or silicate precursors in aqueous solution (see Figure 3). The precursors may be in the form of finely divided powders, gels or colloidal dispersions. The mechanisms of the hydrothermal reactions which occur have been investigated extensively (2,3,17) although these are still not fully understood. However, these generally involve an initial induction period, during which condensation between oligomeric species occurs, followed by nucleation and growth to give crystalline zeolites (Figure 4). It has been proposed that the nucleation process involving oligomeric or colloidal species may take place either homogeneously in solution, or heterogeneously within an amorphous gel phase. Heterogeneous nucleation may also occur at surfaces in the reaction medium (see Figure 4).
induction period PRECURSOR SOLUTION
hydrothermal transformation AMORPHOUS GEL
CRYSTALLINE ZEOLITE (nucleation/ crystal growth)
Figure 3. Schematic steps in the synthesis of a crystalline zeolite by hydrothermal treatment of an aqueous precursor solution.
377
PRECURSOR SOLUTION
HOMOGENEOUS NUCLEATION
SILICATE/ALUMINATE OLIG~ sM~LRIuCTIoPNCIES ~ ~
~
CRYSTALLINE ,
~
ZEOLITE
aggregation
I /_
....... I
Figure 4. Crystalline zeolites may be formed by two different synthesis paths which involve either homogeneous or heterogeneous nucleation as illustrated. The type of zeolite formed can be influenced by many parameters, as has been described in detail (17). Of particular importance are the composition of the precursor solution Si/A1 stoichiometry ; concentration, pH, ionic strength, structure directing agents, the temperature and the time of reaction. The addition of structure directing reagents, such as organic cations, can lead to specific zeolite structures exclusively, e.g. the tetrapropyl ammonium ion, TPA § leads to MFI or silicalite structures. These and other less defined parameters (nature of precursor, stirring, reaction, container etc) may also influence the texture (crystal shape, sizeintergrowth etc.) of the zeolite produced (3,18). From a better understanding of these subtle processes, it has been possible to grow much larger (> 10~tm) zeolite crystals (e.g. MFI) with well defined morphology (19). More recently attention has also been directed to the mechanisms of the initial stages of zeolite formation, which has lead to the synthesis of colloidal zeolites (< 100nm) such as silicalite 1, (20), zeolites A and Y (21), hydroxy sodalite (22) and ZSM-2 (23) by Schoeman and co-workers. Understanding of the species present and the mechanisms involved in the initial stages of zeolite formation in solution has been improved by the recent application of new in situ techniques. Such techniques as small angle scattering of neutrons (24) and X-rays (25), NMR (26) can provide microstructural information under hydrothermal conditions. The nature and control of the zeolite texture, as mentioned above, are very important in the preparation of zeolite membranes and films, which must be free of defects. This will become evident during the following discussion of the different methods which have been employed. Such considerations have been less important previously in the preparation of zeolite powders which have been used in other applications, such as heterogeneous catalysis and adsorption for example.
2.2 Zeolite Matrices
Some of the earliest attempts to produce zeolite membranes have involved the incorporation of zeolite crystals and powders in a matrix. Polymers have been used extensively to form a continuous matrix. Thus Barrer and James (27) reported the first systematic investigations on polymer martrix systems produced by compression molding of finely divided polymer powders and zeolite crystals. Gas permeation measurements were made, although problems
378 occurred due to poor adhesion at the polymer/zeolite interface. These problems of adhesion were largely overcome by Paul and Kemp (28) by dispersing zeolite into a fluid silicone prepolymer. However elastomeric polymers, such as silicone rubber, have a high gas permeability but poor selectivity on their own. Their application has mainly been in the area of pervaporation, to separate alcohols from aqueous solutions for example (29). The use of barrier type, glassy polymer matrices, such as polysulphone has been more successful in gas separation. Thus Yilmaz et al (30) reported the permeation performance of polyethersulphone containing both 13X and 4A zeolites for a variety of gases (N2, O2, Ar, CO2 and HE). Zeolite composite films using a similar concept, have also been prepared in a glassy silica matrix (31). The nature of the zeolite/polymer interface plays an important part in the performance of all of these types of polymer hybrid membranes, and is an aspect which is not clearly understood. Thus poor bonding to the embedded crystal can result in defects leading to a reduction in separation performance. Furthermore because of the low thermal stability of polymers, this type of membrane is not suitable for many potential applications of gas separation. To overcome these drawbacks, wholly inorganic composite membranes have been proposed. These have included zeolite/sepiolite membranes (32) and also zeolite/metal membranes. Caro et al (33, 34) reported an interesting development of the latter in which silicalite crystals were embedded in silver and nickel matrices. By using large crystals (30x30x80~tm) it was possible to preferentially orient these in the metal matrix (Figure 5). These membranes were reported to have high temperature stability (~ 650 K) and were used in the separation of binary mixtures of n-heptane and toluene with promising separation factors (- 4 + 1.5). Their practical application in large-scale gas separation processes is probably limited however.
Figure 5. (a) Membrane containing oriented zeolite crystals obtained by embedding large zeolite crystals in a metal grid followed by electrochemical deposition of nickel or silver. The preferential orientation of the channel structure of the silicalite crystals is illustrated in (b).
379
2.3 In situ hydrothermal synthesis The most widely reported and successful route to zeolite membranes has been in situ hydrothermal synthesis on a substrate. Although a variety of substrates have been used to support the zeolite membranes, those most freauently employed have been porous alumina and stainless steel. In this method the substrate is generally immersed in the zeolite precursor mixture (which may be a clear solution or sometimes an aqueous gel) contained in an autoclave, and then heated for a predetermined time (see Figure 6). The type of zeolite, and the properties (texture, thickness etc.) of the membrane are determined by many factors. These include the chemical composition and nature of the aqueous precursor, the time and temperature of the hydrothermal treatment, and the characteristics of the substrate. The type of zeolite most frequently prepared has been MFI (silicalite, Z5M-5) (35-44). However this route has also been used to synthesize membranes of zeolite A (45-48), zeolite Y (49), mordenite (50) and zeolite P (51). In situ hydrothermal synthesis has also been employed to synthesize membranes containing other molecular sieve materials, related to zeolites, such as A1PO4-5 (52), and SAPO-34 (53).
Figure 6. Schematic arrangement for the in-situ hydrothermal synthesis of a zeolite membrane. The support for the zeolite film is immersed in the precursor solution within the autoclave during the hydrothermal synthesis. By optimising the synthesis conditions, preferential growth of zeolite on the surface of the support can occur.
380
Although the in situ growth route has yielded membranes of several different zeolites which have shown potential in gas separation, it has been claimed to have limitations (9). Thus as Tsapatsis and Gavalas indicate (16), there is little scope for the control of the microstructure of the final films, since synthetic conditions have to be optimized for nucleation and growth in a single - or repeated- batch preparation. The quality of membranes prepared by this route can also be impaired by intercrystal defects, which limits applications in gas separation. To overcome this problem many workers have used repeated batch synthesis. However as noted by Burggraaf in his review (5), the only zeolite membranes of consistent and suitable quality for gas separation have generally been of the MFI-type. It is considered that many reports in the older literature concern defective zeolite membrane systems which although having applications for pervaporation and interesting properties as membrane reactors, are limited in gas separation. In an attempt to minimize defects and decrease the fragility of zeolite membranes, synthetic routes in which the zeolite is formed within the pores of the support, rather than as a thin layer on top of the support, have been employed (35, 36, 54). MFI- type membranes formed inside the pores of m-alumina ceramic supports, in tubular and disc form, have been reported by several workers to give high performance in many gas separations (9, 54). The preferential nucleation and growth of MFI, inside rather than on porous -alumina has been shown to be dependent on several factors, which include the properties of the precursor solution, the reaction conditions (temperature, time) and the pore structure and surface properties of the support (56). This is illustrated in Figure 7 , by the mercury porosimetry results of silicalite membranes prepared under two different conditions using an alumina support containing pores of 0.15 l~m diameter (Figure 7.a). In both preparations the support was immersed in a clear alkaline solution containing silicate oligomers and the tetrapropyl amine (TPA+) template ion.
E
0.3
a)
b)
c)
E :3
>o
0.2
c-
._o U) L
--= a) ._> E o
0.1
0.0
10 3 10 a 101 10 0 10-1 10-z.
10a 101
10o 10.1 10-a
F
10a 101
1
100 10-1 10-a
Pore Diameter [pm] Figure 7. Mercury intrusion curves of (a) an a-alumina support and (b) and (c) zeolite membranes obtained aider different synthesis conditions.
381 When the reaction was carried out at relatively low temperature (130 ~ over a long time (6 days), growth of zeolite was induced within the pores of the substrate. This was evident from the reduction in the pore volume of the support (Figure 7b) and also from SEM analysis. However at higher temperature (190 ~ nucleation and crystal growth was much more rapid, resulting in the formation of an outer layer of larger crystals on the substrate. In this case the pore volume of the support was unchanged, but additional pore volume was created due to the inter-crystalline zeolite voids in the outer layer. A cross-section of such a membrane, formed as an outer layer of large crystals which are inter-growth and bonded to the surface of the porous alumina support is illustrated in Figure 8. Although mechanisms leading to these two different membrane structures are still not fully understood, it appears that at lower temperature, a more prolonged contact of the support with the highly alkaline oligomeric silicate solution favours heterogeneous nucleation at the alumina interface, followed by a slow crystal growth process within the pores. Such subtle effects, involving the nucleation process and the growth at the interface of the ceramic support, may indeed partly explain the greater progress which has been achieved in the synthesis of MFI type membranes compared with other types of zeolite membrane. Thus in the former, the synthesis has generally been carried out with a clear alkaline silicate solution, containing TPA § whereas in the latter a precursor aluminosilicate gel has been employed. The distribution of the zeolite on the support, apart from influencing the mechanical strength and defect properties of the membrane, may also cause differences in gas separation behaviour, as noted by several workers (9, 54). Such effects have been ascribed to differences in the microstructure and inter-connectivity of the crystalline zeolite layers. Improvements in the connectivity between individual crystals has been achieved by different workers by employing several synthesis cycles. Thus Vroon et al (42), claimed that two consecutive hydrothermal treatments were required for the optimum synthesis of MFI zeolite membranes on alumina supports. Alter a single treatment it was found that the lack of crystal intergrowth resulted in a serious defect problem, whereas with three or more treatments the layers became too thick and had a tendency to crack during the thermal treatment required to eliminate the TPA template. The effect of mechanical stress leading to cracking, during the elimination of the template has also been observed by den Exter et al (57).
Figure 8. SEM of the cross-section of silicalite-1 membrane on porous ix-alumina support having a mean pore diameter of 2 ~tm.
382 These workers found that films of randomly oriented crystals were less sensitive to cracking compared to those in which the crystals were preferentially oriented. In the latter configuration the anisotropic stress developed was more likely to yield continuous defects in the crystalline layer. Recently several developments of the in situ hydrothermal route have been reported. These are mainly based on two approaches: firstly to improve the microstructure and control the distribution of the zeolite within the porous support, and secondly to remove defects by processes applied after synthesis. Included in the first approach are methods in which (a) the synthesis gel is infiltrated into the support pores under pressure and (b) where the reactants are separated on either side of the porous support (58,59). In the latter approach, reaction occurs at the interface and subsequent growth of the zeolite crystal barrier may be controlled. This method which is illustrated in Figure 9, has been used to prepare zeolite A membranes within the pores of a tubular a-alumina support.
Figure 9. Schematic illustration of the formation of a zeolite membrane by the counter diffusion of two reacting precursor solutions. The development of a thin concentric zeolite barrier within the pores has been demonstrated by SEM and EDAX measurements.
383 EDAX measurements provide high resolution concentration profiles of different elements (A1, Si, Na) across a section of the tube showing the location of the zeolite layer after reaction. A third development of the hydrothermal route has involved the seeding of the support with crystals of the zeolite to be synthesized in an attempt to control nucleation and crystal growth (47, 60, 61). Several processes to remove defects which remain after hydrothermal synthesis of zeolite membranes have been reported. These include coking treatments (58-62) of MFI - type membranes, which are claimed to block only the non-zeolitic pores, and which result in improved selectivity on n-butane/i-butane isomer separations. Chemical vapour deposition (CVD) treatments have also been reported to be effective as a pore blocking method (63). However, although these post synthetic deposition treatments may lead to improvements in permselectivity, they generally result in reductions in permeability, as has been discussed by Tsapatsis et al (16). Another recent development of the in situ hydrothermal route has been the use of microwave heating (64). This has been applied to synthesize several zeolite types and is claimed to have potential advantages over conventional hydrothermal synthesis, due to the high heating rate. This results in short crystallisation times which in turn can yield crystals with uniform and controlled crystal size and structure. Thus in the synthesis of A1PO4-5 (AFI - structural type) films on anodised alumina, microwave heating resulted in enhanced nucleation within the pores of the substrate. It has also been claimed that convective flow in the substrate pores due to microwave heating can lead to a preferential alignment of the crystals formed (64). Other workers (65) have described the application of microwave heating to form zeolite-A membranes on a-alumina substrates, with a high film density and controlled thickness. However the preparation of highly selective gas separation membranes using the microwave heating method has not yet been reported. Nevertheless this method is considered to have promise in future commercial processes used to produce zeolite membranes (16) due to the rapid and controlled processing conditions which are possible.
2.4 Secondary Growth Processes 2.4.1 Colloidal Zeolites In the previous section we discussed the formation of zeolite membranes by in situ growth of polycrystalline layers on various supports. Membranes of this type have been developed since the early 90's and have shown promising performance in many gas separation applications as will be outlined later. However they do have limitations because of the lack of control of the film microstructure. This microstructure is generally composed of several layers of randomly oriented crystals, within which inter-crystalline defects can be present. Moreover such films generally have a thickness of several tens of microns, which can be a considerable limitation due to the reduction in permeability which results. Another important concept for synthesis, which allows scope for controlling the zeolite membrane microstructure, has been developed during the past five years. This development has arisen from a better understanding of the mechanisms of zeolite formation, which has lead to the synthesis of colloidal zeolite particles. By using such colloidal zeolites, together with more sophisticated techniques for thin film formation on well defined substrates, it has been possible to achieve greater control of the membrane microstructure.
384 Syntheses of aqueous dispersions of colloidal particles of several zeolites have been described recently (20-23, 66). These processes generally start from a clear solution containing the oligomeric precursors, in which homogeneous nucleation occurs under mild hydrothermal treatment to give particles with a narrow size distribution. This size can be controlled, and is generally in the range 50 to < 200 nm. Such zeolite 'sols' are stable (i.e. do not aggregate and precipitate). Tsapatsis and co-workers were the first to use such colloidal zeolites to prepare molecularsieve films, by a process called the secondary growth technique (16). In this process the zeolite sol particles were deposited as a layer on a substrate (eg. a-alumina) and then grown hydrothermally to eliminate intercrystalline porosity. Using variations of this approach these authors have described the preparation of films of MFI (67), LTA (68), LTL (69) and UTD-I (71) zeolites. Such films have been reported to be composed of a thin (--200 nm) layer of highly intergrown, randomly oriented crystals (67). The selective permeability of mixtures of gases (e.g. n-butane / i-butane) have been reported for such membranes (72). It is claimed that the microstructure of the films is better controlled by decoupling the nucleation and growth processes. This approach has also been used to prepare preferentially oriented films by exploiting either the anistropic growth of the seed particles or their initial orientation on the substrate (73 ). In the development of zeolite thin films using colloidal precursors, attention has also been given to the mechanisms of attachment of the colloidal particles to the substrate. The attachment process and the interaction between the particles, can have an important rrle in controlling the microstructure of the film. This has been demonstrated previously in sol-gel processing, to fabricate thin films of oxides and glasses (74). Thus in the work of Tsapatsis et al thin films supported on glass and silicon wafers were prepared by dip-coating with a mixed colloidal dispersion of silicalite and boehmite (67). Progress has also been made using self-assembly processes to fabricate ultra-thin zeolite films. This concept was first described by Yan and Bein (12) to fabricate zeolite-Y on gold surfaces, using thiol-silane monolayers, for application as a chemical sensor. Self assembly techniques using electrostatic interaction between colloidal particles and adsorbed polyelectrolytes in the fabrication of ceramic thin films have subsequently been investigated widely. Cho et al (75) have recently described a development of this method to fabricate thin (-~100 nm) and dense zeolite films on different substrates (silicon, Au, Ag, SiC, SiN etc). In the process described, hexanoic acid is adsorbed on the substrate and the surface of the zeolite particles. Self assembly results from the hydrophobic interaction between the alkyl chains of the amphiphilic molecules to give an organised thin film of zeolite particles on the substrate. In the previous examples, colloidal zeolite particles have been used to form consolidated thin films on well defined substrates. In another novel development, zeolite colloids have been immobilised within the pores of anodic alumina membrane supports. Such membrane supports are available commercially (Anopore| and contain highly uniform cylindrical pores which are aligned normal to the membrane surface. In the development described (76) these pores had a diameter of ~ 200 nm and were filled with zeolite-A colloidal particles with a size of--100 nm. Because the application of colloidal zeolites has been very recent, the evaluation of the membranes for gas separation has been limited apart from the work of Tsapatsis et al. However, further progress is expected in future as this route allows a better control of the membrane microstructure and scope for the use of a wide range of different zeolite types.
385 2.4.2 Laser Ablation Another recent development in which a secondary growth process is used to form zeolite membranes has been described by Balkus et al. (77-79). This route uses a technique of pulsedlaser ablation. In this method a laser beam is employed to evaporate zeolite from a target; vapour species formed are then deposited on a substrate (polished silicon, stainless-steel) held at a controlled temperature. The zeolite thin film so produced is then treated hydrothermally in a secondary process to give an adherent continuous, and sometimes oriented, film with a thickness which can be controlled in a range of > 100 nm to < 1 ~m. This method has also been used to prepare various aluminophosphate molecular sieves (AIPO4 and MeAPO materials - where Me = Co, Fe, Mn, Mg and V) on different substrates. More recently the method has been used to produce silicate-based zeolites of the UTD-I type (80). This zeolite has large pores (10 x 7.5 A), a one dimensional channel system, and a good thermal stability. The membrane was formed with the crystals of UTD-I oriented perpendicular to the support (stainless-steel). Such a membrane was evaluated for the separation of a n-heptane/toluene mixture at room temperature and selective permeation was reported (80).
3. GAS TRANSPORT AND SEPARATION BY ZEOLITE MEMBRANES The processes of gas transport and separation by zeolite membranes have been reviewed recently by Burggraaf (5) and Coronas et al (9). They have concluded that the transport mechanisms involved, particularly for gas mixtures, are complex and depend on many factors. Some of these can be summerized below: (i)
The physical and chemical properties of the gas
(ii)
The temperature and pressure regime used
(iii)
The characteristics of the zeolite (type; crystal size; shape; orientation) in the membrane
(iv)
The texture and microstructure of the zeolite layer (defects; crystal-intergrowth; thickness)
(v)
The properties of the porous support
Some of these factors have been treated in detail in several excellent texts (81-83) concerning gas transport in porous media, and consequently only an outline of their importance will be given here. Firstly we consider the different diffusion regimes which may appply in porous membranes. These depend on the size of the membrane pores and the nature of the interaction of the gas molecules within the pores. These are summarized in Table 2.
386 Table 2. Transport mechanisms of gases in different porous media. Transport mechanism Pore size and classification (IUPAC) .... Viscous Flow >20nm (meso, macro pores)
Knudsen Diffusion Surface Diffusion Capillary Condensation Micropore diffusion (e.g. molecular sieving)
.~ 2 - .~ 10 n m
(mesopores)
Selectivity non-selective
a. = (M1/M2)"1/2 ; M1 < M2
meso-pores
selective
< 2 nm ( m i c r o p o r e s )
very selective
In Table 2 we note that the transport mechanisms of gases in microporous media can be highly selective and may depend on the specific adsorption interaction of the gas molecules in the cages and molecular sieving effects for example. Total selectivity, or sieving, may result when the size of the pore apertures are similar to the dimensions of the gas molecules (see Table 1 and Figure 2). However very high selectivity may also occur with mixtures of gases when the apertures are significantly larger than the molecules, due to the differences in the activation energies of diffusion. This high selectivity for gas separation has lead to the earlier development of other types of microporous membrane apart from zeolite. These include those produced from microporous carbon (84, 85), silica glass (86) and amorphous silica (87), prepared by sol-gel techniques. These materials have an amorphous or glass-like structure, as distinct from crystalline zeolites. Such amorphous structures are better adapted for the formation of coherent membrane layers, within which the micropores form a more continuous network. This advantage of the interconnectivity is however off-set by the less ordered and ill-defined geometry of the structure in these amorphous materials. In single crystal zeolites the pore characteristics are an intrinsic property of the crystalline lattice, but in zeolite membranes secondary pores are present which can affect the gas permeation properties. These secondary pores can arise from intercrystalline spaces, the underlying porous support and indeed macroscopic defects within the zeolite layer. Below an outline of the permeation behaviour of the single and mixed gases in zeolite membranes is given.
3.1 Single Gas Permeation A qualitative description of the permeation behaviour of single gases in zeolite membranes has been discussed in detail by several authors (5, 9). Qualitative descriptions have been based on extensive experimental measurements made with supported MFI-type membranes. Although a quantitative description of gas transport has been given by Burggraaf (9) and others (83, 88, 89), detailed theoretical treatments are complicated by uncertainties in the mechanisms which can operate. Three simultaneous mechanisms have been proposed: permeation through defects, together with activated surface and volume flow in the zeolitic crystals. The transport in defects may occur by a process of Knudsen or viscous flow depending on the size of the pores (meso or macropores). The relative importance of this additional flow may also depend on the temperature and condensibility of the gas (82).
387
Burgraaf (5) distinguished four different regimes for several different gases in high quality MFI membranes. These regions were related to the corresponding adsorption isotherm region for each gas concerned (see Figure 10). These four regimes were typified by the behaviour of a series of alkanes and benzene as described below: (i)
Methane permeated in the Henry Law region of the isotherm. The flux increased linearly with the up-side pressure.
(ii)
Ethane, propane and n-butane permeated in the Langmuir sorption region. Here the behaviour was more complex as described later.
(iii)
Benzene permeated in the isotherm region where saturation occured; here the flux was independent of pressure, but increased with temperature - indicating an activated flow process.
(iv)
For isobutane, having a larger kinetic diameter than n-butane (5.0 compared to 4.3 A), a size exclusion effect occured, and the flux was markedly lower.
For regime (ii), where the permeation process occurs at a temperature/pressure regime corresponding to the Langmuir sorption region (e.g. propane), the flux depends on the temperature (isobaric conditions), as illustrated in Figure 11.
region2
=o
"~
region3
"~ ~.~region 1 Pressure Figure 10. Schematic sorption isotherm of a gas in a microporous zeolite showing three regions ((1)-Henry Law, (2)-Langmuir and (3)-Saturation) where permeation behaviour may differ.
388
Temperature
Figure 11. Schematic temperature dependence of the flux of a sorbed vapour (e.g. n-butane) in a zeolite membrane (cf. regime (ii)). Thus initially the flux increases with temperature because the transport process is activated. This occurs despite a reduction in the pore filling. Aider reaching a maximum, the flux then declines when the effects of the much decreased adsorption take effect. Absolute values of permeance of nitrogen, a non-condensable gas, have been reported by numerous authors for MFI-type membranes at ambient temperature. These cover a wide range (- 10.9 to > 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
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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
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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 (<10 ~m, preti~rrably
Typical conditions for the reaction are given below in Table 2 for the case of H20 without any 02.
405
Table 2. Range of conditions used in experimental studies of YSZ CVD/EVD. Pressure of YC13-ZrC14 side: ZrC14 concentration : YCla/ZrCI4 ratio: H20 concentration: Temperature:
2-5 mbar 1-5 x 10-3 mol/m 3 0.2-0.4, or pure ZrCI4. 5-10x 10.3 mol/m 3 800-1000~
At the pressure and temperature of the reaction the mean free path of the gas molecules is on the order of 30 ~tm, much larger than the pore size of the support, that is generally below 1 ~tm. Consequently, transport within the pores takes place by Knudsen diffusion whereby all species diffuse independently of each other. At these large Knudsen numbers the gas phase reactions are negligible and surface reactions dominate the process. The detailed steps of the surface reaction have not been elucidated but clearly they include adsorption of water and chlorides and surface reaction between the adsorbed species. The gradual narrowing of the pores results eventually in pore closure, i.e., elimination of the pathways connecting the chloride side with the wate rside. After pore closure has taken place, YSZ growth continues by means of solid state diffusion of lattice oxygen and electronholes from the water to the chloride side according to the scheme (Han and Lin, 1994): 1//202 (g) 4- Vo -'~ 0 2 + 2h~ ZrC14 (g) + 202"+ 4 ho --) Zr02 + 2C12+ 2Vo
at the water/YSZ side at the YSZ/chloride side
where Vo, O 2- and ho represent oxygen vacancy, lattice oxygen and electron-hole, respectively. The overall reaction is possible because of the mixed ionic and electrone-hole conductivity of the YSZ solid. In view of the charge transport involved, this phase of deposition is called electrochemical vapor deposition (EVD) (Carolan and Michaels, 1990). The first attempts to prepare thin (<10 ~tm) YSZ membranes on porous substrates and the investigation of the effect of synthesis conditions on membrane microstructure and oxygen permeation properties were reported in the late '80s by researchers at the University of Twente in Netherlands. In a number of publications as well as in two doctoral dissertations (Lin, 1992; Brinkman, 1994), these workers demonstrated controlled deposition of YSZ and other stabilized zirconias inside pores of ceramic substrates such as a-alumina (pore size 0.16 ~tm) and a-alumina-supported y-alumina (pore size <20 nm). Complementary studies on the EVD stage for the fabrication of thin and dense stabilized zirconia layers on the substrate surfaces were also reported by the same workers (Lin et al., 1990, 1992; Brinkman and Burggraaf, 1995). Focusing on the CVD stage which was typically carried out in the temperature range 8001000~ maximum amount of deposited ZrO2 was typically detected near the substrate surface exposed to the metal chloride vapors and extended 3-20 ~tm inside the porous a-alumina support (extent of deposition<0.5 l,tm for ),-alumina), the extend of deposition increasing with increasing temperature (de Haart et al., 1991b; Lin and Burggraaf, 1992; Cao et al., 1993). This result was explained by a Langrnuir-Hinshelwood mechanism of solid deposit growth with the enthalpy of adsorption of the precursors on the substrate pore surface being larger than the activation energy for solid state reaction, and hence an apparent decrease of the
406
overall growth rate (or increase of the extent of deposition) with increasing temperature (see below in this section). The pore narrowing rate of the substrate pores (determined by in situ permeation measurements) was found to increase with increasing bulk concentrations of both metal chlorides and water vapor, decreasing temperature, and decreasing diffusional resistance of the support (defined as the ratio of thickness to pore radius=L/R~ Researchers at the University of New Mexico have elaborated the aerosol-assisted CVD (AACVD) technique to deposit a variety of ceramic films on different substrates for the purpose of developing dense ceramic membranes for oxygen separation. In this approach, suitable metallorganic precursors (of the 13-diketonate family) are dissolved in an organic solvent (e.g. toluene) which is atomized and transported in the form of aerosol droplets towards a heated substrate where the precursors decompose to form the desired oxide phase. Examples of such films include ceria-doped-YSZ, deposited at 300-600~ from Zr(tfac)4, Y(hfac)3 and Ce(tmhd)4 (Siadati et al., 1997), Sr-Co-Fe-O3 perovskite deposited at 550~ from Sr(hfac)2, Co(hfac)3 and Fe(acac)3 (Xia et al., 1998a), and dual-phase Ag/YSZ deposited at 450~ from Zr(tfac)4, Y(hfac)3 and (hfac)Ag(CaHsOS)2 (Xia et al., 1998b). These films exhibited typically columnar microstructure and thickness 0.5-2 ~tm but gas-tightness necessary for separation applications was seldom demonstrated. Table 3 summarizes oxygen permeation flux data of zirconia-based dense membranes made by CVD/EVD on porous alumina substrates. For comparison, data tbr a dense tubular perovskite membrane are also included. Note that at 1000~ and under an 02 feed partial pressure of 0.21 atm, the highest 02 permeation flux was in the 10-4 mol/m2-s range, which is relatively low as compared to the H2 permeation fluxes of the CVD silica or the CVDpalladium membranes which vary in the 10"3-10.2 or 10-2-101 mol/m2-s range, respectively. For this reason, even ultrathin (<1 ~rn) fluorite-type dense ceramic membranes appear less attractive in terms of flux compared to the thicker symmetric perovskite membranes (Stephens et al., 2000), although a Ag/YSZ dual phase membrane made by EVD appears to have higher oxygen permeation flux due to the higher electronic conductivity imparted by the metal phase (Kim and Lin, 2000). Table 3. Properties and fluxes of dense zirconia-based membranes made by CVD/EVD. Workers Membrane Thickness 0 2 flux at 1000~ [ mol m -2 s-1 ] of EVD layer Lin et al. (1992) 1.5x10-4 Y203-ZrO2 5 ~tm Lin et al. (1992)
8rinkman & Burggraaf (1995) Han et al. (1997a) Han et al. (1997b) Stephens et al. (2000)
(on ~-A1203) Y203-ZrO2 (on ~-A1203)
Tb203-Y203-ZrO2 (on ot-Al203) Y203-Zr02 (on ot-A1203) CeO2-YEO3-ZrO2 (on ot-Al203) La-Sr-Fe-Co-Cr-O3 (tubular perovskite)
4.2 Mathematical Modeling of the CVD Phase
0.5 ~m
5.5x10 -4
7-9 lam
3.5-4x10 "4
3 ~tm
6.0x10 -5
4 ~m
4.0x10 4
lmm
2.2xlff 2
407 In addition m the experimental studies, several theoretical papers attempt to model YSZ CVD and compare model predictions with experimental data (Lin and Burggraaf, 1991; Brinkman et al., 1993). Further experimental and theoretical studies related to the CVD/EVD synthesis of dense zirconia-based ceramic membranes and their oxygen permeation properties were published shortly after by Lin and coworkers in an attempt to better understand the CVD/EVD process or improve the oxygen permeation flux of these membranes at elevated temperatures (Lin, 1993; Lin and Burggraaf, 1993; Xomeritakis and Lin, 1994a,b; Han and Lin, 1994; Han et al., 1997a,b). Scanning electron micrographs (SEM) of membrane cross sections have shown in most experimental studies that during the CVD phase of the reaction the deposit layer forms very near the chloride side and has thickness 3-15 ~tm and it takes less than one hour to reach pore plugging (Lin et al., 1990; de Haart et al., 1991; Lin and Burggraaf, 1992; Cao et al., 1993abc; Brinkman et al., 1993). Considerable modeling effort has been carried out to explain the dependence of these characteristics on the reaction conditions. In the models developed the porous structure was described as a collection of cylindrical pores of unitbrm radius R and balances for the chloride reactant (only the ZrCl4 will be considered to simplify the formulation) and water could be written as follows: dN 1 2 - - - Srs(q,c2) (9) dz a dN 2 4 = - - ~ rs(Cl,C2 ) (10) dz a where the indices 1 and 2 refer to the chloride and water respectively, Ni are the molar fluxes of the two species, rs is the reaction rate per unit pore surface area, 2/R is the pore surface area per unit volume, e is the pore volume fraction and z is the position coordinate across in the porous support in the direction of transport. For low-pressure deposition as used in most experiments transport takes place by Knudsen diffusion and the fluxes according to standard capillary models can be written as Ni = __~ DKi dci i = 1,2 (11) dz where x is the tortuosity that accounts for the random orientation of the pores and for deviations from the assumed cylindrical pore shape and Dm is the Knudsen diffusion coefficient, DKi = AKia
i = 1,2
(12)
where 2 18RgT'~ 1/2 AKj = "3 ,, z M )
i=1'2
and Rg is the gas constant and Mi is the molecular weight of species i. The pore volume fraction in Eqs. (9)-(11) above is a function of the radius,
(13)
408
Where go is the initial uniform pore volume fraction. Equation (11) can then be written as
Ni=
eoA Ki a 3 dci 2 dz fa
i = 1,2
(14)
o
On account of the large Knudsen number the chemical reaction takes place on the pore surface and gas phase reactions inside the pores can be neglected. Deposition then involves adsorption of the reactants and surface reaction among the adsorbed species. This heterogeneous reaction is often described by Langrnuir-Hinshelwood (LH) kinetics. If adsorption is nondissociative and both reactants compete for the same surface sites, at adsorption equilibrium the concentrations of the adsorbed species are commonly described by Langmuir isotherms: KiRTci Cis = c T | + RT(KlC 1 + K2c2 )
i = 1,2
(15)
where Ki are the adsorption constants and cT is a constant giving the surface concentration at saturation. These expressions neglect the effect of the product HC1 on account of its rapid removal by convection at the chloride side. At the high temperature of reaction most adsorption sites would be unoccupied so that the isotherms reduce to the linear forms ~~ Cis = cTRTK ic i
(16)
If the reaction between the adsorbed species is rate determining with the adsorption steps being at equilibrium, the rate can be empirically written as (17)
(18)
k - k' (cTRT) m+n K~n K~
where m, n are empirical reaction orders. The major approximation involved in this formulation is that it recognizes only two adsorbed species whereas in reality several would be present in view of the stepwise hydrolysis of the adsorbed chloride. Inserting now the expressions for the fluxes and the reaction rate into Eqs. 9 and 10 one obtains
dz
r(a 3 dcl~ _ 2rk ac~n c~ dz ,/ AK1
d ( a 3 d...~.)
4rk
n
- A--G acI Ca
(19)
(2o
The side of the chloride and water flows will be taken as z=0, and z=L respectively. Thus, the boundary conditions can be written in general as:
409
z = 0 : N1 = kgl (Cl0 - Cl)
(21)
Z = 0 : N2 = - kg2 (c2 - c2')
(22)
z = L :N1 = k'gl (Cl - C l ' )
(23)
z = L : N2 = - k'g2 (C20 - C2)
(24)
where the fluxes Ni are given by Eq. (14) above, C2' and cl'are the concentrations of water at the chloride side and the concentration of chloride at the water side respectively and k S, are mass transfer coefficients in the gas at z=0, z=L respectively. In view of the generally high flowrate of the carrier gas at the two external surfaces the concentrations ci' can be neglected. If in addition the dimensionless parameters ( Biot numbers) kgi L "c/DK, e are large, one can replace the boundary conditions (20), (23) by z = 0 : cl = cl0
(21')
Z = L:C2 = C20
(24')
In the literature the boundary conditions (21) and (22) have also been approximated by (Brinkman et al. 1993; Lin and Burggraaf, 1991): Z = 0 : C2 = 0 Z -L:cl-0 or by z = 0 " dc2 = 0 dz z = L 9 dcl = 0 dz
(22') (23') (22") (24")
When, as observed experimentally, the deposit is formed at or very close to the chloride side boundary conditions (23') and (23") are essentially equivalent and either one is suitable. Under these conditions, however, conditions (22'), (22") are not equivalem and neither one might be adequate. On account of the reaction the pore radius a is a function of the position variable x and decreases gradually according to 0 a = -vsr~ (c 1, c 2) 0t
(25)
where vs is the molar volume of ZrO2. Some of the key experimental findings concern the location of maximum deposition, the width of the deposition zone, the time to pore plugging, and the change of pore size distribution. In numerous experiments, covering a wide range of reactant concentrations,
410 temperature and substrate pore size, the location of maximum deposition (where pore plugging eventually takes place) was at z=O, the chloride side. Moreover, a somewhat surprising feature is that higher temperatures produce less steep profiles indicating lower reaction rate. The negative temperature dependence of the reaction rate is explained by Eq.(18) relating the rate constant k with adsorption constants and a true surface reaction constant such that the overall activation energy is given by E = E ' - m Q1 - n Q2
(26)
where E' is the reaction activation energy and Q~ are the adsorption energies taken as positive quantities. Evidently the net activation energy is negative in these experiments. Maximum deposition at all combinations of reactant concentrations is at the chloride side. In terms of the model the location of maximum deposition will move towards the chloride side by increasing the concentration ratio C2o/C~o,or the diffusivity ratio or by decreasing the reaction order m with respect to the waster. In fact, to obtain the maximum deposit at z=0 it was necessary to either set the reaction order with respect to water m=0, or use the boundary condition (22") (Lin and Burggraaf, 1991). In subsequent work, Xomeritakis and Lin (1994a,b)derived semianalytical expressions for the location of maximum deposition. They used the boundary condition (22') and as a result the position of maximum deposition could be obtained at the extreme point z=0 only when the order with respect to water, n, was set equal to zero. It appears that the difficulties in reconciling the model calculations and the experimental data with respect to the location of maximum deposition are partly due to the boundary conditions used. For large reaction Thiele moduli that are of interest for membrane preparation, the differential equations are very stiff, therefore small changes in the boundary conditions will have a big effect on the results. It would be better, therefore, to use the more general boundary conditions given by Eq. (22) and (23). Another key property is the width of the deposit layer Ld. Approximate expressions have been derived by Xomeritakis and Lin (1994a,b) in terms of the Thiele moduli of the reaction for the two reactants. These expressions for the layer thickness were probably not very sensitive to the boundary conditions used for c2 at z=0 and c~ at z=L. Other model results of interest are the evolution of permeance and the related time to pore closure, the latter being defined as the time when the permeance has been reduced to a specified small fraction of its initial value. These properties are quite sensitive to the pore size distribution and pore geometry that are not taken into account in the fbregoing models and will not be considered here.
5. CVI) OF METALLIC MEMBRANES The CVD synthesis of (mainly palladium-based) metallic membranes for hydrogen separation has attracted increased attention in the last decade because of several potential advantages compared to the more commonly practiced electroless plating technique: (a) the possibility of depositing the metal inside the pores of a porous support, instead of fbrming a metal film on the surface of the support, as is usually the case with plating. In this case, an improved mechanical strength and a higher resistance towards embrittlement is expected for a
411
composite palladium membrane tightly packed inside the pores of a suitable support; (b) simplicity in operation and obviation of the complex wet chemistry associated with electroless plating; (c) better control of the membrane thickness and faster deposition rates. Major challenge in the field is the unavailability of suitable metal precursors with sufficient volatility and thermal decomposition behavior that will guarantee high precursor delivery rates and desirable microstructure of the metal deposit. The first successful application of the CVD process for the fabrication of palladium membranes was demonstrated by Morooka and coworkers (Yan et al., 1994b). These workers employed palladium acetate as source which was decomposed in the macropores (0.2 .am pore diameter) of a 10 mm-long tubular c~-alumina support (supplied by NOK corporation, Japan) at 300-500~ under reduced pressure. The microstructure of the membrane consisted of a 2.am-thick and defective metal layer extending outside of the support, formed most likely by gas phase decomposition of the precursor, adjacent to a palladium-filled zone extending up to 8 .am inside the support which served as the Hz-selective layer of the structure. The membranes exhibited H2 permeance in the range 5x108-5x10 "6 mol/m2-s-Pa and Hz/N2 selectivities in the range 100-1000 at 300-500~ depending on the synthesis temperature which may have a significant effect on the microstructure and grain size of the deposited metal as well as the extent of carbon contamination from the precursor. Improved stability of the membrane was also demonstrated during thermal cycling between 100-500~ in a 100 kPa-H2 atmosphere. Under the conditions employed, however, it was necessary to repeat the deposition process several times in order to prepare a selective membrane in a 40 mm-long support (Morooka et al., 1995b). Parallel with the group of Morooka, a similar tubular a-alumina-supported palladium membrane was developed by Uemiya and coworkers and their results were reported in several conference proceedings or journal papers (Uemiya et al., 1994, 1996, 1997). These workers employed palladium acetylacetonate as metal source which was sublimed at ~-160~ and 1atm of N2 and decomposed inside pores of the partially evacuated support (supplied by Toshiba Ceramics) at-270~ The deposition zone extended up to 8 .am inside the support and deposition times of over 15 h were necessary to achieve sufficient pore plugging. The final membranes exhibited a H2 permeance as high as 3.5-7.0x10 6 mol/m2-s-Pa in the range 300-500~ with a Hz/N2 ratio of 240. In addition to the palladium-based metallic membranes, the group of Uemiya developed metallic membranes based on other precious metals, such as platinum and ruthenium (Uemiya et al., 1997; Kajiwara et al., 2000a) or iridium and rhodium (Kajiwara et al., 2000b) using thermal decomposition of the respective acetylacetonate precursors. These non-palladium o 9 -6 2 p metallic membranes exhibit H~ permeances at 500 C in the range 1.0-3.0xl0 mol/m -s- a and HdN2 ratios up to 100, comparable to the properties of their CVD-palladium membranes, while they offer the additional advantages of higher mechanical resistance against hydrogen embrittlement or chemical resistance against acid gases such as HzS. Different types of palladium membranes deposited inside pores or on the surface of mesoporous y-alumina top layers were also reported by Lin and coworkers, as part of their effort to develop submicron-thick palladium-based membranes by techniques such as CVD/MOCVD and magnetron sputtering. These workers employed a two layer support consisting of a sol-gel derived y-alumina top layer (pore size -~4-6 nm) coated on the surface of home-made macroporous o~-alumina support disks (pore size 0.2 .am). In their earlier work, they employed PdC12 as metal source which was reduced to Pd inside pores of the y-alumina
412 top layers at 450-500~ and reduced pressure (-~1 torr) with the aid of H2 in an opposingreactants scheme (Xomeritakis and Lin, 1996). The employed deposition scheme was the analogue of the metal halide/oxidant reaction scheme adopted by previous workers for the synthesis of metal oxide membranes such as silica or yttria-zirconia (see previous sections). Despite successful pore plugging, this reaction scheme was later abandoned and metal membrane synthesis was attempted using thermal decomposition of palladium acetylacetonate at 300-500~ which appeared more reproducible and easier to control, primarily because of the higher volatility of the metallorganic vs. the halide palladium precursor. Despite the fact that the modified membranes exhibited 3-4 orders of magnitude reduction in He permeance at 25~ vs. the original two-layer support, no satisfactory H2 permselectivity was demonstrated with either membranes beating palladium inside y-alumina mesopores. In the temperature range 22-300~ permeation of both HE and He was activated and the highest ever H2/He selectivity obtained was of order 5 (Xomeritakis and Lin, 1998). This behavior was entirely different from that reported by Morooka and Uemiya when palladium was successfully deposited inside larger pores of plain a-alumina supports. The observed transport behavior must be related to the microstructure of palladium tightly packed inside pores as small as 4-6 nm, combined with possible carbon or chlorine contamination by the employed precursors. To the best of our knowledge, no other study describing successful deposition of Pd membrane inside nanometer-sized mesopores has been published so tar, so that a comparison could be made with the results of Lin and coworkers. H2-permselective membranes were only obtained by thermal decomposition of palladium acetylacetonate at 300-400~ and 1 tort in the presence of excess HE in an opposing-reactants scheme. Under these conditions, 0.5-1.0 lam-thick metallic layers were formed on the surface of y-alumina that exhibited a HE permeance of 1.0-2.0x10 "7 mol/m2-s-Pa and a HE/He ratio of 100-200 at 300~ (Xomeritakis and Lin, 1997, 1998). The transport properties of these membranes were equivalent to those of Pd/Ag alloy membranes prepared by the same workers using magnetron sputtering technique, which suggests that the microstructure, but not purity, is responsible for the unexpectedly low HE permeance of these ultrathin ceramic-supported metallic membranes (Jayaraman and Lin, 1995; Xomeritakis and Lin, 1997; McCool et al., 1999). Since thin (0.5-5 lam) palladium-based metallic membranes became available by CVD or sputtering, H2 permeation behavior that deviated from the well-known solution-diffusion mechanism was also observed. Evidence of surface resistance-controlled H2 permeation was reported by all the above workers, although no detailed study was carried out to elucidate the rate-limiting step in a wide temperature and HE partial pressure range. For example, Lin and coworkers reported activation energies for HE permeation >20 kJ/mol in the range 100-300~ (Xomeritakis and Lin, 1997), which is much higher than the value expected when atomic hydrogen diffusion is rate-limiting (typically <10 kJ/mol). The membrane of Morooka showed a linear dependence of H2 flux on driving force for permeation in the range 300-500~ (although APm was only varied up to 100 kPa) while the membrane of Uemiya had instead a square-root dependence of HE flux on driving force at 500~ However, surface resistance could become rate-limiting at T<300~ as suggested by the of H2 permeation behavior of their platinum membrane (Kajiwara et al., 2000a). At this stage of development in the field, it appears that the exact mechanism of HE permeation through palladium membranes depends on both apparent membrane thickness as well as the underlying microstructure and temperature
413
of operation, and general conclusions cannot be made regarding the exact point of transition from bulk diffusion-limited to surface resistance-limited mechanism of H2 permeation. Table 4 summarizes synthesis conditions and transport properties of CVD-palladium membranes as discussed in detailed above. It is mentioned here that significant research efforts for the development of palladium-based metallic membranes by MOCVD or aerosol-a ssisted CVD have also been carried out by Ward and coworkers and have been reported in several conferences (for example, Deshpande et al., 1994) but no permselectivity was demonstrated so far by this group to the best of our knowledge. Finally, some attempts to prepare CVD-palladium membranes were reported by Meng and coworkers using either PdC12 (Huang et al., 1997) or Pd-acetylacetonate (Meng et al., 1997) with limited success, except for the case of a Pd-Ni alloy membrane that was claimed to be gas-tight based on N2 permeation measurements only. Table 4. CVD Synthesis conditions and pro aerties of Metallic Membranes. Workers Support & Reaction Deposition H2 permeance pore size Scheme temp. and tp mol/mLs-Pa Yan et al. ~-A1203 Pd acetate 300-500~ 10-s-10.6 (1994b) 0.2 ~tm decomp. 2h (300-500~ Uemiya et al. ~-A1203 Pd(acac)2 270~ 3-7xl 0 .6 (1994,96,97) 0.2 pm decomp. > 15h (at 500~ lxl0 ~ Xomeritakis 450-500~ PdC12+H2 ]t-A1203 & Lin ('96) (at 300~ 1-2 h 4-6 nm 2xl 0 .8 Xomeritakis 200-500~ Pd(acac)2 ]t-A1203 & Lin ('98) decomp. (at 300~ 1-2 h 4-6 nm 2x10 -7 Xomeritakis Pd(acac)2 300-350~ y-A1203 & Lin ('98) (at 300~ 1-2 h 4-6 nm +HE (*) Selectivity of H2 over He.
Selectivity H2/N2
100-1000 240 5 (*)
1.1 (') 200 (*)
414 References
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416
Wu, J.C.S., H. Sabol, G.W. Smith, D.L. Flowers, P.K.T. Liu,.l.Membr.Sci. 96 (1994), 275-287. Xia, C., T.L. Ward, P. Atanasova, and R.W. Schwartz, J.Mater.Res. 13 (1998a), 173-179. Xia, C., T.L. Ward, C. Xu, P. Atanasova, and R.W. Schwartz, J.Electrochem.Soc. 145 (1998), L4-L8. Xomeritakis, G., and Y.S. Lin, Chem.Eng.Sci. 49 (1994a), 3909. Xomeritakis, G., and Y.S. Lin, lnd.Eng. Chem.Res. 33 (1994b), 2607-2617. Xomeritakis, G., and Y.S. Lin, J.Membr.Sci. 120 (1996), 261-272. Xomeritakis, G., and Y.S. Lin, J.Membr.Sci. 133 (1997), 217-230. Xomeritakis, G., J. Han, and Y.S. Lin, .l.Membr.Sci. 124 (1997), 27-42. Xomeritakis, G., and Y.S. Lin, AIChEJ.. 44 (1998), 174-183. Yan, S., H. Maeda, K. Kusakabe, and S. Morooka, Ind.Eng.Chem.Res. 33 (1994a), 20962101. Yan, S., H. Maeda, K. Kusakabe, and S. Morooka, lnd.Eng.Chem.Res. 33 (1994b), 616622.
Recent Advances in Gas Separationby Microporous CeramicMembranes N.K. Kanellopoulos (Editor) 2000 Elsevier ScienceB.V. All rights reserved.
417
COMPOSITE CERAMIC MEMBRANES F R O M L A N G M U I R - B L O D G E T T AND SELF-ASSEMBLY P R E C U R S O R S
K. Beltsios, E. Soterakou, N.K. Kanellopoulos Membranes for Environmental Separations Laboratory, Institute of Physical Chemistry, NCSR Demokritos, Agh. Paraskevi, 15310, Greece
I. I N T R O D U C T I O N
la. Basic concepts Chemistry in diminishing dimensions 1 is a current popular means for the generation of fine structural features desirable for applications such as nanocomposites, sensors, nonlinear optics (NLO), piezo-electric devices and asymmetric membranes for gas and vapor separations. The Langmuir-Blodgett (LB) 26 deposition technique (Figure 1) offers a
physical chemical route towards the same structural target, while a subsequent plasma treatment adds a chemistry step to the LB-based approach to nanostructure formation. Plasma converts appropriate organic LB-film forming substances deposited on porous ceramic substrates to ceramic derivatives and yields asymmetric all-ceramic membranes.
A
-----o .
.
.
.
---o
---o
W
0---- amphlphlle
W;
Figure 1. LB deposition of an amphiphile on a hydrophilic porous substrate (S). W: water subphase, A: air. I: First deposition step. The hydrophilic heads are attached to the substrate, and the arrangement of the hydrophobic amphiphile tails make the substrate surface hydrophobic. II: Second deposition step. The arrangement of the second deposited amphiphile layer makes the surface of the substrate hydrophilic again.
418
\ /cy
e-
/ OH
6",\
+
solvent
OH
OH
OH
R
R
....... .pore ......... r
R \ \ S (/ O/
i
R R I J O --Sl--O --SI--O I
~OH
i/
R--Sio--O-jl i
O I
f
I "\ / R O jSi" \O I HO
i
J
,--O--oSi--R ll
R~S./| / O I
J
Si--
I O ~OH I
R-- S i - O I
O
O --
I O -- Si--O
I \ /R Si" O HO/ \ I O I --O- Si--R I
O I
Figure 2. SA deposition of SiCI4 on a hydrophilic porous substrate. SiCI4 in an organic solvent reacts with -OH surface groups and adsorbed H20 molecules and attaches to the pore surface. Pore narrowing is shown in this case, while it is conceivable that pore bridging will be possible for larger size chlorosilanes. Another potential route for the formation of asymmetric ceramic membranes is the, closely related to LB film formation, Self-Assembly3 (SA) technique (Figure 2), which may also be combined with plasma treatment. The successful combination of LB with plasma has been recently demonstrated 79, while only ceramic SA/ compact substrate structures or potential precursor SA/porous substrate structures can be identified in the literature at this point. It is notable that a fully ceramic/SA porous substrate structure may also formed with appropriate SA substances (e.g. SiCl4 or Si2C16), without a need for a subsequent plasma treatment.
l.b. L B and L B - p l a s m a based m e m b r a n e s
The formation of an asymmetric ceramic membrane is often attempted through deposition of a substance that can narrow the surface pores of an available ceramic porous membrane. The LB technique of monolayer transfer is widely used for the deposition of a
419 controlled number of monomolecular layers of appropriate substances (amphiphiles,
selected polymers, elongated or disc-like molecules etc) on top of a smooth compact substrate. In all cases, it is necessary that the substance to be deposited can form a singlemolecule thick, dense and, at the same time, mobile layer on the surface of ultrapure water or another fluid (referred to as the subphase). Here, we will present the basic concepts and provide data pertaining to the formation of asymmetric ceramic membranes by the transferring of LB layers on appropriate porous ceramic substrates (Fig. 1). The use of some form of LB film for separation purposes was already envisioned by Blodgett ~~ The formation of asymmetric membranes by application of a polymerizable monomer or a polymer LB film on a porous substrate received considerable attention after approximately 1968 and work of this type was reviewed some years ago by Tieke 3. The formation of a ceramic ultrathin layer by plasma treatment of fatty acid salt LB multilayer film was first demonstrated by Kalachev et al ~2 in 1993. Certain forms of post deposition surface treatment of LB-derived membrane precursors are known from earlier literature, but those treatments were aiming either at the polymerization of a relatively small LB-deposited substance or the crosslinking of a polymeric LB deposited substance 3.
I.e. SA-based membranes
According to the self assembly (SA) technique of monolayer formation, a reactive substance or surfactant dissolved in an organic fluid is chemisorbed on the surface of an appropriate substrate and forms a densely packed arrangment 5. Reactions such as condensations between appropriate groups of the substrate surface and the SA substance often take place and stabilize further the SA arrangement.
Properly tailored
multifunctional substances may allow for the formation of successive SA layers. The SA technique frequently leads to film structures resembling those obtainable by the LB technique, provided that a compact substrate is used. On the other hand, when a porous substrate modification is attempted by the SA method (Fig. 2), the geometry of
the final structures can be markedly different from those obtainable by the corresponding LB route. This is because in the case of LB deposition the 2-D film is first formed and subsequently transferred; as a result, the surface gaps (: pore mouths) of a porous substrate can be often bridged by the pre-formed layer. In the case of SA deposition, the
420 substance is chemisorbed and densely packed directly on the substrate; as a result, there is a tendency, especially for small size and single active site SA compounds to cover the pore walls rather than to bridge the pore mouths. Further, unless special precautions are taken, the pore wall SA modification need not be limited to the surface of the substrate and a membrane with a homogeneously reduced pore size membrane, rather than an asymmetric membrane will be obtained. Here, we will limit the SA membrane formation discussion to routes that may lead to or contribute towards the formation of an
asymmetric ceramic membrane. II. BASIC PROCESSING
!l.a. LB Isotherms and Deposition An LB isotherm is the two dimensional equivalent of a pressure-volume diagram for a bulk substance. Amphiphile LB small molecules are initially far from each other, but as the area available to the molecules dispersed on the surface of the subphase is reduced, the dispersion becomes a 2-D liquid and finally a 2-D solid, while further compression pushes some of the molecules outside the single layer. The latter process has no realizable analogue in three dimensions, as it corresponds to the expulsion of molecules of a bulk phase to the fourth dimension. Additional important points regarding the behavior of the LB layer are the following: (a) small amphiphile LB molecules do not have a fixed thickness but they enter the third dimension to an increasing degree as compression progresses, (b) the LB film is not a free standing film but a surface phase in some type of equilibrium with the subphase. Also, the types of phases that form and the order (1 st, 2nd etc.) of the transitions that take place between phases need not be the same for two and three dimensions. From the experimental LB isotherm we select a deposition surface pressure (~) corresponding to the state of dense liquid. Depositions require filling the LB trough with a fresh subphase, properly positioning the porous substrate and spreading the LB substance. Subsequently, successive monolayers are isobarically (fixed-n) deposited on the substrate as shown in Figure 1. The number of deposited layers depends on the number of substrate dippings and withdrawals. In case the target top-layer material is a metal oxide, a fatty acid LB substance is chosen and a soluble salt of the metal of interest
421 is added to the subphase. Fatty acid anions and metal cations are LB co-deposited in the form of a salt, while plasma oxidation will subsequently remove the organic part and convert the deposited salt to the metal oxide of interest. When the small amphiphile is replaced by a polymer capable of LB monolayer formation, the isotherm-determination and film deposition procedures remain the same but they should be performed at reduced rates, as macromolecules equilibrate more slowly than small amphiphiles. In addition, a number of differences exist 4'5, regarding the film structure which corresponds to different portions of the isotherm. The most important difference is that a polymer chain usually lies fiat on the subphase surface until a dense monolayer forms, while the small amphiphiles tend to stand upright at high compressions.
II.b. Plasma Treatment
Plasma treatment of the LB -substrate composite is usually necessary when the target is an all-ceramic membrane, because most transferred substances include an organic part. As an oxygen plasma treatment modifies greatly the structure of the top-layer, the presence of few structural imperfections need not affect the integrity of the final membrane top layer, though, certainly, large gaps in the originally deposited material can not be easily amended by the subsequent plasma processing. For a radio frequency (RF) plasma a typical set of processing conditions is the following: Reaction time: 2-5 min. Oxygen Pressure: 10-80 mTorr, Power=300 W and a DC-bias of (-) 80-100 Volt. Plasma reactor and sample arrangements may be selected as to lead to chemical treatment only or to simultaneous chemical treatment and sputtering ~3. All LB/plasma work discussed here is based on arrangements leading to chemical treatment only.
III. PROCESSING OPTIONS lll.a. Choice of ceramic LB substrates
Various porous membranes may be used as substrates, but a low surface roughness appears to be a prerequisite for successful LB transfer 7. Here we will limit our discussion to commercially available membrane substrates that cover two compositions (Vycor silica
422 and Anopore alumina) and pore sizes ranging from 40 A (Vycor) to 0.2 ~tm (Anopore alumina available at 0.02, 0.1 and 0.2 ktm pore diameters). Vycor can be used in acidic environments (in the absence of fluoride ions) but not in strongly alkaline environments. This amorphous silica preserves its porous network up to a temperature in the 800-900~ ~4 range; this fact imposes an upper limit on the temperature of use (in addition to any limitations pertaining to the material of the toplayer). Anodic alumina membranes are vulnerable in strongly alkaline environments, while the membrane behavior in acidic environments depends on the anion (for example, hydrochloric acid may attack them while nitric acid will not). By an appropriate calcination program to a maximum temperature over 850~
anodic alumina membranes
can be converted to a polycrystalline alumina membrane with improved chemical resistance to non-neutral pH conditions ~5. At first sight, the LB deposition on a porous substrate is expected to more difficult, the larger the pore size of the substrate. Nevertheless, we have found that for both siloxane polymers and fatty acid salts, the anodic alumina membranes of all pore diameters examined are better LB substrates than a Vycor membrane. It may also be expected that small amphiphiles can at best bridge pores with a diameter not much larger than the diameter or the length of the LB molecules and only polymer chains can bridge larger pores. While it was already known 3 that various polymers form easily LB films and some of them can be transferred to bridge pores even in the micron range, we have also found that a small amphiphile like Cd arachidate can also bridge quite large pores (0.2 ~tm). The latter finding suggests that the dense liquid 2-D state of a LB film is characterized by considerable lateral coherence and should not be thought as analogous to a 2-D dense assembly of macroscopic objects (discs etc.). Vycor exhibits a rather unusual behavior as a substrate. Vycor surface appears to impose a degree of transfer on the order of 0.7, both to fatty acid salts and to silsesquioxanes, and this observation has been associated to the porosity of Vycor (=0.3=1-0.7) and the presence of silicate protrusions in the surface of Vycor pores 7. Nevertheless, repetitive deposition is possible without a decline of the degree of transfer and, at least, the final membrane (i.e. LB deposition followed by plasma treatment) is characterized by a satisfactory degree and extent of surface modification7"8.
423
lll.b. Deposition Thickness /Number of LB layers The most attractive feature of the LB approach to the asymmetric membrane formation is the possibility of depositing very thin films of a number of compounds. A minimum number of approximately ten layers is usually required for continuous coverage. The LB/plasma approach aims primarily at creating top-layers with a thickness t in the range of 100-200 A, though any t value in the range of 50 to 500 A is a valid target. Much thinner LB layers (e.g. t < 50 A) often lead to discontinuities of the top-layer, while much thicker layers (e.g. t > 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
<0.5
1
0.65 to 0.75
OC
0.9+0.1
lo0.6
3-4
0.7--,1
Pitch Dd,max nmax
0.6
0.7--,1
,not examined
Figure 3. Side view of a sectioned fully ceramic asymmetric membrane prepared from 17 LB layers of Cd arachidate and a 0.2~tm Anopore substrate and subsequent plasma oxidation. D is the deposited layer after plasma oxidation. The arrow indicates the direction of the tubular pores of the substrate.
_>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<6.8 A.
431
2,s 1
2i
f
1,5
1 -i
e__.__.___
0,5 -I
0 0,01
0,1
1
10
Torr
Figure 5. Reduced integral permeability data for an n=10 Cd arachidate/Vycor LB/plasma membrane and various permeates (gases and vapors). The data are plotted in the form of k vs. T/T c, where k is measure of the deviation from Knusden flow (see text), T is the temperature of measurement and Tc is the critical temperature of the permeate. Black circles: 295 K (all seven gases and vapors listed in the text). White circles: a 373 K/CO 2 point, a 363 K/CH 4 point and a 388K/C3H 8 point.
V. P E R S P E C T I V E S At this time, the LB/plasma or SA/plasma routes to asymmetric ceramic membranes are approaches at the infancy stage. What has been demonstrated so far is that LB transfer on porous ceramic membranes is possible both for polymers and small amphiphiles and LB/plasma all-ceramic asymmetric membranes
can
be formed with few or no surface
defects. The SA/plasma route is also expected to yield composite structures of the desired
432 type. In the case of the LB/plasma route it should be noted that the handling of large samples is difficult and fully continuous LB processing is inherently impossible. On the other hand, scaling up of the SA/plasma process should not encounter difficulties of comparable magnitude. In all cases, LB-related technology becomes increasingly more attractive as there is a steeply increasing technological interest for miniaturization. LB/plasma processed asymmetric ceramic membranes may well find applications in microreactor engineering. In this direction we note that LB/plasma deposition processing for the formation of ultrathin top membrane layers containing compounds capable of n-complexation (which can lead to the separation of certain gas pairs e.g. propylene from propane 33) has been suggesteds and needs to be explored. Sensing3 constitutes another technological area requiring the tailoring of small size asymmetric ceramic membranes. LB/plasma membrane processing may become part of the manufacturing of the active component of various types of detectors. For example, odor detectors can be manufactured as follows: Under appropriate reaction conditions, a high surface area (nanoporous) membrane substrate, such as Vycor, may be used for the uniform CVD deposition of an appropriate substance (e.g. SnO234, as a trimethylamine/ fish food decay detector35), without pore plugging. Subsequently, the CVD-modified ceramic membrane can undergo an LB/plasma surface modification; the final composite asymmetric membrane may, for example, permit the flow of the vapor of interest and, at the same time, block moisture s and, thus, lead to an improved signal-to-noise ratio. Finally, as an example of potential uses of the new LB-porous substrate structures outside the field of membranes, we note the possibility of depositing stratum corneum lipids (or alternate layers of stratum corneum lipids and proteins) 36 and determine various diffusion coefficients of the skin.
Acknowledgements Dr. A. Kalachev who suggested the LB/plasma approach and Dr. P. Detemple, Dr. F. Hessel and collaborators (IMM, Mainz) who made early attempts to prepare fatty acid salt/plasma membranes are thanked for their help at the beginning of our work. At subsequent stages, substantial help was provided by Mr. G. Romanos, Prof. G. Tsangaris,
433
Dr. E. Gogolides, Dr.Th. Steriotis and several other co-workers at NTUA and NCSR Dernokritos, Athens.
REFERENCES 1. G.A. Ozin, Nanochemistry: Synthesis in Diminishing Dimensions, Adv. Mater., 1992,4(10), 612. 2. K.B. Blodgett and I. Langmuir, Built-up films of barium stearate and their optical properties, Phys. Rev., 1937, 51,964-982. 3. B. Tieke, Langmuir-Blodgett membranes for separation and sensing, Advanced Materials, 1991, 3(11), 532-541. 4. G.L. Gaines Jr., Insoluble Monolayers at Liquid-Gas Interfaces, Interscience Publishers, NY 1966. 5. A. Ulman, An introduction to Ultrathin Organic Films from Langmuir-Blodgett to Self Assembly, Academic Press Inc, San Diego, 1991. 6. (a) M.E. Petty, Langmuir-Blodgett films, An Introduction, Cambridge U. Press, 1996, (b) D.K. Schwarz, Langmuir-Blodgett film structure, Surface Science Reports, 1997, ~ , 241-334. 7. E. Soterakou, K. Beltsios and N. Kanellopoulos, Asymmetric ceramic composite membranes from Langmuir-Blodgett deposition precursors. I. Deposition of Fatty Acid Salts on Porous Ceramic Substrates, J.Eur. Cer. Sot., 2000, in press. 8. E.Soterakou, K. Beltsios, T. Steriotis and N. Kanellopoulos, Asymmetric ceramic membranes from Langmuir-Blodgett deposition precursors. II. Structure characterization of composite membranes, submitted to the J.Eur. Cer. Soc. 9. E.Soterakou, K. Beltsios and N. Kanellopoulos, Langmuir-Blodgett film properties of linear and ladder siloxane polymers and oligomers, submitted to J. Macrom. Sc., Phys. Ed. 10. K. Blodgett, Film structure and method of preparation, U.S. Patent, 2,220,860, 1940. 11. M.V.d. Auweraer, C. Catry, L. Feng Chi, O. Karthaus, W. Knoll, H. Ringsdorf, M. Sawodny and C.U. Urban, Mono- and multilayers made from discotic liquid crystals, Thin Solid Films, 1992, 210/211, 39-41. 12. A. Kalachev, K. Mathauer, U. Hohne, H. Mohwald and G. Wegner, Low Temperature Plasma Treatment of Monomolecular Langmuir-Blodgett Films, Thin Solid Films, 1993, 228, 307-311. 13. K. Beltsios, G. Charalambopoulou, G. Romanos and N. Kanellopoulos, A Vycor membrane with reduced-size surface pores. I. Preparation and characterization, Journal of Porous Materials, 1999, 6, 25-31. 14. M.J.D. Low and N. Ramasubramanian, The dehydration of porous glass, J. Phys. Chem., 1967, 71 3(~), 730-737. 15. M. Mardilovich, K.E. Holmberg, C. Lofman and E.I. Eriksson, New and Modified anodic alumina membranes. Part II. Comparison of solubility of amorphous (normal) and polycrystalline anodic alumina membranes, J. Membr. Sc., 1995, 98, 143. 16. K. Beltsios, E. Athanasiou, K. Aidinis and N. Kanellopoulos, Microstructure Formation Phenomena in Phase Inversion Membranes, J. Macrom. So., Phys. Ed., 1999, 38(1&2), 125. 17. A. Kalachev, V. Litvinov and G. Wegner, Polysiloxanes at the air/water interface and after transfer onto substrates, Makromol. Chem., Macromol. Symp., 46, 365-370, 1991.
18. F. Embs, D. Funhoff, A. Laschewsky, U. Licht, H. Ohst, W. Prass, H. Ringsdorf, G. Wegner and R. Wehrmann, Preformed polymers from Langmuir-Blodgett films-Molecular concepts, Advanced Materials, 1991, 3__0.),25-31. 19. M. Seufert, C. Fakirov and G. Wegner, Ultrathin Membranes of Molecularly Reinforced Liquids on Porous Substrates, Advanced Materials, 1995, 7(1), 52-55. 20. E. Fitzer, Thermal degradation of Polymers to Polymeric Carbon-An Approach to the Synthesis of New Materials, Angew. Chem., Int. Ed. Engl., 1980, 19, 375-385. 21. Th. Steriotis, K. Beltsios, A. Mitropoulos, N. Kanellopoulos, S. Tennison, A. Wiedenman and U. Keiderling, On the Structure of an Asymmetric Carbon Membrane with a Novolac Resin Precursor, Jr. Appl. Polym. Sc.,1997, 64, 2323-2345. 22. E.Soterakou, K. Beltsios and N. Kanellopoulos, work in progress. 23. S.I. Belousov, E. Sautter, Yu. K. Godovsky, N.I. Makarova and W. Pechhold, Polymer Science, Ser. A, Polysiloxane Langmuir Films. Linear Polysiloxanes, 1996, 38(9), 15321537. 24. E. Sautter, S.I. Belousov, W. Pechhold, N.I. Makarova and Yu. K. Godovsky, Polymer Science, Ser.A, Langrnuir-Blodgett Films of Novel Mesophase Siloxanes, 1996, 38(1), 4955. 25. N. Hagihara, K. Sonogashira, S. Takahashi, Linear Polymers Containining Transition Metals in the Main Chain, Adv. Pol. Sc., 1981, 4__!_1,149-186. 26. W.H. Atwell, Polymeric Routes to Silicon Nitride Fibers, in'Silicon Based Polymer Science', Ed. by J.M. Zeigler and F.W. Gordon Fearon, Advances in Chemistry Series, 1990, 224, 1990, Ch. 32. 27. T.H. Elmer and H. Meissner, Increase of annealing point of 96% SiO2 Glass on incorporation of Carbon, J. Am. Cer. Soc., 1976, 59, 206-209. 28. S. Jiang, Y. Yan and G.R. Gavalas, Temporary carbon barriers in the preaoration of H2l~ermselective silica membranes, Jr. Membr. Sc., 1995, 103, 211-218. 29. S. Sugawara, M. Konno and S. Saito, Gas Permeation through Siloxane of anodic aluminum oxide composite membranes at Temperatures up to 200~ Jr. Membr. Sc., 1989, 44, 151160. 30. K.C. Vracken, L.De Coster, P. Van der Voort, P.J. Grobet and E.F. Vansant, The role of Silanols in the Modification of Silica Gel with Aminosilanes, Jr. Coll. Interf. Sc., 1995, 170, 71. 31. K. Tate, H. Yoshida and K. Yanagida, Pitch for Production of Carbon Fibers, US Patent 4,670,129, 1987. 32. A. Mitropoulos, K. Beltsios, Th. Steriotis, F. Katsaros, P. Makri and N. Kanellopoulos, The combination of equilibrium and dynamic methods for the detailed structural characterisation of ceramic membranes, J. Eur. Ceramic Society, 1998, 1___881545-1558. , 33. H. Jarvelin and J.R. Fair, Adsorptive separation of propylene-propane mixtures, Ind. Eng. Chem. Res., 1993, 3__22,2201. 34. E.Magoulianiti, K.Beltsios, D.Davazoglou, G.Romanos and N.Kanellopoulos, Chemical Vapor Deposition of SnO2 films within the Pores of Vycor Substrates for the control of their Porosity, Proceedings of the Electrochemical Society, 1997, 97(25), 576-583. 35. (a) M. Egashira and Y. Shimizu, Odor Sensing by Semiconductor Metal Oxides, Sensors and Actuators, B, 1993, 13-14, 443-446, (b) P. Althainz, A. Dahlke, J. Goschnick and H.J. Ache, Low temperature deposition of glass membranes for gas sensors, Thin Solid Films, 1994, 241,344. 36. G. Charalambopoulou, K. Beltsios, E. Soterakou, N. Kanellopoulos and A.K. Stubos, 'Langmuir-Blodgett film-based structures as Stratum Corneum models', Proceedings (abstracts) of the Conference 'Drug Delivery for the 3rd Millennium', Pisa, Italy, 1999.
Recent Advances in Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) 2000 ElsevierScienceB.V. All rightsreserved.
435
Nanophase ceramic ion transport membranes for oxygen separation and gas stream enrichment C.G. Guizard and A.C. Julbe Laboratoire des Mat6riaux et Proc6d6s Membranaires, CNRS UMR 5635 Ecole Nationale Sup6rieure de Chimie 8, rue de l'Ecole Normale - 34296 Montpellier Cedex 5, France 1. INTRODUCTION Separation of oxygen from air or other oxygen-containing gas mixtures has become of increasing interest in a number of applications which range from small scale oxygen production equipements (oxygen generators for medical usage) to large scale production plants in combustion processes (oxygen enriched air), energy production (solid oxide fuel cells) or partial oxidation of light hydrocarbons (catalytic membrane reactors) [1 ]. Among the current methods used for oxygen separation and recovery, membranes has arised as a clean, efficient and economical mean of producing oxygen from gas streams. Dense inorganic membranes are of particular interest because of their high permselectivities compared to polymer membranes [2]. Only certain species, namely oxygen ions, are allowed to diffuse through these membranes and this can cause considerable effect on selectivity in separation of gas mixtures as well as on yield and selectivity in oxidation and partial oxidation reactions. Ceramic solid electrolytes dedicated to oxygen transport constitute an important category of membranes. The mobile species are anions and the flux of ions is driven either by an electrical field or by an oxygen pressure gradient. When an electrical field is applied for oxygen transport, the material is preferably electronically insulating whereas if the transport is pressure driven the material must be a mixed (electronic and ionic) conductor. Ceramic ion conducting membranes (CICM) now appear to be offering the best technological and commercial opportunities for oxygen separation applications. Most materials of interest to produce CICM are based on fluorite (AO2) or perovskite (ABO3) related structures. In dense ceramic membranes for which ion transport is via oxygen vacancies, the total flux of oxygen species is then determined by the sum of the bulk permeability and the reaction rate of the molecular oxygen at the interfaces of the membrane with the external gas phases. Many of conducting oxides have a sufficient ionic conductivity to allow their utilization as electrolyte, electrode material or membrane but at elevated temperatures (>800~ There is considerable interest therefore in preparing conducting oxide materials exhibiting novel compositions and/or ultrastructures, and leading to appropriate transport properties at intermediate temperatures. For example, the limiting magnitude of electrical conductivity and the high operating temperature (1000~ of fluorite based oxide ion conductors such as yttriastabilized zirconia (YSZ), is responsible for serious technological problems in solid oxide fuel cell (SOFC) applications. Decreasing membrane thickness is a way of increasing electrical conductivity but the surface reaction inevitably becomes rate limiting in this case.
436 Corrugation at membrane surface or asymmetric membrane structures, with porous interfaces and dense core, have been investigated with the aim of increasing oxygen surface exchange coefficient. A number of candidate materials with perovskite derived structures have been identified as being able to work at lower temperature but long-term reliability under real operating conditions has not been totally demonstrated so far. Beside the considerable increasing number of papers dedicated to CICM and related applications, the aim of this chapter is to provide an insight on the potential contribution of nanophase ceramics and metal/ceramic nanocomposites in the design and preparation of such membranes with higher oxygen transport permselectivity and lower operating temperatures. Current development of CICM can benefit by recent advances in material science, namely nanophase materials, with a number of properties unique to these systems. Nanophase ceramics are inorganic materials with typical microstructural dimensions of less than 100 nm. Such properties as extreme hardness and stiffness or superplasticity, high temperature resistance, chemical inertness and mechanically rigid porous architecture are inherent characteristics of these materials [3]. Moreover when the ceramic is formed of nanocrystallites of less than 10 nm, surface atoms become preponderant in the structure, yielding exacerbated surface adsorption and diffusion as well as catalytic properties towards gas phases. Regarding the specific properties of an arrangement of metal or semiconductor nanoparticles in the sub-10 nm range, charge transport obeys to the physical principle of single electron tunneling. All these aspects can be combined for the investigation of new membranes with oxygen transport properties, based on already described ion conductive ceramic compositions but also on new ceramic or composite metal/ceramic materials. Among affordable methods generally used for the preparation of nanophase materials, the sol-gel process is certainly the most adapted to the preparation of membranes. In the case of CICM a twofold advantage can be expected from sol-gel methods: an homogeneity of the material down to the molecular level due to the utilization of molecular precursors, and a coating process enabling the formation of continuous layers and active phases in one operation starting from the sol stage.
2. OXYGEN TRANSPORT MECHANISMS
2.1. General aspects CICM used in oxygen transport are usually defined as molecular gas tight structures and classified in two categories: solid electrolytes (SE) exhibiting sole ionic conduction and mixed ionic-electronic conductors (MIEC) [4,5]. In the first category, oxygen transport is electrically-driven thank to the presence of an external electrical circuitry with two electrodes on both sides of the membrane, Figure l a. They are known as solid electrolytes or as oxygen pumps able to deliver oxygen at a higher pressure than the air feedstock. This means that the applied potential across the membrane must exceed the back electromotive force arising from the partial pressure gradient of oxygen. In order to be used in electrochemical cells, which is the main application for such electrolytes, they must perform three critical functions: (i) separation of the reactants, (ii) blockage of any internal electronic current between the electrodes so as to force it all to flow through an external circuit, (iii) conduction of the working ions to provide the internal ionic current that must balance the electronic current in the external circuit.
437
Fig. 1. Different membrane concepts for oxygen separation: (a) solid electrolyte cell (oxygen pump), (b) mixed ionic-electronic conductor (MEIC), (c) asymmetric porous membrane with a graded porosity.
In the second category the driving force for overall oxygen transport is the differential oxygen partial pressure applied across the membrane. The flux of oxygen ions is charge compensated by a simultaneous flux of electronic charge carriers, Figure 1b. Compared to the former SE category, MIEC are of a greater interest for membrane applications, i.e. for thin supported membranes able to combine basic characteristics of MIEC and asymmetric porous membranes, Figure 1c, with expected applications in oxygen gas stream enrichment devices or catalytic membrane reactors for partial oxidation of light hydrocarbons. Oxygen transport in CICM consists in a conduction mechanism which occurs via oxygen vacancies. These anion vacancies can result of two types of structures, those obtained by aliovalent doping in fluorite-derived solid electrolytes (Figure 2a) like Zrl_xYxO2x/2 or the one incorporating intrinsic oxygen vacancies in the ceramic crystalline structure. This latter corresponds to enhanced electronic conductive fluorite compounds like pyrochlore A2B2OT, or to perovskite-derived structures (Figure 2b) like brownmillerite A2B2Os. Oxygen mobility in the former materials is not based on an order/disorder transition whereas it is a key parameter for the latter materials. Moreover a mixed ionic/electronic conductivity can exist in the perovskite related structures. It should be also noted that the presence of anion vacancies can introduce protonic conductivity due to water solubility in oxides [45]. Two main factors influence oxygen transport in CICM: the rate of solid state diffusion within the membrane (bulk transport) and the rate at which oxygen molecules can be converted in ionic species on one side of the membrane and recombined in molecular species on the other side (interfacial oxygen exchange) [6]. For the sake of comprehension on how the ultrastructure of the solid can influence oxygen transport performance in CICM, a brief description of these conduction phenomena is given in the following. A more complete insight of oxygen transport mechanisms can be found in a recent review and in the related references on dense ceramic membranes for oxygen separation [7].
438
S
t I
i-
s
O .... 0 .... , 0 I I
- - * ~
i ~ . . J
t
I" I "
9 S
S
~..j
1". I"
s S
,/ ~
- - -~'~
iLL
I
: ' I
S
S S
, f'~
J
I
,,
)
1
9
___."
S
k_J-i I I
r
" I ".
S
S
~.~
9
S
S
:. "1
S
S
' I
S
S
0,0"0"
I I I I I
I I I
'@'
I ! ! ! ! ! ! !
M 4+ (host cation)
0
M 2+ or M 3+(aliovalent cation)
0
Oxygen vacancy
0
i
I I
I
0 I i
___~
- - -(% I
0 2.
,
I
,
I
I ! ! -I=.
! ! I
! I ! . . . .
4 - -
0e
(a)
0
0
(b)
B (transition metal cation)
A (alkali, alkaline earth or rare earth ion)
s
Fig. 2. Representation of fluorite (a) and perovskite (b) related structures.
2.2 Bulk oxygen transport in ion conductive membranes In the case of doped fluorite oxides as yttria stabilized zirconia, the direct substitution of cations of appropriate size for the host lattice cation Zr 4+, not only stabilizes the cubic fluorite structure but also creates a large concentration of oxygen vacancies.
Y203
ZrO~ ; 2Yzr + 300 + Vo.
Then, comparing the total electrical conductivity o-with the oxygen ion conductivity o5, the condition for purely ion conductive ceramic oxide is an oxygen transport number t o nearly equal to one" to - o o/a
~ 1
439 The temperature dependence of the electrical conductivity cr can be empirically written as follows: o- T = A e x p ( - E a / k T ) A is a pre-exponential factor which accounts for such parameters as the jump distance of vacancies, an appropriate lattice frequency and the activation entropy of diffusion ASm. Ea is the activation energy of electrical conduction and is the sum of the mobility enthalpy Ann with the vacancy formation enthalpy AHf or vacancy/aliovalent cation association enthalpy AHA depending if a stoechiometric or non-stoechiometric fluorite structure is considered [8]. In a cubic oxide the conduction Cryfor anion vacancies can be written as: o-v = C~qv/z v where Cv is the number of anion vacancies per unit volume (cm3), and pv is the mobility of charge carriers with a charge qv. Pv = q D / k T where D, the vacancy diffusivity, is a function of the motional free energy AGm. D : D Oexp(- A G , n / k T ) with AG m =
A H
m
-
TAS m
Considering a general term AH, for the vacancy formation energy, Cv : Co e x p ( A H i / 2 k T ) the corresponding activation energy for vacancies can be written as: Ea = AHm + 89AHi Vacancies formation in fluorite oxides is normally achieved through doping with an aliovalent cation. Unfortunately the dopants act as trapping centers for the anion vacancies they create, and a trapping energy AHt ~ AHi exists for a temperature T < Ts, where Ts represents a saturation temperature for freeing the vacancies from the traps. In stabilized zirconia, for example, an activation energy Ea ~ 1eV corresponds to operating temperatures Top > 800~ A purely ionic conduction mechanism is not always the case in fluorite oxide-based electrolytes. A high electronic conductivity is mentioned in the literature [9] for ceria-based electrolytes CeO2.x. From a mechanistic point of view, ceria-based ceramics can exhibit a mixed conductivity due to oxygen ions, electrons and holes. The defect pairs between the oxygen vacancies and aliovalent cations have a great influence on electrical conductivity.
440
Thus the association enthalpy has been shown to be dependent on the relative radii of host and dopant cations. For example, the electrical conductivity of ceria doped with rare earth and alkaline earth oxides was found to be maximum when the radius of dopant ions was similar to the ionic radius of the host ion. A critical radius re was proposed which corresponds to the ionic radius of the dopant whose substitution for the host cation causes neither expansion nor contraction for the fluorite lattice. The critical radii re for divalent and trivalent cations as dopants in ceria correspond to 0.1106 and 0.1038 nm respectively. In the case of vacancies associated to aliovalent doping cations, the activation energy is the sum of the association enthalpy and mobility enthalpy. It is also noted that the activation energies of stoechiometric fluorite compounds are much higher than those of nonstoechiometric compounds and doped solid solutions. This can be understood taking into account the enthalpy of vacancy formation in the former compounds which has a larger value than the association enthalpy in the doped fluorite structure. In other respects, the maximum of the electrical conductivity and the minimum of the activation energy are not necessarily associated with the same dopant concentration, because the pre-exponential factor is also a function of the concentration. Considered now is the case of mixed conducting oxides where the flux of oxygen ions is compensated by a flux of electrons. This is the case of perovskite-related structures which can accommodate a variety of cations in their lattice yielding ceramic materials with intrinsic electronic and/or ionic conductivities. Moreover many of these ordered perovskite-derived structures disorder at elevated temperature and can exhibit high oxygen ion conductivity. According to the Wagner equation which assumes the oxygen bulk diffusion to be the rate limiting step, the interaction of molecular oxygen with the oxide lattice can be represented by the following equation:
1~2 02 + V~;* + 2e = Oo* Provided that at steady state no charge accumulation occurs and that chemical potential gradients of individual charged species can be converted into the virtual chemical potential of gaseous oxygen/Zo.' , the flux of oxygen Jo2 through the membrane can be written as:
1 J02
=
42F
O'elO'to n 2
V/./O 2
O'er +Orion
where F is the Faraday constant, O'el and o%,~ are the partial electronic and ionic conductivities, respectively. Integration of the former equation across the membrane thickness h leads to an equation in which oxygen flux is related to oxygen pressure gradient across the membrane ( P ~ = feed side oxygen pressure and Po~ = permeate side oxygen pressure):
R T l~~~ O'e;O'/o,, d l n 1)o,2 J02 = 42 f 2 h l.e4 Crel "4- O'ton
441 The integrated term (O'el O'ion)/(O'el +O'ion) is defined as the ambipolar conductivity O'amb of the membrane which is generally a function of oxygen partial pressure and may also be written as: O'am b = tio n tel O'total
tion and tet are the
transference numbers for ions and electrons, and O'total -- (Tel -[-C~ion.When the oxygen partial pressure is fixed at one side, measuring the oxygen permeability Jo2on the other side as a function P allows determination of O'amb (prrorP,) : 4 2F2h
RT
Crambaccording to the equation:
[ ~Jo~ ] L~ In P P'orP"=constant
These equations are valid only if the total oxygen transport is predominantly controlled by the bulk volume diffusion and if the diffusion along grain boundaries is negligible [10].
2.3. Interfacial phenomena associated with oxygen ion transport Oxygen exchange at the gas/membrane interface obeys to the following equations in relation with oxygen partial pressures at both sides of the membrane.
P'ga~
1~2
O2+Vo*+Ne---~Oo* II
?
II Oo* --, 1~2 o= + Vo** + 2e
~ P'~as
A simple model has been proposed in the literature that could illustrate what are the ratecontrolling mechanisms at the gas-solid interfaces [6]. This model incorporates interfacial (Re) and bulk (Ro) resistive terms, so that oxygen fluxes (current densities) through an equivalent dense membrane can be represented by the equivalent circuit shown in Fig. 3. Note that Ro is the sum of the solid phase bulk resistance Rb and grain boundaries resistance Rg.
Fig. 3. Equivalent circuit of resistive terms controlling oxygen flux through a dense membrane.
442 In this model the current density j satisfies the equation: j : ri/(R. + Ro)
in which the Nernst Voltage r/, the interfacial Re and bulk Ro resistive terms can be written as: RT 17 = --~- ' Re
RT 1 z F J e and R o
h cr
with z the charge number of the ion, cr the electrical conductivity and h the membrane thickness. The oxygen ion current in a dense membrane can be increased by reducing the thickness of the membrane until Re = Ro, from which a characteristic interfacial length Ld can be calculated, where Ld is determined by the ratio of oxygen self-diffusion coefficient D* (cm2.s l ) to oxygen surface exchange coefficient k, [1,9]. L a = D~/s
It is also useful to note that for most of fluorite and many perovskite oxide materials, Ld has often a value around 100gm. Considering oxygen exchange as the limiting step, membranes of less than 100gm thick will not be advantageous unless the value of ks can be specifically increased. Procedures to bring about this increase could involve : - the deposition of surface active species like nanoparticles of noble metals, - increasing the effective surface area using a graded porous surface layer. The concept of triple phase boundary (TPB) has been applied to CICM and MIEC graded porous layers, used as electrodes as well as electrocatalyst deposited on solid electrolytes, in order to describe oxygen exchange and fuel cell reaction mechanisms between the gas phase and the solid phase. The length of the TPB region is determined through microstructural considerations but its width has to be determined by the oxygen diffusion coefficient within the grains of the relevant oxide electrocatalyst. One example is how oxygen can be collected over the internal surface of a porous cathode structure, showing the importance of parameters such as pore sizes and distribution, tortuosity and pore volume fraction, together with the oxygen ion surface diffusion pathways [5]. 2.4. Contribution of n a n o p h a s e structures and porosity to charge t r a n s p o r t in ion conductive m e m b r a n e s
Taking into account the surface reaction limitation for oxygen transport in fully dense membranes, significant improvement in ionic oxygen transport can be expected from high surface area porous MIEC materials provided that gas diffusion into the pores is not predominant compared to ionic bulk diffusion. Then, a critical question is how under a given oxygen pressure drop across the membrane, the porous structure can affect the ionic conduction in the ceramic grains forming the solid phase. An interesting modeling approach on this question is described in ref. [ 11 ], considering a porous MIEC based membrane. This membrane consists in two symmetrical porous films acting as cathode and anode respectively and separated by a very thin dense interface. The
443 following assumption were made in this work: (1) the drop in chemical potential across the dense interface is negligible, (2) the chemical potential of the gas in the pores is constant, (3) the chemical reaction current results from the difference between the chemical potential of the gas and that of the ions and electrons at the MIEC-gas interface, (4) the porous structure is characterized by three parameters: the porous volume fraction ~b, the pore wall surface area per unit volume S and the tortuosity of the solid phase r~, (5) the pore dimensions are much smaller than the thickness h of the membrane. Moreover, three length scales were used in this model which allow to determine an optimum in membrane porous structure in relation with an enhanced ionic current in the solid phase: the aforementioned interfacial length Ld which determines the transition from diffusion limited to surface reaction limited transport in a non porous membrane, Lg for the variation in the chemical potential of the gas in the pores, and Lp for the equivalent width of the active region of the membrane. The lower is Lp, the higher is the current density across the membrane. In this model the assumption is made that h and Lg are greater than Lp at least by a factor of 3. On the other hand Lp for a porous membrane is given by the equation:
L, One can see that the enhancement in ion current increases with S 1/2. Results obtained with this model are reported in Table 1. They show that the ionic current can be increased by a factor of 77 compared to a dense membrane, in the case of fine grained structures with individual grain sizes d of about 30 nm.
Table 1 Calculated length scale Lp and ion current enhancement ImJls in porous membranes with Ld = 100~tm, 1 - ~b= 0.69, and rs = 1.16, for diffrent values of S and related grain sizes d [ 11 ].
S
d
Lp
ImJI=
(cm "1) 106 105 104 103
(~tm) 0.030 0.30 3 30
(~tm) 0.77 2.4 7.7 24
77 25 8 3
A schematic representation of a porous membrane based on this model is shown in Figure 4. It appears that a significant enhancement of ion current in the solid phase can be expected from a nanophase ceramic porous structure in which grain sizes are typically less than 30 nm. Another important concern is the lower limit for individual grain sizes in a porous MIEC membrane in order to maintain both ionic and electronic conductions in the solid phase. An answer to this question can be found considering nanocrystalline structures in gas-sensing [12] or catalyst materials [13]. In gas sensing materials based on metal oxide electrolytes, o~ygen is recognized by an electrochemical reaction taking place via three-phase contact between the solid electrolyte, a metal electrode (generally platinum) and the gas phase.
444
i i,.,,.
--.,.:z_,zr
I .,.]
10-20nm
individual grains r
80 ["
~
S = 106 cm -1
60
I p
!p,,
~
+h/2 -h/2
"0 p,>p,,
(a)
.~ 4 0
2 O-h~2
0
~ 0
+h/2
(b)
Fig. 4. Nanophase porous MIEC membrane; (a) schematic representation of the porous membrane cross section showing ionic oxygen transfer on both sides of the membrane under an oxygen partial pressure gradient P ' > 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
451 fluxes through dense SrCo0.sFe0.203-~ membranes were measured in the temperature range 620-920~ under various oxygen partial pressure gradients, showing a change in the apparent activation energy of overall permeation above 770~ which was attributed to the orderdisorder transition. The oxygen permeation mechanism in perovskite-based ion conductors is very complex and prediction of oxygen flux performance for practical use is not an easy task. For example the cubic perovskite La0.2Sr0.sCu0.4Co0.603-5has high electronic and ionic conductivity at high temperatures but tends to decompose when submitted for more than 400h to an oxygen partial pressure gradient above 950~ [46]. The systems (Bal_xSrx)2In205 and Ba2(Inl.xGa• were investigated by means of electrical conductivity measurements and dilatometry. The transition temperature Td was found to be related to a tolerance factor (t) = {(ro+rA)=v/2.t.(ro+r~)}, calculated from the ionic (r) radii in the ABO3-type structure" The tolerance factor is taken equal to 1 for an ideal perovskite structure. In the case of Sr2+ or Ga 3+ substitution, with (0 ___x < 0.2), Td linearly decreased as the tolerance factor approached 1 so that the substitution of Sr2+ in place of Ba 2+ heightened the order-disorder temperature whereas the substitution of Ga 3§ in place of In 3§ lowered the transition temperature [47]. In other respects characterization of oxygen transport in the pseudo-binary oxide LaCoO3-LaGaO3 suggested that introduction of Ga 3§ in the Co 3+ sublattice leads to insulating cobalt ions [48]. More recently, LaGaO3based perovskites were found to exhibit efficient ion conductivity, comparable with that of CeO2-based oxides. In particular LaGaO3 doped with Sr for La and Mg and Co for Ga have been pointed out to have very high ion conductivity. The power density for this electrolyte was claimed to be 0.77 W cm "2 at 800~ compared with 0.06 W cm -2 for YSZ at the same temperature [49]. The purpose here has not been to provide an extensive review of the numerous studies dealing with conductive perovskite-based materials but just to highlight the large variety of available oxide systems in this category of compounds. The major problem still present is that, as well as being stable against undesirable polymorphic transformations such as vacancy ordering, they must resist decomposition to other phases under reducing conditions. This is important for membrane application devices in which a low oxygen partial pressure exists in the permeate side of the membrane. It can be concluded from current works that though they are still very promising, until now these materials did not satisfy entirely the requirements on high ion conduction at low temperature and/or long-term stability under a reduced oxygen partial pressure.
3.3. Nanocomposite materials incorporating both ionic conducting and electronic conducting phases As mentioned before in Sections 3.1 and 3.2, it has been found very difficult to realize all the requirements attached to the production of highly selective oxygen semi-permeable dense membranes with one single component material. Another concept based on a composite material has been proposed in the literature [ 18,50,51 ]. The composite consists of two phases: one being an ion conductive material (ceramic electrolyte), the other being an electronic conductor (noble metal). According to the TPB concept the electronic conductive phase can also promote surface reactions. Such composite materials with uncoupled ionic and electronic conduction can be schematized by two interpenetrated percolative phases, as shown in Figure 9.
452
Fig. 9. Dual-phase membrane material with uncoupled ion and electron transports in two different phases.
According to this concept, YSZ/Pd dual phase composites were investigated showing a much larger oxygen permeability for a percolative composite (40 vol% Pd) than that of a non percolative composite (30 vol% Pd) [50]. Data were collected in the temperature range 900 to 1000~ The authors went to the conclusion that the viability of the dual-phase concept was proved in terms of electrical charge balance between the two phases though the limiting step of the process remained the transport of ions through the YSZ phase. A similar study was reported for a YSZ/Pt composite material [51] but the Pt content was far below the percolation threshold. Bulk and microporous YSZ/Pt materials were investigated by complex impedance spectroscopy in the temperature range 200-600~ in an oxygen atmosphere. This method provided the possibility to distinguish between bulk material, grain boundary and electrode polarization effects on electrical conductivity of the composite material. One important characteristic of these systems was the absence of surface area (< lm2/g) for the highly sintered bulk material while a high specific surface area was measured for the microporous system (140 m2/g at 500~ 30 m2/g at 1200~ The Pt-free YSZ bulk material was taken as the reference for conductivity measurements. In the highly sintered dense bulk system, Pt containing YSZ ceramics showed a lower overall conductivity compared to Pt-free samples. This has been explained by a blocking effect on ion transport of Pt particles which seems to increase drastically the grain boundary resistance of the samples. Simultaneously, a lower activation energy conductivity was found, which was attributed to oxygen adsorption equilibrium at the YSZ/Pt grain interfaces. The measured conductivities for all microporous samples was lower than for bulk samples but the Pt containing system exhibited an improved conductivity compared to its Pt-free counterpart. One reason put forward has been the highly dispersed Pt nanoparticles in the high surface area YSZ phase. These results are consistent with the conclusions of Section 2.4, which describe the contribution to charge transport of nanophase porous structures containing metal particles.
453 4. DESIGN, PREPARATION AND CHARACTERISTICS CONDUCTIVE CERAMIC OXIDE MEMBRANES
OF
OXYGEN
ION
4.1. Existing methods for membrane preparation Preparation of dense ceramic discs or tubes have been described as a convenient way for measuring oxygen permeation through dense oxygen permselective ceramic materials as well as for inserting them in membrane reactor devices. Those dense ceramics obtained by powder sintering are considered as bulk material, yet they are close to the situation of a self-supported thick membrane, Figure 10.
9 Pressed ceramm9 disc .
.
.
.
.
(a)
, i-
- ' ~ " --~
Extruded ceramic . mic ..................a tube _~~~'~',',~]_
I
Dense ceramic material. made of sintered grains
03)
Fig. 10. Flat (a) or tubular (b) oxygen ion conductive membranes with a dense structure obtained by powder sintering.
Dense membrane discs in the system Sr-Co-Fe-O have been produced by pressing and sintering of powders at high temperature. For example a perovskite powder was prepared by grinding and heating at 1000~ a mixture of Co and Fe single metal oxides with Sr carbonate (Co304, Fe203, SrCO3). Starting from this powder, 8 mm and 13 mm diameter discs with typical thickness of a few millimeters were formed and sintered at 1160~ [44]. Another study described the preparation of thick membrane tubes by plastic extrusion starting from perovskite powders in the system La-Sr-Fe-Co-O, using the following precursors: La(NO3)3, SrCO3, Co(NO3)2.6H20 and Fe203 [43]. In a first step, a tube in the green state was obtained by extrusion of a slip containing the powder and several additives (solvent, dispersant, binder and plasticizer). According to conventional ceramic heat treatments, the firing step was carried out with a slow heating rate up to 400~ in order to facilitate removal of gaseous species formed during decomposition of organic additives. After the organics were removed, a faster heating rate was used up to the final sintering temperature (1200~ at which material sintering was achieved within 5-10 hours in a stagnant air atmosphere. The tube dimensions were typically of 30 cm length, 6.5 mm in diameter, with wall thickness in the range 0.251.20 mm. One specific advantage of supported membranes, Figure l la, compared with the previously described thick membranes, Figure 10, is the possibility to attain a lower thickness. Actually, a thinner membrane has the potential to increase the permeation rate, depending on the kinetics limit of the oxygen surface transfer. Several approaches to thin film fabrication have been reported including vapor deposition techniques [52,53], sputtering [54], tape
454 calendaring [55,56], particulate suspension deposition [57,58], and the sol-gel process for which a detailed description is given in Section 4.2. Specific requirements must be answered for the successful preparation of CICM on porous supports: dense and defect-free membrane layer; chemical compatibility between the support and the membrane material; similar thermal expansion coefficients; and mechanical integrity of the entire system under thermal cycles. The following examples of CICM preparation illustrate major existing problems as well as novel appropriate methods to overpass these problems. In an extensive study, several methods for the preparation of supported membranes with the composition SrCo0.sFeOx were investigated [59]. Regarding the compatibility between the membrane and available porous ceramic supports, a-alumina supports were found to react with Sr-Co-Fe-O compounds at temperatures as low as 800~ whereas SrZrO3 was formed with zirconia supports. Among the tested supports, only MgO was found to be inert up to 1000~ In terms of thermal expansion coefficients, the values for the two materials are very close (- 14 x 10"6 ~ up to 1100~ and therefore, MgO was considered as an attractive support for Sr-Co-Fe-O based membrane compositions. Preparation of thin membranes ( - l g m ) was attempted from citrate or nitrate salt precursors. Casting solutions from these precursors were prepared with a film-forming appropriate viscosity. An excessive inner surface roughness for MgO supports has been pointed out as the main reason for unsuccessful crack-free membrane production. Another way has been to prepare thick supported membranes (30 to 100 gm) by a spray deposition technique from an aqueous slurry of Sr-CoFe-O powders. In fact densification of the membrane was difficult to achieve, due to the constraints generated by the support in the layer. Normally, because the membrane is bonded to the support, shrinkage is restricted to the direction perpendicular to the surface. Finally, a melting and recrystallization approach was evaluated on the supported films. The recrystallized film obtained after melting at 1500~ for 0.5 hour remained a pure phase, even though extensive cracking was observed. An original method has been proposed dealing with the preparation of dense hollow fibers and tapes of LaxSrl.xCoyFel.yO3.z using a standard manufacturing route for polymeric membranes based on a phase inversion process [56]. In this method, shaping is carried out by tape casting on a highly porous support or by a spinning technique. In a first step, a suspension of a polysulfone/ceramic powder mixture with a high ceramic powder content was prepared in N-methyl-2-pyrrolidone. The ceramic structure then formed by phase inversion in a water or isopropanol bath. The polysulfone was removed at 600~ for 1 hour, and the ceramic pieces, tapes or fibers, were sintered for 24 hours at 1225~ The final products were claimed to be nearly dense with the correct perovskite structure. Another way described as a suitable method to achieve fully dense and defect-free thin films on a porous substrate is the deposition onto a green substrate of very fine powder colloidal suspensions [57]. This so called "colloidal suspension technique" was used to form bilayer structures consisting of highly porous substrates and dense films of zirconia, ceria and perovskite mixed conductors (SrZrO3, SrCeO3, and La SrCoFeO3), suitable for gas separation, membrane reactors and SFOCs. Compatible materials for the dense electrolyte layers and the porous substrates were selected. Then, fabricating dense films of 5-40 gm was achieved by careful control of the sintering profile (shrinkage vs. temperature) and the magnitude of the shrinkage of the materials. It has been shown with such defect-free bilayer structures, that limitations can be shifted from the electrolyte to interfacial and charge transfer resistance as well as mass transfer polarization at high current densities. In the case of SFOC applications
455 the possibility to work at lower temperatures means systematic studies of altemative cathode materials and electrode microstructures.
Fig. 11. Schematic representation of an asymmetric supported membrane (a) and a composite infiltrated membrane (b).
A versatile concept based on porous infiltrated membranes, Figure 11b, has been discussed in the recent literature with the aim to develop affordable membrane reactor technologies [60]. Indeed these membranes, in which the material is deposited inside the pores of a robust porous support, have a good thermo-chemical resistance, a low sensitivity to the presence of defects, a sufficient thickness allowing the control of permeability, and are easily reproducible. A number of synthesis methods are adapted to the preparation of such composite infiltrated membranes. Among these methods, the chemical vapor deposition infiltration (CVI) revealed useful to prepare almost dense silica/~,A1203 composite membranes, highly permselective to H2 [61] and commercially available (Media Process Technology Inc). Nevertheless the CVI method should be difficult to apply to MEIC membranes with a perovskite-based structure as far as several precursors must be used simultaneously in the infiltration process and must yield the correct crystalline structure. The direct impregnation of a porous support with salt solutions has been reported in the literature for the synthesis of perovskites/otA1203 composite membranes used as combustor for volatile organic compounds [62]. However this method, when using multi-step impregnation, is not well adapted for a precise control of the composition in multi-component membrane oxide materials. The solvothermal synthesis can also be used for the direct growth of a crystalline material inside the pores of a porous support. Mainly used until now for preparing infiltrated zeolite membranes, this method could be of interest for ion conductive membranes. Finally the sol-gel process, as described hereafter, is also a very attractive, simple and versatile method for the preparation of supported ceramic membranes, in particular those resulting from an impregnation method.
456
4.2. New preparation methods by the sol-gel process Improvements expected for CICM can result from the utilization of porous nanophase ceramics as discussed in Section 2.4. In other respects, the sol-gel process has been proved to be a very efficient technique for the preparation of supported ceramic membranes. Two solgel routes can be used for preparing thin supported membranes [63,64]: one is based on colloid chemistry in aqueous media, the other relates to the chemistry of metal-organic precursors in organic solvents. Membrane processing by this method is generally achieved through four main steps as shown on the diagram provided in Figure 12.
SOL (colloidal particles in aqueous media)
SOL (inorganic polymers in organic media)
1 Sol deposition on a porous substrate
I
Gel formation
membrane coating I
Drying and firing at intermediate temperature (T < 400~
Material sintering
(T >_400~
~
removalof solvent.and organics membrane material consolidation
Fig. 12. The different steps involved in sol-gel processing of supported ceramic membranes.
457 The preparation of mesoporous zirconia supported membranes by the sol-gel process was reported some years ago [65]. More recently, it has been shown that nanosized individual grains can be obtained in catalytic materials and ceramic membranes using improved sol-gel techniques [66]. For example, one of the methods which were investigated [67] and later on used for the preparation of commercial ceramic nanofilters, consists in the utilization of organic sols containing nanosized metal oxide clusters stabilized by an organic shell made of acetylaceton ligands. Resulting ceramic nanofilters made of a microporous zirconia layer with individual grains of 6 nm, and supported on a porous ceramic substrate have been developed up to an industrial scale by ORELIS (Groupe Rhodia, France). The commercially available tubes are 120 cm long and 25 mm in diameter with a multichannel geometry. In relation with the preparation of perovskite-type ceramic materials, sol-gel derived nanophase crystalline structures have been described in the literature. A sol-gel method was used for the preparation of LaCoO3 starting from Co(Ac)2.2H20 and La203 dissolved in nitric acid [68]. After adding stearic acid, the sol was entirely dehydrated and cooled to ambient temperature to form a gel. On thermal treatment of the gel up to 900~ the perovskite structure formed at about 450~ and resulted in loose black well-crystallized ultrafine particles with sizes in the nanometer range (28 to 89 nm depending on the temperature). In an other work [69], a sol-gel process was developed for preparing thin films and fine powders of LaMnO3 with perovskite-type structure. Used precursors were lanthanum and manganese acetylacetonates dissolved in a mixed solution of methyl alcohol and ethylene glycol (or methyl alcohol and propionic acid) to give a spinnable organic sol. This sol was used to form thin supported films for which a perovskite-type lanthanum manganite phase was obtained at 450~ in the presence of polyvinyl alcohol additive. Here also the mean crystallite size at 480~ was as small as ca. 50 nm. It can be concluded that in both cases the sol-gel process considerably decreased the crystallization temperature of perovskite-type structures and yielded crystallites of less than 100 nm which is a typical intrinsic characteristic of nanophase ceramics. In spite of inherent electrical conduction problems attached to the reduction of Ce 4+ in Ce 3+, ceria-based materials are very attractive for oxidation catalysis and a number of their properties are of relevant interest for CICM applications. Apart from its 02 storing/releasing function used in Three-Way Catalysts (TWC), ceria is suggested to promote noble metal dispersion, to increase the thermal stability of host ceramic matrices like alumina, to promote the water gas shift and steam reforming reactions activity at the metal-support interfacial sites, and to promote CO removal through oxidation with lattice oxygens. A recent paper [60], reports on the preparation by the sol-gel process of a series of nanophase ceramic materials with a very high oxygen mobility in the system CeOz/AlaO3/CaO. Sol-derived materials were prepared from Al(OSBu)3, Ca(OMe)a and Ce(acac)3.xH20 precursors. Sol-to-gel transition was obtained by dissolving the precursors in hexylene glycol and then adding water for hydrolysis and condensation reactions. For some of the samples, a noble metal (1.5wt% Pd) was incorporated in the material by dissolving Pd(acac)2 directly in the sol. The gel was dried at 50~ under reduced pressure and thermally treated in air at 450~ and 700~ For a chemical composition of 0.25CeO2-0.65A1203-0.10CaO, XRD patterns showed an amorphous material at 450~ and a crystallized CeO2 phase at 700~ with no evidence of A1203 crystallization. Confirmation of the structural evolution with temperature was provided by HRTEM analysis. The material is totally amorphous at 450~ whereas a large number of CeO2 nanocrystallites with mean particle sizes of 4 nm and embedded in an amorphous alumina matrix, were detected at 700~ With ceria nanocrytallites of about 4 nm, the
458 proportion of surface atoms can be as high as 30 to 60% depending on the particle sizes distribution [3]. The H2-TPRd technique (see Section 4.3) was of particular interest for comparing oxygen mobility in this sample and in a reference sample in which the mean ceria particle size was 12 nm. After an oxidative heating pretreatment of the sample at 700~ the oxygen mobility was evaluated by measuring the consumed H2 during a reducing heat treatment. For all samples the presence of Pd particles was necessary to clearly observe oxygen exchange with the materials. The extremely high oxygen mobility observed in Figure 13 for this type of material, compared with its reference counterpart, is attributed to the number of surface atoms significantly larger than in the reference sample (15-30%). As suggested in Section 2.4, it can be expected that such porous thin solid film electrolytes with a large inner surface and incorporating highly dispersed noble metal particles accessible to gas phase, would allow a higher oxygen reaction rate and an enhanced oxygen conductivity, especially at low temperature.
H 2 consumption (~tmol H2/g) 2.6. /~ b) Mean CeO2crystallite 2.2. ,~ size = 4 nm 1.81.4 ~ 1.00.6" 0.2~
f:
~ , \
100
a) Mean CeO2crystallite size= 12nm
200
300
400
500
600
700
Temperature(C) Fig. 13. TPR spectra of two CeO2-A1203-Pd samples dispersed in amorphous alumina. Mean ceria crystallite sizes at 700~ 9a) 12 nm, b) 4 nm.
If different preparation ways of sol-gel derived MIEC ceramic powders have been described in the literature, only a few attempts concern the preparation of supported CICM by the sol-gel process. One example is the utilization of the sol-gel polymeric route to fabricate supported thin porous layers (ca. 300 nm) of the perovskite-type La0.3Sr0.7CoO3.~ [70]. A spincoating technique was used for casting the layer on porous or- and T-A1203 disc shaped supports. The main phase formed upon heating in air above 400~ was cubic perovskite, although traces of SrCO3 and of an unknown phase were observed up to 800~ Above this temperature, limitation in the utilization of these membranes arose from strong chemical interactions occurring between the deposited perovskite layer and the alumina support. The sol-gel process has also been described as a suitable method to deposit a thin doped zirconia interfacial layer (0.850 ZrO2 - 0.110 Sc203 - 0.004 A1203) on a ceria sheet (Ce0.sGd0.202-d) [71]. The role of the thin interfacial film was to overcome the problem of instability of ceria in a reduced atmosphere. In such a case, the film has to be as thin as possible in order to retain
459 the low ohmic loss in the electrolyte. The sol-gel process was used because it provides a simple coating method able to achieve submicronic film thicknesses. Nevertheless this kind of interfacial very thin layer can not be considered as a membrane. In fact two major problems have to be solved for a successful utilization of the sol-gel process in supported CICM fabrication. One is the choice of porous supports which have to keep chemically inert towards the deposited conductive material in a large temperature range, the other is the possibility to achieve thicker supported layers (> ~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.
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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 (<10 ~tm thick) of a nanoporous carbon film supported on (a) a mesomacroporous inorganic solid or (b) a carbonized polymeric structure. The typical effective pore diameters of these membranes (3-10~) are comparable with the size of the gas molecules being separated. The surface chemistry of the carbon pore walls can be complex, ranging between non-polar to highly polar. Thus, the gas molecules diffusing through the nanopores are essentially adsorbed on the pore walls and the transport is caused by surface diffusion under a chemical potential gradient across the pore. The following sections review the published literature on NCM in the areas of (a) classification of membrane structures and gas transport mechanisms, (b) membrane preparation, (c) data representation for gas separation, (d) relative advantages, (e) applications, (f) molecular engineering, and (g) pore size determination.
476
illli
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4
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"~,...
IIII!
II1'
2 - Tetrabromo
Bis A polycarbonate
].., ]..,
I!111
]...
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1 - Poly(triazole) 3
v
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III
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I.:
'
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3 - Polypyrrolone 2
94 - P o l y ( t e r t - b u t y l
.
acetylene)
.
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,
6 - MSC
Membrane
(9)
!II ......
100 .,.I.,.I !111111. ,,1.,,I I! Iiilt. ,.1.,.I II llllJ'. ..... 10-1
2
3
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2
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101
2
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10 2
2
1!
3
10 3
2 3
10 4
Po2 ' Barrer Figure 1 Example of 0 2 permeance - O2/N2 permselectivity relationship for polymeric membranes.
GAS TRANSPORT THROUGH NCM The basic modes of gas transport through the nanoporous carbon membranes are described by Figures 2a and 2b. They show cartoons of idealized carbon pores which selectively permeate some components of the feed gas mixture through them. The feed gas is passed over one side of the membrane at a relatively high pressure (pH) while the other side of the membrane is maintained at a relatively low pressure (pL). Two different situations may arise: (a) If the pores of the carbon membrane are smaller than some of the feed gas molecules, then only those molecules which can enter the pores are selectively adsorbed on the pore walls at the high pressure side. The adsorbed molecules then diffuse on the pore surface to the low pressure side where they desorb into the gas phase. The separation of the gas mixture, in this case, is primarily caused by the differences in the molecular sizes of the feed gas components, and the smaller molecules of the mixture are preferentially permeated through the membrane. Figure 2a schematically depicts that situation. The smaller molecules (component B) preferentially diffuse through the carbon pores over the larger molecules (component A). These membranes are called the Molecular Sieve Carbon (MSC) membranes in the literature [9-12].
477 (b) If the pores of the carbon membrane are larger than the diameters of the feed gas components, then the larger and/or the more polar molecules of the mixture are selectively adsorbed on the pore walls at the high pressure side. The adsorbed molecules then selectively diffuse on the pore surface to the low pressure side where they desorb into the gas phase. The separation of the gas mixture, in this case, is primarily caused by the differences in the molecular size, polarizability and the polarity of the feed gas molecules. Consequently, the larger and the more polar molecules of the mixture are more selectively adsorbed by the carbon pores and they are preferentially permeated through the membrane. Furthermore, the more selectively adsorbed molecules can hinder the flow of the less selectively adsorbed molecules through the void space between the pore walls (if any). Figure 2b schematically depicts that situation. The larger and the more polar molecules (component A) of the feed mixture selectively permeate over the smaller and less polar molecules (component B). These membranes are called the Selective Surface Flow (SSF) membranes in the literature [ 13-20]. Clearly, the effective pore diameters of the MSC membranes (3-5A) will be smaller than those for the SSF membranes (5-10A) because most gas molecules of separation interest have molecular diameters between 2.5-6.0A. In practice, a distribution of pore sizes may exist in the carbon membranes, and one of the above described gas transport modes may be predominant. However, the pore size distribution must be very narrow for the membranes to be effective for practical gas separation by either modes. A critical requirement for successful use of these membranes is the absence of even a minute fraction (ppm) of larger pores (>30A) in their structure which can make the membrane "leaky" and destroy its separation selectivity. ,=,.
A-rich 9" Product \
; : ":
B-rich Product
./..
0 Pore
9 0
0
~
\Carbofi\
High Pressure
0
Pore
9 9
o-B
(a)
] ~IP ~I~ ~i~~
A-rich Product
9
Low Pressure
O-A
] B-rich ~ ~:{ [ Product ~\ \ , 1
HighPressure
LowPressure
O-A
0. B
(b)
Figure 2 Schematic mechanisms of gas transport through Nanoporous Carbon Membranes: (a) MSC Membrane, (b) SSF Membrane.
478 By the same token, the presence of intermediate size pores (10-30A) in a SSF membrane will introduce a significant quantity of Knudsen flow through the void space of these pores. Since Knudsen selectivity for gas separation is generally meager, these pores can suppress the overall selectivity of separation [30-33]. The actual mechanism of transport of the adsorbed molecules on the carbon pore walls is activated surface diffusion (hopping). It is driven by the chemical potential gradients of the adsorbates across the thickness of the membrane, and the surface diffusivities of the adsorbates are exponential functions of temperature. The concentration dependence of the surface diffusivities of the adsorbates can be complex functions of adsorbate loadings [30-33].
PREPARATION OF NCM Both the MSC and the SSF membranes are produced by carbonization of polymeric substrates. This is achieved by heating the polymer under vacuum or in presence of an inert gas. However, different polymeric substrates, carbonizing temperatures and conditions, and heating and cooling protocols are used for production of these membranes. Both types of membranes are subjected to activation or passivation processes by exposure to O2, air, CO2, etc. at various temperatures after the carbonization steps. The properties of the final NCM product obviously depend on the art of its manufacture. MSC Membranes Koresh and Soffer successfully prepared a MSC membrane in the hollow fiber configuration by pyrolysis of a thermosetting polymer composed of cellulosic or phenolic resins as well as poly-acrylonitrile [9-11 ]. Different types of MSC membranes were produced by varying the preparation conditions. The resulting membranes selectively permeated the smaller components of a gas mixture, for example, 02 from N2, He from N2, Hz from CH4, CO2 from N2 or CH4, C3H6 from C3H8, and N2 from SF6. More detailed separation characteristics for some of these mixtures are given in Table 1. MSC membranes of different pore diameters could be produced by heat treating the membranes at different temperatures. Figure 3 shows the pure gas permeabilities of Ha and CH4 through a MSC membrane as a function of heat treatment temperatures. The permeabilities of both gases go through maximum values at a temperature of 600-650~ [ 10]. Koros and coworkers prepared a MSC membrane by carbonizing an integrally-skinned asylnlnetric hollow fiber membrane made of a polyimide [21,25]. The properties of the final product depended on various factors such as carbonization temperature, carbonization conditions (vacuum or inert gas purge), nature of inert purge gas and its flow rate, etc. These membranes also selectively permeated the smaller molecules of a gas mixture, for example, 02 from N2, CO2 from CH4 and N2, and Ha from CH4. Table 1 gives the separation characteristics for these membranes. These authors studied air separation by their MSC membranes in much detail [25] and found that (a) carbonization under vacuum produced a MSC membrane with higher O2/N2 selectively but lower 02 permeability than the membrane
479 produced by carbonization under inert gas purge, (b) higher purge flow rates produced a membrane with larger O2 permeability but lower O2/N2 selectively, (c) higher pyrolysis temperature produced a membrane with larger O2/N2 selectively but lower 02 permeability (presumably because of smaller carbon pores). There was, however, a substantial variation in the membrane performance from batch to batch of production. The O2/N 2 separation performance was deteriorated by the presence of H20 in the air feed [23]. It was found that the negative effect of moisture in feed air could be reduced by coating the MSC membrane with a thin layer of a hydrophobic polymer such as teflon [24]. It was also found that the performance of the MSC membrane for O2/N2 separation was severely reduced (lower 02 permeability and O2/N2 selectivity) by the presence of trace hydrocarbon contamination such as vacuum pump oil in the feed air [22]. However, the properties of the membrane could be largely restored by flushing them with gaseous propylene [22]. Table 1. ,,Examples of Separation., Characteristics of MSC Membranes. Feed Pressure (atm)
Temperature (~
02 (1) + N2 (2)
3.7 1.0
25.0
0.21 -
H2 ( 1 ) +
2.4
-
0.50
28.0 4.4
50.0 80.0 -
0.50 0.50
28.0 1.0
50.0 25.0 65.0 35.0 -
0.10 0.50
Gas Mixture*
Feed Pensn_.eance (P/f) of C_omposition .Component .!,,** (yl) (GPU)
CH4 (2)
CO2 (1) + CH4 (2)
-
C3H6 (1) + 9 C3H8(.2) .... Air(l)+ SF6 (2)
-
......
16.0 3.6 P = 0.17 GPU-cm (1700 Barrer)*** 168.2 365.5 -1000 180 60 91 -35 -~7.3 -1190 (?)_ 4.2 183 365
_~_~12
Reference
13.6 10.0 7.1 ...... 450 500 200 630 175.3 50 28 163.3 20.0 25.0 12-15 >1000
21 29 9 21 12 26 27 21 12 26 29 28 37 12 12
*Component 1 is smaller and selectivelypermeated. **1 GPU (Gas PermeationUnit) = SCC/(cm2,S.cmHg) x 10-6 ***1 Barrer = SCC-cm/(cm2.S,cmHg) x 10"1~ Tanihara, et al. also produced a MSC membrane by pyrolysis of an asymmetric polyimide hollow fiber [26]. The membrane selectively permeated H2 from CH4 (Table 1). The presence of trace amounts of toluene (7500 ppm) in the feed gas did not affect the membrane performance over a long test period. They observed a qualitatively similar effect of heat treatment temperature on the membrane performance as shown by Figure 3 [27].
480
Morooka, et al. prepared a MSC membrane by coating the outer surface of a porous alumina support with a BPDA-pp'ODA polyimide film and carbonizing the polymer at 600-900~ [28]. The membrane selectively permeated CO2 from CH4 (Table 1). Figure 4 shows the permeance (Pi/g ) of various pure gases through this MSC membrane at 65~ The molecular sieve nature of the membrane is clearly demonstrated by the fact that pure gas permeance decreases as the molecular size of the gas increases. The figure also shows that subsequent mild oxidation of the MSC membrane with O2 (300~ for 3 hours) increases the pore size, which increases the permeance of all gases through the membrane while retaining a very narrow pore size distribution, so that the MSC characteristics are still exhibited. Prolonged exposure of the membrane to air at 100~ slowly decreased the permeance of several gases through the membrane but they were restored by heating it in N2 at 600~ for 4 hours.
0.9 24
0.8
22
0.7
2O
L_
,..
i.._
t~
m t'N
L.
0.6
18
~[II L.
r
0.5
16
,.,,
0.4
14
~
0.3
12
0.2
10
0.1 300
400
500
600
T, ~
700
4=-800
Figure 3 - Permeabilities of pure H2 and CH4 through a MSC membrane produced at different heat treatment temperatures: open circles - CH4; closed circles - H2 Centeno and Fuertes [29] prepared a MSC membrane by pyrolysis of a phenolic resin (Novolak) supported on a macroporous carbon substrate (pore size 1 pro). The membrane had a thickness of--2 gm and the estimated pore openings were 4.2A in diameter. It exhibited selectively of separation of 02 from N2 and CO2 from CH4 and N2 (Table 1). The pure helium permeance through the membrane as a function of pyrolysis temperature exhibited a behavior similar to that shown by Figure 3 and the permeances of various pure gases through the membrane exhibited a behavior similar to that given by Figure 4, confirming that it was a MSC membrane.
481
He
"C4Hlo
CO.
F6
10 "6 10 .7 A
"T, C"
!
10 a
(I,1 o,1" L_
r
1 0 -9 v
E
I. 1 0 "10
1 0 "11
%. 0.2
0.3 0.4 0.5 0.6 Kinetic Diameter (nm)
Figure 4 - Permeance of various pure gases through a MSC membrane at 65~ 9 closed circles - fresh membrane; open circles - oxidized membrane.
SSF Membranes The selective surface flow (SSF) mechanism of transport of the components of a gas mixture through a porous carbon matrix was originally demonstrated by Barrer and coworkers [30-33]. They used a compressed cylindrical plug of non-porous carbon black particles with interparticular void pore diameters of at least 20-85A. Thus, a significant fraction of flow across the plug was through the void space (Knudsen flow) which reduced the overall transport selectivity for separation of gas mixtures. Recently, a new class of nanoporous SSF carbon membranes was produced by Air Products and Chemicals, Inc. of U.S.A. by (eL) coating the bore side of a porous alumina tube (<1 ~tm pore diameter) with a layer of polyvinylidene chloride-acrylate terpolymer latex containing 0.1-0.14 gm polymer beads in an aqueous solution (4 wt % solid), (b) drying the coat under N2 at 50~ (c) pyrolysing the film under a dry N2 purge at 600~ and (d) passivating the nascent carbon film by heating in an oxidizing atmosphere at 200-300~ Only a single coat of the latex and a single heating step were used [ 13-16]. The resulting carbon membrane was 2-3 gm thick containing a very narrow distribution of 5-6A pores [ 15].
482 The membrane selectively permeates the larger or more polar molecules of a gas mixture, for example, C2-C4 hydrocarbons from H2, CO~ from H2 and CI-I4, and H2S from H2 and CH4. Extensive data for separation of these mixtures are published in the literature. Several examples will be given in later sections. Table 2 shows the pure gas permeabilities of H2, CH4, C2H6, C3Hs, and C4H10 through a SSF membrane of 2.5 ~m thickness supported on a macroporous graphite sheet having 0.7 ~tm pores [ 13]. It also shows the component permeabilities from a gas mixture of hydrogen and hydrocarbons. These permeabilities were calculated using the definition given by Equation (1). It may be seen that the permeabilities of the most weakly adsorbed components (H2 and CH4) are drastically reduced in the presence of the higher hydrocarbons compared to their pure gas permeabilities. The most selectively adsorbed component (C4H10)permeates through the membrane at a very high flow rate from the mixture followed by C3H8and C2H6. In other words, the order of permeabilities of the hydrocarbons follow the order of their strength of adsorption on the carbon. Consequently, the selectivities of separation of ChilI0 and C3H8 over H2 by the SSF membrane are very high. These selectivities are far different from those obtained by ratios of pure gas permeabilities which demonstrates the role of competitive adsorption and surface diffusion in determining the separation performance of the SSF membrane. It should be recognized that C3H8 will be the most selectively adsorbed component in absence of CaHI0 and the permselectivity between C3H8and H2 will be much larger than that given by Table 2 in such a case. Similarly C2H6-H2 selectivity will be higher than that reported in Table 2 if the higher hydrocarbons were absent. Another key observation from Table 2 is that the adsorption of higher hydrocarbons effectively blocks the permeation of H2 through the void space (if any) in the carbon pores. Finally, the data of Table 2 demonstrates that the conventional approach used for design of polymeric membrane systems (component permeabilities from mixtures are equal to those for pure gases) cannot be used for designing SSF membrane systems. This point will be elaborated in the next section. DATA REPRESENTATION FOR GAS SEPARATION BY NCM Table 2 demonstrates that the separation characteristics of a NCM cannot be easily described in terms of pure feed gas component permeabilities (Pi) and ideal permselectivities ((xij) as in the case of most polymeric membranes. Due to selective adsorption on carbon walls, these properties depend on (a) the local gas phase partial pressures of the components at the high and low pressure sides of the membrane, (b) the corresponding multicomponent adsorption equilibria on the carbon wall, (c) the multicomponent surface diffusities of components on the
483 Table 2. Permeabi!ities Qf Hydrogen and Hydrocarbons Through a SSF M embra13e at 295 K
Pure Gas Permeabilities (P~ (BaiTers)
Mixture Permeabilities (Pi)* (Barrers)
H2
130
CH4
Components
Permselectivity (PHydrocarbon/PH2) Pure Gas
Mixture
1.2
1.0
1.0
660
1.3
5.1
1.1
Cat-I6
850
7.7
6.6
6.4
C3H8
290
25.4
2.3
21.2
C4H10
155
112.3
1.2
93.6
*Gas composition in high pressure side" 41.0% H2, 20.2% CH4, 9.5% C2H6, 9.4% CsHs, and 19.9% C4H10;PH = 4.4 arm, pL = 1.0 atm
wall, (d) hindered diffusion of smaller molecules through carbon pore void space, (e) extent of molecular sieving at the high pressure side carbon pore mouth, and (f) heterogeneity of the carbon membrane structure, etc. These properties vary along the length and thickness of a practical membrane and are generally not known. We, therefore, recommend the use of overall rejection (130 and recovery (oti) of component i of the gas mixture of the system, as defined by Figure 5, for describing the gas separation performance by NCM. The rejection of component i is given by the fraction of that component (relative to feed gas) leaving the membrane at the low pressure side. The recovery of component i is given by the fraction of that component (relative to feed gas) leaving the membrane at the high pressure side. All flow rates and gas compositions for the membrane system of Figure 5 can be defined by experimentally specifying 13i as a function of c~i of a key component, the feed gas conditions and its flow rate, and pH and pC [ 16]: H~h Press.ure Side: P yF(1-13i) "~ = Z yF (1- I~i ) ; yiP = Z--~iFi1 :13~)
(6)
Low Pressure Side: W yiZl3i F - 1-2Y~'(1-13i) ; yW = 1-2yV(1-13i)
(7)
484 Equations (6) and (7) assume that there is no low pressure purge used in the system. The only other experimental variable needed to completely define the system is (A/F) as a function of ~i of the key component for a given pH, pL, and y~ [19]. This relationship provides the membrane area (A) needed for a given separation. All published data for gas separation by SSF membranes used the above described protocol (14-20). Figure 6 shows an example for separation of CO2 from a mixture with CH4 and H2 [ 19]. The more polar (although not the largest) CO2 molecules were selectively adsorbed over CH4 and H2 on the SSF membrane and they preferentially permeated through the membrane. The selectivity for CO2, however, was not infinite. Thus, a CH4 + H2 rich gas stream was produced as the high pressure effluent gas and a CO2 rich gas stream was produced as the low pressure effluent gas. The figure plots experimentally measured 13co2 and 13CH4 values as functions of c~H2 for a feed gas containing 52% CO2 + 37% H2 + 11% CH4 at 20~ and pL values were, respectively,-3.0 and 1.0 atmospheres. values as functions of ~t r~2 9
The pr~
The figure also plots (A/F)
All published data for gas separation by MSC membranes, on the other hand, report permeabilities and permselectivities analogous to those for the polymeric membranes (Table 1) despite the fact that even pure gas permeabilities through these membranes can be strong functions of gas pressures due to adsorption on the carbon surface. Figure 7 plots the pure gas permeabilities of He, 02, Ar, H2, CO2, N20, and CH4 against the average pressure applied across a MSC membrane [10]. The permeabilities for the weakly adsorbed gases (He, O2, Ar, and H2) do not show any pressure dependence. However, the permeabilities of the more strongly adsorbed gases on the carbon (CO2, N20, and CH4) show that Pi substantially decreases with increasing [(pH + pL)/2]" This behavior can be easily explained by assuming a Langmuirian adsorption isotherm on the carbon for these gases. It can be shown [10] from Equations (1) and (3) that for a pure gas obeying the Langmuir adsorption isotherm [C = aP/(1 + bP)] and having a constant surface diffusivity (Di), the permeance (Pi) would be independent of pressure in the Henry's law region [C = KP] of the adsorption isotherm (case for He, 02, Ar, and H2) and Pi should decrease with increasing pressure in the nonlinear region of the adsorption isotherms (case for CO2, N20, and CH4). The variables a, b, and K are constants. Consequently, one cannot describe the separation performance of these gases through the MSC membrane using a single value of Pi or otij. The data of Figure 7 is also a proof of the adsorption-surface diffusion mechanism of transport through the MSC membrane pores. RELATIVE ADVANTAGES OF NCM The unique mechanisms of gas transport through the NCM provide the following practical advantages" (a) The fluxes of migrating molecules through the NCM can be very high because the energy barriers for surface diffusion of molecules on carbon are relatively low compared to those for
485
Membrane Area - A Ceramic Support
,--SSF \ Membrane
....
C "11 FeedGasatP [ _ . . _ ( M FHC ) . . . , . I ~~ ....... ~, ~ r-low Hate, J~II To GC Mole Fraction, ~yF
"~
Membrane Holder
i ' "" i'"-' L Low Pressure Effluent at pt. Flow Rate, W Mole Fraction, Yi*
Recovery of Component i = PyiP/Fy~= ai Rejection of Component i = Wy~'/FyF = 13i Area per Unit Feed Flow = A/F i
ii
iii
ii
High Pressure Effluent at pH Flow Rate, P Mole Fraction, y~
o~ i + 13i = 1
iiii
Figure 5 - Schematic drawing describing the separation characteristics of a NCM.
1.0 l
pH - 30 psig pL- 1 psig
.8
\
~-_ 0.6
20
l
\
A/F " " ' . r ~ ~ \ CH
J
10
O
E
0.4 0.2 00
Feed: 0
0.2
LL 0
0
0.4
0.6
0.8
1.0
0
(ZH2 Figure 6" Separation characteristics of SSF membrane for CO2-CH4-H2 gas mixture (52% CO2, 37% H2, 11% CH4).
486
4
,-
10
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I
1.4
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t_ L.
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6
~"
4 I
,
L. (9 t_
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a.
1.2
0.6 ~ " 13. 0.4
Lilt v
2
0.2 0
1
2
3
4
5
6
A v e r a g e Pressure A c r o s s Membrane, x 10 3 Torr 13 r
~
1 1 r ~
~
9r
~
7r
- 3.0 "
CH4
N20 1
2
3
r
2.0
~,
L_
1.5
co2
- 1.0
r
0
- 2.5
4
5
6
A v e r a g e P r e s s u r e A c r o s s M e m b r a n e , x 10 3 Torr
Figure 7: Permeabilities of various pure gases through a MSC membrane as functions of average pressure across the membrane.
transport of gases through a conventional polymeric matrix. This eliminates the need for having ultra thin membranes. (b) The selectivity of separation by the MSC membrane is based on size difference between the feed gas molecules relative to the carbon pore size, and that by the SSF membrane is based on (i) size, polarizability and polarity differences of the feed gas molecules, (ii) relative surface diffusivities of the adsorbed molecules, and (iii) hindered diffusion of less strongly
487 adsorbed molecules through the void space. These interactions between the migrating molecules and the carbon pores can provide very high selectively of separation. (c) A combination of properties (a) and (b) can simultaneously provide a high selectivity and high flux for the transport of selectively adsorbed components, thus breaking the barrier imposed by polymeric membranes. (d) The SSF membrane can be operated using a relatively low value of P~ and a near ambient value of pL because the true driving force for the transport of a gas through the pores of a SSF membrane is determined by its specific adsorbate loading gradient across the membrane. A large adsorbate loading of the selectively adsorbed component of feed gas mixture can be achieved at a relatively low value of pH. In contrast, the gas solubility in a polymer matrix is generally a linear function of its pressure which requires a relatively larger value of Pn for the polymeric membrane to be efficient. (e) The high pressure effluent gas from a SSF membrane system is produced at the feed gas pressure and it is enriched in the smaller or less polar molecules (less selectively adsorbed) which often constitutes the desired product. Thus, the need for product gas recompression (required by a polymeric or MSC membrane) is eliminated. (f) The NCM can be operated at higher temperatures, can be tolerant to corrosive atmospheres, and its separation properties can be altered by molecular engineering (controlling pore size and surface polarity of the carbon). A comparison between the separation performance of the SSF membrane and a polymeric membrane (glassy polytrimethyl silylpropyne, PTMSP) was carried out for production of H2 enriched gas from a fluid catalytic cracker (FCC) off gas containing 20% H2, 20% CH4, 8% C2H4, 8% C2H6, 29% C3H6, and 15% C3H8 [16] because of their similar permeation characteristics. The feed gas was available at a pressure of 3.0 atmospheres and at ambient temperature. The separation objective was to reject the hydrocarbons through the membrane and produce a H2 enriched gas with high H2 recovery. Both the SSF and the PTMSP membranes were formed on identical macroporous alumina supports. Both membranes selectively permeated the hydrocarbons over H2. Figures 8a and 8b show the hydrocarbon rejections as functions of H2 recovery for the SSF and the PTMSP membranes, respectively. They show that much higher rejections of C2-C3 hydrocarbons can be achieved by the SSF membrane than the PTMSP membrane for any given H2 recovery. Table 3 compares the performance of these two membranes for a H2 recovery of 60%. It shows that a H2 enriched gas containing much less quantities of the heavier hydrocarbons can be produced at the feed gas pressure by the SSF membrane compared to that by the PTMSP membrane. This demonstrates the superiority of a SSF membrane over a polymeric membrane for the separation of interest. A comparison between the potential separation characteristics of a MSC membrane and the polymeric membranes is shown by Figure 1. The MSC membrane can offer a much larger permselectivity for 02 over N2 [9] while retaining a very large 02 permeability.
488 Table 3. Comparative Separation performance of SSF a,nd P.TMSP Membranes for FCC Offgas. at a Hz Recovery_ of 60%
Gas Components
Component Rejections SSF PTMSP
High Pressure Product Compositions (%) SSF PTMSP
C3H8
98.2
86.0
1.16
6.33
C3H6
98.8
86.0
1.49
12.20
C2H6
94.1
76.0
2.30
6.33
C2H4
93.3
72.0
2.03
5.79
CH4
52.0
46.0
41.46
32.73
H2
40.0
40.0
51.56
36.19
APPLICATIONS OF NCM Several interesting applications of the MSC membranes are proposed by the Carbon Membranes LTD of Israel [12] who manufacture a hollow fiber MSC system. These include (a) removal of SF6 from air, (b) separation of CO2 from a mixture with CH4 such as landfill gas, (c) production of 02 enriched air, (d) separation of C3H6 from C3H8 which is a difficult distillation problem in petrochemical industry, and (e) separation of H2 from CH4. Table 1 reports the published performance data for these separations by the company. It may be seen that the MSC membrane offers very attractive permeance and permselectivity for the smaller component of all of these mixtures. However, the product gas (low pressure effluent from membrane) may require recompression if the smaller component constitutes the desired product. The SSF membrane has been tested for several potential industrial applications by Air Products and Chemicals, Inc. of U.S.A. [20]. They include (a) recovery of H2 from refinery waste gases, (b) recovery of H2 from Pressure Swing Adsorption (PSA) waste gases used in purification of H2 from Steam Methane Reformer (SMR) off-gas, and (c) separation of bulk H2S from H2 and CH4. Refinery waste gases typically contain low purity Hz (15-40%) in conjunction with bulk amounts of C2-C4 hydrocarbons. The gas pressure is generally low (3-10 atmospheres). Consequently, it is not economic to extract H2 from such a stream and it is burnt to recover its fuel value. The SSF membrane can enrich H2 from such a stream by rejecting most of the higher hydrocarbons (C3-C4). The Ha enriched stream which is available at feed gas pressure
489 100 O
= m
90 80
m ~
o m
o
70 A Propylene
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i
Ill
I
Ethylene
O Ethane
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IIIIL
Propane
9 Methane
......... 30 35
40
45
50
55
60
65
70
75
% Hydrogen Recovery (a) 100 90
0 "~"
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o
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o
mmm=
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Porpanm Ethyle:e
50
() Ethane
40 30 30
35
40
45
50
55
60
65
70
75
% Hydrogen Recovery (b)
Figure 8 - Separation characteristics of (a) SSF and (b) PTMSP membranes for FCC off-gas (20% H2, 20% CH4, 8% C2H4, 8% C2H6, 29% C3H6, and 15% C3H8); pH = 3.0 atrn, pL = 1.0 atm.
490 can be compressed and further purified to essentially pure H2 by PSA [ 16, 20]. A schematic process diagram for this application is given by Figure 9a. An example of the performance of the SSF membrane for such application using FCC off-gas as feed was described earlier (Figure 8a, Table 3). They show very high efficiency of the SSF membrane for rejecting C3C4 hydrocarbons from mixtures with H2. The membrane was pilot tested for this application [17] at a refinery site. Hydrogen is conventionally produced by steam-methane reformation. The reactor effluent is then shifted to enhance H2 production, cooled, and purified in a PSA to obtain pure H2. The PSA waste gas is typically dilute in H2 (--35%) and available at low pressures (<1.7 atmospheres). It is burnt to recover its fuel value. A SSF membrane can be used to recover enriched H2 (>55%) from the PSA waste gas at feed pressure by rejecting CO2 and CH4, followed by recompression and recycling to the original PSA system as shown by the schematic drawing of Figure 9b. This can substantially increase the overall H2 recovery of the integrated SMR-SSF-PSA system from 75% to 85+% [19]. An example of the SSF membrane performance for such application using PSA waste as feed was described earlier (Figure 6). The CO2 and CH4 rejections were, respectively, 79 and 65% at a H2 recovery of 60%. Removal of bulk H2S (>20%) from CH4 or H2 at a moderate pressure (<10 atmospheres) can be a major technical hurdle. The SSF membrane can be used to reject HzS from such mixtures [18,20]. Figures 10a and 10b, respectively, show the rejections of HzS as functions of H2 and CH4 recoveries by the SSF membrane for different feed gas compositions. More than 90% H2S can be rejected at 70% H2 or CH4 recovery when the partial pressure of HzS in feed gas is moderate (>3.8 atmospheres). The enriched H2 and CH4 products are obtained at feed gas pressure. Figure 9c shows the schematic of a two-stage SSF process system in combination with a Thermal Swing Adsorber (TSA) which can be used to produce pure H2 with an overall H2S rejection of 98.3% and overall H2 and CH4 recoveries of 70-80% [ 18,20]. M O L E C U L A R ENGINEERING OF SSF MEMBRANES
The pore size of the SSF membrane can be altered by controlled oxidation with air and CO2 [34]. The surface polarity of the SSF membrane can also be increased by judicious oxidation of its surface by treating it with copper acetate (catalyst)-nitric acid solutions [35,36]. The oxidized membrane can selectively remove water vapor from air at a moderate feed pressure (--3-4 atmospheres). The polar SSF membrane surface selectively adsorbs and permeates the water vapor. 70-80% of the water vapor can be rejected with very little air loss. About 99% of feed air is recovered at feed pressure. The flow of air molecules through the membrane is blocked by adsorbed H20. Figure 11 shows a set of performance data by the modified SSF membrane for air drying using two different N2 purge (countercurrent) rates at the low pressure side. The variable (S/F) represents the ratio of purge gas (S) to feed air (F) flow rates. This demonstrates how an originally hydrophobic SSF membrane can be molecular engineered to create a hydrophilic membrane.
491 Product Hydrogen Refinery Waste SSF Membrane
Gas
Hydrogen PSA
H 2 + ( CI - C4)
To Fuel (a)
PSA Feed G a s H2, CH4, C O 2 , CO |
Pure H2 ,,
|
- l
~_1 Hydrogen ~'-[ J PSA
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--
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~
~
i
,~
I
CH 4 or
He
,SA
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~/////////////////////////////////////////////AI
.
HeS Enriched Gas
l (e)
Figure 9" Schematic flow sheets for various SSF membrane-PSA-TSA hybrid systems: (a) H2 recovery from refinery waste gas, (b) Hz enrichment from PSA waste gas, (c) bulk HzS-H2 separation.
492 100 9O 0~ r 0 o (o -~ (D9 9:
80 70
-
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9 5 0 % H2S
I
I
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30
40
50
60
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80
90
100
H 2 Recovery (%) (a) 100 , 908070-
A
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e,mml I
n,
-1-
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-\
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L
3010-~ 00
,
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1 9
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\\
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"
45% HzSatPH=0.239MPa
O
5 0 % H2S a t P H = 0 . 4 4 6 M P a I
I
I
I
I
I
10
20
30
40
50
60
CH 4 Recovery
70
80
90
100
(%)
(b) Figure 10 - Separation characteristics of SSF membrane (a) H2S-H2 mixture, (b) HzS-CH4 mixture at different feed gas compositions and pressures.
493
100
ill
=qU!mmuu| !
ii
. . . . .
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91 . . . . . . . . . . . 40
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|
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i
|
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H20 Rejection
\
80
90
100
(%)
Figure 11 - Separation characteristics of SSF membrane for air drying at different purge gas to feed gas flow rates. PORE CHARACTERIZATION OF SSF MEMBRANES There is no reliable tool for characterization of truly nanoporous (3-10A diameter) and amorphous materials. Direct scans of the SSF membrane surface (produced in sheet form) by Atomic Force Microscopy (AFM) and Scanning Tunneling Microscopy (STM) revealed the surface roughness of the membrane (both methods) as well as clearly defined deep regions (STM only) which are presumed to be holes [15]. The size of the hole was estimated to be ~4.5A. These findings, however, were not very conclusive. An indirect method was developed to estimate the average pore size of the SSF membranes by measuring pure CH4 diffusivity (DcH4) through them and comparing that value with the diffusivity of CH4 through zeolite pores of known dimensions [15]. Figure 12 shows the reference plot of methane diffusivity through pores (diameter, dp) of various sizes. Molecular diffusion dominates the flow when the pores are large in diameter (>1000A). Knudsen diffusion is the controlling mechanism in the pore diameter range of 20-1000A. Activated surface diffusion dominates the transport for nanopores (<10A) where the gas diffusivity drops extremely rapidly with slight decrease in the pore size.
494
Comparison of the measured CH4 diffusivity through the SSF membrane with the reference curve of Figure 12 indicated that the membrane pores were in the range of 5-6A. A sensitivity analysis of the pore size distribution of the membrane showed that the distribution was indeed very narrow [15]. Recently, Centeno and Fuertes used this technique to obtain a pore diameter of-~4.2A for a MSC membrane [29]. These results are consistent with the physical requirement that the pores of the SSF membrane should be larger than the pores of the MSC membrane.
10 o
=
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=-" 10-2 . .=
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T=295K
,"
-"=
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dp, Angstroms Figure 12 - Estimated diffusivity of methane as a function of pore diameter at 295K. SUMMARY Nanoporous Carbon Membranes (NCM) for gas separation can be successfully produced by pyrolysis of polymeric films. The separation characteristics of these membranes depend on the pores size and surface chemistry of pore walls. They are determined by the nature of the polymer precursor, method and conditions of pyrolysis and post treatment protocols. The molecular sieve carbon (MSC) membranes selectively permeate the smaller molecules of a gas mixture through the pores. The selective surface flow (SSF) membranes selectively permeate the larger and/or the more polar molecules of a gas mixture through the pores. The transport mechanism through the pores of the carbon membranes is adsorption and surface diffusion in both cases. The average pore sizes of the MSC membranes are smaller (3-5A) than those for the SSF membranes (4-10/~). However, a very narrow pore size distribution is needed for these membranes to be practical.
495 The permeance and permselectivity of gases through these membranes will generally depend on gas pressure, composition, and temperature on both sides of the membrane due to selective multicomponent adsorption and multicomponent surface diffusion of the molecules on a heterogeneous surface. Thus, it may be needed to describe the separation characteristics of the membranes in terms of the actual performance such as the rejection of components and membrane area per unit feed gas flow rate as functions of the recovery of a key component. Several potential applications of MSC membranes include (a) air separation, (b) removal of SF6 from air, (c) C3H6-C3H8 separation, (d) CO2-CH4 separation, and (e) CH4-H2 separation. The SSF membrane has been tested for (a) enriching H2 from a refinery waste gas containing C2-C4 hydrocarbons, (b) recovery of H2 from SMR-PSA waste gas, and (c) separation of bulk H2S from H2 and CH4. Both membranes can simultaneously exhibit high permeance and permselectivity of the preferentially transported molecules unlike the conventional polymeric membranes. The SSF membrane, however, produces a gas stream enriched in the smaller and less selectively adsorbed component of the feed mixture at feed gas pressure. This can be advantageous when such components constitute the desired product. The MSC membrane will require recompression of desired product gas in such a case. The pore size and surface chemistry (polarity) of the NCM can be altered by simple techniques (heating, surface oxidation, etc.) in order to change the adsorption and surface diffusion characteristics of the transported molecules. A water selective SSF membrane for gas drying was prepared by this approach. Reliable characterization of nanopores (size, shape, distribution, and surface chemistry) cannot be done by today's technology. An indirect method based on CH4 diffusion measurement through the NCM is found to be a reasonable approach. REFERENCES
1. Scott, K., "Handbook of Industrial Membranes," Elsevier Science Publication, Oxford, U.K. (1995). 2. Ho, W. S. W., and K. K. Sirkar, "Membrane Handbook," Van Nostrand Reinhold, New York (1992). 3. Kesting, R. E. and A. K. Fritzsche, "Polymeric Gas Separation Membranes," John Wiley, New York (1993). 4. Stem, J. A., J. Membrane Sci., 94, 1 (1994). 5. Koros, W. J., and G. K. Fleming, J. Membrane Sci., 83, 1 (1993). 6. Blaisdell, G. T., and K. Kammermeyer, Chem Eng. Sci., 28, 1249 (1973). 7. Ruthven, D. M., and S. Sircar, "Distillation and Other Industrial Separations," AIChE Publication, 1, 209 (1997). 8. Robeson, L. M., J. Membrane Sci., 62, 165 (1991). 9. Koresh, J. E., and A. Softer, Sep. Sci. Tech., 18, 723 (1983). 10. Koresh, J. E., and A. Softer, J. Chem. Soc. Faraday Trans I., 82, 2057 (1986). 11. Softer, A., and J. E. Koresh, "Separation Device," U.S. Patent 4,685,940 (1987). 12. Carbon Membranes Ltd., Israel, Trade Literature.
496 13. Rao, M. B., S. Sircar, and T. C. Golden, "Gas Separation by Adsorbent Membranes," U.S. Patent 5,104,425 (1992). 14. Rao, M. B., and S. Sircar, J. Membrane Sci., 8__55,253(1993). 15. Rao, M. B., and S. Sircar, J. Membrane Sci., 110, 109 (1996). 16. Anand, M., M. Langsam, M. B. Rao, and S. Sircar, J. Membrane Sci., 123., 17 (1997). 17. Naheiri, T., K. A. Ludwig, M. Anand, M. B. Rao, and S. Sircar, Sep. Sci. Tech., 3__22,1589 (1997). 18. Parillo, D. J., C. M. A. Thaeron, and S. Sircar, AIChE J., 4_.33,2239 (1997). 19. Sircar, S., W. E. Waldron, M. B. Rao, and M. Anand, Sep. Purif. Tech., 1___7711 , (1999). 20. Sircar, S., M. B. Rao, and C. M. A. Thaeron, Sep. Sci. Tech., 3__44,2081 (1999). 21. Jones, C. W., and W. J. Koros, Carbon, 3_.22,1419 (1994). 22. Jones, C. W., and W. J. Koros, Carbon, 3_.22,1427 (1994). 23. Jones, C. W., and W. J. Koros, Ind. Eng. Chem. Res., 3__44,158 (1995). 24. Jones, C. W., and W. J. Koros, Ind. Eng. Chem. Res., 34, 164 (1995). 25. Geiszler, V. C., and W. J. Koros, Ind. Eng. Chem. Res., 3__55,2999 (1996). 26. Yanihara, N., H. Shimazaki, Y. Hirayama, S. Nakanishi, T. Yoshinaga, and Y. Kusuki, J. Membrane Sci., 16__9_0,179 (1999). 27. Y. Kusuki, H. Shimazaki, N. Tanihara, S. Nakanishi, and T. Yoshinaga, J. Membrane Sci., 134, 245 (1997). 28. J. Hayashi, M. Yamarnoto, K. Kusakabe, and S. Morooka, Ind. Eng. Chem. Res., 3_6, 2134 (1997). 29. Centeno, T. A., and A. B. Fuertes, J. Membrane Sci., 160, 201 (1999). 30. Barrer, R. M. AIChE-I Chem E (London) Syrup. Ser. No. 1, pp. 112-121 (1965). 31. Ash, R., R. M. Barrer, and C. G. Pope, Proc. Royal Soc., A271, 19 (1963). 32. Ash, R., R. W. Baker, and R. M. Barrer, Proc. Royal Sot., A299, 434 (1967). 33. Ash, R., R. M. Barrer, and P. Sharma, J. Membrane Sei., 1, 17 (1976). 34. Rao, M. B., S. Sircar, and T. C. Golden, "Composite Porous Carbonaceous Membranes," U.S. Patent, 5,507,860 (1996). 3 5. Golden, C. M. A. T., M. B. Rao, and S. Sircar, Proceedings of Fundamentals of Adsorption 6, (Ed) F. Meunier, Elsevier, Paris, pp. 1083-1088 (1998). 36. Rao, M. B., S. Sircar, and T. C. Golden, "Carbonaceous Adsorbent Membrane for Gas Dehydration," U.S. Patent 6,004,374 (1999). 37. Yamamoto, M., K. Kusakabe, J. Hayashi, and S. Morooka, J. Membrane Sci., 13___33,195 (1997).
RecentAdvancesin Gas Separationby MicroporousCeramicMembranes N.K. Kanellopoulos(Editor) 2000 ElsevierScienceB.V.All rightsreserved.
497
Microporous inorganic and polymeric membranes as catalytic reactors and membrane contactors E. Driolil'2 and A. Criscuoli 1 1 Research Institute on Membranes and Modelling of Chemical Reactors at University of Calabria, Via Pietro Bucci, Cubo 17/C, Arcavacata di Rende (CS) 87030 Italy 2 Department of Chemical Engineering and Materials, University of Calabria, Via Pietro Bucci, Cubo 17/C, Arcavacata di Rende (CS) 87030 Italy
Microporous membranes, both inorganic and polymeric, find applications in operations like microfiltration and gas separation. In last years their use as catalytic membrane reactors and, more recently as membrane contactors has also been faced. The combination of reaction and separation upon a membrane was suggested already by Michaels (reported in [1]); the goal was to attain higher conversions by shifting the product distribution of equilibrium reactions through the selective permeation of at least one of the reaction products. When catalytic materials are deposited into the membrane pores the membrane acts both as reactor and as separator. Until '80s polymeric membranes were developing quickly. Polymers, however, can only withstand relatively mild chemical and thermal conditions and many researchers suggested that applications of membrane reactors would probably be confined to high-value biotechnological products. The significant recent developments in the manufacture of both ceramic and metal membranes increased the interest in the use of these new systems in chemical reactors at more severe operating conditions than those sustainable by the polymeric ones. High thermally and chemically stable inorganic membranes with relatively small and homogeneously dispersed pores were attained and are constantly under development in many research groups all over the world. Microporous membranes can be used also to promote mass transfer between phases. In membrane contactors the membranes, microporous and hydrophobic, are mostly used for mass transfer applications between two immiscible phases (gas scrubbing, stripping, solvent extraction, osmotic distillation). The interface between phases is created into the pores of the membrane and the mass transfer is obtained mostly by diffusion (see Figure 1). The membranes can be manufactured into small-diameter hollow fibers that provide a very high surface area to volume ratio. When a temperature difference is established across the fibers, the difference of vapour pressures promotes a vapour transport through the pores allowing the concentration of aqueous solutions (membrane contactors used for membrane distillation operations). Basic properties of membrane reactors and membrane contactors and examples of fields in which they can find application are reported and discussed in the following.
498
Fig. 1. A scheme of a membrane contactor.
1. M E M B R A N E S USED
Depending on reaction conditions (temperature, pressure etc.) in membrane reactors can be used both inorganic and organic membranes. Both types of membranes can be divided into symmetric and asymmetric. The first ones are tmiform along all the thickness, the second ones have an upper microporous selective layer on a porous layer which gives a mechanical support at the membrane structure. In this way it is possible to combine the selectivity of the microporous membrane with the permeability of the porous support. In general, higher permeabilities are obtained with thinner membranes because permeation rate is inversely proportional to thickness. However, the membrane must be thick enough to avoid formation of cracks and pinholes during its preparation or during use. An optimal thickness exists because as the membrane becomes too thin the higher permeation also of reactants results in a decrease of conversion [2]. Usually, asymmetric membranes are preferred due to higher permselectivities achievable. Organic membranes can be divided into rubbery polymers and glassy polymers. When an amorphous polymer is heated, if the temperature becomes higher than the "rubbery transition temperature", Tg, the polymer passes from the glassy state to the rubbery one. Normally, rubbery polymers show high permeabilities for gases, that means high productivity, while glassy polymers present high selectivities, so they allow to have high purity. Materials used for inorganic microporous membranes are alumina, titanium, silica, zirconium, vycor glass, zeolites. Zeolites are the main group of microporous membranes having potential applications as membrane reactors. This is due to their regular structure with
499 pores of molecular size, high acid resistance, thermal stability up to 600 ~ and inherent catalytic activity. In contrast to ceramic membranes, large gas separation factors can be obtained by using porous membranes having pore size less than about 2 nm, such as zeolite. In membrane contactors hydrophobic polymeric membranes are normally used (e.g. polypropylene ones). The interface at which the mass transport occurs located at the pore entrance. Studies on preparation and characterisation of microporous membranes with high hydrophobicity, appropriate microporosity and thickness are also in progress [3]. New symmetric microporous membranes made of an amorphous perfluoropolymer have been
Fig. 3. A SEM imagine of an asymmetricmicroporousmembrane
500 prepared and their pore size distribution has been determined by using atomic force microscopy imaging. The preliminary experiments on the liquid water permeability of these membranes showed that up to 10 bar the water flux is practically zero, confirming their high hydrophobic character. The development of microporous ceramic membranes with controlled, stable and narrow pore-size distribution, allows the application of these devices also when more severe operating conditions are present. Figures 2 and 3 show SEM imagines of symmetric and asymmetric microporous membranes. 2. BASIC PROPERTIES OF CATALYTIC MEMBRANE REACTORS A catalytic membrane reactor (CMR) is defined as a combination of a heterogeneous catalyst and a permselective membrane that allows one component of a mixture to selectively permeate through it (see Figures 4 and 5).
Fig. 5. A section of a membrane reactor with catalyst packed in the lumen side. Case in which the membrane allows the selective removal of a product.
501
Membranes of different shapes can be employed. The common tubular and disk shapes have low packing densities (low filtration area per unit volume) but are easy to maintain. In the tubular configuration a permselective membrane tube separates two gaseous regions. Reaction takes place on a heterogeneous catalyst that is located in the porous structure of the membrane, on the surface of the membrane, or in one of the two regions. The permeate stream can flow countercurrent, cocurrent, or perpendicular (crossflow) to the feed stream. In additional to disks, tubes and monoliths, high packing-density geometries (e.g., hollow fiber) of inorganic membranes have also been attempted. A CMR can have many advantages over a separate catalytic reactor and downstream separation units. One distinct advantage is that combining two process, which are normally carried out separately, will lower capital costs, since separations can account for 70% of a chemical plant's cost [2]. The appropriate reactor design can improve yield or reaction selectivity, and this can also decrease downstream separation costs. Some other advantages that can be mentioned are: 1) The removal of one of the reaction products as it forms to increase the conversion in reactions limited by thermodynamic equilibrium. The conversion that can be obtained is limited by permeation of the reactant(s) unless a highly selective membrane is used. The removal of one of the reaction products can serve also to prevent its further reaction to undesirable products. 2) The controlled addition of one of the reactants through the membrane allows to work with a more uniform concentration on the catalyst surface than in a standard tubular reactor. This results in a better control of the reactor performance (e.g., in exothermic reactions, the thermal runaway can be avoided). 3) The membrane can separate two zones of reaction, and only one component (one of the products of reaction 1) can permeate through the membrane to serve as a reactant for reaction 2. Heat can transfer across the membrane from the exothermic to the endothermic reaction. In this way, it is possible to carry out two reactions in the same device. 3. APPLICATIONS OF MEMBRANE REACTORS Microporous membrane reactors can be used for carrying out both high temperature and mild temperature catalytic reactions [4]. For high temperature catalytic reactions inorganic membranes are normally used, e.g. microporous glass membranes, while polymeric membranes are employed when mild operating conditions are present. The majority of reactions studied in membrane reactors refers to the ability of the membrane to selectively remove a product by diffusion with a consequent increase of the conversion for equilibrium limited reactions. In microporous membranes the diffusion transport is mainly of the Knudsen type and the lighter species preferentially permeate. In the following part some results presented in literature relatively to microporous membrane reactors are reported. Weyten et al. [5] used a silica membrane, with a permselectivity of 110 for hydrogen/propane at 500~ for the propane dehydrogenation. Under well-chosen process conditions a membrane reactor effect is found. The conversion of propane to propene increases with at least a factor of 2, so that at 500~ a conversion can be obtained belonging to the thermodynamic equilibrium of 600~ The advantage is then that the commercial catalyst can
502 be used for a much longer time (at least 50 times) than at 600~ regenerated.
before it has to be
Itoh (reported in [6]) studied the dehydrogenation of cyclohexane to benzene using a reactor packed with Pt/A1203 catalyst. At 473 K and 1 atm, the equilibrium conversion was only 19%. The removal of hydrogen through a membrane made of a vycor glass tube with a mean pore size of 40 A increased the conversion up to 45%. Styrene nowadays is produced by two processes: i) dehydrogenation of ethylbenzene and ii) as a by-product in the epoxidation of propylene with ethylbenzene hydroperoxide and Mo complex-based catalysts. The former process accounts for more than 90% of the worldwide capacity, which is approximately 13 106 t/year. The latter process is commercialized by ARCO Chemical (formerly Oxirane) and by Shell. Approximately 1.2 106 t/year are currently produced with this technology [7]. The main problems in the actual ethylbenzene dehydrogenation process are: - the need for a reactant recycle, owing to the low conversion achieved per pass (due to thermodynamic limitations); the need for high steam-to-hydrocarbon ratios; the high endothermicity of the reaction; a slight irreversible deactivation of the catalyst (the lifetime is usually about two years). Membrane reactor, in order to shift the equilibrium and to carry out the reaction at lower temperature has been proposed to give a solution to the above described problems. The catalytic dehydrogenation of ethylbenzene to styrene !o enhance the conversion has been studied, for example, by Wu et al. (reported in [6] ). The authors studied the reaction in a CMR ranging between 600~ and 640~ The catalytic dehydrogenation of ethylbenzene has been enhanced because the hydrogen was separated through a commercial alumina membrane tube with 40 A pore diameter. The conversion increased about 15% compared to the conversion in a packed bed reactor. -
-
-
A growing interest on the water-gas shift reaction assisted by a CMR appeared in the recent literature. A ceramic catalytic membrane reactor (CCMR) has been used by Bracht et al. [8]. The development of optimum combination of S- and C1- catalyst resistant (standard Fe/Crcatalyst; Co/Cr-, and Co/Mn-catalysts) and a CCMR (silicamembrane) for the WGS reaction was considered in order to proof the feasibility of a process for cost effective and energy efficient hydrogen conversion recovery from coal-derived gases as a means of CO2 control. They have shown that in a conventional Integrated Gasification Combined Cycle power plant the efficiency penalty and system complexity is reduced to a minimum when the fuel gas (mainly hydrogen and carbon dioxide) is separated at high temperature by using a CCMR. Damle et al. [9] developed a simplified but interesting process model to simulate a catalytic membrane WGS reactor. Their model assumes the membrane reactor as isothermal, and continuous chemical reaction equilibrium on the feed side. For example, their analysis considered the effect of stage cut (0.05-0.9) and pressure ratio (Pr = 2; 5; 10; 20) on CO conversion at different H20/CO molar ratio (2:1; 3:1; 4:1) both for Knudsen diffusion
503 separation and for low gas separation factors. Considering a typical cher gasifier exit composition as feed composition (48.6% H2, 21% CO2, 17.3% CO, 13.1% N2 on a dry basis), their conclusion was that a multistage process is necessary to increase the hydrogen product concentration beyond 80%. Seok and Hwang [10] evaluated the performance of the WGS reaction by a CMR using porous Vycor glass coated with ruthenium(III) chloride trihydrate. The reaction has been carried out under various operating conditions of temperature, pressure and feed composition. The highest conversion of CO obtained was of 85% at lower temperature (430 K, 157~ with respect to industrial processes with a consequent energy saving. The metathesis of alkenes is a major development in hydrocarbon chemistry in recent years. Propylene methathesis, just like any other olefin methathesis, is essentially a thermoneutral catalytic rupture and re-formation of carbon-carbon double bonds and results in an equilibrium composition of reactants and products. The catalyst and membrane used were rhenium oxide supported on alumina and porous Vycor glass, respectively [10]. The methathesis reaction was carried out in the temperature range of 20-22~ The maximum equilibrium conversion is 34% for a conventional fixed bed reactor, while using the membrane reactor it was reached a value of 40%. The limitation seen in the conversion improvement is mainly due to the poor membrane selectivity. A more selective membrane for the product will improve the conversion and will divide the product stream into two: one is the reject stream which is concentrated in the least permeable species, ethylene. The other is the permeate stream, enriched in the most permeable species, butene. Synthesis gas can be produced by partial oxidation of methane. This reaction can be either catalytic or high-temperature non catalytic. The catalytic partial oxidation of methane in membrane reactors has been studied by different authors. Santos et al. [11] selectively converted methane to synthesis gas using a Ni/A1203 catalyst inside a modified ceramic membrane. The reactor was divided into two zone: a first zone behaved as a conventional fixed bed reactor; in the second zone some of products could preferentially diffuse out of the reactor. At 800~ 1 bar and using a sweep gas flow rate of 500 cm3/min, the conversion was a little bit lower than 98% (equilibrium value = 93.5%). An interesting result consisted in the possibility to operate at higher pressures: at higher pressures there is a decrease in the methane conversion because of the unfavourable equilibrium shift; however, the use of the membrane reactor allowed an increase of conversion which compensated the lower equilibrium values. Bishop et al. (reported in [12]), tested the oxidation of volatile organic carbons (VOCs) in a porous honeycomb monolithic ceramic membrane filter in the pores of which an oxidation catalyst has been deposited. More than the 99% of removal efficiency has been found. Omata et al. ( reported in [2] ) studied the selective oxidative coupling of CH4. They used a PdO catalyst supported by MgO, which was deposited on a ceramic membrane. The formation of C2 hydrocarbons was carried out near 1000 K by feeding air to the tube side of the membrane and CH4 to the shell side. The catalyst was on the shell side. They reported three advantages of this arrangement:
504 - Air could be used instead of 02 as the reactant without introducing large amounts of N2 into the exit stream. Neither N2 nor O2 was detected in the gas phase in the CH4 stream; - The rate of C2 formation per unit surface area was higher; - The selectivity increased significantly: selectivities greater than 90% were measured in the CMR, while for a supported catalyst selectivities were as low as 50%. McGrath and Ergas (reported in [ 12]) used a microporous polypropylene hollow fiber module to remove toluene from air and convert it. The air containing toluene was fed to the tube side while an aqueous solution with an enzyme was circulated at the shell side. By working at inlet concentrations of 100 ppm, the 98% of toluene has been removed. Microporous membranes can be applied also for the opposing reactant fed. In this case, reactants are fed at the opposite side of a catalytically active membrane and the point in the membrane at which they meet determines the reaction region. To avoid the slip of reactants, it is important to have fast reaction rates. Several reactions have been studied by using this type of configuration [ 13 - 15]. For the NOx destruction a 70% of conversion with a selectivity for nitrogen up to 75% has been achieved in a temperature range of 300-350~ by using vanadium oxide as catalyst [ 16]. Membrane reactors can serve to selectively extract chemicals or biochemical reaction products, improving the performance of the fermentation and enzymatic transformations [ 17]. In the wastewater treatment, microporous membrane reactors find also interesting applications. By feeding water contaminated by trichloroethylene to the tube side of microporous polypropylene hollow fiber contactor while circulating a methanotrophic bacterium at the shell side, removals of the order of 78.3%-99.9% (depending on the water residence time: 315 min) have been achieved [ 18]. Table 1 shows some other examples of reactions carried out by using microporous membrane reactors. 4. APPLICATIONS OF MEMBRANE CONTACTORS Several are the applications of membrane contactors both under study and already at commercial level. They cover liquid-liquid extractions, gas absorption and stripping, waste water treatment. Figure 6 shows a commercial module (from Hoechst Celanese). Oxidative membrane gas absorption for mercury removal from gas streams is possible by using these devices [19]. This application is especially advantageous over the use of a conventional absorber when mercury vapours are present in low concentrations, because in this case a very low amount of absorption liquid is required. In conventional absorption processes the use of these low quantities of liquid in a large gas flow would, in fact, lead to severe operating problems. The absorption liquid used in this study is based on oxidising agent. For oxidiser with high reaction rate, liquid flow rate hasn't any effect on the mass transfer. For low reaction rate there is an influence and higher mass transfer coefficients are achieved at higher liquid flow rates. PTFE membranes are required to withstand the strongly oxidising absorption liquids.
505
Table 1 Some examples of reactions carried out by using microporous membrane reactors Reaction Membrane Steam reforming of methane
A1203
Dehydrogenation of methanol
Glass
Dehydrogenation of ethane to ethylene
A1203
Dehydrogenation of propane to propene
A1203
Dehydrogenation of n-butane to butene
A1203
Dehydrogenation of cyclohexane to benzene
A1203
Dehydrogenation of ethylbenzene to styrene
A1203
Hydrogenation of nitrobenzoic acid
Calcium aluminum silicate
Oxidative dehydrogenation of methanol
A1203
Oxidative dehydrogenation of propane
zeolite
Oxidation of methane
ZrO-CaO-A1203
Hydrogenation of dehydrolinalcol
stainless steel
Decomposition of H2S
7-A1203
Decomposition of ammonia
ceramic
Larsen [20] presented some results relative to the removal of SO2 from fuel gas streams by an absorbent solution. A microporous hydrophobic membrane has been used for contacting. The entire process involved three steps: absorption, electrodialytic regeneration of spent absorbent solution, vacuum membrane stripping. Shell and tube module design do not provide well defined flow conditions of both the liquid and the gas phases, that are necessary for achieving good mass transfer between the two phases. Based on such mass transfer considerations, the short gas residence time required for suitably selected membranes and the requirement of large interfacial area per unit volume, several suitable module designs were developed which allow to obtain the required removal. A 95% of SO2 removal at a gas side pressure drop of less than 800 Pa has been achieved.
506
Fig. 6. A commercially available (Hoechst Celanese Corporation) membrane contactor
Membrane contactors have shown to be useful also for the water carbonation. Criscuoli and Drioli [21] obtained interesting water carbonation. The influence of several parameters on the performance of the process has been illustrated. In particular, low water and high CO2 flow rates (80 and 315 ml/min, respectively) lead to reach higher CO2 concentration. CO2 concentration was increased by increasing CO2 pressure and reducing
507 temperature. The same degree of water carbonation of traditional processes (1-5 g/l) has been achieved by operating with 1.4 m 2 of membrane area. Hollow fiber contactor could be used in mass transfer operations with contacting of two and three phases [22]. In both two or three phase systems, and even in multiphase systems, interfaces are immobilized in microporous walls. Planar hollow fiber elements can be assembled for contacting also four phases where the membrane phase is flowing perpendicularly to hollow fibers with two types of solutions selectively stripping different solutes. Way of operation of an hollow fiber contactor can influence its performance. For example, by introducing the pulsation of the membrane phase it is possible to increase the mass transfer rate up to 60%. Hollow fiber contactors were tested for recovery of metals and organic contaminants from aqueous solutions and for separation of carboxylic acids and drugs produced in fermentation. Semmens et al. [23] used microporous hollow fiber membranes for delivering gas to water. Water is forced past microporous fibers with micropores in the range of 0.1-1 microns and the lumen of the fibers was pressurized with oxygen. When the oxygen pressure was higher than the bubble point of the membrane, oxygen flowed through the micropores and formed bubbles on the outside of the membrane. Bubble size less than 100 microns diameter can be formed by manipulating the gas fluxes across the membrane and the water velocity past the fibers. A pilot plant for extractions of chlorinated and aromatic compounds from wastewater where hollow fiber microporous membranes are employed, has been developed in The Netherlands. The individual contaminant level was reduced to less than 10 pg/1 (reported in [24]). Wikol et al. [25] made the ozonation of tap water using a microporous PTFE hollow fiber module (DISSO3LVE, W.L. Gore&Associates, Elkton, MD). Target dissolved ozone concentration, 2-10 ppm, has been obtained at the following conditions: Total pressure, 1 kg/cm2; T, 25~ Feed gas ozone concentration, 235 g/m3; Water flow rate, 15 1/min. Membrane contactors can be used also for microemulsion production. The properties of emulsions such as stability, creaming and rheological behaviour depend on the particle diameter distribution. Generally, it is desirable to obtain emulsions of uniform particle diameter such as monodispersed emulsion for studying the interfacial phenomena of particles that affect the physical properties of emulsions directly. The preparation of monodispersed emulsion of desired particle diameter is difficult to achieve by the commercial apparatus. Emulsification by microporous membranes, applied to date mainly for preparing food emulsions, allows to obtain emulsions with narrow particle diameter distribution [26]. The dispersion phase under pressure is emulsified into the continuous phase by passage through a microporous membrane. Monodispersed emulsions could be prepared if porous membranes of uniform pore size were available. For preparing a monodispersed emulsion it is important that the membrane surface is not wetted by the dispersion phase. Thus, for preparing oil/water emulsions, the microporous membrane has to be hydrophilic to wet well with continuos (water) phase, and be hydrophobic tbr water/oil emulsions. In order to prevent wetting of the membrane surface by the dispersion phase, emulsifiers are generally added to the continuous phase [27].
508 Membrane emulsification seems to be a very promising method to solve the problem of preparing monodispersed and stable emulsions. Besides the experiments carried out till now are mainly related to the food area, the concept on which the membrane emulsification method is based, can be extended to all the applications in which emulsions are involved. Figure 7 shows the formation of an emulsion through the membrane.
Permeation of dispersion phase under pressure
Continuous
phase
I, ii!e:i
@
--
ii,e iie iim
Fig. 7. Emulsion formation through the membrane
Membrane contactors find market acceptance mainly for deoxygenation of Ultra Pure Water (UPW) for the semiconductor industry and for bubble-free carbonation lines. Ultrapure water with less than 1 ppb dissolved oxygen can be obtained. Today, several systems are installed both in large central loop and in Point of Use stations [28]. The use of membrane contactors for the carbonation of beverages began with the successful installation in a Pepsi bottling plant in the USA. Since 1994, this plant has been the most efficient bottler when comparing carbon dioxide usage among various Pepsi plants [28]. 5. CONCLUSIONS Microporous membranes find interesting applications for membrane reactors and membrane contactors operations. Most of the studies made show that a CMR usually operates at higher yields, better reaction selectivity or lower costs than a separate catalytic reactor and downstream separation units. In last years, improvements achieved in the inorganic membranes manufacture allowed their application for a wider range of reactions, e.g., high temperatures ones. Further improvements in their permselectivity, thermal, chemical and
509 mechanical stability coupled to a suitable module design and engineering are at the basis of their introduction in the industrial world. Membrane contactors with their high surface/volume ratios represent a very interesting media for promoting the mass transfer between phases in controlled way. Commercial applications are already present (e.g, electronical industry or bubble-free carbonation lines). Their potentialities in facilitating mass transfer both in liquid and gas phases suggest other interesting opportunities in the extraction or adsorption of gases, in the design of artificial organs. Membrane systems less expensive, more chemically stable, cleaner and more efficient will help in this intent. REFERENCES
1 2 3
8
9 10
11 12 13 14 15 16 17 18
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