Characterization of Porous Solids II

Studies in Surface Science and Catalysis 62 CHARACTERIZATION OF POROUS SOLIDS II

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Studies in Surface Science and Catalysis Advisory Editors: B. Delmon and J.T. Yates

Vol. 62

CHARACTERIZATION OF POROUS SOLIDS II Proceedingsof the IUPAC Symposium (COPS 11). Alicante, Spain, May 6- 9 , 1 9 9 0 Editors

F. Rodriguez-Reinoso Departamento de Quimica lnorgdnica e Ingenieria Quimica, Universidad de Alicante, Apartado 99, Alicante, Spain

J. Rouquerol Centre de Thermodynamiqueet de Microcalorimetrie, CNRS, 7 3003 Marseille, France K.S.W. Sing Department of Chemistry, Brunel University, Uxbridge, Middlesex UB8 3PH, U.K. and

K.K. Unger lnstitut fur Anorganische Chemie und Analytische Chemie, Johannes Gutenberg-Universitat,0-6500Mainz, F.R.G.

ELSEVIER

Amsterdam - Oxford - New York -Tokyo

1991

ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhahstraat 25 P.O. Box 2 1 1, 1000 AE Amsterdam, The Netherlands Distributors for the United States and Canada:

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Library o f Congress Cataloging-in-Publication Data

IUPAC Symposium. C O P S (2nd : 1990 : Alicante. Spain) Characterization of porous solids I1 : proceedings of the IUPAC Symposium, C O P S 11. Alicante. Spain. May 6-9. 1990 I editors, F. Rodriguez-Reinoso ... [et al.1. p. cm. -- (Studies in surface science and catalysis ; 62) Includes bibliographical references and indexes. ISBN 0-444-88569-2 1. Porous materials--Congresses. I. Rodrjguez-Reinoso. F., 194111. International Union of PGre and Applied Chemistry. 111. Title. IV. Title. Characterization o f porous solids 2. V. Title: Characterization of porous solids two. VI. S e r i e s . TA418.9.P6196 1990 620.1'16--d~20 91- 10354 C1P

ISBN 0-444-88569-2

0 Elsevier Science Publishers B.V., 199 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./ Physical Sciences & EngineeringDivision, P.O. Box 330,lo00 AH Amsterdam, The Netherlands. Special regulationsfor readers in the USA -This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the publisher. No responsibility is assumed by the Publisherfor any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Although all advertising material is expected to conform to ethical (medical) standards, inclusion in this publication does not constitute a guarantee or endorsement of the quality or value of such product or of the claims made of it by its manufacturer. This book is printed on acid-free paper. Printed in The Netherlands

V

CONTENTS

Preface

XI11

Characterization of porous solids: an introductory survey K.S.W. Sing

1

Simulation of adsorption in model microporous graphite D. Nicholson

11

Theory of adsorption in micropores Z. Tan and K.E. Gubbins

21

Sorption of gases on microporous solids: pore size characterization by gas sorption S.W. Webb and W.C.Conner

31

Analysis of the percolation properties of a real porous material G. Mason and D.W. Mellor

41

The five types of porous structures and their hysteresis loops V. Mayagoitia

51

Model study of the combined effect of heteroporosity of macroscopic heterogeneity gas relative permeability of porous solids N.K. Kanellopoulos, J.K. Petrou and J.H. Petropoulos

61

Percolation theory of capillary hysteresis phenomena and its application for characterization of porous solids A.V. Neimark

67

Modelling of mercury intrusion and extrusion M. Day, I.B. Parker, J. Bell, M. Thomas, R. Fletcher and J. Duffie

75

Wetting phenomena in porous solids: Mechanisms and models A. Winter

85

The contact angle of liquids in porous media U. Demlehner

97

The main principles of modelling of porous solids. Models of systems with needle-like particles A.P. Karnaukhov

105

Adsorption-desorption hysteresis in porous networks D.K. Efremov and V.B. Fenelonov

115

VI

The determination of the pore size distribution of porous solids using a molecular model to interpret nitrogen adsorption measurements C.A. Jessop, S.M. Riddiford, N.A. Seaton, J.P.R.B. Walton and N. Quirke

123

Standardisation, reference materials and comparative measurements for surface area and pore characterisation E. Robens and K.-F. Krebs

133

Fractal characterization of the porosity of organic tissue by interferometry M. Sernetz, H.R. Bittner, P. Bach and B. Glittenberg

141

Determination of surface properties of porous solids K.S. Birdi, D.T. Vu, S.I. Andersen, A. Winter, H. Topsrae and S.V. Christensen

151

A new apparatus for continuous adsorption. Application to the characterization of microporous solids H. Ajot, J.F. Joly, F. Raatz and C. Russmann

161

A new mercury intrusion-retraction simulator used as a means for the characterization of porous materials C.D. Tsakiroglou and A.C. Payatakes

169

Film surface area measurements for microporosity and surface roughness analysis G.P. Johnston, D.M. Smith, A.J. Hurd and P. Pfeifer

179

Some problems about gas adsorption isotherm measurements by automated procedures in manometric devices J.L. Ginoux and L. Bonnetain

189

Morphological influences on unsteady gas diffusivities in porous solids W. C. Conner, S.W. Webb, P. Buckley, S.V. Christiansen, G. Parthun, J.A. Hansen and H. Topsrae

199

Textural characterization of ultrafiltration membranes by thermoporometry and liquid flow measurement J.F. Quinson, N. Nameri and B. Bariou

209

Characterization of the surface fractal dimension of evaporated silver and gold films through adsorption isotherm measurements J. Krim and V. Panella

217

Influence of pore structure parameters on the intraparticle pressure change during adsorption S.E. Scholl and A.B. Mersmann

225

VII

Neutron scattering investigation of adsorption processes in model porous systems J.D.F. Ramsay and R.G. Avery

235

Small angle and ultra-small angle scattering techniques for characterization of porous materials J.C. Dore and A.N. North

245

Gel-precipitated oxide gels with controlled porosity-determination of structure by small angle neutron scattering and adsorption isotherm measurements J.D.F. Ramsay, P.J. Russell and S.W. Swanton

257

Small-angle neutron scattering study of fumed silica powder compaction A.J. Hurd, G.P. Johnston and D.M. Smith

267

The determination of permeability and binary gas diffusion coefficients in novel forms of porous carbons S.B. Bhowmik, S.P. Waldram, R. McMurray and S.R. Tennison

273

Pore-size analysis for permeability estimation in porous material T. Sat0

283

The effects of pore and particle geometry on NMR diffusion measurements in adsorbed liquids S . Bahceli, A.R.S. Al-Kaisi, K. Krynicki and J.H. Strange

293

Pore size analysis of wet materials via low-field NMR D.M. Smith and P.J. Davis

30 1

Characterization of microporosity and surface homogeneity by the study of argon and nitrogen isotherm crossing and measurement of differential enthalpies of adsorption J.M. Martin-Martinez, F. Rodriguez-Reinoso, Y. Grillet, F. Rouquerol and J. Rouquerol

311

Adsorptive properties of activated carbons prepared from kevlar J.J. Freeman, F.G.R. Gimblett, R.A. Hayes, Z. Mohd. Amin and K.S.W. Sing

319

Modification in porous texture and oxygen surface groups of activated carbons by oxidation M. Molina-Sabio, M.A. Muiiecas-Vidal and F. Rodriguez-Reinoso

329

Adsorption of methanol and water by charcoal cloth A.M. Gonplves da Silva, M.M.L. Ribeiro Carrott, P.J.M. Carrott and M.M. Brotas de Carvalho

341

VIII

Influence of coal preoxidation and reactive gas flow rate on textural properties of active carbons J.A. Pajares, J.J. Pis, A.B. Fuertes, A.J. PCrez, M. Mahamud and J.B. Parra

347

Evaluation of microporosity in steam activated brown coal humic acids chars T. Siemieniewska, K. Tomkow, J. Kaczmarczyk, A. Albiniak, Y. Grillet and M. FranGois

357

Induced porosity in activated carbons by catalytic activation A. Linares-Solano, M. Almela-Alardn, C. Salinas-Martinez de Lecea, M.J. Muii6z-Guillena and M.J. IllPn-G6mez

367

Characterization of activated carbon: an approach to the activation process by SAXS and optical microscopy J.M. Guet, Q. Lin, A. Linares-Solano and C. SalinasMartinez de Lecea

379

Dynamic micropore structures of micrographitic carbons during adsorption K. Kaneko, T. Suzuki, Y. Fujiwara and K. Nishikawa

389

Characterization of the porosity of activated charcoals by adsorption from solution J. FernPndez-Colinas, R. Denoyel and J. Rouquerol

399

The porosity of textile fibre surfaces A. McInally, R.R. Mather and K.S.W.Sing

409

Further comments on low pressure hysteresis in activated carbons: effect of preparation method F. Rodriguez-Reinoso, J.M. Martin-Martinez, A. Linares-Solano and R. Torregrosa

419

Multi-stage micropore filling of N, and Ar by microporous carbon fibers K. Kakei, S. Ozeki, T. Suzuki and K. Kaneko

429

Porous structure of synthetic active carbons N.T. Kartel, A.M. Puzy and V.V. Strelko

439

Evaluation of microporosity in activated carbons with high ash (Cr20,) content M.A. Martinez-Shchez, J.M. Martin-Martinez, A.C. OrgilCsBarcel6, F. Rodriguez-Reinoso and M.J. SellCs-PCrez

449

Influence of coal oxidation on coke porosity J.J. Pis, R. MenCndez, J.J. Lorenzana, A.J. PCrez, H. Marsh and E. Romero

459

IX

Comparative studies of the microporous structure parameters evaluated from the adsorption isotherms of various adsorbates on activated carbons M. Jaroniec, J. Choma, F. Rodriguez-Reinoso and J.M. Mart in-Mart inez

469

Estimating micropore sizes in activated carbons from adsorption isotherms B. McEnaney and T.J. Mays

477

A comparative study of the porous structure of active carbons using benzene and water adsorption, inmersion calorimetry and liquid chromatography K.H. Radeke and P. Briickner

491

Mercury porosimetry of porous glass and active carbon preloaded with n-decane or water H. Lentz and Y. Zhou

499

Sorption of hydrocarbons in silicalite-1 and Nay zeolites J.A. Hampson, R.V. Jasra and L.V.C Rees

509

How can an adsorption system show phase transition. A case study on the adsorption of p-xylene in ZSM-5 D. Pan and A.B. Mersmann

5 19

Crystallochemical structure of zeolite micropores and adsorptionenergetic characteristics G.U. Rakhmatkariev, A.A. Isirikjan

525

Sorption of argon and nitrogen on network types of zeolites and aluminophosphates H. Reichert, U. Muller, K.K. Unger, Y. Grillet, F. Rouquerol, J. Rouquerol and J.P. Coulomb

535

Porosity of silicas: comparison of nitrogen adsorption and mercury penetration D.R. Milburn, B.D. Adkins and B.H. Davis

543

Characterization and stability of porous structure of titanium-silicalite by sorption methods G. Lmfanti, F. Genoni, M. Padovan, G. Petrini, G. Trezza and A. Zecchina

553

Study of the pore network of dealuminated faujasites by water vapor adsorption M.H. Simonot-Grange, A. Elm’Chaouri, M. Nafis, G. Weber, P. Dufresne, F. Raatz and J.F. Joly

5 65

Estimation of pore structure parameters for silica and carbon sorbents by macromolecular adsorption N.A. Eltekova and Yu.A. Eltekov

575

Formation of secondary pores in zeolites during dealumination: influence of the crystallographic structure and of the %/A1 ratio H. Ajot, J.F. Joly, J. Lynch, F. Raatz and P. Caullet

583

Vacuum thermal stability and textural properties of attapulgite J.M. Cases, Y. Grillet, M. Franqois, L. Michot, F. Villieras and J. Yvon

591

Characterisation of porous SiO2-Al20, sol-gels: model heterogeneous catalysts P.A. Sermon, T.J. Walton, M.A. Martin Luengo (Yates) and M. Yates

599

Effect of La(II1) on the thermal stability of Al-pillared montmorillonite J.M. Trillo, M.D. Alba, R. Alvero, M.A. Castro, J. Poyato and M.M. Tobias

607

Evolution of porosity during conversion of n-alumina to a novel porous a-alumina fibre M.H. Stacey

615

Evolution of the texture and the thermic stability of a pilc-A1 with varying dialysis time C. Pesquera, F. Gonzalez, I. Benito and S . Mendioroz

625

Microstructure of ex-hydroxide magnesium oxide & products of rehydration M.M.L. Ribeiro Carrott, P.J.M. Carrott, M.M. Brotas de Carvalho and K.S.W. Sing

635

Texture and surface properties of supported metallic oxide catalysts: Na-doped, titania and alumina-supported vanadia M. del Arco, E. Hernandez, C. Martin, I. Mateos and V. Rives

645

Sorption of water vapour by partially decomposed calcium hydroxide K.S.W. Sing, C.R. Theocharis and D. Yeates

653

Texture and sintering of zirconium dioxide-yttrium oxide ceramics A.J. Lecloux, S . Blacher, P.-Y. Kessels, P. Marchot, J.L. Merlo, F. Noville and J.P. Pirard

659

The porosity and permeability of macrodefect free cements K.S.W. Sing and M. Yates

669

XI

An appraisal by M.I.P. of the changes induced in the microstructure of complex sulfide ores by reactive thermal treatments in H2 and N2 M. Fatemi-Sadr and P. Bracconi

677

The adsorption of water vapour by microporous solids P.J.M. Carrott, M.B. Kenny, R.A. Roberts, K.S.W. Sing and C.R. Theocharis

685

Porosity of ancient Egyptian mortars J. Ragai, K.S.W. Sing and M. Yates

693

The porous structure of polymeric sorbents of different nature L.D. Belyakova

70 1

Determination of spatially resolved pore size information B. Ewing, P.J. Davis, P.D. Majors, G.P. Drobny, D.M. Smith and W.L. Far1

709

The influence of porous structure and external morphology on the activity of catalyst spheres prepared by the sol-gel method A.Q.M. Boon, C.J.G. van der Grift, A.J.W. van Veldhuizen and J.W. Geus

717

Characterization of porosity and pore quality in sedimentary rocks M.E. Cather, N.R. Morrow and I. Klich

727

Surface characterization of an upper-permian carbonate rock by N2 adsorption P.J. Mnller, P. Frykman, N. Stentoft and Chr.B. Koch

737

The adsorption of sulphur by macroporous materials L. Daza, S . Mendioroz and J.A. Pajares

747

The differences in the adsorption processes in micro and supermicropores 0. Kadlec

759

Author Index

77 1

Keyword Index

775

Studies in Surface Science and Catalysis (other volumes in the series)

779

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XI11

PREFACE

Since 1958, when the first major conference on porous solids was held at Bristol, U.K., considerable progress has been made in the development and characterization of porous materials. The subsequent international symposia held in 1978 (at Neuchfttel, Switzerland) and in 1983 (Milan, Italy) were well supported and led to the decision to arrange further symposia at regular intervals. As a result the first IUPAC Symposium on the Characterisation of Porous Solids (i.e. Cops I) was held at Bad Soden, F.R.G., in 1987, after which it was decided to hold COPS I1 at Alicante, Spain, in 1990. Following the success of COPS I, the Scientific Committee wanted to encourage a wide range of scientists and technologists to participate in COPS I1 and to provide them with the opportunity to authoritatively assess the progress which had been made in theoretical, experimental and applied research. The Symposium was organised by Professor F. RodriguezReinoso and his colleagues of the Departamento de Quimica Inorghica e Ingenieria Quimica. It consisted of a plenary lecture by Professor K.S.W. Sing, 153 oral and poster presentationsmd an extensive exhibition of equipment. It brought together 222 participants from 29 countries. This volume contains 82 of the papers which were selected and deemed worthy of publication. The organizers wish to express their special thanks to IUPAC for sponsoring the meeting and to the Ministerio de Educaci6n y Ciencia, Universidad de Alicante and Repsol Petr6leo for its generous support which made it possible to hold COPS I1 at Alicante. It has been decided that COPS 111 will be held at Marseille, France in 1993. F. Rodriguez-Reinoso, J . Rouquerol, K.S. W. Sing and K.K. Unger

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F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids II 1991 Elsevier Science Publishers B.V., Amsterdam

CHARACTERIZATION OF POROUS SOLIDS: Kenneth S.W.

A N INTRODUCTORY SURVEY

Sing

Department o f Chemistry, B r u n e l U n i v e r s i t y , Middlesex, UB8 3PH, U n i t e d Kingdom.

Uxbridge,

BACKGROUND The widespread i n t e r e s t in porous solids i s well i l l u s t r a t e d by t h e multifarious n a t u r e o f t h e c o n t r i b u t i o n s t o t h i s volume. Much o f t h e w o r k r e p o r t e d was u n d e r t a k e n o n materials o f technological importance such as adsorbents, c a t a l y s t s a n d constructional materials a n d t h e solids s t u d i e d include carbons, oxides, cements, clays, polymers, zeolites a n d metal films.

In view o f t h i s wide d i v e r s i t y o f interest, it i s p e r t i n e n t t o a s k whether such a b r o a d l y based symposium i s l i k e l y t o b e u s e f u l from a scientific standpoint. T h e f i r s t IUPAC Symposium o n t h e Characterization o f Porous Solids was h e l d in 1987 (i.e. COPS I, Elsevier, 1988) a n d it was e v i d e n t In h i s i n t r o d u c t o r y then t h a t t h e r e was a need f o r f u r t h e r systematic w o r k . paper, E v e r e t t d r e w attention t o some o f t h e o u t s t a n d i n g problems i n c l u d i n g the important requirement o f p r e d i c t i n g technological performance from t h e r e s u l t s o f characterization measurements. T h i s became a l l t h e more u r g e n t w i t h t h e development o f advanced materials a n d shape selective catalysts which r e q u i r e t h e application o f sophisticated characterization techniques. T h e way was t h e r e f o r e p r e p a r e d f o r t h e COPS I I Symposium t o b e h e l d in 1990 a n d t h e o p p o r t u n i t y was t h e n t a k e n t o review t h e status o f t h e more traditional techniques s u c h as a d s o r p t i o n a n d fluid penetration alongside t h e newer experimental techniques a n d computational procedures (e.g. small angle scattering, computer simulation a n d molecular modelling). This introductory s u r v e y i s n o t designed t o p r o v i d e a systematic appraisal o f t h e w o r k described here, but r a t h e r t o set t h e scene f o r these Proceedings of an important symposium. TERMINOLOGY AND MODEL SYSTEMS

'

The ubiquity o f porous materials has led t o confusion in t h e usage o f such terms as 'micropore', 'macropore', ' t o t a l p o r e volume' a n d ' i n t e r n a l area'. In t h e IUPAC classification o f p o r e size, t h e micropore w i d t h i s t a k e n to n o t exceed about 2 nm ( 2 O R J . t h e mesopore w i d t h t o be in t h e r a n g e 2-50 nm In r e c e n t years a n d t h e macropore w i d t h t o b e above about 50 nm ( 0 . 0 5 pm). these d e f i n i t i o n s have s e r v e d u s well, especially in t h e c o n t e x t o f gas adsorption a n d m e r c u r y porosimetry, but it i s becoming i n c r e a s i n g l y clear t h a t some refinements a r e r e q u i r e d a n d t h a t account should b e taken o f p o r e shape. It i s a p p a r e n t t h a t t h e p o r e s t r u c t u r e s o f many systems o f technological importance (e.g. building materials) a r e made up o f cracks, cavities a n d channel n e t w o r k s o f v a r y i n g size, shape a n d c o n n e c t i v i t y . On the other hand, p o r e s t r u c t u r e s can now b e p r e p a r e d w h i c h a r e remarkably u n i f o r m a n d correspond f a i r l y closely t o model systems.

2 Zeolitic s t r u c t u r e s o f high S i / A I r a t i o a r e generally q u i t e d i f f i c u l t t o synthesise in t h e form o f l a r g e c r y s t a l s . It i s t h e r e f o r e n o t e w o r t h y t h a t Unger a n d h i s co-workers have been able t o synthesise l a r g e c r y s t a l s o f T h i s has enabled Reichert e l a l t o g a i n a ZSM-5, Silicalite 1 a n d ZSM-48. much i m p r o v e d u n d e r s t a n d i n g o f t h e i n t r i n s i c p r o p e r t i e s o f these zeolites t h a n was f o r m e r l y possible. Molecular seive carbons can now b e p r e p a r e d from v a r i o u s polymeric p r e c u r s o r s . High-resolution electron microscopy has revealed t h a t t h e pores a r e predominanently slit-shaped. O t h e r systems w h i c h e x h i b i t slit-shaped pores a r e t h e p i l l a r e d clays a n d c e r t a i n inorganic oxides p r o d u c e d by t h e controlled thermal decomposition o f p a r e n t h y d r o x i d e s s u c h as Ca(OHI2 a n d Mg (OH) 2 . K a r n a u k h o v has classified p o r o u s solids as spongy a n d corpuscular. Many c o r p u s c u l a r systems a r e unconsolidated o r o n l y weakly aggregated. If t h e area o f contact between a n assemblage o f g l o b u l a r p a r t i c l e s i s small t h e system w i l l behave in some ways as a non-porous powder (e.g. w i t h respect t o gas adsorption). If t h e powder i s subjected t o compaction o r heat treatment it w i l l t e n d t o u n d e r g o a n i r r e v e r s i b l e change. T h e weakly-bonded aggregate i s t h u s c o n v e r t e d i n t o a more compact agglomerate w i t h a well-defined p o r e s t r u c t u r e . Systems o f t h i s t y p e a r e discussed by Karnaukhov, Mason, Ramsay a n d others. D u b i n i n a n d h i s co-workers f i r s t suggested t h a t micropores should b e sub-divided i n t o t w o groups, w h i c h a r e now usually termed ultramicropores a n d supermicropores. Ultramicroporous solids ( o f p o r e w i d t h < ca 0.7 nm) a r e l i k e l y t o e x h i b i t molecular sieve properties, whereas supermicroporous solids g e n e r a l l y have l a r g e r i n t e r n a l areas a n d p o r e volumes w h i c h a r e accessible t o a w i d e r r a n g e o f a d s o r p t i v e molecules. If these somewhat inelegant terms a r e t o b e retained it would b e desirable t o define t h e ranges o f size more p r e c i s e l y in relation t o p o r e shape (e.g. s l i t s a n d c y l i n d r i c a l channels). It i s obvious t h a t as t h e p o r e w i d t h i s r e d u c e d a n d approaches molecular dimensions so t h e absolute magnitude o f t h e p o r e volume becomes more d i f f i c u l t t o evaluate. For t h i s reason it has been recommended t h a t t h e t e r m effective pore volume should b e employed a n d t h e operational p r o c e d u r e used for i t s evaluation c l e a r l y specified.

The COPS-I Symposium (Elsevier, 1988) p r o v i d e d t h e f i r s t o p p o r t u n i t y for a n e x t e n s i v e discussion o f t h e r o l e o f f r a c t a l analysis in t h e characterization o f t h e t e x t u r e o f solids. A l t h o u g h some aspects a r e open t o c r i t i c i s m t h e r e i s l i t t l e d o u b t t h a t f r a c t a l geometry has been shown t o b e a useful tool in t h e analysis o f data obtained w i t h porous solids o r r o u g h surfaces. T h e studies by K r i m a n d Panella, Johnston e t al, Dore a n d N o r t h a n d Sernetz a n d h i s co-workers i l l u s t r a t e t h e application o f f r a c t a l geometry for t h e analysis of v a r i o u s t y p e s o f experimental data obtained w i t h r o u g h surfaces a n d p o r o u s materials. A t t h e v e r y least, t h e proponents o f f r a c t a l analysis can j u s t i f i a b l y claim t h a t t h e approach p r o v i d e s a systematic basis for t h e analysis o f experimental data obtained w i t h s t r u c t u r a l l v complex nlHerials. U n f o r t u n a t e l y , t h e r e s u l t s o f t h e analysis a r e ofte; difficult to interpret! ADSORPTION Experimental Techniques T h e measurement o f a d s o r p t i o n a t t h e g a s / s o l i d i n t e r f a c e continues t o b e one o f t h e most p o p u l a r techniques f o r t h e s t u d y o f microporous a n d

3 It i s n o t s u r p r i s i n g t h e r e f o r e t h a t many papers in t h i s mesoporous solids. symposium a r e concerned w i t h t h e determination a n d i n t e r p r e t a t i o n o f gas adsorption data.

Great advances have been made in t h e development o f automated equipment f o r a d s o r p t i o n isotherm measurements, but it i s n o t always easy t o o b t a i n reliable data. Robens a n d Krebs stress t h e d e s i r a b i l i t y o f c a l i b r a t i n g new i n s t r u m e n t s w i t h t h e a i d o f reference materials a n d Ginoux a n d Bonnetain also d r a w a t t e n t i o n t o some o f t h e l i k e l y sources o f e r r o r in isotherm measurements. The papers by Conner, Kaneko, Rouquerol, U n g e r a n d t h e i r co-workers u n d e r l i n e t h e importance now attached t o t h e determination o f p h y s i s o r p t i o n isotherms a t v e r y low levels o f surface coverage o r fractional micropore filling, i.e. in t h e r e g i o n o f v e r y low p / p o . Such high resolution a d s o r p t i o n (HRADS) measurements have been shown t o b e especially u s e f u l f o r t h e characterization o f the a d s o r p t i v e p r o p e r t i e s o f zeolites, aluminophosphates a n d molecular sieve carbons. Another b e n e f i t o f automated instrumentation i s t h a t t h e detailed course o f a n isotherm can b e established o v e r a n y pre-selected r a n g e o f p/po. Equipment o f t h i s t y p e o p e r a t i n g in t h e mode o f continuous flow was f i r s t used by Rouquerol a n d h i s co-workers in conjunction w i t h microcalorimetry The results o f f o r s t u d y i n g changes in state o f t h e adsorbed phase. continuous a d s o r p t i o n measurements a r e also r e p o r t e d h e r e by Ajot e t al. Micropore F i l l i n q It is now generally agreed t h a t p h y s i s o r p t i o n w i t h i n t h e n a r r o w e s t micropores ( i .e. t h e ultramicropores) does n o t i n v o l v e monolayer formation, but instead takes place p r e f e r e n t i a l l y a t v e r y low p / p o ( i n i t i a l l y a r o u n d p / p o / v T h i s process i s associated w i t h enhanced adsorbent-adsorbate interactions a n d r e s u l t s in a n appreciable d i s t o r t i o n o f t h e a d s o r p t i o n isotherm. T h e mechanism o f p h y s i s o r p t i o n in t h e wider micropores ( i .e. t h e supermicropores) i s much less well understood, but appears t o i n v o l v e cooperative adsorbate-adsorbate interactions so t h a t a d s o r p t i o n takes place a t somewhat h i g h e r p / p o (-0.01-0.2) by an assemblage o f molecules, i.e. giving quasi-multilayer formation. In t h i s connection it i s o f i n t e r e s t t o n o t e t h e f i n d i n g s o f Nicholson a n d T a n & Gubbins. These two p a p e r s deal w i t h a d s o r p t i o n in model slit-shaped pores w i t h i n a g r a p h i t i c s t r u c t u r e ; t h e former by t h e application o f g r a n d canonical emsemble simulation t o follow t h e a d s o r p t i o n o f a r g o n a n d t h e l a t t e r by t h e use o f meanf i e l d density-functional t h e o r y t o model t h e behaviour o f methane a n d ethane. These studies appear t o s u p p o r t t h e view t h a t favourable circumstances e x i s t f o r t h e filling o f pores o f p a r t i c u l a r dimensions (in relation t o t h e molecular diameter) a n d p o i n t t h e way f o r f u r t h e r w o r k .

T h e q u e s t i o n o f t h e v a l i d i t y o f t h e Dubinin-Radushkevich ( D R ) equation continues t o a t t r a c t a good deal of attention. Many a u t h o r s s t i l l use t h e DR p l o t f o r t h e assessment o f t h e micropore volume whilst o t h e r s a r e more cautious in t h e i r i n t e r p r e t a t i o n o f t h e d e r i v e d values o f micropore volume a n d p o r e width. Confirmation i s p r o v i d e d in a p a p e r by Rodriguez-Reinoso a n d h i s co-workers t h a t excellent agreement can b e obtained between t h e values o f micropore volume obtained by extrapolation o f DR p l o t s a n d t h e corresponding a -plots p r o v i d e d t h a t c e r t a i n conditions a r e f u l f i l l e d - namely t h a t t h e microposre size d i s t r i b u t i o n i s n o t too broad. T h e Alicante scientists also draw a t t e n t i o n t o t h e d i f f i c u l t y o f o b t a i n i n g suitable non-porous reference materials when dealing w i t h microporous carbons h a v i n g high a s h contents. Kaneko a n d h i s co-workers have n o t e d t h a t some DR p l o t s appear t o e x h i b i t a succession o f linear regions. These features a r e i n t e r p r e t e d in terms of a multistage mechanism o f micropore filling, i.e. an extension o f t h e p r i n c i p l e s o f p r i m a r y a n d cooperative micropore filling.

4 As McEnaney a n d Mays p o i n t out, t h e simple DR equation i s based o n t h e assumption t h a t t h e micropore s t r u c t u r e i s homogeneous, i.e. t h a t a l l t h e micropores in t h e adsorbent g i v e t h e same characteristic a d s o r p t i o n potential, E Since t h e equation has a v e r y general mathematical form, t h i s requirement'cannot b e tested by simple inspection o f t h e DR p l o t a n d t h e r e i s l i t t l e d o u b t t h a t most microporous solids a r e s t r u c t u r a l l y heterogeneous.

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To overcome t h i s problem Dubinin, McEnaney, Stoeckli a n d Kadlec have proposed generalised forms o f t h e DR equation w h i c h in p r i n c i p l e should b e applicable t o heterogeneous microporous solids. In practice, t h e main problem in a d o p t i n g t h i s approach i s t o a r r i v e a t a u n i q u e solution for t h e p r o b a b i l i t y d e n s i t y f u n c t i o n o f E a n d hence t h e micropore size d i s t r i b u t i o n . These aspects a r e discussed in &me detail by McEnaney a n d Mays.

As mentioned earlier, a d s o r p t i o n microcalorimetry i s a n invaluable technique f o r s t u d y i n g t h e thermodynamic p r o p e r t i e s o f adsorption systems. The paper by Martin-Martinez e t a l p r o v i d e s a good example o f how adsorption e n t h a l p y measurements can y i e l d a clearer understanding o f the mechanisms o f micropore filling a n d surface coverage. A n improved isosteric method has been developed by Rees a n d h i s co-workers. T h e i r measurements have revealed energetic heterogeneity in t h e adsorption o f ethane a n d propane by Silicalite I . Jessop e t a l have developed a novel p r o c e d u r e f o r computing t h e p o r e size d i s t r i b u t i o n from n i t r o g e n isotherm data. T h e method i s based o n t h e application o f mean-field t h e o r y f o r t h e calculation o f a set o f isotherms c o r r e s p o n d i n g t o pores o f g i v e n w i d t h a n d it i s claimed t h a t t h e molecular model p r o v i d e s a realistic representation o f t h e adsorbed fluid in pores of a l l sizes a n d t h a t t h e method can t h e r e f o r e b e used f o r b o t h micropore a n d mesopore analysis. A limited number o f comparisons have been made w i t h more conventional methods o f p o r e size analysis, but it i s p r o b a b l y too e a r l y t o judge t h e success o f t h i s i n t e r e s t i n g approach. A d s o r p t i o n Hysteresis It i s well k n o w n t h a t c a p i l l a r y condensation in mesopores i s generally associated w i t h hysteresis. Progress has been made in linking t h e characteristic shapes o f c e r t a i n h y s t e r e s i s loops w i t h t h e n a t u r e o f t h e p o r e s t r u c t u r e , but much remains t o be done t o e x p l a i n t h e mechanisms of mesopore filling a n d emptying. T h e p a p e r s by Mayagoitia, Neimark a n d Efremov a n d Fenelonov o n t h e r o l e o f porous n e t w o r k s show how f u r t h e r p r o g r e s s can b e made by t h e systematic computer-assisted analysis o f a number o f c a r e f u l l y selected model systems. The fundamental question o f whether t o adopt t h e adsorption o r desorption b r a n c h of t h e h y s t e r e s i s loop f o r mesopore analysis remains unresolved. Indeed, it seems l i k e l y t h a t t h e r e i s no simple answer, but t h a t t h e computational p r o c e d u r e should b e g o v e r n e d by t h e p o r e geometry a n d n e t w o r k configuration.

F o r many years it was t h o u g h t t h a t a n y h y s t e r e s i s appearing before t h e onset o f c a p i l l a r y condensation was t h e r e s u l t o f slow e q u i l i b r a t i o n o r inaccurate measurements. It i s now known, however, t h a t t h e r e a r e two t y p e s of low-pressure h y s t e r e s i s which a r e associated w i t h p a r t i c u l a r systems. The f i r s t i s a well-defined h y s t e r e s i s loop appearing a t p/po/v 0.1 a n d g i v e n f o r 'This loop has been s t u d i e d example by N2 isotherms o n HZSM-5 a t 77K. in some detail by MUller a n d Unger, who a t t r i b u t e it t o a phase transformation T h e p r e s e n t paper by Pan a n d Mersmann ( l i q u i d - l i k e t o solid-like s t r u c t u r e s ) . p r o v i d e s a somewhat d i f f e r e n t explanation based o n a combination o f localized a d s o r p t i o n o n a r a n g e o f surface sites a n d i n t e r a c t i o n between adsorbed molecules.

5 The second t y p e o f low-pressure h y s t e r e s i s extends down t o much lower p r e s s u r e a n d i s d u e t o e i t h e r a n i r r e v e r s i b l e change in t h e adsorbent (e.g. swelling o r surface chemical change) o r t o t h e slow passage o f molecules t h r o u g h v e r y n a r r o w p o r e entrances o r between small aggregated Rodriguez-Reinoso a n d h i s co-workers now r e p o r t new r e s u l t s particles. w i t h microporous carbons, w h i c h reveal t h a t t h e development o f low-pressure hysteresis i s dependent o n t h e atmosphere ( C O z o r a i r ) in which t h e carbons The a u t h o r s o f f e r t h e t e n t a t i v e explanation t h a t t h e a r e activated. appearance o f t h i s t y p e o f h y s t e r e s i s i s associated w i t h t h e development o f d i f f e r e n t surface s t r u c t u r e s . Adsorption o f Water Vapour A number o f papers in t h i s volume a r e concerned w i t h t h e adsorption o f water vapour, which is o f g r e a t importance in t h e c o n t e x t o f gas separation o r r e s p i r a t o r y protection. Since a c t i v a t e d c a r b o n f i l t e r s have a low a f f i n i t y f o r water vapour, v e r y l i t t l e p o r e b l o c k i n g o c c u r s a t low r e l a t i v e h u m i d i t y . However, i f t h e r e s p i r a t o r i s used in a humid atmosphere o r t h e c a r b o n p r e v i o u s l y exposed t o water vapour, t h e adsorption e f f i c i e n c y i s seriously impaired. The w o r k o f C a r r o t t e t a l has revealed t h a t Silicalite i s in e f f e c t more h y d r o p h o b i c t h a n a n y microporous carbon s t u d i e d so far, since it has both low a f f i n i t y a n d low capacity f o r water vapour. It i s suggested t h a t t h e low water capacity i s d i r e c t l y related t o t h e t u b u l a r n a t u r e o f t h e i n t r a c r y s t a l l i n e channels in Silicalite a n d t h a t a thin l a y e r o f hydrogen-bonded water molecules can more easily form w i t h i n t h e slit-shaped pores o f a c t i v a t e d carbons. A d s o r p t i o n f r o m Solution A d s o r p t i o n from solution measurements have been employed f o r many years t o characterize i n d u s t r i a l adsorbents, but t h e data obtained a r e o f t e n Rouquerol a n d h i s co-workers have now made a difficult to interpret. systematic s t u d y o f a series o f a c t i v a t e d charcoals in w h i c h t h e r e s u l t s of adsorption from solution a r e compared w i t h data obtained by gas a d s o r p t i o n B y a d a p t i n g t h e @ -method, t h e y have shown t h a t a n d immersion calorimetry. t h e adsorption o f benzene from ethanol solutio8 is comparable w i t h t h a t o f n i t r o g e n from t h e gas phase a n d t h a t t h e a d s o r p t i o n from solution data obtained w i t h p r o b e molecules o f d i f f e r e n t shape p r o v i d e a u s e f u l means o f s t u d y i n g t h e enlargement o f mciropore entrances. Another i n t e r e s t i n g s t u d y o f solution a d s o r p t i o n r e p o r t e d h e r e i s t h a t o f Eltekova a n d Eltekov o n t h e a d s o r p t i o n o f macromolecules by mesoporous It i s e v i d e n t from t h i s w o r k t h a t t h e a d s o r p t i o n o f these carbons a n d silicas. large solute molecules can b e optimised by c o n t r o l o f t h e p o r e s t r u c t u r e a n d it is tempting t o suggest t h a t 'micropore filling' e f f e c t s should b e t a k e n i n t o account. F L U I D PENETRATION AND FLOW As E v e r e t t has p o i n t e d o u t (see COPS I , Elsevier, 1988, p.7). t h e d e n s i t y o f porous solids i s n o t a s t r a i g h t f o r w a r d concept. A problem o f i n t e r p r e t a t i o n arises when t h e volume occupied by a g i v e n mass o f solid appears t o b e dependent o n t h e fluid (gas o r l i q u i d ) displaced. This disparity is indicative o f differences in t h e degree o f penetrationof t h e f l u i d s i n t o t h e p a r t i c u l a r pore s t r u c t u r e a n d may b e t h e r e s u l t o f e i t h e r molecular s i e v i n g o r t h e effects o f capillarity. Wetting behaviour i s o f t e n discussed in terms o f contact angle measurements, but t h e paper by Demlehher draws a t t e n t i o n t o t h e d i f f i c u l t y o f

6 obtaining agreement between contact angles determined by d i f f e r e n t methods. A way o f a v o i d i n g t h e contact angle problem i s discussed in t h e paper by Winter, which deals w i t h w e t t i n g a n d displacement o f liquid in single pores a n d c a p i l l a r y networks. Another problem i s t h e swelling which occurs when porous polymers a r e immersed in organic l i q u i d s o r even subjected t o vapour However, Belyakova has f o u n d t h a t t h i s may be minimised by t h e sorption. choice o f a d s o r p t i v e a n d c o n t r o l o f p / p o . M e r c u r y Porosimetry M e r c u r y porosimetry i s featured in many o f t h e c o n t r i b u t i o n s t o t h i s volume. Indeed, it i s now one o f t h e most popular methods available f o r t h e characterization o f a wide r a n g e o f porous materials a n d t h e d e r i v e d p o r e The method i s sizes a r e o f t e n quoted in t h e patent a n d technical literature. based o n t h e non-wetting n a t u r e o f m e r c u r y a n d t h e application o f t h e Washburn equation. T h e volume o f m e r c u r y p e n e t r a t i n g i n t o a porous solid i s determined as a f u n c t i o n o f t h e applied pressure, which i s assumed t o be d i r e c t l y related t o t h e p o r e width. In spite o f t h e g r o w i n g p o p u l a r i t y o f m e r c u r y porosimetry a n d t h e ready availability o f excellent automated equipment, t h e i n t e r p r e t a t i o n o f t h e m e r c u r y i n t r u s i o n - e x t r u s i o n data i s s t i l l f a r from clear. The values o f surface tension a n d contact angle which must b e i n s e r t e d in t h e Washburn equation a r e s t i l l u n c e r t a i n - as a r e t h e limits o f applicability o f t h e equation itself. Other problems include t h e r e v e r s i b l e o r i r r e v e r s i b l e deformation o f t h e p o r e structure, which undoubtedly occurs w i t h some corpuscular o r weakly agglomerated systems.

Many d i f f e r e n t explanations have been proposed f o r t h e appearance o f i n t r u s i o n - e x t r u s i o n hysteresis which appears t o b e a u n i v e r s a l feature o f m e r c u r y porosimetry. The paper by Day e t al helps t o p r o v i d e a b e t t e r u n d e r s t a n d i n g o f t h i s phenomenon a n d also t h e related i r r e v e r s i b l e entrapment o f mercury. The I C I scientists have extended a n d improved t h e By n e t w o r k model approach o r i g i n a l l y used by Haynes, Mann a n d Conner. computer simulation o f a three-dimensional n e t w o r k it i s possible t o model t h e pathways o f advancing a n d receding m e r c u r y threads a n d explore t h e effects o f b l o c k i n g a n d k n o c k i n g o u t pores. The w o r k i s s t i l l in progress, but t h e comparisons w i t h real systems made so f a r indicate t h a t a mechanism i n v o l v i n g t h e spontaneous nucleation o f t h e m e r c u r y meniscus a t t h e s t a r t o f e x t r u s i o n i s untenable a n d t h a t some form o f a i r seeding i s p r o b a b l y essential. C a r e f u l experimental w o r k in t h e IC I laboratories has confirmed t h a t a high level o f r e p r o d u c i b i l i t y can b e achieved in p a r t i a l intrusion, scanning a n d r e c y c l i n g experiments. Lentz a n d Zhou have c a r r i e d o u t a n i n t e r e s t i n g investigation o f t h e effect on m e r c u r y i n t r u s i o n o f p a r t i a l l y filling t h e pores w i t h another liquid. T h e y explain t h e i r r e s u l t s by postulating a change in t h e contact angle, but t h i s explanation i s open t o question in view o f t h e complexity o f t h e p o r e s t r u c t u r e s s t u d i e d so f a r . However, it should b e r e w a r d i n g t o c a r r y o u t more w o r k of t h i s t y p e w i t h c a r e f u l l y selected systems. Davis a n d h i s co-workers have extended t h e i r investigations o f well-defined porous silicas. They r e p o r t f a i r l y good agreement between t h e p o r e volumes a n d p o r e size d i s t r i b u t i o n s determined by m e r c u r y porosimetry a n d n i t r o g e n adsorption, but lack o f agreement between t h e corresponding surface areas. ( T h e l a t t e r values calculated from t h e m e r c u r y i n t r u s i o n c u r v e s a r e These a n d o t h e r appreciably h i g h e r t h a n t h e corresponding BET-areas) r e s u l t s u n d e r l i n e t h e u r g e n t need f o r more fundamental w o r k t o p r o v i d e a more r i g o r o u s basis f o r t h e i n t e r p r e t a t i o n o f m e r c u r y porosimetry data.

.

F l u i d Flow T h e r a t e o f movement o f f l u i d s i n t o a n d t h r o u g h porous media i s o f g r e a t importance in a g r i c u l t u r e , c i v i l engineering, catalysis a n d separation As Conner e t a l p o i n t out, many attempts have been made t o technology. correlate permeability ( o r t r a n s p o r t resistance) w i t h t h e morphology o f a However, it i s n o t s u r p r i s i n g t o find t h a t no simple c o r r e l a t i o n porous solid. can b e f o u n d between t h e t r a n s p o r t p r o p e r t i e s a n d t h e p o r o s i t y as s t u d i e d by Another complication i s t h a t gas a d s o r p t i o n o r m e r c u r y porosimetry. adsorption k i n e t i c s a r e notoriously d i f f i c u l t t o model a t t h e molecular level. Thus, a l t h o u g h gaseous d i f f u s i o n in zeolites a n d molecular sieve carbons has been widely studied, t h e data in t h e l i t e r a t u r e show many anomalies a n d inconsistencies. The problems encountered in experimental permeability studies a r e Quinson e t al; discussed in a number o f papers (e.g. Sato; Bhewmik e t al; A n unexpected development o f high permeability in Sing a n d Yates). porous p l u g s o r membranes i s o f t e n t h e r e s u l t o f uneven macropore o r c r a c k formation during manufacture, storage o r operation (e.g. dimensional changes In t h e i r s t u d y o f model systems, Kanellopoulos a n d h i s o f membranes). co-workers discuss t h e effects o n gas permeability o f d i f f e r e n t forms o f n e t w o r k heterogeneity. It appears from t h i s a n d o t h e r studies t h a t similar changes in permeability a n d percolation thresholds may o r i g i n a t e in q u i t e d i f f e r e n t ways a n d h i g h l i g h t s t h e need f o r caution in t h e i n t e r p r e t a t i o n o f permeability data. A n a l t e r n a t i v e approach i s p r e s e n t e d in t h e paper by Mason a n d Mellor, which follows t h e e a r l i e r w o r k by Mason (see COPS I ) o n In t h e i r p r e s e n t paper, a t t e n t i o n i s g i v e n t o percolation a n d n e t w o r k theory. beds o f packed spheres a n d it i s c o n c l u d e d t h a t s u c h systems can b e t r e a t e d However, as n e t w o r k s a r r a n g e d in t h e form o f t h e 3-D diamond lattice. simulation o f drainage a n d imbibition appears t o indicate t h a t t h e b o n d a n d c a v i t y sizes a r e n o t randomly d i s t r i b u t e d t h r o u g h o u t t h e n e t w o r k . Mass t r a n s p o r t The role o f t h e p o r e s t r u c t u r e in mass t r a n s p o r t in adsorbents a n d catalysts i s discussed in t h e papers by Scholl a n d Mersmann a n d Boon e t al. In t h e former s t u d y , which i n v o l v e s modelling t h e a d s o r p t i o n kinetics, allowance i s made f o r t h e e f f e c t o f v a r i a t i o n o f total p r e s s u r e o n concentration a n d temperature p r o f i l e s w i t h i n a spherical p a r t i c l e a n d t h u s simulate t h e T h e o t h e r s t u d y by Boon e t a l i s conditions o f p r e s s u r e swing adsorption. concerned w i t h t h e behaviour o f porous oxide-based c a t a l y s t spheres p r e p a r e d by t h e sol-gel method. A l t h o u g h t h e y deal w i t h v e r y d i f f e r e n t systems a n d circumstances, these t w o papers b o t h d r a w a t t e n t i o n t o t h e importance o f macroporosity in d i f f u s i o n c o n t r o l a n d mass t r a n s p o r t . M I SC ELLAN EOUS TECH N IQUES Microscopy A l t h o u g h t h e y do n o t appear t o occupy a prominent place in t h e p r e s e n t volume, microscopic techniques continue t o p l a y a v i t a l r o l e in t h e Thus, confidence can b e gained in characterization o f many porous materials. the i n t e r p r e t a t i o n o f adsorption o r flow data if independent evidence can b e obtained o f p o r e shape o r t e x t u r e u n i f o r m i t y . T h e paper by Pis e t a l p r o v i d e s a good example o f t h e application o f optical microscopy. In t h i s case,image-analysis has been used t o p r o v i d e a q u a n t i t a t i v e evaluation o f t h e number, size a n d shape o f pores in cokes The r e s u l t s a r e compared w i t h t h e p r o d u c e d by p r o g r e s s i v e oxidation. m e r c u r y i n t r u s i o n data a n d t h e t w o techniques shown t o b e complementary.

8 The use o f thin section analysis a n d fluorescent microscopy f o r t h e s t u d y o f sedimentary oil-bearing r o c k s i s described in t h e paper by Cather e t al. H i g h resolution electron microscopy i s f e a t u r e d in many o f t h e papers presented here. A l t h o u g h TEM i s n o t easy t o apply, it has been used successfully t o s t u d y micropore a n d mesopore shape in s u c h d i v e r s e systems as modified zeolites (e.g. in t h e w o r k o f A j o t e t a l l , alumina f i b r e s (by Stacey) a n d t h e thermal decomposition p r o d u c t s o f Mg(OH)2 ( R i b e i r o C a r r o t t e t a l l . T h e successful outcome o f these a n d o t h e r studies has t o a l a r g e e x t e n t depended o n t h e c a r e f u l a t t e n t i o n g i v e n t o thin sectioning o r o t h e r forms o f T h e application o f SEM i s o f course less demanding a n d sample preparation. i s o f p a r t i c u l a r value f o r t h e i n v e s t i g a t i o n o f p a r t i c l e / c r y s t a l shape a n d aggregate s t r u c t u r e . SEM i s now g e n e r a l l y r e g a r d e d as an extremely u s e f u l a n c i l l a r y tool f o r s t u d y i n g t h e morphology a n d secondary p o r e s t r u c t u r e o f zeolites, oxides a n d carbons a n d o f multicomponent systems such as cements. Small A n g l e S c a t t e r i n g T h e use o f small angle s c a t t e r i n g techniques f o r s t u d y i n g porous solids i s well established, but it i s o n l y in r e c e n t years t h a t t h e i r full potential has been appreciated. Several p a p e r s in t h e p r e s e n t symposium i l l u s t r a t e t h e application o f small angle n e u t r o n (SANS) a n d X - r a y (SAXS) scattering. Ramsay a n d A v e r y have c o n t i n u e d t o a p p l y SANS in t h e i r studies o f porous oxides: in t h e i r p r e s e n t paper t h e y u t i l i s e H 2 0 / D 2 0 m i x t u r e s t o investigate mechanisms o f p o r e filling a n d conclude t h a t s i g n i f i c a n t differences a r e apparent between t h e state o f adsorbed water in mesoporous silicas a n d microporous ceria. In another paper, Ramsay a n d h i s co-workers r e p o r t t h e f i n d i n g s o f e x t e n s i v e SANS a n d adsorption studies o f a r a n g e o f h y d r o u s oxide gels in a polymer m a t r i x . Stacey has used SANS along w i t h gas adsorption a n d TEM t o investigate The t h e development o f p o r o s i t y in alumina f i b r e s made by Sol-gel methods. SANS p a t t e r n s were a n j m n e t r i c a n d t h i s together w i t h o t h e r evidence indicated O t h e r SANS studies a r e t h a t t h e pores were s t r o n g l y a x i a l l y aligned. r e p o r t e d by Dore a n d N o r t h a n d H u r d e t al. The w o r k by t h e former a u t h o r s i n v o l v e d an i n v e s t i g a t i o n o f H O/D,O in p o r o u s silica a n d oil-bearing rocks. It is e v i d e n t t h a t t h e f r a c t a l dimensionality as calculated from t h e s c a t t e r i n g data i s d i f f e r e n t f o r n e u t r o n s a n d X-rays. This difference is attributed to t h e presence o f 'occluded pockets' in t h e i n t e r f a c i a l r e g i o n in giving d i f f e r e n t e f f e c t i v e roughness factors f o r n e u t r o n s a n d X-rays. Spectroscopic a n d o t h e r methods O f t h e numerous techniques r e f e r r e d t o in t h i s volume a n d n o t discussed so far, special mention must b e made o f F T l R a n d NMR. These techniques may b e a p p l i e d in many d i f f e r e n t ways a n d f o r v a r i o u s reasons i n c l u d i n g s t u d y o f t h e p o r e s t r u c t u r e a n d t h e p r o p e r t i e s o f adsorbed o r occluded material. F T l R i s especially u s e f u l f o r t h e characterization o f surface species a n d t h e state o f adsorbed molecules. A s t u d y o f s u p p o r t e d o x i d e catalysts i n v o l v i n g F T l R a n d a d s o r p t i o n measurements i s r e p o r t e d by Rives a n d h i s co-workers a n d t h e use o f F T l R as a n a n c i l l a r y technique i s r e f e r r e d t o in several o t h e r papers. NMR measurements have been c a r r i e d o u t in t h e c o n t e x t o f image analysis (NMRI) o f p o r e s t r u c t u r e s (Ewing e t al), determination o f d i f f u s i v i t i e s o f adsorbed species (Bahceli e t al) a n d t h e p o r e s t r u c t u r a l analysis o f wet materials (Smith a n d Davis). Such techniques as F T l R a n d NMR have t h e g r e a t advantage t h a t t h e y impose v e r y l i t t l e p e r t u r b a t i o n o n t h e system. In c o n t r a s t techniques s u c h as thermoporometry may i n d u c e s t r u c t u r a l changes. T h i s method, which i s

9 based o n t h e relation between p o r e size a n d t h e f r e e z i n g p o i n t o f c a p i l l a r y condensate, i s f e a t u r e d in t h e paper by Quinson e t a l o n t h e t e x t u r e o f polycarbonate membranes. CONCLUSIONS AND RECOMMENDATIONS

It i s g r a t i f y i n g t o see t h a t t h e characterization o f porous solids i s now a t t r a c t i n g t h e attention o f many d i s t i n g u i s h e d mathematicians, scientists a n d technologists a n d t h a t steady p r o g r e s s i s b e i n g made in modelling t h e behaviour o f idealised p o r e s t r u c t u r e s a n d in a p p l y i n g new a n d improved experimental techniques. On t h e o t h e r hand, it is e v i d e n t t h a t a number o f It i s hoped t h a t t h e following general fundamental problems remain unsolved. recommendations w i l l help t o p o i n t t h e way f o r w a r d in p r e p a r a t i o n f o r COPS I l l . 1. E v e r y e f f o r t should b e made t o a p p l y experimental techniques in a complementary manner r a t h e r t h a n t o t e s t t h e r e s u l t s o f one p r o c e d u r e against those o f another. T h e main a t t r i b u t e s o f t h e most p o p u l a r techniques s u c h as gas adsorption a n d m e r c u r y porosimetry a r e already well k n o w n a n d it i s equally important t o recognise t h e i r limitations. 2. T h e r e i s an u r g e n t need f o r t h e f u r t h e r development a n d p r o d u c t i o n o f a range o f well-defined porous adsorbents a n d membranes. A t t e n t i o n should b e g i v e n t o t h e uniformity o f p o r e size a n d shape a n d t o mechanical a n d thermal s t a b i l i t y .

The lead t a k e n by Robens a n d o t h e r s in t h e d i s t r i b u t i o n o f information a n d reference materials should b e encouraged a n d s u p p o r t e d by the a p p r o p r i a t e national a n d i n t e r n a t i o n a l organizations.

3.

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F. Rodriguez-Reinoso et al. (Editors), Characterization of Porous Solids II 0 1991 Elsevier Science Publishers B.V., Amsterdam

11

SIMULATION OF ADSORPTION IN MODEL MICROPOROUS GRAPHITE

DAVID NICHOLSON Department of Chemistry, Imperial College of Science, Technology and Medicine, London SW7 2AY, U.K.

SUMMARY Grand ensemble Monte Carlo simulations have been carried out for Lennard-Jones models of Ar and N, in model graphite pores. The potentials were initially validated using plane surface experimental data for graphite. The pore model consisted of graphite 0001 planes separated by integer multiples of the graphite interplanar separation (D=0.3375nm) with H=3.0,4.0 and 5.OD where H is the C-centre to centre distance across the pore. Isotherm and isosteric heat curves are reported which support the view that intermolecular cooperative interactions are important in micropore filling. Zero coverage heats show little enhancement above the plane surface values, but cooperative effects produce quite substantial increases in pq,, at higher coverage. INTRODUCTION Nitrogen and Argon are both used extensively as adsorptives for the characterisation of porous materials, particularly at 77.5K. In spite of the ubiquity of such measurements, many fundamental questions remain to be answered in regard to these adsorption systems. Computer simulation can be a valuable technique to this end because it affords the opportunity to elucidate the behaviour of clearly defined model systems and relate this to experimental observation.

Provided that the

simulation can be based on reliable premisses, it may then be possible to restrict the types of model which are feasible, even though exact emulation of experimental observation may be difficult. Adsorption in micropores is of particular interest in this context because, whilst the importance of micropores is now widely recognised, it is difficult to obtain simple well characterised microporous adsorbents, of indeed to be confident that such materials have been discovered, given the difficulfy and complexity of interpretation. The present study is based on three assumptions: (i) Properly executed simulations give a valid account of the statistical mechanics of the system under investigation. (ii) Potential functions which are able to reproduce the main features of the bulk adsorptives and of adsorption on plane surfaces, can be carried over to pore models. (iii) Micropores in graphite are formed by separation of 0001 graphite planes held apart at integer multiples of the interplanar spacing in graphite (taken as 0.3375nm here).

12 The adsorptives were modelled using the 12-6 potential model with the parameters given in Table 1, where

E,,

o, and E

~

om . are the potential well depths and hard sphere diameters for the

adsorbate and adsorbate adsorbent potentials respectively. Clearly this is less satisfactory for N, than for Ar since, in spite of the fact that free rotation is to be expected to reduce the quadrupole effects in the bulk phase above 40K, it is not necessarily the case that this also applies to the adsorbate. This reservation seems to be borne out by the results reported below. Nevertheless it has proved valuable here to be able to compare two similar models which differ only in their molecular parameters. Because of its particular combination of molecular size and interactions the Ar-graphite system is difficult to model with precision at the temperature of interest. A useful touchstone for evaluating model potentials is provided by the liquid to incommensurate solid transition exhibited by this system at 77.5K. It is also of interest in the present context to know how porosity affects this transition.

TABLE 1. Properties of the model adsorptives a

(E,/k)/K

oJnm

Ar

120 95.2

0.3405 0.375

N,

62.5 52.1

2.0 2.0

0.96 1.0

0.4 1.23

For nitrogen a superficially similar transition is observed but here the larger size and weaker intermolecular interactions of the nitrogen molecules ensures that the adsorbate on graphite exists as commensurate structures near to monolayer coverage on graphite, and the transition is from a liquid

to a commensurate solid state. PORE MODEL AND SIMULATION METHODS The dimensions of the pore models studied are listed in table 2. Here H is the distance between C-centres in opposite planar pore walls, D is the separation of the graphite planes (taken as 0.3375nm) and H'=H-D. In keeping with the integer separation model adopted here it was assumed that the ABAB stacking of nonporous graphite would be maintained for the pore structure. It would of course be of some interest to examine this assumption further, especially for the smallest pore size. A notable feature of table 2 is the difference in the number of hard sphere diameters inside the pore for each adsorbate. In the 12-6 model the interlayer spacing in an fcc lattice is very close to o, so that whereas an integer number of layers of Ar is readily accommodated in this packing this is not the case for N,.

Schoen and co-workers (1) have noted interesting effects in the singlet distribution

functions arising from imperfect accommodation in pores of different widths whereby a new layer

13 gradually ‘squeezes in’ as the pore width is increased. The present work shows how this behaviour affects the shape of adsorption isotherms. In all the pore models studied a double minimum is retained in the adsorbent potential field, but overlap effects produce an attractive field even at the pore centre. The simulations were carried out in the grand (v,V,T) ensemble. The molecular interactions were cut off at the surface of a cylinder, with axis normal to the graphite planes, of radius 3.50, centred on a ’trial’ molecule. Long range corrections, using a mean field assumption (4) and frequently updated

TABLE 2. The Pore Model

II

H/D

H/nm H’/nrn H’/aA, H’/o,,

5.0 4.0 3.0

1.688 1.350 3.965 3.600 1.350 1.013 2.975 2.701 1.013 0.675 1.982 1.800

stacking

AB AA AB

II

densities, from the singlet distribution across the pore, were applied at each step. The validity of this procedure was verified by carrying out a few simulations with cutoff at 5.00. The pressure was calculated from the corrected chemical potentials assuming ideal gas behaviour for the vapour phase. Various initial configurations were investigated, including pores which had been filled at very high pressures; commensurate and incommensurate states and empty pores. Hysteresis was observed in the H=5.OD and in the H=3.OD pores for Ar, but not for N., observed at H=7.000,,

In previous work with N, hysteresis was

but not at H=5.000a, (=5.55D) (2,3). Once the existence of a stable and

reversible configuration had been established, subsequent runs were initiated by readjusting the pressure to the desired value and permitting filling or emptying to proceed until a new converged region was reached. The length of simulation run depended on pressure, degree of filling and initial configuration; averages were taken over at least 1 . 5 ~O6 1 configurations; uncertainties in isotherm points is ca 0.05% but can be as high as 5% in the q , values in the region of the maxima since these are calculated as fluctuations (4).

RESULTS FOR PLANE SURFACES The adsorbate-adsorbent potential was modelled on the basis of summation over 12-6 potentials using the familiar truncated Fourier expansion representation (5). The height of the surface barriers was modified, as described in detail elsewhere (6,7,8), by introducing a parameter h, such that 1=-1gives a smooth surface, and hzl raises the surface barriers by a factor of (l+h) compared to the corrugation from an unmodified 12-6 potential. A second adjustable parameter Q was introduced to allow for the possibility of repulsion between adsorbate atoms in the adsorbed layer adjacent to the

14 wall. A fuller discussion of these parameters has been given elsewhere (8); the values used in this work are summarised in table 1, li

Fig. 1. Adsorption on a planar 0001 graphite surface at 77.5K. Experimental data ( + +) and simulation results (...O...)for argon (left hand panel)and for nitrogen (right hand panel). Surface coverage, 8, is in units of close padted incommensurate monolayers for the argon and in u n i t s of c o m m e n s u r a t e monolayers for the nitrogen.

111

9 Ra

Fig. 1 shows the plane surface isotherms for the system studied. It is to be noted that whereas the experimental liquid-incommensuratesolid transition for Ar (9,lO) is well reproduced by the simulation, the strength of the liquid-commensurate solid transition in N, (10,ll) is greatly overstated. For the Ar simulation the potential was readjusted to compensate for corrugation effects so as to produce close agreement between the heats at zero coverage from simulation and from experiment (8). This was not done for N, since these heats were already high (pq,,(O=O)=14.1 from simulation compared to an estimated value of 13.1 from experiment). It is probable that improvement could be achieved for the N, by resort to a diatomic model with quadruples (12). The accurate reproduction of transitions over

a very small range of coverage affords a particularly stringent test of the potential functions and highlights the sensitivity of adsorption isotherms to changes in the interaction energy as noted in earlier work (7,8). ADSORPTION IN MODEL MICROPORES The adsorption isotherms for Ar, plotted as coverage versus pressure, are shown in Figs. 2, 3 and 4 and those for N, in Figs. 5 and 6. In this form comparison with the plane surface simulation can readily be made. It is clear that pore structure has less effect on the nitrogen adsorption than on the argon adsorption; for the latter the pore filling pressure is shifted by roughly an order of magnitude for each pore width. For N, the shift is approximately half of this, reflecting the weaker interaction between N, molecules compared to that for Ar (table l ) , and is one indication of the importance of cooperative interactions in pore filling. The Ar isotherm for H=5.OD (Fig. 4) has an essentially type IV character and follows the plane surface isotherm very closely up to 8-0.83 at this point it branches, the lower branch has a transition, similar to that observed on the plane surface, from a liquid-like to an extremely stable

15 1.o

0.8

-

0.6

-

0.4

-

8

0.03

Fig. 2. Ar adsorption in a model pore with H=3.OD, H’=l.980 at 77.5K. The inset shows the initial Henry’s law region. Coverage is in units of incommensurate monolayers on the plane surface

0.02

0.01

0.00 0.0 0.5 1.0

I

0.2

-

-

-

0.0

.,.

1.5 2.0 2.5 3.0

__________-___----0.5

0.0

1.0

1.5

2.0

2.5

I

a

3.0

3.5

Fig. 3. Ar adsorption in a model pore with H=4.OD, H’=2.97o at 77.5K. The dotted line shows the adsorption on a plane surface. Coverage is in units of incommensurate monolayers on the plane surface

2.5

I ~‘~/atnr

2.0

1.5

e 1.0

0.5

0.0

Fig. 4. Ar adsorption in a model pore with H=5.OD, H’=3.98o at 77.5K. The dotted line shows the adsorption on a plane surface. Coverage is in units of incommensurate monolayers on the plane surface

+ .....

e&..

P

1 , 5

f5

25

35

Io * P / ~ ~

45

16 solid-like monolayer, (as judged by the very low free energy calculated from the pressure virial (4)). There is then a transition to the filled state. The upper branch remains stable over a wide range of pressure. The thermodynamic transition pressure could be determined by Gibbs ensemble 'pore-pore' simulations (13). The N, isotherm in the H=5.OD pore is also type IV, the plane surface isotherm is again followed to the pre-transition coverage, where the adsorbate forms stable monolayers on the

two surfaces but no sharp liquid-solid transition occurs. In contrast to the Ar isotherm, adsorption beyond the monolayer then continues up to 8-1.2 before the whole pore fills. The departure from the plane surface behaviour at this stage is mainly attributable to an incipient layer in the centre of the pore which is manifested in the singlet distributions as a weak double maximum, whereas Ar shows singlet distribution function maxima only at the pore walls up to the point at which filling occurs. The differences in isotherm shape are therefore related to the inability of the pore to accommodate an exact number of fcc layers of N, within the pore width chosen for the model. A striking difference between these two isotherms is the complete absence of hysteresis for the nitrogen. This strongly suggests that hysteresis is largely an artefact of the simulation; its occurrence for Ar being related to the much stronger Ar-Ar interactions, and to the well-known inability of simulation to produce crystalline structures from disorganised starting configurations. For N, the interactions are much weaker and fcc structures within the pore are not possible.

Fig. 5. Adsorption of 12-6 nitrogen at 77.5 in model graphite pores. H=4.OD, H'=2.70 (0); H=5.OD, H'=3.& (A); plane surface (...O...)

Fig. 6. Adsorption of 12-6 nitrogen in a model graphite pore with H=3.OD, H'=l.80. The inset shows the initial Henry's law region.

17 In the H=4.OD pore the isotherms change their character, that for N, is close to type I, departure from the plane surface isotherm occurs when 8> 0.5 and there is again a remaining vestige The stronger interactions between Ar atoms lead to a much more of the monolayer transition at 8-1 .l. rapid rise above the plane surface adsorption in this isotherm (Fig. 3). No clear filling transition is apparent for either adsorbate at H=4.OD but the concave shape of the Ar isotherm to the 8 axis associated with adsorption well above the plane surface level is strongly indicative of the way in which pore structure acts to enhance the effects of intermolecular interactions. In the smallest pore studied (H=3.OD) a strong transition is observed (Figs. 4 and 6), but this is now a sub-monolayer transition akin to that which occurs at these low coverage in larger pores and on plane surfaces, but usually masked, as it is here for the H=4.0 and 5.OD pores, by the small pressure scale over which it can be resolved. This is illustrated by exhibiting the initial Henry's law region for the H=3.OD isotherms. Adsorption on the plane surface is now quite negligible over the pressure scale of these graphs. The Ar isotherm again exhibits a much sharper transition than that for N, and it is possible that a narrow hysteresis loop exists in this region. As before, no hysteresis loop was found for the N, isotherm where the transition is also much more gradual. The Ar isotherm fills to a complete monolayer between p-2.5~10.~ atm and 2 0 ~ 1 atm. 0 ~ Adsorption occurs even more .~ slowly above the transition for N, than for Ar and is not complete until ~ - 1 0 atm. At the next pore size (H=2.OD), according to the model investigated here, potential overlap is such that Ar is only weakly attracted, and N, is excluded under normal pressures. It is worth noting that a similar model, based on expanded graphite spacings (14), would accommodate both adsotptives. The isotherms can alternatively be displayed as fractional filling plotted against relative pressure. The relative pressure at which pore filling occurs is similar for both adsorptives for the H=3.OD and H=4.OD pores, being approximately 7 ~ 1 0and . ~ 2 ~ 1 0respectively. .~ At H=5.OD however the relative pressures of the filling transition are O.O2(N,) and 0.002(Ar). There is ambiguity about the definition of fractional filling because of the uncertainty concerning the state of the adsorbate. Argon

liq. 1.05 1.13

sol.

liq.

sol.

liq.

sol.

0.909 1.03

0.894 1.04

0.903

0.902 1.21

0.965 1.22

0.968

to be solid-like, both because of the temperature (T*=0.67) and because of the very nearly exact is expected accommodation of the fcc lattices. For N, the Situation is less clear, the liquid state would seem to be the more probable at this temperature, however singlet distribution functions (Fig. 7) show that ordered layering occurs, suggesting that a solid-like state exists within the pores, even though the

18 layers are not always complete. The values of fractional filling, W/W, within the filled pores, show that neither the liquid, nor the solid hypothesis is entirely satisfactory: solid densities are not reached, but densities are in excess of those of the bulk liquid - especially for N., No significant trend with pore size is apparent in table 3 for Ar, but the N, density increases in the DNo smaller pores.

'I 6 .

Fig. 7. Singlet distribution functions for n-n at a pressure of 0.02 atm (P/PO=0.016). The full line is for the H=5.OD pore, the p ( l ) triangles for the plane surface.

,

2 .

0 .

I

-2 0.5

t.0

1.5

20

25

30

3.5

I

4.0

z/a

The isosteric heat curves are shown in Figs. 8 and 9. The plane surface curves exhibit characteristic maxima with cusped minima near to the transition, as observed in experiment and 40

35-

7

25

5

30-

3:

. I

25

.

lo ~

--

*.-*.-*

f

20

% -

Fig. 8. lsosteric heats of adsorption for argon in model graphite pores at 77.5K plotted against coverage, 8. H=3.OD (v);H=4.OD (0); H=5.OD (A); plane surface ( 0 )

10

Fig. 9. lsosteric heats of adsorption for 12-6 nitrogen in model graphite pores plotted against coverage (commensurate monolayer units). Symbols as in Fig. 8.

19 discussed elsewhere (7). Up to a coverage of 8=0.8,the heats for the 5.OD pores show only minor departure from the plane surface data, but the maximum is stronger. In the 4.OD pore initial slopes are noticeably steeper; it is likely that maxima also occur here but if so they were not resolved in these simulations. The increasing importance of intermolecular interactions is demonstrated more clearly in the heats for the smallest (H=3.OD) pores which have high initial slopes and are displaced well above the plane surface curve. The enhancement of the initial heat (Sq,,(e=O)) is small in the H=3.OD pores and negligible for the larger pores (table 4) TABLE 4. lsosteric heats of adsorption at zero coverage Plane HID= surface

5.0

4.0

3.0

Ar enhancement

15.03

15.2 1.01

15.50 1.03

17.00 1.13

N* enhancement

14.10

14.28 1.01

14.62 1.04

16.35 1.16

DISCUSSION AND CONCLUSIONS The isotherms and heat curves reported here differ in many respects from those normally associated with experimental results (14,l 5) from adsorption in graphite micropores. Typically these give fairly smooth type I isotherms, and heat curves which decrease rapidly from an initial maximum; the latter may show inflections but do not have maxima at high filling.

One reason for these

differences may be the difficulty in making measurements at sufficiently high resolution, even with present day equipment; another could stem from the inevitability of pore size distributions in experimental materials. The model examined here also suffersfrom several defects and uncertainties,

thus, even if the basic tenet of integer spacings is accepted, there is uncertainty about the graphite plane spacings (14) and the role played by graphite edge planes which could be very significant, as could wedge rather than parallel geometry. Nevertheless a number of observations may be made which have consequences both for future simulation studies as well as for the interpretation of experimental data: (i) The simulation results emphasise again (7,8)the extreme sensitivity of isotherms (plotted in the usual way as adsorption versus pressure) to small modifications in the interaction potentials. Qualitative differences,such as sharpness of a transition as well as quantitative differences may result from such changes. (ii) The mechanism of micropore filling is responsive to these changes in two ways: firstly even quite a small increase in the potential at a wall, due to overlap from the potential at the opposite wall

20 significantly alters the adsorption at a given pressure; this effect is amplified by the consequent increase in the adsorbate intermolecular field acting initially in a lateral direction. In the present work this is clearly seen in the difference between the 5.OD and the 4.OD pores; in the former overlap effects are insufficient to perturb the normal monolayer formation process, it is only when second layer adsorption begins that the influence of pore structure is evident; at this stage second layer molecules from opposite pore walls can interact strongly with each other and pore filling occurs. In the smaller pores both overlap effects and adsorbate interactions from the opposite wall can occur simultaneously and reinforce one another leading to a cooperative process. These phenomena are manifested in the change in initial slope and final maximum of the differential enthalpy curves, especially those for the smallest pore. It is possible that some of this 'intermolecular enhancement' is seen in experimental data for real materials with size distribution as high initial isosteric heats; if so its presence would be difficult to distinguish from surface heterogeneity enhancement. In any case no other feature of the present model can account for the high initial heats observed experimentally. (iii) Differences between Ar and N, as a probe are shown to be manifested in ways other than mere size effects. These come about firstly because the cooperative effects referred to above are magnified as E increases and secondly because of the more subtle influence of perfect or imperfect accommodation of the molecules by the pore. ACKNOWLEDGEMENTS I wish to thank the University of London Computer Centre for a generous allowance of computer time and Dr. N.G. Parsonage and Prof. W.A. Steele for helpful discussions.

REFERENCES 1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

M.Schoen, D.J.Diestler and J.H.Cushman, J.Chem.Phys. 87, 5464 (1987). J.P.R.B.Walton and N.Ouirke, Mol. Simulation. 2,361 (1989). N.A.Seaton, J.P.R.B.Walton and N.Quirke, Carbon, 27, 853 (1989). D.Nicholson and N.G.Parsonage, "Computer simulation and the statistical mechanics of adsorption", p.97, Academic Press (London,New York) (1982). W.A.Steele, Surface Sci. 82, 817 (1973). D.Nicholson, L.A.Rowley and N.G.Parsonage, Mol. Phys. 44,629, (1981). D.Nicholson and N.G.Parsonage, J. Chem. SOC..Faraday Trans.2, 82, 1657 (1986). D.Nicholson, R.F.Cracknell and N.G.Parsonage, Mol. Simulation, in press (1990). Y.Grillet, FRouquerol, J.Rouquerol, J. Chim. Phys. 2,179 (1977), J.Coll. and Interf. Sci. 70, 239, (1979). Y.Lahrer, J.Chem. Phys. 68,2257, (1978). D.M.Butler, G.B.Huff, R.W.Toth and G.A.Stewart, Phys. Rev. Lett. 35,1718, (1975). J.Talbot, D.J.Tildesley and W.A.Steele, Mol. Phys. 1331 (1984). A.Z. Panagiotopoulos. Mol. Phys. 62,701, (1987). K.Kakei, S.Ozeki, TSuzuki and K.Kaneko, J. Chem. SOC.Faraday Trans. S, 371 (1990). K.Kaneko, T. Suzuki, K. Kakei, Langmuir, 5,879,(1989). D.Atkinson, P.J.M.Carrot, Y.Grillet, J.Rouquerol and K.S.W.Sing, Fundamentals of Adsorption p.89, ed. A.I.Liapis, (Engineering Foundation, New York) (1987).

s,

21

F. Rodriguez-Reinoso et al. (Editors), Characterization of Porous solids II 0 1991 Elsevier SciencePublishersB.V., Amsterdam

THEORY OF ADSORPTION IN MICROPORES Ziming Tan and Keith E. Gubbins School of Chemical Engineering, Cornell University Ithaca, New York 14853, U.S.A. ABSTRACT We test three theories for adsorption and capillary condensation in pores against computer simulation resulcs. They are the Kelvin equation, and two forms of density functional theory, the local density approximation (LDA) and the (nonlocal) smoothed density approximation (SDA); all three theories are of potential use in determining pore size distributions for mesoporous solids, while the LDA and SDA can also be applied to microporous materials and to surface area determination. The SDA is found to be the most accurate theory, and has a much wider range of validity than the other two. The SDA is used to study the adsorption of methane and methane-ethane mixtures on models of porous carbon in which the pores are slit-shaped. We find that an optimum pore size and gas pressure exists that maximizes the excess adsorption for methane. For methaneethane mixtures we show the variation of selectivity with pore size and temperature. INTRODUCTION Although adsorption data and mercury porosimetry are widely used to characterize porous materials [l], the classical methods for interpreting such data rely on equations that are more than 40 years old, and are of uncertain validity, particularly for micropores and small mesopores.

The most important

of these equations are those of Brunauer, Emett and Teller (BET), Kelvin, and Dubinin and Radushkevitch (DR) and their modified forms [l]. The BET equation neglects adsorbate-adsorbate interactions, heterogeneity of the surface, and variations in properties of adsorbed layers after the first; nevertheless, it usually gives a good account of low pressure adsorption, especially for nonporous materials.

The Kelvin equation assumes (a) the vapour phase is ideal, (b) the

liquid phase is incompressible,with a molar volume that is negligible compared to the gas, and (c) the system is large enough for the surface tension to be a useful concept.

Assumptions (a) and (b) will lead to significant errors at

higher temperatures, especially as the capillary critical point is approached, while approximation (c) will lead to increasing errors as the pore size decreases.

Thus, molecular dynamics simulations of small drops of Lennard-

Jones molecules [ 2 ] have shown that the surface tension

-y

departs significantly

from its bulk liquid value for drop diameters below about 140 (u- molecular diameter), and for drop diameters below 7-8u surface tension ceases to have any

22

meaning (e.g., the various thermodynamic equations involving -y are inconsistent). A similar breakdown occurs in using the Kelvin equation for pores whose diameters are in this region [ 3 1 . The DR equation introduces a single adjustable parameter to characterize the pore-fluid system, and is essentially empirical in nature. Statistical mechanics provides a more reliable and general approach to interpretation of adsorption and porosimetry experiments. At the present time the two most promising approaches are density functional theory and direct molecular simulation (Monte Carlo or molecular dynamics).

The simulation

approach [ 4 ] has the advantage that the statistical mechanical equations are solved exactly for the prescribed model of the pore geometry and intermolecular interactions; it is relatively easy to incorporate surface structure and heterogeneity and a variety of pore geometries and irregularities. The principal disadvantage is cost; a simulation for a single state point usually takes one to several hours on a fast computer.

The density functional theory [ 5 ]

calculations are faster by about one to two orders of magnitude, and provide both more detailed insight and higher accuracy than the classical methods currently in use.

Two principal forms of the theory exist, a local and a nonlocal form

(these terms are defined in the following section), the nonlocal form being the more accurate. The nonlocal theory gives a good description of adsorption and phase transitions in slit pores of all widths, and of cylindrical pores for pore radii down to about 1.60; it describes all six classes of isotherms [l], including step-like ones (class VI), and is good for both subcritical and supercritical temperatures. Its principal limitations are its failure for very narrow cylindrical pores (it does not predict the correct one-dimensionallimit), and its failure to predict the solid-liquid transition for the adsorbate. It has

so

far only been applied to pores of simple geometry having smooth

structureless walls; for more complex pores it is not yet clear whether the theory will offer major advantages over direct simulation methods.

The local

form of the theory has been used recently by Seaton et al. [ 6 ] to obtain pore size distributions from nitrogen isotherm data on carbons. In this work, following a brief description of the density functional theory (Sec. 2 ) ,

we report tests of the theory and of the Kelvin equation against

computer simulation results (Sec. 3 ) .

We also describe (Sec. 4 ) an application

of the density functional theory to the adsorption of methane and methane-ethane mixtures in model carbon pores. MEAN FIELD DENSITY FUNCTIONAL THEORY The fluid-in-pore system is treated as an inhomogeneous fluid at fixed temperature T and chemical potential solid walls of the porous material.

p

in an external field v(r) exerted by the

For this choice of independent variables,

(p,T,V), the appropriate free energy that must be minimized at equilibrium is

23

the grand potential, 0

=

-pV+rS, where p is pressure and S is surface area.

The procedure in density functional theory [S] is to introduce a grand potential functional n[p(r)]

that has the properties that it is uniquely defined once the

density profile in the porous material, p(r),

is defined, and has its minimum

value at equilibrium. We must now write an approximate expression for n[p(r)], and minimize it with respect to p(r) to find the equilibrium density profile. In the mean field approximation, the grand potential functional can be written in the form [3,5,7,8]:

The first two terms on the right side of this equation represent the contribution to the Helmholtz energy due to the short range repulsive intermolecular potential between the fluid molecules, the third term is the corresponding contribution to the Helmholtz energy due to the long range intermolecular potential, ulong(r), in the mean field approximation (setting the pair correlation function in this term equal to unity), and the last term is the contribution from the external field v(r) due to the solid. In the first two terms a(r) is the Helmholtz energy density at the point r in the pore, aid being the ideal gas part and acon the (excess) configurational part due to (repulsive) intermolecular forces.

The

ideal gas part is exactly local, i.e. it can be calculated as the Helmholtz energy density of a uniform fluid whose density is the same as that of the nonuniform fluid at the point r , i.e. p(r).

The second term on the right

contains aconrwhich is nonlocal; i.e. it depends not only on the local density p ( r ) at r in the pore, but also on the density at neighboring points around r. Much attention has been paid to this term in the last few years by theorists,

and current theories can be divided into two forms: (a) the local density approximation (LDA), in which aeon is treated locally, i.e. to the local density p(r);

-p

is simply set equal

and (b) a nonlocal smoothed density approximation

(SDA), in which acOn is calculated as the value for a uniform fluid whose molecules interact with repulsive forces only, andwhose density is some smoothed value p(r).

In both the LDA and SDA this uniform fluid of purely repulsive

molecules is approximated by a fluid of hard spheres of diameter d.

This

approximation is known to be quite accurate, provided d is chosen suitably; often the Weeks-Chandler-Andersenformula is used [9]. In the SDA the smoothing of the density around the point r of interest is intended to account for the effects of the large density gradients that exist in small pores, and is found to work well provided the recipe to calculate

7

is chosen to give an accurate account

of the properties of the uniform fluid. Several such recipes exist [7]. In our

24

work we have chosen to use the one due to Tarazona [ 8 ] , in which 7 is calculated by comparing the first few terms in the virial expansion of the direct correlation function for hard spheres with those from the known Percus-Yevick result. The resulting theory is both tractable and reasonably accurate. It has been extended to mixtures by Tan et al. [lo]. COMPARISON OF THEORIES AND SIMULATION We first compare our SDA results for the excess adsorption per unit of surface area with the grand canonical Monte Carlo (GCMC) simulation results of van Megen and Snook (vMS) [ll]. Calculations were carried out for a LennardJones (LJ) fluid with parameters modeling ethylene in a slit-like carbon pore with a 1 0 - 4 - 3 potential for the solid-fluid potential [12] (see next section). The excess adsorption per unit area, rs, is defined as

where

p(z)

width.

is the density profile, pb is the bulk density, and H is the pore

In Fig. 1 is shown ps

(supercritical) and H* (H/u,)

- 5.

(r$J

Here u1 and

c1

-

s

=

1.35

are the LJ parameters for

ethylene. An adsorption isotherm for a subcritical temperature, T" H"

-

vs p*b ( ~ ~ for 2 ~T*) (kT/a,)

=

0.95, and

10 is shown in Fig. 2. In the SDA results in Figs. 1 and 2 a temperature

I

T' = 1.35

1

0 GCMC (this work)

I

01 0

A GCMC (van Megen and Snaak)

o GCMC (van Megen and SnOOk)

- SDA

- SDA

0 .I

0.2

0.3

0.4 I

0

I

0

0.2

4

I

0.4

0.6

0.8

1.0

P/P"

Fig. 1 Adsorption isotherm for ethylene in carbon pores at a supercritical temperature, ' T 1.35.

-

Fig. 2 Adsorption isotherm for ethylene in carbon pores at a subcritical isotherm, T* = 0.95. The metastable regions predicted by the SDA are included.

25 dependent hard sphere diameter was used [12]. Good agreement between the SDA and computer simulation is found in both cases. In Fig. 3 , we compare the LDA, SDA, and Kelvin equation with molecular dynamics (MD) simulation results for LJ

fluids in cylindrical pores using the results of Peterson et al. [3]. The Kelvin equation is

where po is bulk fluid vapor pressure, y and vL are the surface tension and molar volume of the liquid, N is Avogadro's number, k is Boltzmann's constant, and R is pore radius. Calculations were carried out for a LJ fluid with Ar parameters in a cylindrical pore with a CO, solid wall. F o r the temperatures shown, the SDA results are in reasonable agreement with the simulation.

The LDA gives

noticeably poorer predictions, but better than the Kelvin equation in general. The Kelvin equation is much poorer at the higher temperature, as expected. We note that in the SDA calculations shown in Fig. 3 (taken from Peterson et al. [3]) the hard sphere diameter was taken to be independent of temperature; somewhat better results are to be expected if the temperature dependence is accounted for [12]. RESULTS FOR ADSORPTION IN CARBON PORES We report here results for LJ fluids and mixtures in a model pore of slitlike geometry.

Following our earlier work [12,13,14],the fluid-fluid pair

interaction was described by a cut-and-shiftedLJ potential. The fluid potential parameters [15] chosen to model methane (1) and ethane (2) were: u1

=

cl/k = 148.1K,

0.381nrn

u2

=

0.395nrn,

c2/k

=

243.0K

The 10-4-3model was used for the solid-fluid potential [15]:

with parameters modeling a carbon graphite surface [15]: us

=

0.340nm,

a,/k

=

28.OK,

A

=

0.335nm,

ps

=

114nn1-~.

26 I/' i ; T' = 0.7

R'

Fig. 3 Capillary condensation conditions for IJ Ar in a GO2 cylinder at T* 0 . 7 (left) and 0.85 (right).

-

The cross-parameters, osf and e s f , were calculated using the Lorentz-Berthelot rules. Pure Methane We have examined the excess adsorption per unit of volume of pure methane, which is defined by

In Fig. 4 are displayed the excess adsorption isotherms,

r,,

for H

=

1.9 nm at

temperatures T from 200 K, which is near the bulk fluid critical temperature, to 296 K.

Each isotherm exhibits a maximum. The isotherms are very similar in

shape for the temperatures shown. for We are particularly interested in how the maximum excess adsorption, rvm, versus H. an isotherm varies with pore width, H. In Fig. 5 , we have plotted rvm The results show that for each temperature there is an optimum pore width that maximizes the adsorption. At H" = 1 . 6 4 , rvm falls to zero. For pore sizes below this value we found no adsorption in the pore. Methane/Ethane For the binary mixture, we focussed on the selectivity of component 2 (ethane) relative to component 1 (methane), which is defined as

21

1.5

I.o

0.5

L’ -60

0

Fig. 4 Adsorption per unit pore volume; methane in carbon pores for H = 1.9 nm.

..-- -

I II I 0-

I

I

I

I

z96 K

-- ----__

I

I

Fig. 5 The maximum excess adsorption of methane in carbon pores, rm, vs H.

6.0

,'

H+

I Z - ;1. ' ~ 3

T' = 2.0 (296)

' ,

: e(30.56)

.I , Yb,CH4 = Os ! '"'..~ '\ I ii' ....... --._ ; -._-.. ! 8 - ;: ,. -, \'....... '.C '\

-- - _ -237K -_

'.

I

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

;1:

..__ .............

i!

s

.;I'

I

i /

......252..........

- --- . - -.-. ....................... -._ -

--- -- --- - - - - -26'-

-226-

I

4-,

--

326 3.5 -

I

20

40

60

30

40

Fig. 7 Selectivity of ethane at fixed bulk mole fraction for H 3.05 nm for several temperatures.

Fig. 6 Selectivity of ethane versus pressure at T 296 K and H 3.05 nm for several bulk gas compositions.

-

20

10

0

-

-

where ybl is the mole fraction of methane in the bulk phase, and x1 is the overall mole fraction of methane in the adsorbate phase, given by

In Fig. 6 are displayed the selectivity versus the bulk pressure p for different bulk mole fractions for a fixed pore size, H

=

3.05nrn.

For a solution with high

concentration of methane, (e.g., ybl = 0 . 9 at this temperature), the isotherm passes through a maximum and levels off as the pressure increases.

This type

of S-p isotherm is typical for a fluid at supercritical conditions (we note that the capillary critical point depends on the bulk mole fraction).

For results

at low concentration of methane (e.g.,ybl= 0.1 at this temperature), however, the isotherm exhibits a second maximum.

This type of isotherm seems to occur

when the temperature is near the capillary critical point. The result shown in Fig. 6 is for a rather large pore.

For the ybl values

indicated above, the bulk critical temperatures are 301, 2 6 2 , and 206 K, respectively. The corresponding capillary critical points are shifted to lower values as the pore size is decreased [ 3 ] .

We therefore expect that at a smaller

H value, e.g., 1.0 nrn, S-p isotherms for T

=

296

K will fall into the first type

discussed above for most yhl values.

Fig. 6 Selectivity of ethane versus pressure at T 296 K and H 3.05 nm for several bulk gas compositions.

-

-

Fig. 7 Selectivity of ethane at fixed bulk mole fraction for H 3.05 nm for several temperatures.

-

29

In Fig. 7 we show isotherms for several temperatures from supercritical to sub-critical at fixed bulk mole fraction and pore size. At high temperatures (296 and 326 K) the isotherms are of the first type, passing through one maximum. As the temperature is lowered (252 and 267 K) , the second maximum develops, showing the second type of isotherm. Finally at sub-critical temperatures (237 K) a gas-liquid phase transition occurs. CONCLUSION The SDA form of density functional theory gives generally good results, particularly when the temperature dependence of the hard sphere diameter is accounted for.

It is much superior to both the LDA and the Kelvin equation,

giving a good description of slit-like pores

for all pore widths and

temperatures, and of cylindrical pores for radii down to about 1 . 6 ~ .The Kelvin equation fails for small pores and also for higher temperatures, especially near the capillary critical point.

The SDA should provide a powerful tool for

interpreting adsorption data to characterize pore size distributions and surface area. Since it can describe the whole isotherm over a wide range o f temperatures (in contrast to the Kelvin equation) it should allow a more complete and reliable characterization of porous materials. The calculation of the supercritical adsorption of LJ methane in carbon pores suggests that there exists an optimum pore size for methane adsorbed in porous carbon. At a fixed temperature, the maximum excess adsorption per unit of pore volume passes through a global maximum for a particular pore width.

The

selectivity isotherm for methane-ethane mixtures shows different shapes when the temperature changes. At high temperatures, it passes through a maximum. When the temperature is near the capillary critical one, a second maximum appears. As the temperature is further lowered, phase transition occurs. ACKNOWLEDGMENT We thank the Gas Research Institute and National Science Foundation (grant no. CTS-8914907) for support of this work.

30 REFERENCES

10

11

12 13 14

15

S.J. Gregg and K.S. W. Sing, Adsorption, surface area and porosity, Academic Press, Landon (1982). S.M. Thompson, K.E. Gubbins, J.P.R.B. Walton, R.A.R. Chantry and J . S . Rowlinson, A molecular dynamics study of liquid drops, J. Chem Phys. 81, 530 (1984) . B.K. Peterson, K.E. Gubbins, G.S. Heffelfinger, U. Marini Bettolo Marconi and F. van Swol, Lennard-Jones fluids in cylindrical pores: Nonlocal theory and computer simulation, J. Chem. Phys., 88, 6487 (1988). M.P. Allen and D.J. Tildesley, Computer simulation of liquids, Clarendon Press, Oxford (1987). R. Evans, The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids, Adv. Phys., 28, 143 (1979). N.A. Seaton, J.P.R.B. Walton and N. Quirke, A new analysis method for t h e determination of the pore size distribution of porous carbons from nitrogen adsorption measurements, Carbon, 27, 853 (1989); C.A. Jessop, S.M.Ric?diford, N.A. Seaton, J.P.R.B. Walton and N. Quirke, The determination of the pore size distribution of porous solids using a molecular model to interpret nitrogen adsorption measurement, paper presented at IUPAC Symposium on Characterization of Porous Solids, Alicante, Spain, May 6-9, 1990. C.G. Gray and K.E. Gubbins, Theory of molecular fluids, Vol. 2, Ch. 8, Clarendon Press, Oxford, in preparation (1991). P. Tarazona, Free-energy density functional for hard spheres, Phys. Rev. A, 31, 2672 1985); some of the equations in this paper are incorrect; corrected versions are in P. Tarazona, U. Marini Bettolo Marconi and R. Evans, Phase equilibrium at fluid interfaces and confined fluids: Nonlocal versus local density functionals, Mol. Phys., 60, 573 (1987). J.D. Weeks, D. Chandler and H.C. Andersen, Role of repulsive forces in determinig the equilibrium structure of simple liquids, J. Chem, Phys., 54, 5237 (1971). Z. Tan, U. Marini Bettolo Marconi, F. van Swol and K.E. Gubbins, Hardsphere mixtures near a hard wall, J . Chem. Phys., 90, 3704 (1989). W. Van Megen and I.K. Snook, Physical adsorption of gases at high pressure, I. The Critical Region, Mol. Phys., 45, 629 (1981); Physical adsorption of gases at high pressure 111. Adsorption in slit-like pores, Mol. Phys., 54, 741 (1984). Z. Tan and K.E. Gubbins, Adsorption in carbon micropores at supercritical temperatures, J . Phys. Chem., 94, 6061 (1990). 2 . Tan, K.E. Gubbins, F. van Swol and U. Marini Bettolo Marconi, Mixtures confined to narrow slit pores: Computer simulation and theory, Proc. Third Internat. Conf. on Fund. Ads., Sonthofen, FRG, in press (1990). 2 . Tan, F. van Swol and K.E. Gubbins, Lennard-Jones mixtures in cylindrical pores, Molec. Phys., 62, 1213 (1987). W.A. Steele, The physical interactionof gases with crystalline solids, Surf. Sci., 36, 317 (1973); The interaction of gases with solid surfaces, Pergamon, Oxford (1974).

F. Rodriguez-Reinoso et al. (Editors), Characterization 0fPorou.s Solids II 1991 Elsevier Science Publishers B.V., Amsterdam

31

SORPTION OF GASES ON MICROPOROUS SOLIDS: PORE SIZE CHARACTERIZATION BY GAS SORPTION STEVEN W. WEBB and W. CURTIS CONNER, Department of Chemical Engineering, University of Massachusetts, Amherst, MA, 01003 USA ABSTRACT Characterization of micropores in zeolite crystals may be performed by automated, dynamic, high resolution adsorption. Of the systems considered only nitrogen over ZSM-5 silicalite at 77 K shows an anomalous hysteresis/transition in the micropore sorption isotherm. The presence of aluminum, steaming of the zeolite or thc use of argon @ 77 K or C02 @ -6O'C eliminates the transition and hysteresis. Framework aluminum tends to reduce pore volume and to broaden the pore size distribution. Steaming reduces pore volume, broadens pore size and generates a significant amorphous phase, presumably largely aluminum. The measured pore volume, but not necessarily the pore dimensions, depend on the equilibration time during adsorption. INTRODUCTION It is well known that zeolites enhance selectivity based on the size of their intracrystalline pores. Zeolite crystals exclude or capture molecules based on the ratio of molecule size to pore size. Measurement of pore size by crystal size (e.g., X-ray diffraction) fails to account for the influence of the dynamics of the crystal structure, the dynamics of the sorbing molecules or the interaction between zeolite pore and sorbed molecule. The crystals and/or sorbed phase after sorption may be structurally different from the bulk phase and/or unfilled zeolite. The pore sizes determined in an X-ray analysis may be different from those present during sorption. Thus, it is preferred to study zeolite morphology by a combination of structural and sorption analysis. In this manner, it is possible to study both the state of the zeolite crystals and the state of the sorbed phase and to infer how these influence the amount of sorption of gas phase molecules and the effective micropore size. Solids characterization may be performed by Si29 NMR or XRD. With Si29 NMR, changes in the crystal dimensions due to sorption have been observed (refs. 1-3). Sorbed phase characterization can be studied by volumetric sorption. Thermodynamically simple molecules (e.g., spherical and small) at low temperatures arc used to study pore volume and sizes. A novel, automated, low pressure sorption instrument (Omicron Tech., Berkcley Heights, NJ, USA) has greatly simplified the analysis of zeolites. The technique has recently been named High Resolution Adsorption (HRADS). PORE SIZE CHARACTERIZATION BY HRADS Pore sizes are determined by the amount of sorption of a gas at pressures far less than its saturation pressure. At equilibrium, the free energies of the gas and pore-condensed phase must be equal. The free energy of the sorbed phase depends on the surface energy and the interaction between the pore walls and sorbed molccules. The free energy of the gas is related to its pressure. Sorption in micropores requires very low relative pressures, p/po, attained either with low partial pressures or with high PO. Experimentally, either case proves more difficult than normal mesopore adsorption since quantitative high vacuum is difficult to control and at high po increasing the total amount of sorption is reduced. Also, at low pressures heat transfer is poor and maintcnance of thcrmal equilibrium becomes more difficult. The use of an automated instrument overcomes some of these problems.

Adsorption may c o n f i i the pore size distribution (PSD) and the pore types in the zeolite crystal identified by XRD. However, the crystalline morphology of zeolites during adsorption is not static. The framework may flex or deform with accumulation of a sorbed phase. Structural alterations in the crystal due to sorption have obvious implications for the performance of zeolites in separation/catalysis. Sorption in pure ZSM-5 (i.e., no amorphous phase) is Type 1. However with some adsorbents, transitions (i.e., abrupt change in isotherm slope) and hysteresis, (i.e., sorption and desorption isotherms which do not overlay) have been observed over ZSM-5. The cause of hysteresis and transitions may include, 1) Sorbent: a configurational relaxation of the sorbed phase which depends on the concentration of sorbed molecules; 3-D or 2-D "freezing" or surface phase splitting which alters the density of the sorbed phase. 2) Crystal: a crystallinerearrangement, flexing, or swelling of the crystal structure. 3) Structural: a multimodal PSD or pore network effectsrelated to pore fillinglemptying. Hysteresis in micropore sorption was originally claimed to be due to swelling of the micropores that traps sorbed molecules (ref. 4). Evidence for pore swelling was found (ref. 5) by observing hysteresis in particle volume, conductivity, as well volume adsorbed. This early work was done with microporous carbon, a soft, amorphous solid. With rigid oxide crystals, swelling is not be expected. However, at large length scales the crystal network can flex resulting in distortion of the pore shapes and effectivesizes. Flexing of zeolite crystals has been observed in recent Si29 NMR results (refs. 2-3). Zeolites can undergo crystalline rearrangement. For instance, high silicon ZSM-5 and ZSM-11 undergo a monoclinic-orthorhombic transition at temperatures of 67 and 47°C respectively (ref. 3). Crystalline rearrangement during sorption will alter the pore sizes and could lead to an abrupt transition in the isotherm. However, this effect is equilibrium driven and should occur at a single point (pressure and temperature). Therefore, while a transition in the isotherm can be explained by a crystalline rearrangement, hysteresis cannot. Molecular rearrangement in the gas phase is essential to configurational diffusion in the confined pore space. If it occurs fast, relative to the rate of change of pressure, pore diffusion will be fast and not limiting. If it is slow, then equilibrium will not be maintained and the data will be meaningless. Very low pressures (P), large molecules (low Dconfigurational) and large crystals (Rcrystal) will require very slow pressure changes. For this reason, static sorption (dP/dt = 0) and finite equilibration times must be used for zeolite sorptions.

Pressure changes must also be much slower than the phase transformation rate. If pressure is increased too quickly, non-equilibriumcondensation (i.e., spinodal) may occur. The sorbed phase will be of lower density than is thermodynamicallyfavored. This effect may be due to insufficient freedom in the micropores to permit facile molecular relaxations necessary to create an equilibrium sorbed phase within normal observable times. At some degree of excess pressure (pressure deviation from the thermodynamic phase transition), the metastable condensed phase may relax. Relaxation of molecules in the sorbed phase may cause a change in density which will abruptly alter the micropore filling and produce a transition. For instance, during increasing pressure the density of the sorbed phase may abruptly increase as the sorbed phase goes from a metastable "liquid" to a more stable "ice". During desorption, an amount of under pressure will be required to reform the "liquid phase. Molecular relaxation can be so constrained in the narrow zeolite pore that a condensed, non-equilibrium phase is "frozen" in the pore. This type of transition is analogous to a spinodal decomposition; a spontaneous rearrangement of non-equilibrium phases to stable equilibrium which occurs at a certain amount of excess pressure. Spinodal rearrangement is facilitated by nucleation. For highly localized sorption (e.g. H-bonding or aluminum

33

sites in the lattice), rearrangement may be so fast as to preclude spinodal effects and eliminate the observed transition. Freezing of condensed nitrogen and argon has been reported (refs. 5-6) by microcalorimetric studies over graphitized carbons. Abrupt transitions in sorption isotherms were coincident with increases in the isosteric heat of adsorption. A surface phase transition is claimed. A transition during sorption of p-xylene was observed over ZSM-5 at 70°C by Olsen (ref.7) which they also ascribed to an ordered packing of sorbed molecules. As this represents a ciensification of adsorbed species compared to the liquid, it should be a distinct phase and there would be an associated phase transition for its forrnation.either from the gas or from the liquid states. The spinodal phenomena could explain both hysteresis and the transition. The effect should be experimentally observable if the relaxation time is similar to the experimental times. For zeolite powders, gas phase transport times will be of order 0.1-10 seconds, far less than experimental static equilibration times (> 10 minutes). Sorbed phase relaxation times are unknown but may be large enough to be observed. SORFTION IN ZEOLITES: QUANTITATIVE THEORY Sorption in ZSM-5 particles using nitrogen at 77 K was reported by Unger and Muller (ref.8). Hysteresis was observed at a relative pressure of around 0.1 and spanned a pressure range of 0.05 p/po. At this pressure, most of the micropores are filled. Since the crystals were large, the effect of interparticle surface sorption is minimized. They found that hysteresis was sensitive to three factors: 1) Aluminum and/or cation content: only silicalite (Si/Al> 500) showed hysteresis.

2) Tempcrature: higher temperature (90 K) caused the transition to move to a lower relative pressure.

3) Polarizability of the sorbing gas: argon has no permanent dipole and showed no hysteresis. Venero and Chiou (ref. 9) measured sorption isotherms over ZSM-5, CaA and NaY zeolites using both nitrogen at 77K and argon at 86K. They found that argon gave more accurate predictions of pore sizes of physical mixtures of zeolites than nitrogen. Sorption in micropores can occurs by condensation (refs. 10-11). rather than by multilayer physisorption. Condensation in pores less than 20 8, corresponds to less than 5 sorbent molecules between the pore walls. The Kelvin model is inappropriate for modelling sorption since an equilibrium phase, with continuum properties of surface tension and molar volume, does not exist. The critical parameter controlling the sorption isotherm in micropores is the ratio of pore size/molecule size. The effect of packing of sorbed molecules may be important. The volume of sorbed molecules alone will underestimate the pore volume simply due to the manner in which the sorbed molecules pack in the condensed phase. Unlike a bulk liquid phase in which free fluctuations produce a single phase density, the condensed phase in a micropore is constrained to few configurations leading to many possible densities. The particular density of the sorbed phase will depend on how the phase was assembled during micropore filling. These details of sorption are of no consequence for conventional analysis of meso and macropore sorption. One of the simplest quantitative models was proposed by Horvath and Kawazoe (ref.12) developed for adsorption in active carbons. It is employed in these studies to compare different zeolites, but, recognizing thc differences between active carbons and zeolites, it is only a qualitative measure of pore dimensions. This method (denoted "H-K) is based on statistical thermodynamics of the adsorbed gas molecules on surfaces. They use a 106 Lennard-Jones potential model to relate the free energy of a sorbed gas molecule to the distance between the gas molecule and solid surface. The smallest pore size is constrained by the diameter of the sorbent molecule (e.g., for nitrogen: 3.65 8,). Sensitivity increases with decreasing pore size. The comparison between the pore size predicted by the Kelvin and H-K theories is shown below in figure 1.

34

Pore 2.0 Size

(nm)

1.5

.o

1

0.5 0.0

1 0 . ~.w4 1 0 . ~

lo-'

Relative Pressure, p/p,

ion

Figure 1: Horvath-Kawazoe vs. Kelvin Equation Quantitative Relationship Between Equilibrium Pressure and Micropore Diameter EXPERIMENTAL We studied six (6) zeolite powders, the first four of which were supplied by Haldor Tops@, Denmark and the last two were supplied by Mark Davis of Virginia Polytechnic Institute and by Union Carbide Corp. 1) ZSM-5; silicalite with Si/A1=500, 2) a higher aluminum ZSM-5 zeolite with Si/A1=36, 3) a "mildly" steamed ZSM-5 zeolite with Si/A1=43, 4) a "severely" steamed ZSM-5 zeolite with Si/Al=108

5 ) ZSM-11 6) VPI-5; an aluminophosphate (ref. 14). The crystal sizes were unknown;particle sizes were less than 1 micron. The solids were prepared by drying under vacuum at 350°C for 12 hours at torr . Sorption was studied using an Omnisorb 360 automated sorption instrument (Omicron Technology, USA). By performing a dead volume correction with helium, instrument software calculates the amount sorbed;using the H-K model, the pore size distribution is calculated. Sorbents were: nitrogen at 77 K (liquid nitrogen, p e l atm.), argon at 77 K (liquid nitrogen, po=200 torr), and carbon dioxide at -58°C (dry ice-acetone, p p l atm.). Isotherms were collected in two ways: (1) statically from to 0.1, followed by dynamic from 0.1 to 0.3 p/po and (2) dynamic ad/desorution from 0.01 to 1.0 and back to 50 tom. Static sorption is used to study micropore sizes. Dynamic sorptions explore mesopores and hysteresis in sorption in a quasi-equilibrium manner. The static method base case was 1.5 scc ( 5 minutes add time at 0.3 sccm) of gas charged to the system (volume -47 SCC)followed by an 8 minute equilibration per point. The gas charge determines the resolution and pressure range of the static isotherm. If the sample is weakly sorbing, then a smaller charge is required to resolve thc micropore pressure range. The base case corresponds to a characteristic time of 8+5 =13 minutes per static point. This time is considerably longer than the expected gas phase diffusion time and may be longer than the relaxation time for molecules in the condensed phase. Nevertheless, the equilibration time was varied to look for a phase relaxation influence. The base case dynamic isotherm was collected at 0.3 sccm (47/0.3=150 minute characteristic time). Different flow rates were used to test for a dynamic effect on the transition (which occurs outside the micropore filling pressure range).

35 Desorptions are limited to -50 torr with the current instrument configuration. At low sorbate pressures during desorption, the amount of sorbate leaving the solid becomes so low that the outlet valve is unable to maintain the set flow rate and the analysis fails. RESULTS AND DISCUSSION Nitrogen Isotherms at 77 K Dynamic nitrogen isotherms are shown in Figure 2. Calculated micropores volumes are listed in Table 1. The presence of aluminum causes a reduction in microporosity. Steaming causes a further drop in microporosity perhaps by creation of an amorphous aluminum phase. Steaming, used to reduce framework aluminum, results in the creation of a significant amorphous phase and the redistribution of the crystalline phase to smaller pore sizes. Figure 3 shows the very low pressure (nitrogen at 77 K) region of sorption ("static" base case). The silicalite sorption profile is identical to that reported by Unger and Muller (ref.8). The isotherms and pore size distributions of all three ZSM-5 zeolites are similar. Hysteresis is observed for the silicalite. Our results agree with Unger and Muller (ref.8) and show that the presence of aluminum and/or steaming of the ZSM-5 eliminates hysteresis with nitrogen. PSD's (H-K model) are shown in Figure 4; mean sizes (volume basis) are shown in Table 2. The silicalite ZSM-5 and its higher aluminum companion show peak pore sizes at 5 and 10 A. The ZSM-11 has a sharp peak at 7.4 8,. Both the mildly and severely steamed zeolites have featureless PSD's indicating that most of the micropores are destroyed by steaming. The VPI-5 aluminophosphate has a broad size distribution and mean size of 15.5 A. This compares with a size determined by XRD of 12.6 8, (ref. 13).

'

@ 150 M

v

38 100 e,

-5

>

50

Si/A1>500; UCC)

8

QY

v)

1

aii

ZSM-5 ( s k e d ; Si/A1=43) 0 . - , . I I . , . I 0.0 0.2 0.4 0.6 0.8 1.0 Relative Pressure (p/pO)

-

50

P

0.0

0.2 0.4 0.6 0.8 Relative Pressure (p/pO)

Figure 2: Nitrogen Full Ad/Desorption Isotherms for Selected Zeolites at 77 K

1.0

36

200 175 150 125 100 75 50 25

5 (Si/Al=108; sev. stmed)

0 10-1 loo Relative Pressure (p/po) >ow Pressure Nitrogen Isotherms for Selected Zeolites at 77 K

Figure

Areon Isotherms @ 77K All isotherms are Type I with no hysteresis or transitions. Lack of hysteresis was also found (ref. 12) with argon isotherms at 87 K. The lack of transitions and hysteresis may be due to the greater stability of the condensed phase with argon at this temperature. Micropore volumes (Table I) are ordered the same as nitrogen. Figure 4 shows the low pressure argon isotherms. Venero and Chiou (ref. 9) found that argon (87 K) providcd more accurate pore size discrimination than nitrogen. We find that argon does not discriminate between these zeolites as well as nitrogen does. TABLE 1 Micropore Volumes at Various Temperatures and Sorbenls (measured at 0.3 p/p,)

Zcolite

Sorbcnt

ZSM-5 nitrogen' VPI-5 nitrogen ZSM-5 nitrogen ZSM- 11 nitrogen ZSM-S/Steamed niuogen ZSM-5 argon2 ZSM-5 argon ZSM-S/Steamed argon VPI-5 co23 ZSM-5

co2 COZ co2

ZSM-5 ZSM-11 ZSM-SIS~CZUTIC~ C02

Tempcrature (K) 77 77 77 77

Si/A1 Ratio

77

43 500 36 43

77 77 77 21s 215 215 215 215

(dim) 500

__

36 _.

__

500 36

__

43

Micropore Volume (cc/g) 0.227 0.196 0.195 0.112 0.104 0.207 0.153 0.041 0.215 0.172

0.128 0.108 0.096

l:based on condcnsed phase (liquid) dcnsity of 0.818 gramlcc or 0.00156 cc-liquidlcc-gas 2: based on condensed phase (solid) density of 1.477 grarnlcc or 0.001207 cc-solidlcc-gas 3: based on condensed phase (solid) density of 1.265 gxarnlcc DI 0.001550cc-solidlcc-gas

37 TABLE 2 Pore Size Averages and Pore Volume Using the Horvath-Kawazoe Model with Nitrogen at 77K (0.3 cc step with 8 minutes equilibrate/ pt.) Zeolite Si/A Pore Average Ratio Volume (cc/g) Pore Size (A) ZSM-51 500 0.227 1.4 ZSM-11 __ 0.112 7.4 ZSM-5 36 0.195 9.0 ZSM-S/Steamed 43 0.104 12.6 VPI-5 __ 0.196 15.5 1:

bimodal distribution with peaks at 11 and 5.4 8,

-d

-E 0 v)

12

-

10

w 3

.M

U

O

6

E

4

s

ZSM-5 (Si/Al=36) ZSM-I1 (UCC) ZSM-5 (Si/AI=108) sev. stmcd

.$? 2

so

0.4

0.9

1.4

Pore Size (nm)

1.9

Figure 4: Calculatcd Micropore Size Distributions for Selected Zeolites (Nitrogen at 77 K) Argon Isotherms 0 77K Figure 5 shows the complete argon isotherms. All isotherms arc Type I with no hysteresis or transitions. Lack of hysteresis was also found by Ungcr and Muller [ref. 81 with argon isotherms at 87 K. The lack o l transitions and hysteresis may be due to the greater stability of the condensed phase with argon at this temperature. Micropore volumcs (Table 1) are ordered the same as nitrogen. The reason for the diffcrences between the pore volumes for ZSM-5 and ZSM-11 are unknown but are undoubtedly due to some difference between the sample morphology. Careful inspection of the curves for ZSM-5 in figure 5 show that the desorption branch docs not meet the adsorption branch. We are convinced that this is an cxperimental/analytical artefact. It is not real. Figure 6 shows the low pressure argon isotherms. Venero and Chiou [ref 91 found that argon (87 K) provided more accurate pore size discrimination than nitrogen. We find that argon does not discriminate between these zeolites as well as nitrogen does.

2 E 200j

200

.bO

3 0

150

3 P

175 150 125 100

ZSM-5 (SdAk36)

z ;;

50

2 2 5

0 0.0 0.2

0.6

0.4

0.8

Relative Pressure (p/pO)

Figure 5: Argon Addcsorption Isotherms for Selected Zeolites at 77 K

3, amed)

lo-*

1.0

10-1

loo

Relative Pressure (p/po) Figure 6: Static, Low Pressure Argon Isotherms for Selected Zeolites at 77 K

Carbon Dioxide Isotherms 0 215K Figure 7 shows the addesorptions to 0.3 p/po. The VPI-5 zeolite, which has the largest transition pressure and largest pores, shows pronounced hysteresis. The micropore volumes are shown in Table 1. The increase in transition pressure with higher sorption temperature provides incentive to study micropores with higher temperature sorbates. The micropore volume trend is maintained for nitrogen, argon and carbon dioxide. At the higher temperature (where relaxation and transport processes are presumably faster) there is no increase in micropore volume. Thus, activated sorption, gas diffusion and phase relaxation in the micropores is either much longer, or shorter, than the base case experimental time. This is welcome confirmation of the ability of the static volumetric technique to produce consistent isotherms. 150

13 loo

SM-5 (Si/Ab500) ZSM-5 (Si/A1=36) ZSM-11

50

-5 (Si/A1=43) smcd

P 0.0

0.1 0.2 0.3 Relative Pressure (p/po)

0.4

Figure 7: Ad/Dcsorption Isotherms for Carbon Dioxide for Selected Zeolites at -6O'C

39 AdsorDtion Dvnamics and Hvstercsis Only two isotherms showed hysteresis; silicalite with nitrogen at 77 K and VPI-5 with carbon dioxide at 215K. The VPI sample did not show a pronounced transition and therefore, its non-ideal isotherm is perhaps attributable to a residual small pore amorphous phase. This would be an artifact of the synthesis and has little to do with micropore adsorption. Figure 8 shows dynamic isotherms for various experimental times for ZSM-5 silicalite powder with nitrogen at 77 K. and Figure 9 shows the calculated H-K PSD's from these isotherms. The zeolite pore sizes are not afrcctcd by experimental dynamics. While some resolution is lost, the size distributions are insensitive to expcrimcntal time. The zeolite pore sizes are not affected by experimental dynamics but the pore volumes are effectcd. These rcsults provide confidence in the ability of HRADS to quantitatively size micropores. h

10 1

%

-

Pu 200 v

38

8 min. equil. + 0.2 sccm

100

v1

-z P

0 0.00 0.05 0.10 0.15 0.20 0.25 0.30

Relative Pressure (p/po) Figure 8: Sorption over Silicalite at Varying Experimental Times (Nitrogcn at 77 K)

0.0

0.5

1.0 1.5 Pore Size (nm)

2.0

2.5

3.0

Figurc 9: Porc Size Distribution of Silicalitc at Varying Equilibration Times (Nitrogcn at 77K)

However, it is observed that the Gumulative effect of instrument time is significant and influences the total

d This . means that the amount sorbed dcpends on how the micropores are filled. Longer equilibration time during micropore filling results in less gas sorbed (a more dcnse condcnsed phase) which is an indication of a significant and observable phase relaxation dynamic. Apparently, over 30 minutes is required between data points during micropore filling to achieve equilibrium. Slower flow rate of gas during dynamic sorplion results in more gas sorbed (a lower condensed phase dcnsity, which is counterintuitive) and deviation from Type I behavior. However, the pressure at which the transition occurs is insensitive to experimental times. Pressure range remains 0.15-0.25 and volume change remains constant. The proposcd spinodal relaxation occurs much faster than the experimental times observcd and is indcpcndent of thc dcnsity or thc sorbed phase. The same dynamic experiments were performed with a powder ZSM-5, Si/A1=36. This zcolitc docs not give a transition. The same trends were observed. The dynamics of the adsorption experiment arc important in determining pore volume; however, pore size is relatively insensitive to cxperimcntal dynamics. Howcver, we €ound that with this zeolite, equilibration times of 15-30 minutes produce identical isotherms. Phase relaxation in this solid is apparently faster than in silicalite. The presence of significant aluminum in the framework may incrcase relaxation (perhaps by providing more nucleation sites) and help stabilize thc sorbed phase. This would bc consistent with the influence of aluminum on hysteresis.

40 CONCLUSIONS Nitrogen isotherms at 77 K reproduce the results of Unger and Muller (ref. 8). Only silicalite/nitrogen demonstrates hysteresis. The presence of aluminum and steaming of the zeolite eliminate hysteresis. Nitrogen sorption at 77 K is capable of accurately determining micropore size. ZSM-5 has a bimodal pore size distribution; ZSM-11 has a single sharp peak at 7.3 A. The VPI-5 aluminophosphate has a much larger pore size, 15.5 A, which is comparable to that measured by x-ray diffraction. Argon isotherms at 77 K are qualitidlively similar to nitrogen. Hysteresis is not observed which indicates that increased stability of the condensed phase by sorbing structurally simple gases eliminates hysteresis. Argon isotherms can distinguish pore size diflerenccs as wcll as nitrogen. Carbon dioxide isotherms at -65°C are without hysteresis. Transition pressures are much Ilighcr than with nitrogen and therefore more easily resolved without resorting to high vacuum conditions. The CO2 isotherms can discriminate between the different zeolites tested. C02 shows hysteresis only with VPI-5 large pore size solid which is probably an artifact of that particular solid. Pore size distribution is not greatly influenced by experimental times used in the adsorption. Thus, HRADS is a good technique for micropore size analysis. Volume sorbed depends on experimental times, thus, estimation of pore volume by HRADS may not be reliable.Condensed phase relaxation or a spinodal decomposition in the micropores during adsorption is the probable cause of hysteresis in sorption over high silica ZSM-5. Localized sorption, encouraged by the presence of aluminum, eliminates the hysteresis by decreasing the phase relaxation time and preventing the formation of a metastable state. ACKNOWLEDGEMENTS This work was supported by the Petroleum Research Fund of the America1 Chemical Socicty under grant under grant 22916-ACS. REFERENCES 1. C. Fyfe, G. Kennedy, C. De Schutter, and G. Kokotailo, I. Chem.Soc., Chem. Comm., .54, (1 984) - , 2. G.T. Kokotailo et al., Proceedings of the Seventh International Zeolite Conference, KodanshdElevier, Tokyo, pp. 361, 1986 3. W.C. Conner, P. Vincent, P. Man, and J.Fraissard, Catalysis Letters 4(1) (1990) 75. 4. J.C. Arne11 and H.C. McDermott, Proceedings of the 2nd International Congress on Surlace Activation, 11, pg.122, Butterworth, 1957. 5. J. Rouquerol, S . Partyka and F. Rouquerol, J. Chem.Soc., Far. Trans. I 7 3 (1977) 306-314. 6. Y. Grillet, F. Rouquerol and J. Rouqerol, J. Col. and Int. Sci. 20(2) (1979) 239-244. 7. D.H. Olsen, G.T. Kokotailo and J.L. Lawton, J.Physica1 Chemistry 85 (1981) 2238-2243. 8. K.K. Unger and U. Muller, "Characterization of Porous Solids" K.K.Unger (Ed.) Elscvicr, \ - -

1 088

9.

10. 11. 12. 13.

A. Venero and J. Chiou, Charactcrization of Zeolites by Gas Adsorption at Low Pressures, unpublished, Omicron Technology Corporation, Berkeley Heights, NJ, USA, 1988. M.M. Dubinin, J. Colloid and Interface Science, 23 (1967) 487-499. E.G. Derouane, J.M. Andre, and A.A. Lucas, J.Catalysis, 110 (1988) 58-73. G. Horvath and K. Kawazoe, J. of Chem. Eng. Japan, 16(6) (1983) 470-475. M.E. Davis, C. Montes, P.E. Hathaway, J.P. Arhancet, D.L. Hasha and J.M. Garccs, Physicochemical Propeties of VPI-5, submitted to J.Am.Chem.Soc.(l989).

F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids I1 0 1991 Elsevier Science Publishers B.V., Amsterdam

41

AHALYSIS OF TEE PERCOLATIOI PROPERTIES OF A REAL POROUS HATERIAL Geoffrey KASOB’ and David W. KELLOR’

’

Department of Chemical Engineering, Loughborough University of Technology, Loughborough, L e i c e s t e r s h i r e , England.

BP Research Centre, Chertsey Road, Sunbury-on-Thames,

Kiddlesex, England.

WHHABY A packing of 3,367 equal s p h e r e s f o r which t h e c e n t r e c o o r d i n a t e s were accurately known w a s d i s s e c t e d i n t o 14,870 i r r e g u l a r t e t r a h e d r a l pores. The drainage and imbibition curvatures a s s o c i a t e d with t h e s e pores were calculated using t h e Haines insphere approximation. The network of interconnections of t h e t e t r a h e d r a w a s calculated. Drainage and imbibition of t h e network were simulated using a percolation model. Residual entrapment w a s not modelled. I t is concluded t h a t t h e b e s t regular lattice approximation t o t h e real i r r e g u l a r network is t h e diamond lattice. However, n e i t h e r t h e bond sizes, nor t h e c a v i t y sizes are randomly s i t u a t e d on t h e network and t h e e f f e c t of t h i s non-randomness is t o s i g n i f i c a n t l y s h i f t t h e percolation threshold.

IIITBODUCTIOII The a p p l i c a t i o n of percolation theory t o t h e behaviour of f l u i d s i n porous media h a s led t o increased understanding network-related

effects.

of

drainage-imbibition

h y s t e r e s i s and o t h e r

The primary outcome h a s been t h e r e a l i s a t i o n t h a t f o r

many of t h e processes t h a t o c c u r i n a pore space, such as drainage-imbibition, desorption-adsorption

and mercury porosimetry, t h e network of connections is of

paramount importance ( r e f s 1, 2).

So important, i n f a c t , t h a t a l m o s t any network

w i l l e x h i b i t most of t h e f e a t u r e s sought t o be modelled.

A s a result work h a s

tended t o concentrate, n o t so much on understanding t h e actual network s t r u c t u r e o f real

porous

materials, but

on

including

increasingly

mechanisms so a s t o model decreasingly important e f f e c t s .

sophisticated

conditional

I t h a s become customary

i n computer modelling of percolation behaviour t o use lattice network structures r a t h e r than random s t r u c t u r e s . probably

because

of

the

ease

The cubic

of

labelling

programmes as three-dimensional a r r a y s .

lattice has been

the

t h e m o s t popular,

interconnections

in

computer

B u t , i n t h e background, The Great Question

of percolation theory ( r e f . 3 ) remains unanswered - Vhat is t h e n e t w o r k structure

of real materials and which, if any, of t h e regular lattice s t r u c t u r e s m o s t c l o s e l y m o d e l s it?

W e r e p o r t here a n a n a l y s i s of t h e network s t r u c t u r e of a real porous

material, a l b e i t only a random packing of equal s p h e r e s , and show t h a t , from a

percolation s t a n d p o i n t , it is best modelled by t h e diamond lattice s t r u c t u r e . The Great Assumption of percolation modellers is t h a t some property (usually “pore radius” f o r drainage-imbibition)

of t h e bonds (or sites) of t h e network is

42

randomly distributed across the structure.

This assumption is made both because

it s e e m s reasonable, and also because the behaviour of models using it seem to closely follow the behaviour of real systems.

But there is little evidence,one way

or the other, concerning its validity, although it is known that for the pores in a porous material both the site sizes and bond sizes cannot simultaneously be Ye also report here the percolation properties of

randomly distributed (ref. 4 ) .

our real pore network and show that, although the correlation between adjacent bond (and site) sizes appears small, the effect on the percolation threshold is large.

It may well be that it is not enough to nominate a lattice, and a bond or site distribution, but a bond (and site) correlating factor may also be needed to fully describe a pore network with regard to its percolation behaviour. DluYSIs

In 1960 Finney reported the measurement of the coordinates of 3,367 spheres in a random sphere packing (ref. 5).

The purpose was to see if this structure was a

practical model of liquid structure.

These sphere centre coordinates have been

used by other workers to model the structure of liquids and glasses but, so far, noone s e e m s to have used them as the model of the pore structure of a porous material. In order to sub-divide the void space of a random sphere packing, some kind of irregular individual pore has to be defined.

For various reasons we have used the

irregular tetrahedron defined by four adjacent sphere centres as the unit cell of the pore space.

Such a unit cell has a sphere at each vertex and has four

windows, one on each face, and a void space in the centre.

The cell has four

connections (the faces) to the neighbouring cells and these connections are the windows (or constrictions) in the pore space.

These constrictions dominate

Imbibition is determined by wider parts of the pore space.

drainage behaviour.

For modelling the imbibition of wetting fluids the interior of the tetrahedral cell gives the broadest part of the pore. The tetrahedral cell is thus a sensible subdivision into pores when capillary properties are to be modelled. The division of the sphere packing

into tetrahedra has

the practical advantage that only

“neighbouring spheres” have to be found, and, in a mathematical sense, this is unambiguous.

The division, whilst technically easy, does require considerable

computational effort (ref. 6), and will be described elsewhere.

CAPILLARY PBOPGBTLGS OF FQRES Because imbibition and drainage behaviour are to be modelled, we require the This involves calculating

capillary properties of the individual tetrahedral pores. the

curvature of

menisci

in

non-axisymmetric, converging-diverging pores

something that cannot yet be done

-

-

and consequently we have fallen back on the

43 "Haines insphere" probably

(ref.?)

involves

t o g i v e meniscus curvature.

roughly

equal

proportional

error

This is imprecise in

the

window

but

menisci

(associated with t h e bonds of t h e network and drainage) and t h e c a v i t y menisci (associated with t h e s i t e s , and hence imbibition). The coordinates of t h e Finney packing gave 14,870 t e t r a h e d r a l pores. window

The

(bond) meniscus curvature d i s t r i b u t i o n w a s calculated, using t h e i n s p h e r e

approximation and is shown i n Figure 1. t h e bonds of t h e network.

There were 30,719 windows and t h e s e were

Likewise, t h e imbibition curvatures, one f o r each pore,

were calculated and t h e i r curvature d i s t r i b u t i o n is shown i n Figure 2.

O OZ5

I

C"W0t"W

F i g u r e 1. D i s t r i b u t i o n of meniscus c u r v a t u r e s f o r t h e 30,719 windows i n t h e network c a l c u l a t e d u s i n g t h e Haines i n s p h e r e a p p r o x i r a t i o n .

curvature

F i g u r e 2. D i s t r i b u t i o n of meniscus c u r v a t u r e s f o r t h e 14,870 s i t e s i n the network c a l c u l a t e d u s i n g t h e Haines i n s p h e r e approximation.

THB DETVOBI[ Each t e t r a h e d r a l pore was numbered.

Then, for each pore i n t u r n , t h e numbers

of each of t h e neighbouring pores were evaluated. ( r e f . 8).

Full d e t a i l s are given elsewhere

This a r r a y s t o r e d t h e s t r u c t u r e of t h e network.

A convention w a s

44 adopted in which the outside of the packing was numbered as tetrahedron zero and consequently,when drainage was simulated, the outside of the packing network could readily be identified. DRAIBAGE A computer programme was written to simulate drainage of the packing.

The

Rules for Drainage were:

Rule 1 : Rule 2:

I n order t o drain, a cell must be connected to at least one immediate neighbour which is already empty of wetting fluid, In order t o drain from an erpty neighbouring cell, the "current curvature" nust exceed the critical curvature (given by the Haines insphere) of the face which connects the cell to its empty neighbour.

It should be noted that these rules do not permit entrapment of liquid by disconnection of the continuous liquid phase. The packing starts full of fluid with the current curvature set to zero.

The

current curvature was then incrementally increased and the total volume (and number of cells) drained at that curvature was calculated using the Rules for Drainage. Access to the packing

WAS

assumed to be over the entire outer surface (the pore

numbered zero was taken to be initially empty).

The results are shown in Figure 3 .

curvature

Figure 3 . Volume and Number Fraction Full against meniscus curvature for drainage of the packing from the outside surface. The similarity of these curves indicates that there is little correlation between cell volume and drainage curvature for the individual cells. Note also that This is because the packing there is no sharp percolation threshold. is small relative to its surface area. Two main conclusions can be drawn from Figure 3 .

The first, and most obvious,

is that the Number Fraction emptied corresponds closely with the Volume Fraction

emptied.

This indicates that there is no correlation between pore drainage

curvature and pore volume.

The lack of such a correlation is not intuitively

obvious but is obviously relevant to percolation modellers because "number emptied" is usually the variable calculated.

The second conclusion is that even though the

45

packing contains over 14,000 pores, it is still far too small. is the lack of any sharp percolation threshold.

The indicator here

The rounded breakthrough between

curvature 4 and 7 is caused by the sample being too small. precise threshold posed an interesting problem.

How to find the

The usual solution would be to

increase the size of the network or adopt repeating boundary conditions.

But this

was not possible in our case because the source packing was of fixed size and had no regular lattice structure. access to the outside.

So we adopted the alternative approach and limited

For the initial drainage simulation all the faces on the

outside were taken to be accessible.

There were 1958 of them.

Let us define a

"sample size ratio" (S,)

S, = total number of tetrahedral pores/number of faces accessible which, for the initial simulation was

S,

14870 / 1958 = 7.6

=

Ideally S,

would be infinite or, at least, very large.

increased so

the 1,958 accessible faces was decreased.

The 14,870 could not be Faces on the outside of

the packing were randomly selected and considered to be non-accessible. drainage simulation was re-run. Sample Sample Sample Sample Sample

A

B C

D E

1958 982 187 22 9

accessible accessible accessible accessible accessible

The

There were 4 repeat simulations (B to E ) faces faces faces faces faces

S, = SR = S, = S, = S, =

7.6 15.1 79.5 675.9 1652.2

In effect, Sample E is more that 200 times larger than A and is equal to around 3x10'.

tetrahedral pores.

The results are shown in Figure 4.

Of course having

such a limited number of access points (9 for Sample E) gives rise to statistical lumpiness near breakthrough but the clear fact is that the Sample D gives a much better developed percolation threshold than Sample A . The curves shown in Figure 4 are for a simulated drainage process. In normal percolation variables the curves would show the accessible number fraction of bonds (or sites) plotted against the probability of a bond being available.

Since we

know the number frequency of the bond meniscus curvatures it is easy to transform the variable called "meniscus curvature" into "probability of a bond being larger than a particular meniscus curvature".

We can now plot the percolation graph for

the number of accessible sites (not bonds, note, because pore volume relates to sites in drainage (ref.2)) on a percolating bond network (Figure 5).

46

Figure 4 . Fraction emptied during drainage using limited access to the outside of the packing. The restriction of the number of windows on the surface of the packing through which the non-wetting phase enters sharpens up the percolation threshold.

Drainage of the bond network plotted in conventional Figure 5. percolation variables. This Figure is similar to Figure 4 but with the transformation of the x-axis into probability. Figure 5 shows that the critical percolation threshold (p,.*) for this network is pr- = 0.51 (*O.Ol).

This is a surprising value, corresponding approximately to the

threshold value for a 2-D square lattice.

Using the approximation that in 3-D, at

the percolation threshold, about 1.5 bonddnode have to percolate (ref. 9), gives an expected value of pEP = 0.375. than expected.

So the actual percolation threshold is much larger

There could be two explanations:

this actual network is not

regular, and the bonds are not necessarily situated at random.

To test the

significance of the bonds not being sited at random, the bond sizes were randomly re-assigned across the whole network and the drainage simulation was repeated. Now, the percolation threshold was p c P = 0.38 (f0.01) (Figure 6 ) , which was significantly different to 0.51 for the real packing.

The percolation threshold of

47

0.38 is close to that of the 3-D diamond lattice (0.3903 (ref. 101, a structure with

four bonds meeting at each site.

So there is evidently sufficient correlation

between adjacent bonds in the real packing to significantly shift the percolation threshold.

08

Y

e

\

0 6

o4 z

,

,

Randamired , Sample E ,

c

E

,

0 2

- _- - _ _

00 01

02

03

0 4

05

06

07

08

09

Probability

Figure 6 . A repeat of the drainage simulation using the same network of connections as Figure 5 but with the bond sizes randomly reassigned to give a completely random structure. Row the percolation threshold occurs at the expected value indicating that the real network does not have the bond sizes sited at random. The conclusions for drainage of the real network are: the the the iii) the

i) ii)

2-D square lattice gives the correct percolation threshold, network of connections can be reasonably well approximated by diamond lattice, bond sizes cannot be assigned at random.

These conclusions give percolation modellers three options: Use the square lattice and assume that bonds are situated at random, Use the diamond lattice and find out how adjacent bonds should be correlated, c) Use the Bethe lattice with bonds situated at random and with the bondlnode ratio chosen to give the correct percolation threshold.

a) b)

Option b) has the disadvantage that it cannot currently be done! Option a) will be good for some predictions but is only two-dimensional and will certainly break down if two phase permeabilities are calculated.

Also,

the square network

only approximates the percolation threshold and only certain percolation properties are known for this lattice. percolation threshold

and

Option c) has the advantage of flexibly matching the giving

analytic functions (ref. 11,

disadvantage of using an unreal network. time will tell.

but

has

the

Which option is best in practice only

48

IHBIBITIOI

Imbibition is closely related to drainage: the network remains the same but now it is the number of accessible sites on the site tree that is required.

The

meniscus imbibition curvature for a tetrahedral pore can be approximated by the Haines insphere and Figure 2 showed the curvature frequency distribution. The Rules for Imbibition were:

Rule 1 : Rule 2:

In order to fill, a cell Rust be connected to at least one ianediate neighbour which is already filled with vetting liquid, For a pore to f i l l from a filled neighbouring cell, the "current curvature" must be below the critical curvature (given by the Haines insphere) of the body of the pore,

Again, these rules preclude any residual entrapment of the non-wetting phase.

A computer programme was written incorporating these Rules and the imbibition of the packing was simulated.

There were six simulations, one of the disaggregated

set, and five others (A to E) in which access to the outside of the packing was restricted in order to sharpen the percolation threshold.

The number of access

cells was made to match the number for the drainage simulation and consequently the SR values for Samples A

- E are identical to the values previously tabulated for

drainage. The results, in terms of meniscus curvature, are shown in Figure 7. curvature threshold associated with imbibition is 5.85 (i0.05).

The

Again, as in

drainage, the capillary pressure can be related to the probability of a tetrahedral pore filling and Figure 7 can be transformed into conventional percolation variables, this time the fraction of accessible sites on the site tree.

0

2

in

12

Figure 7. Imbibition of the real pore network in terms of meniscus curvature. Bate that the network needs restricted access to the invading phase if it is to show a pronounced percolation threshold. Transforming Figure 7 into the conventional percolation variables gives Figure 8 , from which it can be seen that the percolation threshold is 0.32 (f0.01).

The

percolation threshold of the 2-D square lattice for site percolation is 0.59

49

(ref. 9 ) ,

so,

unlike drainage (involving bonds), the 2-D lattice is a very poor

approximation for imbibition.

The site percolation threshold of the 3-D diamond

lattice (ref. 9) is 0.43,which is also widely different.

Could it be that, like the

window radii, the cavity radii are not randomly situated on the lattice?

The site

network was randomised by rearranging the site sizes on the same network of connections and the imbibition simulation re-run for the Sample E condition. results are shown on Figure 9.

The

Bow the percolation threshold has moved to

0.44 (iO.Ol), virtually the value for the diamond lattice, thus confirming that the

real network approximates to the diamond lattice, and that the sites are not situated at random.

3 Prabobiliiy

Figure 8. Imbibition of the real network in terms of conventional percolation variables. Note that the percolation threshold for this, (the site problem), is significantly different to the expected value of 0.43 (ref. -9) for the diamond lattice.

,I/,

0 0 0 1

0 2

03

0 4

05

06

,

,

,

07

08

09

n

Probobility

Figure 9. Imbibition (the site problem) of the network with the site sizes re-distributed at random on the same network. The effect of having the sites randomly distributed is to move the percolation This means that the sites in threshold to that of the diamond lattice. the real network are not distributed randomly.

50 The conclusions f o r imbibition are t h a t : i) t h e 2-D square l a t t i c e g i v e s t h e wrong p e r c o l a t i o n t h r e s h o l d , i i ) t h e network c a n be r e a s o n a b l y approximated by t h e diamond l a t t i c e , i i i ) t h e c a v i t y s i z e s are not d i s t r i b u t e d a t random b u t are s u f f i c i e n t l y correlated t o s i g n i f i c a n t l y s h i f t t h e percolation threshold.

coIcLusIoIs For percolation s t u d i e s , t h e regular diamond lattice is a good approximation t o t h e irregular network of pores i n a random packing of s p h e r e s . However, t h e c o n s t r i c t i o n s

(bonds) which dominate drainage are not randomly

s i t u a t e d i n t h e real network but are c o r r e l a t e d such t h a t " l i k e s repel" and t h i s s i g n i f i c a n t l y s h i f t s t h e percolation t h r e s h o l d , making t h e network harder t o d r a i n . There is a similar non-randomness

i n t h e d i s t r i b u t i o n of t h e c a v i t i e s (sites) which

determine imbibition but, i n t h i s case, it is t h e r e v e r s e c o r r e l a t i o n and it makes t h e network easier t o f i l l .

ACKIOVLEDGEICBITS W e thank Professor J.L.

Finney, Birkbeck College, f o r permission t o u s e h i s

s p h e r e centre coordinates, and

Dr

A.C.

Vright,

University

of

Reading,

for the

resolution of t h e Finney coordinates i n t o t e t r a h e d r a .

REFEJZEICES 1

G. Mason, Determination of the Fore Size Distributions and Fore Space In terconnectivity of Vycor Pomus Glass f m m Adsorption-Desorption Hysteresis Capillary Condensation Isotherms, Proc. Roy. Soc., 4156 (1988) 453-486.

2

G. Mason, Site and Bond Fractions on Bethe Trees, Powder Technology, 39 (1984) 21-28.

3

G. Mason, Porous Haterials and Fercolation Theory, i n K.K. Unger et al. (Eds), C b a r a c t e r i s a t i o n of Porous S o l i d s , Blsevier, Amsterdam, 1988, pp 323-332.

4

(Y. L i ) Yu, V.G. Laidlaw and I.C. Vardlaw, Sensitivity of Drainage and Imbibition to Pore Structures as Revealed by Computer Simulation of Displacement P m e s s , Advances i n Colloid and I n t e r f a c e Science, 26 (1986) 1-68.

5

J.L. Finney, Random Fackings and the Structure of Simple Liquids. I The Geometry of Random Close Packing, Proc. Roy. Soc., 319A (1970) 479-494; also, J.L. Finney, Random Fackings and the Structure of the Liquid State, PhD Thesis, University of London, 1968.

6

A.C. Vright, Personal communication.

7

V.B. Haines, Studies on the Fhysical Pmperties of Soil, J. Agric. Sci., 1 7 (1927) 264-290.

8

D.V. Mellor, Random Close Packing of Equal Spheres; Structure and Implications for Use as a Xadel Fvmus Xedium, PhD Thesis, Open University, 1985.

9

J.M. Ziman, Had& of D i s o r d e r : The T h e o r e t i c a l Physics of D i s o r d e m d Systems, Cambridge University P r e s s , 1979.

Borogenaauely

10 F.A.L. Dullien, Porous Hedia: F l u i d Transport and Pare S t r u c t u r e , Academic P r e s s , Bew York, 1979.

51

F. Rodriguez-Reinosoet al. (Editors),Characterization of Porous Solids II 0 1991 Elsevier Science PublishersB.V., Amsterdam

THE FIVE TYPES OF POROUS STRUCTURES AND 'THEIR HYSTERESIS LOOPS VICENTE MAYAGOITIA Departamento de Quimica Universidad Autonoma Apartado Postal 55-534, Mexico 13, D. F., MQxico

Metropolitana-Iztapalapa

ABSTRACT Porous materials are classified within five types according

to

the

relative positions of their site- and bond- size distributions. l'his leads to a better understanding of the morphological aspects of the porous medium as well as an assessment of the different mechanisms arising during capillary condensation and evaporation. For each one of these types of materials, relevant char-acteristicscan be recognised in their hysteresis loops. I NTRODUC'TION

The classification of adsorption hysteresis loops has been always stated in Lerms of the appearance of these curves, e.g. their shape or extension. Among the most important classifications, that of de Boer (ref. 1 ) i s based 011

a combination between the steep or sloping character of the adsorption and

desorption branches, while Everett's classification (ref. 2 ) emphasizes the extent of the region of relative pressures at which hysteresis occurs. A classification adopted by the IUPAC (ref. 3 ) considers four types of loops, vliich are identified according to the slope of the boundary curves. I t has been intended, a posteriori, t o relate these shapes of hysteresis loops to some processes of filling by capillary condensate or evaporation of the liquid held

in a pore, and in order to justify the existence of these

mecharijsms. several models of the pore geometry have been consjdered. The shape of a hysteresis loop is influenced by many factors, porous structure being the dominant one of them and for this reason i t appears as the basic property of our classification. Moreover, instead of looking for types of hysteresis loops, we prefer to define types of porous structures. What we propose is the folfowing:

- first, to classify the porous materials according to the most relevant characteristics which define their morphology, or the precise seqaence of element sizes throughout the network, statistically expressed, follcwed by

- air investigation about the relationship between the geometrical properties of the porous network and the possible mechanisms for vapour-liquid and

52

liquid-vapour phase transitions to take place in it, and then finally

- to predict the shapes of the hysteresis loops produced by each type, in such a way that the most important features of these loops can be explained satisfactorily in terms of cohesive and adhesive interactions and

the

statistical properties of the porous network. However, before proceeding with the above sequence, it would be better to start with an analysis of both the classical vision and the newest aspects of fluid transitions in pore space. THE MAIN CAUSES OF ADSORPTION HYSTERESIS Even if real structures may be very complicated in shape, in this work very simple geometries will be mentioned exclusively. Some authorities in this field (ref. 4). have recommended to lose generality in order to gain clarity. Everett (ref. 5). in his remarkable review of adsorption hysteresis, has extensively discussed about possible explanations for the existence of such phenomena. In the present contribution only some of the most common causes of hysteresis have been considered, although it has to be recognized that other factors can be more determinant at some particular conditions, e.g. the failure of the liquid phase in an extreme state of stress (ref. 6 ) or the contact angle hysteresis within the isotherms (ref. 7). Katz (ref. 8 ) pointed out that any convenient theory of adsorption must take into account the two following causes of hysteresis in pores: a delay in the formation of hemispherical menisci and the impossibility to have a liquid-vapour transition inside an element in which a liquid-vapour meniscus

*

is absent

.

In reality, the interaction between voids and the capillaries linking them is a little more complex, and is present in condensation as well as in evaporation. Consider that the porous medium can be visualized as a COMeCted network of alternated elements, the sites, or voids, and the bonds or necks. Then, if the connectivity, C, is the number of bonds meeting at a site, each void possesses C entries. Sites "opened at several poles" are the counterpart of what is very popular for bonds: "bonds opened at both ends". This last characteristic drastically alters the behaviour of phaseI

transitions. Let us assume, for the sake of simplicity, that the bonds lead directly to the free vapour phase. During condensation then, a sequential Foster (ref. 9 ) and Cohan (ref. 10) principally contributed to establishment of the delayed meniscus theory.Everett and Haynes (ref. 4). Broekhoff and de Boer (ref. 11) made very substantial contributions to understanding of these phenomena. Kraemer (ref. 12) and McBain (ref. developed the ink bottle theory.

the and the 13)

53

filling, according to

their size, can arise for bonds, following the

cylindrical geometry. In this way, bonds fill on their own. On the other hand, it is impossible for a site to fill on its own unless the C bonds have been previously filled. The requirement to fulfill in this case is clear: all these bonds must possess radii in such a way that r1, r2 ,.... r C < R / 2 .

If

several bonds remain unfilled, the meniscus located in the pore lacks continuity, and its advancement to fill completely the site with condensate is impossible, even if this element is in a saturated state. In the event of only one of the bonds being empty, the meniscus can advance straightforwardly into the site to fill it together with the remaining empty bond. Now, if one of the bonds possesses a radius r1 equal to that of the site, this fills reversibly only if r2 , . . . rC < R / 2. For any other case condensation in the site is controlled by the biggest bond among the remaining r2 to rC. Anyway, an hysteretic behaviour would always be inherent to bonds labeled as r2,. . rC. Condensation and evaporation in porous networks obey the above arguments, but are complicated because of the possibility of many different menisci paths within the network. Quinn and McIntosh (ref. 14) were the first to stress the importance of this pore- blocking effect during evaporation. Everett (ref. 15) and Barker (ref. 16) gave an explanation of the fundamental aspects of it. More recently, assisted and hindered transitions arising from cooperative effects all along the network have been pointed out by Morioka and Kobayashi (ref. 171, and by Mayagoitia et al. (ref. 18). Cooperative behaviour during condensation seems to be the rule rather than the exception. The consideration of all these mechanisms leads to the conclusion that the morphology, or the precise sequence of element sizes throughout the network,

". . .controls,.. to

a

major

. . . the

extent,

condensation-evaporation

characteristics"(ref. 19). FORMER TYPES OF POROUS STRUCTURES As Everett

(ref. 19) noted, the so-called pore- size distribution

"

...

involves, in fact, two statistical functions rather than one". These two statistical functions are the site and the bond- size distributions. With respect to the overlap between these distributions, three situations are possible (ref. 20): I

- a zero or very low overlap, in which case the sizes of sites and bonds are notably different. The sizes of elements are disposed across the network completely at random. Types I to 111. t

-

- a large overlap causes a structuration of the elements in the network. A

*

This structuration has been observed recently by means of Monte Carlo methods (ref. 21).

54

size- segregation effect arises.There form regions of big e1ements:big sites and bonds linked together, and somewhere apart there lie regions constituted of smaller elements reunited. Type IV.

- an overlap tending to completeness. The size- segregation effect is so strong that the network is broken into a collection of "homotatic" regions, each of them possessing sites and bonds of the same size, the bonds of which

*

behave in practice as independent . Type V. Dealing

again with

a

situation of

nearly

zero

overlap,

the

two

distributions could lie very far apart or, conversely, very close to each other. Three situations still arise:

- the distributions are

so

far apart, as to avoid any interaction between

sites and bonds during capillary condensation, Type I,

- there exists an intermediate situation in which bond-site interactions are moderate, Type 11, or finally

- the distributions lie so close to each other that even before the onset of the independent filling of bonds, all the sites are already, by virtue of their

size,

in

a

state

of

supersaturation,

i.e.

are

eligible

for

condensation, and the transition depends only on the state of their bonds. Type 111. REQUERIMENTS FOR THE PREDICTION OF HYSTERESIS CURVES In principle, an estimation of the hysteresis and scanning curves from a twofold size-distribution and connectivity is possible. The aspects that appear to be absolutely unavoidable to deal with are the following:

- a critical analysis of the morphology of the adsorbent, allowing a proper treatment of the interactions between the elements of the network. i.e., low overlapped structures are fully random media, consequently pore-blocking effects are very important to consider. On the other hand, for structures displaying an overlap tending to completion, pore blocking is absent,

so

that

it would be a serious error to incorporate percolation relationships in the treatment (ref. 22).

-

all kind of possible interactions between the elements of the network,

assisted or hindered, must be envisaged, and we draw attention specially to the cooperative phenomena pccurring during capillary condensation, a subject that has been very scarcely treated (ref. 18, 20).

*

the

analysis performed

should

be

the

most

precise,

then

domain

The real impossibility of having rigorously the same size for sites and bonds in the same region is not to be considered as a serious problem, as long as the bonds completely control the condensation- evaporation characteristics.

55 complexions,rendering the state (empty or full with capillary condensate) of both sites and bonds, in terms of their size, can be represented.

- adsorbate/adsorbent interaction is to be taken into account by means of an adsorption potential that not only leads to the development of an adsorbed layer but

that also modifies drastically the Kelvin equation and

the

conditions of capillary condensation and evaporation to take place (ref. 11).

If one could ignore the influence of this potential the uncorrected Kelvin equation would lead to a critical radius of curvature, Rc. Kelvin equation renders a value R as well as another value R

2

instead of Rc,

in place of R

C

The corrected

for a spherical geometry,

/ 2 for a cylindrical geometry,

both as functions of the relative pressure. Table 1 presents some comparative values for the condensation of nitrogen at 77 K. TABLE 1. Influence of the adsorption potential on the condensation of nitrogen at 77 K in sites (hollow spheres), R1, and bonds (hollow cylinders), R2.

I

1 I

II

**

**

Critical radius

True condensation radius

True condensation radiui

20

38

25

40

65

41

60

91

56

80

115

70

100

139

84

200

256

147

300

368

208

as defined by the non-corrected Kelvin equation

The new parameters, R 1 and R2, must replace the former ones in all the expressions describing interactions during capillary condensation, evaporation and scanning (ref.20.22).

- finally,in order to represent the hysteresis and scanning curves for a I

particular adsorbate/adsorbent pair, it is required to be acquainted with all the relevant information about the .nature of both components and their interaction, as well as for all the difficulties involved in the definition of such a system.

56

CALCULATION OF HYSTERESIS LOOPS A very complex method of calculation, taking into account all these five

remarks is being tested by us. and constitutes perhaps the most complete approach to the investigation of the texture of a porous material and the behaviour that a condensable fluid is undergoing in it.

This method is

probabilistic (analytic) in nature. First of all, the twofold distribution and a value for C are imposed. For a given relative pressure, values of R

1 and R2, as well as the thickness of the adsorbed layer for all sizes of sites

and bonds are calculated. With the relative pressure kept fixed again, the degree of filling for sites and bonds of every size is calculated by means of eqns. (24) to (39) of (ref. 2 0 ) and ( 1 ) to (51) of (ref. 22) and for all kind of

envisaged

processes:

ascending

and

descending boundary

curves

and

scanning. Afterwards the overall degree of filling is calculated by means of eq. (52) of (ref.22), but in a more refined manner as the adsorbed layer has been taken into account. The use of this method provides adsorption-desorption curves very similar to those observed for real porous materials. Figs. 1-8 show theoretical isotherms for the adsorption of nitrogen at 77K in different types of porous structures. For instance in cases labelled as types I ,

I1 and

I11

(i.e. those

corresponding to zero overlap), a common characteristic is a very steep descending boundary curve (see Figs. 1-41. As in these structures the sizes of the void elements are disposed throughout the network totally at random, the porous medium (initially saturated with condensate) is invaded by vapour at a percolation threshold, so that the reason for the abrupt fall of the descending curve. From type I to type 111, the hysteresis loop decreases in width, while at the same time the adsorption layer becomes more important. For a type 111,

the slope of

the adsorption branch, within a great

extension of the hysteresis loop, is higher than that corresponding to the desorption branch. Here cooperative phenomena during adsorption are more intense than during desorption. This has not been mentioned by previous authors. A comparison between Figs. 3 and 4 shows that, other structural parameters

being constant, a variation of the connectivity (which drastically alters the I

shape of the isotherm for type I structures) does not influence significantly the appearance of the isotherm again for type I 1 1 structures.Experimenta1 curves for the adsorption of vapour at 298 K in model mesoporous carbons (ref. 2 3 ) consisting of monosized spheres forming a regular array resemble closely to those found in figs. 3 and 4. Very complicated calculations are involved in type IV structures that it

51

VERALL EGREE F FILLING

I 1

VERALL lEGREE F FILLING

I

RELATIVE PRESSURE

RET-ATLYE PRESSURE

Fig. 1. Type I structure.

Fig. 2. Type I1 structure.

1

1VERALL IEGREE

I F FILLING

7 i

b

RELATIVE PRESSURE

Fig. 3. Type I11 structure with C = 3.

oh

RELATIVE PRESSURE

F-g. 4. Type111 structure w i t h C = 6.

Comparison of some adsorption hysteresis cycles, calculated from twofold distributions, f o r several types o f porous structures.

58

. . OVERALL DEGREE OF FILLING

o

OVERALL DEGREE OF FILLING

.

.. . . e

0

RELATIVE PRESSURE

1

Fig. 5. Type V. Small pores.

0

RELATIVE PRESSURE

1

Fig. 7. Type I. Ascending scanning curves.

0

RELATIVE PRESSURE

o

1

Fig. 6. Type V. Big pores

0

RELATIVE PRESSURE

1

Fig. 8. Type 11. Ascending scanning curves.

Comparison of some adsorption hysteresis cycles, calculated from twofold distributions, f o r several types of porous structures.

59 has been impossible for the moment to obtain adsorption isotherms. Fig. 5 corresponds to a type V (overlap between size distributions tends to completeness) material, made of small pores. There exists an initial plateau at the upper part of the descending boundary curve. This is not at all due to the existence of a pore-blocking effect, since the hypothesis employed have nothing to do with this phenomenon. The plateau is better understood in terms of the delayed meniscus theory, so that this effect gains a great importance in the characterization of the porous medium. Fig. 6 is an isotherm for a solid (type V) made of big pores, which closely resembles the adsorption isotherms found f o r globular carbon samples, where the particles are partially coalesced (ref. 2 3 ) . Scanning curves were also calculated for types I and I 1 and the results are shown in Figs. 7 and 8 . It is expected that an analysis of the scanning curves corresponding to real materials, will extend and complement the textural information obtained from the boundary curves. The method of calculation here outlined constitutes a powerful tool for the determination of the textural properties of a porous solid. NEW CLASSIFICATION OF POROUS MATERIALS The above results and discussion seem to confirm the appropriateness of a classification published elsewhere (ref. 2 0 ) . However it is necessary to stress the importance of the adsorption potential

(amerely

in the

development of the thickness of the adsorbed layer). We have also learned from our Monte Carlo results to explore the porous morphology in relation with the intensity of the overlap. Consequently, this classification can be improved on the basis of the following remarks: TYPE I. A material should be considered as such if there is not overlap at all and if i t there is a span of radii in which there are no elements between RZ(RBB) and RI(RSs). (RBB denotes the biggest bond, while Rss is the smallest

site).

TYPE 11. This is the general case of low overlap, meaning for this a value as the network has not been yet

of such parameter between 0 and 30 %, structurated appreciably.

A material of reduced overlap having practically all the I elements within a span of radii between R (R 1 and R (R 1 (R is the 2 SB I BS SB TYPE 1 1 1 .

size of the smallest bond and R

BS

is that of the biggest site).

TYPE IV. A network having a significant overlap. TYPE V. A situation in which overlap is larger than 85 %.

60

CONCLUSIONS The arguments relating a porous structure and its morphology to mechanisms

of phase transitions

-

specially vapour-liquid transitions - reveal to be

highly consistent. A previous clasification of porous structures within five types was improved by considering recent results of Monte Carlo estimations of porous morphology and the role of the adsorption potential.

ACKNOWLEDGEMENT This work was supported by the National Council of Science and Technology of Mexico (CONACyT).

LITERATURE CITED 1

2 3 4 5 6

J. H. de Boer, in D. H. Everett and F. S. Stone (Eds.1, Structure and Properties of Porous Materials, Colston Papers, Vol. 10, p. 90, Butterworths, London, 1958. D. H. Everett, in E. A Flood (Ed.1, The Solid-Gas Interface, Vol 2, p. 1059, Marcel Dekker, New York, 1967. K. S. W. Sing, D. H. Everett, R. A. W. Haul, L. Moscou, R. A. Pierotti,J. Rouquerol and T. Siemieniewska, Pure and Appl. Chem., 57 ( 4 ) (1985) 612. D. H . Everett and J. M. Haynes, J. Colloid & Interface Sci. 38 (1972) 125. D. H. Everett, in E. A. Flood (Ed.1, The Solid-Gas Interface, Vol 2, pp. 1055 - 1113, Marcel Dekker, New York, 1967. C. G. V. Burgess and D. H. Everett, J . Colloid Interface Sci., 33 (1970) 611.

7 8

9 10 11 12 13 14 15

16

17 18

R.Zsigmondy, Z . Anorg. Allgem. Chem., 7 1 (1914) 356. S . M. Katz, J. Phys. Chem., 53 (1949) 1166. A. G. Foster, Trans. Faraday SOC., 28 (1932) 645. L. H. Cohan, J. Am. Chem. SOC., 66 (1944) 98. J. C. P. Broekhof-fand J . H. de Boer, J. Catalysis, 9 (1967) 15. E. 0. Kraemer,in H. S . Taylor (Ed.1, A Treatise on Physical Chemistry p. 1661, New York, 1931. J. W. McBain, J. Am. Chem. SOC.,57 (1935) 699. H. W. Quinn and R. Mc Intosh, in J. H. Schulman (Ed.1, Surface Activity, Vol. 2, p. 122, Butterworths, London, 1957. D. H. Everett, in D. H. Everett and F. S . Stone (Eds.1, Structure and Properties of Porous Materials, Colston Papers, Vol. 10, p. 117, Butterworths, London, 1958. J. A. Barker, in D. H. Everett and F. S . Stone (Eds.1, Structure and Properties of Porous Materials, Colston Papers, Vol. 10, p. 125, Butterworths, London, 1958. Y. Morioka and J. Kobayashi, J. Chem. SOC.Jpn.. 2 (1979) 157. V. Mayagoitia, F. Rojas and I. Kornhauser, J. Chem. SOC., Faraday Trans.

1, 8 1 (1985) 2931. 19 D. H. Everett, in E. A Flood (Ed.1, The Solid-Gas Interface, Vol 2, p. 1083, Marcel Dekker, New, York, 1967. 20 V. Mayagoitia, F. Rojas and I. Kornhauser, J. Chem. SOC.Faraday Trans. 1, 84 (1988) 785. 2 1 M.J. Cruz, V. Mayagoitia and F. Rojas, J. Chem. SOC.Faraday Trans. 1, 8 5 ( 8 ) (1989) 2079. 22 V. Mayagoitia, B. Gilot, F. Rojas and- I. Kornhauser, J . Chem. Soc., Faraday Trans. 1, 84 (1988) 801. 23 F. Hojas, Ph. D. Thesis, University of Bristol, England, 1982.

61

F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids XI 1991 Elsevier Science Publishers B.V., Amsterdam

MODEL STUDY OF THE COMBINED MACROSCOPIC HETEROGENEITY GAS SOLIDS

EFFECT OF HETEROPOROSITY OF RELATIVE PERMEABILITY OF POROUS

N.K.Kanellopoulos,J.K.Petrou and J.H.Petropou1os Physical Chemistry Laboratory Nuclear Research Aghia Paraskevi Attiki,Greece.

Center,

15310

S-ry

A model study of the combined effect of macroscopic heterogeneity and heteroporosity on the relative gas permeability of a porous solid, as a function of the fraction of pore volume occupied by a foreign sorbate, is reported. The heteroporous solid was modelled as a regular capillary network with randomly varying capillary radius, characterized by the radius distribution and the structure of the network, notably network connectivity. Macroscopic heterogeneity was introduced by allowing the local porosity of the solid to vary along or across the axis of permeation. Model calculations were performed for various macroscopic and microscopic parameter nalues, in order to obtain a realistic assessment of the relative importance of the respective effects and the way in which they combine to produce the final observable result. Introduction In previous work [1-41 it was shown that the relative permeability of porous solids is an important source of information about their pore structure. For the simulation of the pore structure, a network model has been employed, consisting of a regular array of nodes joined together by cylindrical capillaries of randomly varying radius r. The model is completely characterized by the capillary radius probability distribution f(r) and the connectivity of the network , n ~ , given by the number of capillaries meeting at each node. However, in practice, exploitation of relative permeability measurements is hindered by macroscopic nonhomogeneities, in the form of e.g. non-uniform porosity produced in the common It has been demonstrated [ l ] that pelletization procedures[S] the effect of macroscopic heterogeneity on the initial slope of the relative permeability curves can be very significant and hence cannot be ignored in practice. In addition, it has been shown that the effectiveness factors of catalysts formed by compression can be [6]. greatly affected by macroscopic heterogeneities However, a realistic model capable of representing the behavior of a mesoporous non-homogeneous pellet over the full range of relative permeability is, as yet lacking. Such a model is presented here. Macroscopic inhomogeneity is represented by making the the local porosity E of the pellet (in the form of a slab) a function of the normalized spatial coordinate oPa-

The overall fractional pore volume of porous medium occupied by foreign sorbate is given by

Here, Pg (v?g) is calculated in the Knudsen regime , by the effective medium approximation (EMA), namely [4]. This treatment yields

.

where g( q)=p rm3 (p-t) ( p=const ) represents the conductance of a pore in the actual network in the Knudsen regime (neglecting effects of finite pore length) and gM is the corresponding conductance of a pore in the effective medium network (composed of pores of equal conductance); g# is proportional to Pg!vs) The observed overall permeability coefficient Pg is given in terms of the corresponding local values Pg by

.

(a) in the case of axial heterogeneity (q=x)

L

J

64

(b) in the case of radial heterogeneity (q=w)

0

,The effect of the heterogeneity and heteporosity on the PR(vS) curves, over the whole range of vs, is illustrated in a Figure 1. The heteroporoustypical set of results of heterogeneous curves (denoted by HH) are compared with the corresponding homoporous-heterogeneous (OH), heteroporoushomogeneous (HO) and homoporous-homogeneous ( 0 0 ) media. The similarity of the effects of axial (radial) heterogeneity and the low (high) network connectivity nT should be noted. These cases present the characteristics of a serial (parallel) pore array, where narrow (wide) pores dominate [ 2 ] . Thus, the respective PR(vs) curves lie below (above ) that corresponding to the 00 case. In addition, as in the case of connectivity [ 2 ] , the effect of heterogeneity is more(1ess) profound in the lower (upper) parts of the curves. Thus significant shifts of the percolation thresholds can be caused by heterogeneity effectcs. Finally it is noteworthy that, although the combined effect of heteroporosity and heterogeneity is usually cumulative, there important exceptions to this. A striking case in point is afforded by the crossing of the OHX and HHX curves at n ~ = 4 ;at higher vs the deviation caused by the heterogeneity alone is greater than the combined effect of both the heterogeneity and the heteroporosity porosity. Figure 1 shows that the dexiations between the uniform and the non-unizorm porosity P R ( V ~ )curves are larger (smaller) at high {low! vs. This indicates that the effect of the inhomogeneity is more (less) evident in cases where the condensation (adsorption) mode of sorption is more predominant. This effect is shown more clearly in Figures 2 and 3 for the hypothetical cases of pure condensation and pure adsorption respectively.

1

\\ t

O2

Pa

0

Fig.1: Results of model relative permeability calculations representative of N2 at I 1 K for homoporous-homogeneous ( 0 0 ) , heteroporous-homogeneous (HO), homoporous-heterogeneous (OH) and heteroporous-heterogeneous (HH) media of slab geometry. For the homoporous medium rm=3.4 nm and for the homogeneous medium ~=0.40. The cases of heteroporosity and heterogeneity are reperesented respectively by the T ( p ) and ~ ( q ) functions shown in the insets. Values of salient parameters: a=0.3 nT=4(---),18(-- - ) , &0=.23, kl=1.5,k2=0 ( E O / E ~ ~ ~ = ~ . ~

h

rm(l)/rm(0)=1.58,~=0.40)),

Lv=.02/n,X(Y) denote cases of axial and (radial) heterogeneity.

65

In Figure 2 it is illustrated that homoporous heterogeneous in the axial direction ( O H X ) are steeper than the corresponding heteroporous heterogeneous curves HHX. This is attributed to the fact that pore blocking by condensation is more efficient in the former case , since it takes place only in the smaller porosity section of the plug; on the contrary, for the case of heteroporous heterogeneous system ( H H X ) , the pore blocking is less efficient, since small pores are blocked along the whole x-axis. The opposite holds for the case of y-inhomogeneities. The homoporous heterogeneous curves ( O H Y ) are less steep than the corresponding heteroporous heterogeneous ( H H Y ) curves and present values at the percolation threshold. This is due to higher V ~ F the fact that for the homoporous heterogeneous case (OH) at the percolation threshold all the pores are blocked except for the largest pores at the largest porosity section, whereas for the heteroporous heterogeneous case at the percolation threshold several large pores are open along the y-axis. Figure 3 shows that for the case of homogeneous plugs the effect of heteroporosity is important only for the low connectivities. The heteroporous homoporous ( H O ) curve is lower, since the constriction caused by the smaller core radius pores cannot be by-passed, due to the low connectivity [ 7 ] . The heteroporous heterogeneous ( H H X ) curves are lower than the coresponding homoporous heterogeneous ( O H X ! curves due to the constriction effect of the smaller pores in the heteroporous case. This explains the crossing of the low connectivity HHX and OHX curves of Figure 1. The homoporous heterogeneous ( O H X ) curve at n ~ = 4is higher than heteroporous heterogenous ( H H X ) in the initial pure adsorption portion of the curve in agreement with Figure 3; and the opposite holds in the lower section of the curves, where the pure condensation mode of sorption is predominant, in agreement with Figure 2.

0.1

f

0,s

PR

08

v,

-

t

0 8' vs

Fig.2: PR curves as in Fig.1 for the hypothetical case of pure condensation.

-

Fig.3: PR curves as in Fig.1 for the hypothetical case of pure adsorption.

66

References 1 N.K.Kanellopoulos, J.H.Petropoulos and D.Nicholson,Effect of Pore Structure and Macroscopic Non-homogeneity on the Relative Gas permeability of Porous Solids, J.Chem.Soc., Faraday Trans. 1, 81 (1985) 1183 2 N.K.Kanellopoulos and J.K.Petrou, Relative Permeability of parallel and serial capillary models with various radius distributions,J Membrane Sci.,35 (1987) 21 3 D. Nicholson and J.H.Petropoulos, Gas relative permeability in the capillary network model, J.Chem.Soc., Faraday Trans. 1,80 (1984) 1069. 4 J.H.Petropoulos, J.K.Petrou and N.K.Kanellopoulos, Explicit relation between relative permeability and structural parameters in stochastic pore networks, Chem.Eng. Sci.,44 (1989) 2967 5 C.G.Goetze1, Treatise on Powder Metallurgy, Interscience, New York, 1949 ; Vol.1, Chaps. 8,9. 6 S.Kasaoka and Y. Sakata, Effectivess factors for nonuniform catalyst pellets, J. of Chem.Engr. of Japan, Vol. 1, 2 (1968) 138. 7 N.K.Kanellopoulos, J.K.Petrou and J.H.Petropoulos, Realistic modelling of the interaction of vapors with densely packed spherical particles, Part 11: Relative permeability, J. Colloid and Inter.Sci., 96,1,(1983) 101.

F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids I1 1991 Elsevier Science Publishers B.V., Amsterdam

PERCOLATION THEORY OF CAPILLARY HYSTERESIS PHENOMENA AND APPLICATION FOR CHARACTERIZATION OF POROUS SOLIDS

67

ITS

A.V. NEIMARK Institute of Physical Chemistry of the USSR Academy of Sciences. Moscow (USSR) ABSTRACT

A statistical theory of capillary hysteresis phenomena in porous media has been developed. The analysis is based on percolation theory and pore space network models. New methods for computation of porous structure parameters are proposed as application. The main results are: - percolation theory of adsorption hysteresis in mesoporous materials with hysteresis loops of H1 and H2 type by IUPAC classification and corresponding methods of pore size distribution computation; - theory of cooperative capillary condensation in stochastic channels network based on three-component bond percolation problem; - theory of hysteresis loop scanning isotherms of adsorption and desorption in stochastic cavities and throats network based on mixed bond-site percolation problems. INTRODUCTION

The presence of adsorption hysteresis is the special feature of all adsorbents with a rnesopore structure. The adsorption and desorption isotherms differ appreciably from one another and form a closed hysteresis loop. According to the IUPAC classification four main types of hysteresis loops can be distinguished: H1, H 2 , H3 and H4 (ref. 1). Experimental adsorption and desorption isotherms in the hysteresis region provide information for calculating the structural characteristics of porous materialsporosity, surface area and pore size distribution. Traditional methods for such calculations are based on the assumption of an unrelated system of pores of simple form, as a rule, cylindrical capillaries. The calculations are based on either the adsorption or the desorption isotherm, ignoring the existence of hysteresis in the adsorption process. This leads to two different pore size distributions. The question of which of these is to be preferred has been the subject of unending discussion. In this report a statistical theory of capillary hysteresis phenomena in porous media has been developed. The analysis is based on percolation theory and pore space networks models, which are widely used for the modeling of such processes by many authors (refs. 2-10). The new percolation methods for porous structure parameters computation are also proposed.

68

RESULTS AND DISCUSSION Cooverative character of adsorvtion vhenomena. In real materials the pores are connected to one another and form a three-dimensional network. The interconnection of pores accounts for the cooperative character of adsorption phenomena. In capillary condensation the effect of the initiation of condensation in the wide pores appears after condensation in the narrow pores adjacent to them. The delay in desorption from the wider pores is stipulated by its blocking by the narrower ones. These cooperative effects cannot be allowed for by a model of unrelated pores: the requirements for filling or emptying of a given pore depend not only on its own characteristics but on the characteristics of adjacent pores as well. The influence of interconnection effects is diagrammatically illustrated on the example of a simple system consisting of one wide capillary of radius p p and two capillaries of radius p1 (see Fig. 1): Capillary condensation in cylindrical capillary of radius p occurs at one value of relative pressure x+ (x=p/ps) and desorption at another value of relative pressure x-. The values x+ and x- depend on pore radius p , moreover x - ( p ) > x + ( p ) . In this inequality the capillary hysteresis on the level of one capillary is displayed. It is conditioned by the difference of the mechanisms of capillary condensation and desorption. Capillary condensation occurs by means of spontaneous filling at the moment of the loss of adsorption film stability on the internal surface of capillary. This process is not reversible. Desorption occurs at the moment of equilibrium meniscus formation on the open end of capillary.

Fig. 1. Hysteresis loops in a model system of three capillaries.

69

In the system of unrelated pores the adsorption and the desorption isotherms form two hysteresis loops (Fig, la). In the case the wide capillary is connected with the narrow one the second loop disppears (Fig. lb). After the condensation in the narrow capillary in the place of capillaries intersection the equilibrium meniscus is forming and condensation in the wide capillary occurs reversibly at such relative pressure x = x - ( p 2 ) as its emptying under desorption. In the other situation, when the wide capillary is blocked by narrow ones (Fig. lc) , the hysteresis loop transforms essentially. In this case the adsorption process is going on as in the previous one, but the desorption process is quite different. The desorption from the wide pore occurs only after the emptying of blocking narrow pores at x = x - ( p l ) . On this simplest example we see that interconnection effects have essential influence on capillary condensation and desorption processes, and on the shape of hysteresis loop. Ought to remark, that in the literature the main attention was attracted to the blocking effects under desorption, but the effects of capillary condensation's initiation were avoided. Usually the authors assume that the condensation in the network of pores occurs as in the system of unrelated pores (Ref. 1,8). Both these effects displace the isotherms of adsorption and desorption towards smaller relative pressure as compared with the system of unrelated pores. Hence it follows: 1) the pore size distribution, calculated in the frameworks of unrelated pores model, gives the decreased values of pore radii; 2 ) the distribution obtained on the bases of adsorption isotherm, differs from the distribution obtained on the bases of desorption isotherm. Cooperative effects can be taken into account by means of network models, reflecting the special features of the pore structure more fully, than a system of unrelated pores. Network models of Pore structure. It is useful to distinguish two different network models. The first one used for the adsorbents exhibiting a hysteresis loop of type H1 is the network of channels. The second one used for the adsorbents exhibiting a hysteresis loop of type H2 is the network of cavities and constrictions. These models are the particular cases of more common model of the network of cavities and channels. In the first case we suppose that the pore space consists of intersecting channels of different sizes and the main pore volume

is concentrated in the networks bonds (Fig. 2a). In the second case we suppose that the main pore volume is concentrated in the network sites imitating the pore cavities connected by more narrow pore constructions (Fig. 2b). V

Fig. 2. Hysteresis loops of type H1 (a) and of type H2 (b) and corresponding pore space models: network of channels (a) and network of cavities and constrictions (b). Some results in Dercolation theory of adsomtion hysteresis. By means of percolation theory it is shown that the difference in the properties of the hysteresis in the adsorbents characterized by the loops of type H1 and type H2 can be explained in the frameworks of these models(refs. 5-7, 11). The particular attention is spared to the scanning isotherms. The course of isotherms scanning loop of type H1 is quite different from the course of isotherms scanning loop of type H2. In the first case the scanning isotherms form closed loops inside the main loop (Fig. 2a). In the second case the scanning isotherms of desorption, starting from the main adsorption branch, that finish in the point A of the beginning of hysteresis. On their turn the scanning isotherms of adsorption, starting from the main desorption branch, finish in the point C of the end of hysteresis. Analogous behavior is typical for isotherms scanning internal hysteresis loops as well. This difference was explained by the peculiarities of porous structure, which are taken into account in the network models mentioned above. The theory of cooperative capillary condensation in stochastic network of channels is developed. The corresponding mathematical problem is reduced to a three-component bond percolation problem. At a given relative pressure x in the network of channels three types of bonds are distinguished: subundercritical channels of equivalent size p < p + ( x ), intermediate- of size p + ( x )< p < p - ( x ) and overcritical - of size p > p - ( x ) . Here functions p + ( x ) and p - ( x ) determine the equivalent sizes of pores in which the capillary condensation and desorption are observed at relative pressure x .

71

The problem of design of the isotherms scanning the loop of type H2 is reduced to mixed bond-site percolation problem (ref. 6). The special methods for calculating the pore size distribution in adsorbents having loops of type H1 and H2 are suggested (refs. 5, 7). Their principal innovation is that they employ simultaneously information obtained experimentally from both the adsorption and the desorption branches of the isotherm. These methods are used in new versatile software for characterization of porous solids (ref. 12). The detailed description of percolation method for the interpretation of hysteresis loop of type H1 is given below. Percolation method for calculatinq the Dore size distribution (loor,

H1) The problem on desorption from the network of channels along the main desorption branch is the classical problem on bond percolation. In the network two types of bonds are distinguished: overcritical - of pore p > p - ( x ) and undercritial - of size p < p - ( x ) . At the process of pressure reduction down to a given value x the desorption occurs not from the all undercritical pores (as would be in a system of unrelated channels) but from only those pores which are forming connected system of undercritial pores looking on the external surface of the sample. The point E of the transition from the gently sloping section of desorption isotherm to the sharp one corresponds to the percolation transition - to the forming of connected system of overcritical pores and the beginning of desorption from the sample's volume. In the point E the portion of overcritical bonds in the network is equal to the percolation threshold p c . The portion Q-(x) of channels, got free of capillary condensate at given value x, is determined by the connectivity function of the network:

Here p,(p-(x)) is the portion of overcritical channels of size p > p (x). The connectivity function Q,(p) is to be calculated by means of percolation theory. The model of network of channels proposed that equivalent sizes and other geometrical characteristics of pores are not correlated. This assumption produced the following equation between isotherms of adsorption V+(x) and desorption V-(x) at x<xB ( x B

72

corresponds to the beginning of capillary condensation).

Equation ( 2 ) permits to calculate the portion Q-(x) of free pores at desorption. On the base of the comparison of this value obtained from experimental data with the theoretical value (1) we can determine the portion p,(p-(x)) of overcritical pores. So the integral pore size distribution function is equal to

where QC(-') is the function inverse to the connectivity function

Q,(P)

-

This equation constitutes the basis of the percolation method for calculating the mesopores size distribution. The main theoretical problem is the determination of the connectivity function Q,(p) for given network. For a three-dimensional network we have obtained interpolation formulae which describe with required accuracy the course of connectivity function over the whole range of p : for O

0.6

55.2

_ _ _ 41.4

34.5 E E J.J

5

7 1 9 7

LOG10 PRESSURE (Pa)

PARTIAL INTRUSION DATA 0.6

0.5

0.4

r: 0.2

0.1

0

80

THE MODEL Network Definition The three-dimensional model network is based on a cubic lattice.

The

lengths of the pores are all equal to one unit and the radii of the pores are allocated as random values from a log-normal distribution using a NAG library routine. A pseudo-random generator is used with a fixed seed s o that reproducible runs can be achieved.

Reduced connectivity was achieved by

randomly deleting pores from a network by "knock-out",and blind pores were created by blocking access to a node at one end of the pore. A network containing 30 x 30 x 30 segments was used. Algorithm Details Intrusion and extrusion were assumed to be determined by the Washburn equation. Intrusion.

The lattice is scanned to find all the pore critical pressures.

These are ordered in ascending size and the pressure increased in steps to achieve each critical pressure in turn. equivalent pore is investigated to

see

As each pressure is reached the if Hg exists at either end.

If not,

the next pressure is taken. If Hg at the entrance is trapped, the next pressure increment is made with no further action.

Filling occurs when the

mercury has a continuous path to the outside. When this occurs both end nodes are checked for other super critical pores. All empty pores of greater diameter connected to this critical pore are filled. All pores containing trapped mercury encountered during this procedure are now flagged as no longer trapped. An air seed is flagged when mercury is present at both ends of the critical pore.

No air seeds are created above their critical pressure

as we do not model the sequence of filling, only the logic.

The scanning

process continues until the designated proportion of the network is filled. Extrusion.

The pressure is dropped in the reverse of the sequence for

incrementation. The critical pore is examined. If no Hg exists at one end, and a liquid path exists to the outside, then that pore is emptied. Pores connected to the emptying end are further examined for the possibility of emptying because new Hg/air interfaces have been created. Mechanisms Preliminary capillary experiments indicated that where filling takes place from both ends and a seed is trapped within the capillary, emptying will take place, but when filling is from one end, reduction of applied pressure alone is not sufficient to cause the capillary to empty. Two theoretical mechanisms of intrusion/extrusionin the network were

considered, as follows:-

81

tlb 3

NETWORK A

10

0

6.6

7

6.8

7.2

7.6

7.4

-778.2 8.4

8

7.8

8.6

LOGlO PRESSURE (Pa)

FIG 4

'lo 100

80

MECHANISM II: EFFECT NETWORK A

3 T-f-i-inirusion

-

~

r

--1 ,

1 follows intrusion

-1

L-_ -

OF KNOCKOUT

I

z

$

.-,-------

70

3

5

601

I

5

50

2

40-

n

30 20 10

0

1

-

No K n o c k o u t

-

-

I

2 in 6 K n o c k o u t

I1 II

4I !

6

I

I

I I

1

6.4

I

I

6.8

I

I

7.2

I

I

7.6

LOGlO PRESSURE (Po)

I

,k-8

. . --I--

8.4

8.8

82

FIG 5

MECHANISM II: EFFECT OF KNOCKOUT NETWORK A

60

50

10

0

I

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A mechanism which proposes the spontaneous nucleation of the mercury

meniscus at the start of extrusion. path exists to the outside. their

own

Pores always empty if a continuous

Pores which fill at pressures other than

Pc will be trapped.

Pores which fill at their critical

pressure have at least one path to the outside bath consisting of larger diameter pores.

If a pore fills at a higher pressure than its own

critical pressure, then all paths to the outside have at least one pore of smaller radius. own

I1

These will empty at higher pressures to the pores

critical pressure and leave this pore trapped.

A mechanism (multiseed) in which the presence of a disturbing influence

is assumed necessary to encourage the mercurylair interface to be created.

Following Mann ( 3 ) , the idea of a single interface, or an air

seed interface with two menisci which exist within any pore filled from both ends at its critical pressure, and which persists because of the high pressure of trapped gas, was considered. Both ends of the pore have to be investigated separately.

If no filled path exists to the

outside, the whole set of pores visited are flagged as trapped and do not take further part in the extrusion process. Results of Modelline, The two mechanisms were applied to networks based on the mean pore radius of sample A derived from intrusion data and two unimodal distributions of pore radii including one similar to that of sample A , with or without a reduction in connectivity via blinding or knocking out pores, running three intrusion/extrusioncycles per network.

This does not imply that the network

represents sample A , and so will be referred to as network A .

In each case

the cycles were examined for hysteresis, the extent of hysteresis, the amount of entrapment, and whether re-intrusion followed the path of extrusion or first intrusion, as a function of connectivity. Results are reported in Table 5 and Figs 3 , 4 , 5 , 6 . Discussion and Conclusions The experimental findings can be summarised as follows. Hysteresis between intrusion and extrusion was reproducible in all cases, and there was no significant time dependence. observed in all cases

:

Entrapment at the end of first extrusion was

it was reproducible and permanent in the time scale

of the experiment. Re-intrusion has the analytical form of first intrusion in all cases.

Partial intrusion resulted in a lower level of entrapment and

narrowing of hysteresis compared to full instrusion. The level of entrapment and the width of hysteresis were proportional to the extent of intrusion. Discussion of modelling is confined to network A .

It was found that a

decrease in contact angle will generate hysteresis, but not entrapment, in any system, and has not been considered further. Mechanism I did not predict

84 hysteresis for a network with connectivity of six, and required a minimum knock-out of 86% of pores to generate hysteresis in which intrusion and extrusion were separate and parallel.

In all cases, re-intrusion followed

the path of extrusion and so did not accord with experimental observations. Mechanism I1 predicted partial hysteresis for a network with full connectivity. From zero knock-out to 50%, re-intrusion followed first cycle intrusion, as observed experimentally, but as knock-out increased above 50%, the path of re-intrusion tended to move back towards the path of extrusion. Partial instrusion resulted in a narrowing of the hysteresis l o o p and a decrease in the level of entrapment, as observed experimentally. REFERENCES 1 2 3 4

D H Everett, "Characterisationof Porous Solids", p 229. Society of Chemical Industry, 1979. W C Conner, J Catal 83, 336, 1983 R Mann, Chem Eng Science 34, 1203, 1979 N C Wardlaw, Powder Technology 29, 127, 1989 This is a collaborative project between Catalysis Research Centre (Billingham), Analytical and Physical Sciences Group (Runcorn), and Petrochemicals Group (Wilton) of ICI Chemicals and Polymers Ltd.

ACKNOWLEDGEMENTS The authors wish to acknowledge valuable discussions with Prof K S W Sing, Brunel University, and Dr D Nicholson, Imperial College, throughout this project .

85

F. Rodriguez-Reinoso et al. (Editors), Characterization of Porous Solids I1 0 1991 Elsevier Science Publishers B.V., Amsterdam

WETTING PHENOMENA IN POROUS SOLIDS: MECHANISMS AND MODELS

A. Winter Geological Survey of Denmark, Thoravej 8, DK-2400 Copenhagen NV, Denmark

ABSTRACT The purpose of this paper is to describe physical mechanisms and mathematical models of disordered porous solids relevant for studies of wetting phenomena in such media. Two distinct levels of investigation are considered: a. the level of a single pore, b. the level of a network of capillaries. Investigations of wetting phenomena at the single pore level include a description of two different wetting regimes. Furthermore, a criterion for stability of thin wetting films is described. The class of mathematical models of porous solids pertaining to the level of a network of capillaries is that of fractal constructs. Applicability of such models to description of porewall roughness is discussed. WETTING PROBLEM: OPEN AND CONFINED GEOMETRIES Wetting phenomena in porous solids involve three coexisting phases: fluid (liquid A or gas), liquid B and solid. In order to describe the interfacial properties of such systems one needs three interfacial tensions, 71v,ysl, and ysv,pertaining to the liquid-fluid-, solid-liquidand solid-fluid interfaces, respectively. An important parameter in studies of wetting phenomena is the spreading coefficient,

S, defined as follows

s = ysv

- Ysl - Ylv

(1)

Two different situations may occur, one where S is negative and another with S being positive. In the former case the liquid wets the underlying solid partially, i.e. a liquid drop placed on the solid does not spread spontaneousIy and the contact line, separating the three coexisting phases, makes a well-defined angle, 0 , with the substrate. In the second case (S > 0), the liquid spreads spontaneously on the solid. More specifically, a thin liquid film separating the fluid phase and substrate is created ( 0 = 0). According to Antonow’s rule (ref. ll), the solid-fluid interfacial tension is given by the following expression

Ysv

= Ylv

+ Ysl

(2)

or, equivalently, S = 0. It should be noted that Antonow’s rule is sometimes violated. This may happen, for instance, when the three-phase system under consideration is described by two order parameters (ref. 11).

86

Experimental investigations of configurations of the wetting- and nonwetting phases in square-sectional capillaries have shown that the wetting fluid tends to occupy the four corners of the capillary. On the other hand, the center of the capillary is filled by the nonwetting phase, see Figure 1. Triangular - Like Channel

a

C

t Brine

I

(Porewal I) phase 1

I

d

Fig. 1. Configuration of the "oil-water'' interface in a square-sectional capillary tubing: (a) 45' plane. (b) and (c) 90° plane (Figure l(b)) shows the case of strong adverse pressure: only corners of the capillary are wetted; Figure l(c) shows the case of weak adverse

pressure: porewalls are entirely wetted). The close-up l(d) shows the thin film (dotted) consisting of N molecules surrounded by the bulk aqueous phase consisting of N-M molecules. An important question is to what extent the wetting phase is present outside the four corners. This problem has been treated theoretically by Joanny and de Gennes (ref. 7). They assumed that the wetting phase is influenced by two kinds of forces: van der Waals forces favoring the existence of a wetting film and the adverse pressure, A p , opposing its formation. In the case of a horizontal capillary shown in Figure 1, the adverse pressure is identical to the capillary pressure, i.e. the difference in pressure, A p c , between the wetting- and nonwetting phases.

Thus, according to the Laplace equation APC = rY

(3)

where Ape is the capillary pressure, y is the interfacial tension between oil and water phases and r is the mean curvature of the interface. In particular, Joanny and de Gennes (ref. 7) have shown that the wetting film extends beyond the four corners of the capillary provided that the adverse pressure exceeds certain critical level, ApCr,given by the following expression

where S is the spreading coefficient and A is the Hamaker constant. Theoretical underpinnings of the problem of presence or absence of thin wetting films in square-sectional capillaries are given in the subsequent section. STABILITY O F THIN WETTING FILMS AND THICKNESS TRANSITIONS Thin wetting films can be considered as phases extending in two lateral dimensions only. Consequently, most of their properties are controlled by forces originating from molecules residing in the ambient, three-dimensional bulk phases. In particular, this is always the case when thickness of the wetting film is smaller than the range of intermolecular interactions. Such interactions typically extend from a few to hundreds of atomic diameters. In the case shown in Figure 2a the chemical potential of the a m , p 3 ~ is, the same as that in the 3D film phase under the same conditions. On the other hand, in the case where there are overlapping force fields originating from the two interfaces of the thin film (cf. Figure 2b), the chemical potential deviates from its value in the 3D phase. More precisely,

~ ~ f (=hP )~ + D pez(h)

(5)

where p e z is the chemical potential that a molecule residing in the 2D film phase has in excess (or deficiency) as compared with its counterpart placed in the 3D phase. The properties of the overlapping force fields may vary from one case to another depending on their origin. Consequently, the excess chemical potential, pez , can be influenced by forces underlying adsorption at the film surfaces, dispersion forces or electric forces acting between charged film surfaces. It should be noted that the excess chemical potential of the film phase is related to the so-called disjoining pressure, II(h) , introduced by Derjagin and his co-workers. It is defined by the following formula (ref. 5)

88

(6)

k ( h ) = - v H( h )

where v the volume per molecule in the 3D phase, i.e. in the infinitely thick film. The problem of dependence of the disjoining pressure function on film thickness has been studied by Dzyaloshinskii, Lifshitz and Pitaevskii (ref. 6).

phase 1 phase 1 3D

phase 2 phase 2 a

b

Fig. 2. Schematic cross-section of a thin film between two bulk phases: (a) the force fields of the two film interfaces do not reach each other, (b) overlapping of the force fields originating from the two film interfaces. Consider now a thin film configuration shown in Figure 2. The thin wetting film 3 is assumed to consist of a one-component liquid squeezed between two plane-parallel 3D phases 1 and 2 representing a porewall and nonwetting liquid, respectively. Let us assume that the positions of the dividing surfaces have been chosen according to the usual conventions (ref. 4). The wetting film is assumed to consist of N molecules. Its thickness can be determined from the following expression

h = (v/A)N

(7)

where v is the volume per molecule in the infinitely thick (3D) film phase and A is film area. In order to formulate the stability conditions for the thin film phase, assume that it M molecules. The chemical potential of the M-N molecules, exterior to the film phase, is denoted by p . The Gibbs free energy of the entire system, G, , is given by the following expression assuming that M >> N: is a part of a larger system containing

G,(N) = ( M - N ) p

+ G ( N )+ constant

where G (N)is the Gibbs free energy of the wetting film. The Gibbs free energy of a finite size, one-component film phase of N molecules can be stated as follows (refs. 8J2)

89

where 1130 is the Gibbs free energy which the finite-size film phase would have had it were a part of a 3D phase of the same composition and @ ( N )is the excess free energy of the

film due to the work associated with the formation of its two interfaces. The system will be in stable thermodynamic equilibrium when its Gibbs free energy fulfils the conditions (dG,/dN)~,,,,,t = 0 and (d2Gs/dN2)A=const > 0. Combining equations (5), (7) and the stability criteria stated above, one can derive the following conditions for the stable equilibrium

P f ( h )= P

and d t”f(h)/dh> 0

(11)

where p is the chemical potential of the contacting 3D phase. If only eq. (lo), is satisfied, but dPf(h)/dh hmin. On the other hand, the thickness range corresponding to the descending portion of the p f ( h ) , results in unstable thermodynamic equilibrium of the is termed a -film and its wetting film. In the stable case, the thinner film ( h 5 h,,,) thicker counterpart ( h 2 h,i,) is termed /? -film. Thus, the wetting film can appear in two thickness states, each representing a distinct 2D phase. One concrete example of a situation with the sigmoidal p f ( h ) dependence is when the dominating components of the disjoining pressure are those representing the molecularand ionic-electrostatic molecular interactions, i.e. II(h)= A / h 3

+B/h2

(13)

where A is the Hamaker constant and B is another constant representing the ionicelectrostatic forces. In this case, the augmented Young-Laplace equation is as follows (cf. eq.(3)

90

where I' = 1/R1+ 1/Rz (R1 and R2 are the orthogonal radii of curvature). In the center of the tubing to the following form

2 = 0 and the Young-Laplace equation (14) degenerates

h3 - ( B / A p ) h+ A / A P = 0 where A P = AP, - y/Rz

hmax

hmin

h

Fig. 3. Portion of a thin film chemical potential isotherm. cc -film and /3 -film of different thickness coexist at p = p e . h,,, and hmin are the equilibrium thin film thickness correspondinq to pmaz and pmin , respectively. Equality of the two hatched areas follows from Maxwell s rule. The above considerations indicate that presence or absence of thin wetting films in square-sectional capillaries can be explained by different values of the excess chemical potential of the wetting film in the two cases. Such changes of the excess chemical potential also appear in certain enhanced oil recovery schemes. This problem is taken up in more details in the subsequent section. MOBILIZATION PROCESSES AND WETTING: SINGLE PORE LEVEL This section describes an experimental study of mobilization of a drop trapped in a square-sectional capillary by a microemulsion slug (refs. 1, 2). Its main purpose is to give a concrete example of a situation where thin film phases appear in a complex industrial process (here: enhanced oil recovery processes at the microscale). The sequence of events observed during mobilization of entrapped drops of a non- wetting phase in a square-sectional capillary is as follows (cf. Figure 4): 1. The front of a microemulsion slug is approximately 25 microns from the back of the drop. The trailing interface of the nonane suddenly retracts and contacts the slug of microemulsion. This is probably due to a film of brine surrounding the front of the

91

slug. The high concentration of the surfactant in this film seems to be responsible for a steep change in the interfacial tension between the wetting- and nonwetting phases in the rear part of the drop. The drop jumps backwards toward the slug and returns to a stable configuration (cf. Figures 4-1and 4-2). 2. The rear interface of the drop is locally ruptured by the front of the microemulsion. The observed phenomena (strong rippling and rapid expansions and contractions of the interface) are probably caused by local changes in the interfacial tension (Marangoni effect) (cf. Figure 4-3).

3. Marangoni effect initiates internal circulation inside the drop. In particular, isolated parts of the drop, close to its rear interface, become emulsified. Consequently, an internal interface separating the emulsified and nonemulsified parts of drop is created. The rolling motion inside the drop is responsible for the transport of its non-emulsified parts to the surface (cf. Figure 4-4). 4. At the final stage of mobilization the whole drop becomes emulsified. The microemul-

sion slug bypasses the drop which snaps-off through the constriction (cf. Figures 4 5 and 4-6). The sequence of events described above is by no means unique: it is extremely sensitive to a composition of the microemulsion. Nevertheless, it provides an excellent illustration of complexity of physicochemical mechanisms governing stability and thickness transitions in thin film phases. WETTING PHENOMENA IN POROUS SOLIDS This section extends our discussion of wetting regimes in a single pore to the level of a network of pores. As the porous solids are structurally extremely complex, this section focuses only on one property affecting wetting phenomena: fractal nature of porewall roughness. A number of recent papers support the hypothesis that, at least in some cases, roughness is indeed fractal (ref. 9). As a concrete example of a model porous medium consider a geometrical construct shown in Figure 5 . Its cross-section consisting of polygonal grains and square-sectional pores in is shown in Figure 6. The porespace is a prespecified range of cutoffs, lmin5 1 5 I,,,, assumed to be initially entirely filled with a wetting phase. The oil phase migrating from the source rock into the reservoir zone displaces the resident wetting fluid. The natural question to be posed is whether wetting films extend beyond the corners of capillary tubes. Assume that the adverse pressure, favoring presence of wetting films, is represented by the van der Waals dispersion forces. In that case all tubes for which the capillary pressure is smaller than the critical pressure given by eq. (4)will have wetting films entirely covering the porewalls. In the remaining tubes wetting films will be retained only in the corners (cf. Figure 6). The above hypothesis concerning distribution of the wetting phase in a fractal porous solid has been tested by considering a capillary pressure measurement using the porous plate method. In capillary pressure measurements the porous sample is initially totally filled with the water phase. A nonwetting phase ( e g oil) is then gradually injected into the sample. As the injection pressure increases, more and more water is removed from the solid. At each step of the experiment the wetting phase appears in one of the two regimes shown in in Figure 1. It seems reasonable to assume that at the end of the desaturation

92

Fig. 4. Enhanced oil recovery at the microscale: mobilization of a trapped nonane drop by a microemulsion slug (modified after (ref. 1)). Detailed explanation of the 6 stages of the mobilization process are given in the text. process all (or almost all) pores retain the wetting phase only in corners of capillary tubes. However, in the case of extremely smooth pores the wetting phase in thin films connecting the corners must also be considered.

93

A simple derivation shows that for the class of fractal porous media shown in Figure 5, the capillary pressure, P,, and the saturation of the wetting phase, S, , are linked by the following relation (cf. Winter, in preparation)

where D is the fractal dimension of the porewalls characterizing their roughness and S, is the part of the wetting phase remaining ineorners of tubings.

Fig. 5 . Three-dimensional view of the fractal construct used as a model porous medium. By fitting the results of capillary pressure experiments (cf. Table I) to the above expression one gets the following values of the fractal dimension for the two cases: D1 = 2.40 and D2 = 2.29. The correlation coefficients are 1.00 and 0.99, respectively. The shape of the distribution function of pore sizes is, of course, a crucial parameter controlling wetting regimes in fractal porous media: depending on its properties, the fraction of pores in one of the two wetting regimes varies affecting many important properties of the medium, such as, e.g. its ability of fluid transport.

94

a

b

Fig. 6. Cross-section through a fractal porous medium showing the configuration of the thin film phase in the pores. Only pores with sizes below the critical threshold level are entirely wetted. In the remaining pores the presence of the film phase is controlled by the magnitude of the adverse pressure: (a) the porewalls are entirely wetted; (b) the film phase appears in corners only.

95

FINAL REMARKS The fundamental mechanisms governing wetting phenomena in disordered porous solids have been described. At the level of a single pore, a square-sectional-pore has been used both as an experimental and theoretical tool in wettability studies. At the level of a network of pores, a fractal porous network has been introduced to describe roughness of porewalls. A fractal dimension associated with this network has been found from the capillary pressure curve. Thus, two parameters emerge as the decriptors of wetting phenomena in a complex porous network: (a) at the single pore level: the exponents in monomials in the film thickness descibing the disjoining pressure isotherms (cf. eq. (13). These exponents charaterize solidliquid interactions and do not change as the configuration of liquids in the pore space varies (ref. 13). At the level of a network of pores: the fractal dimension describing roughness of porewalls. (b) More work, combining information derived from thin film physics at the single pore level and utilizing fractal geometry at the network level, is necessary to assess the applicability of the approach described in this paper to evaluation of wetting phenomena in real life industrial processes.

ACKNOWLEDGEMENTS This work was supported by the EC Research Contract No. RIlB-0290-C(AM).

Saturation

PC

Saturation

PC

(fraction)

psi

(fraction)

psi

0 2 3.97 7.96 15.9 31.2 64 160

1 0.163 0.098 0.063 0.043 0.027 0.016 0.007

1

0.155 0.100 0.069 0.047 0.033 0.020 0.011

0

0 3.97 7.96 15.9 31.2 64 160

Table I. Results of capillaly pressure measurements. Only the 6 last measurements, corresponding to water saturations smaller than 0.069, have been used in the computations of the fractal dimension.

96

REFERENCES 1. Arriola, A., Ph.D. Thesis, University of Kansas, 1983.

2. Birdi, K.S., Vu, D.T. & Winter, A., Proceedings of the IV-th European Symposium on Enhanced Oil Recovery, Hamburg, October 27-29, (1987) 945. 3. Birdi, K.S., Vu, D.T. and Winter, A., Experimental Studies of Mobilization Mechanisms in Square-sectional Capillaries, (in preparation). 4. Croxton, C., Introduction to Liquid State Physics, J. Wiley and Sons, 1975. 5. Derjagin, B.V., Churaev, N.V., Muller, V.M., Surface Forces, Plenum Publishing Corporation, New York, 1987. 6. Dzyaloshinskii, I.E., Lifshitz, E.M., Pitaevskii, L.P., Sovjet Physics JETP, vol. 37, (1960) 161. 7. Joanny, J.F., de Gennes, P.G., C.R. Acad. Sc. Paris, t. 299, serie I1 no. 10 (1984) 605. 8. Kashchiev, D., Surface Science, vol. 225, (1990) 107. 9. Katz, A.J., Thompson, A.H., Physical Review Letters, vol. 54, no. 12, (1985) 1325. 10. Lenormand, R., Zarcone, C. & Sarr, A., J. Fluid Mechanics, vol. 135, (1983) 337. 11. Rowlinson, J.S., Widom, B., Molecular Theory of Capillarity, Oxford University Press, 1982. 12. Rusanov, A.I., Phasengleichgewichte und Grenzflaechenerscheinungen,Akademie Verlag, Berlin, 1978. 13. Toledo, P.G., Novy, R.A., Davis, H.T. and Scriven, L.E., International Workshop on "Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Solids", Riverside, CA, October 11-13, (1989). 14. Winter, A., in: Phase Transitions in Soft Condensed Matter, T. Riste & D. Sherrington (eds.), pp. 237-243, Plenum Publishing Corporation, New York, (1989) 237. 15. Winter, A,, International Journal of Physicochemical Hydrodynamics, vol. 9, no. 3-4, (1987) 589. 16. Winter, A., in: Mathematics of Oil Recovery, P. King (ed.), to be published by Oxford University Press. 17. Winter, A., Stability of Thin Wetting Films and Wettability Reversal in Reservoir Rocks, presented at the Symposium on findamentals of Fluid Transport in Porous Media organized by Institut Francais du Petrole, May 14-18, 1990, Arles, France (in preparation).

F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids I1 0 1991 Elsevier Science Publishers B.V., Amsterdam

97

THE CONTACT ANGLE OF LIQUIDS IN POROUS MEDIA U. Demlehner Wacker-Chemie GmbH, Dept. F/PK 20, D-8263 Burghausen, FRG

SUMMARY We developed a method to determine the contact angle of a liquid penetrating a porous medium by a non-linear fit ofthe continuously measured liquid uptake over a period of some minutes. This method makes it possible to measure the contact angle without any additional assumptions on completely wetting reference liquids. The method was applied to porous glass frits with water, toluene, and different silicone oils. The measured contact angles ranging from 60' to 80' are much higher than the equilibrium contact angles on glass. INTRODUCTION The determination of the contact angle between a liquid and a solid material is of fundamental importance for the characterization of the wetting behaviour of the solid's surface. There exist a plenty of methods to measure the contact angle if the solid surface is non-porous and smooth, since the contact angle may then be measured by optical methods and in an equilibriumstate (ref 1). The determination ofthe contact angle between powder particles with irregular surfaces and a liquid is much more difficult. The powder may be compressed to a tablet showing a macroscopically smooth surface. Experiments and theory have shown that the contact angles measured on the outer surface of compressed powder cakes do not represent thermodynamically consistent equilibrium values (ref. 1). Methods for the determination of the contact angle between a liquid and the inner surface of a powder cake base in most cases on the capillary force which drives the liquid into the powder cake. The counter pressure to balance this capillary pressure is determined with the Bartell method (refs. 1,2,3). A widely used technique is the imbibition method based on the Washburn equation (refs. 1,4). Using this method, the rate ofcapillary penetration is measured either by observing the raise ofthe liquid penetrating the powder cake or by continuously registering the weight ofthe imbibed liquid (reE 5). Ifthe evaporation ofthe liquid is negligiblethe weight loss ofthe liquid reservoir may alternativelybe registered (ref 6). A premise for the imbibition method is the preparation of at least two totally identical powder plugs, one for the measurement with a reference liquid and the other one for the measurement with the liquid under investigation. From the experimental standpoint it is virtually impossible to prepare two powder cakes with identical pore system properties. The reference liquid has to be a completely wetting liquid with a contact angle of 6 = 0' (cos 6 = 1). Since the contact angle between this reference liquid and the powder surface cannot be measured by a direct method, the assumption 0 = 0' can never strictly be proofed. Furthermore, a contact angle measured by the imbibition method is an advancing contact angle and, therefore, not identical with the corresponding equilibrium contact angle.

98

The arguments listed above show that an imbibition method has to be developed, which makes the reference liquid unnecessary and which allows the determination of the contact angle with one sample of a

porous substrate and one liquid. This very method is an absolute method, i. e., no additional assumptions concerning the contact angle are necessary. THEORY Our approach uses the fact that the Washburn equation is an approximate solution for the liquid imbibition into a vertical capillary (refs. 1 , 4 , 7 , 8 , 9 ) . The equation of motion for a liquid raising in a vertical capillary with constant radius ris eq. 1, where his the height ofpenetration at time f, g the gravity constant, 71 the dynamic viscosity, p the gravimetric density and 0 the surface tension ofthe liquid.

If the porous body is modelled by a bundle of vertical capillaries with equal and constant radius r, the height ofpenetration h may be replaced by the liquid uptake per unit area p ofthe bundle (eq. 2). CL

= PPh This model may be extended to any porous body with constant cross section and porosity p , if r is

considered as an equivalent capillary radius or, simply, as an unspecified geometrical parameter. The differential equation for the liquid uptake per unit area p of a porous body is now eq. 3 with the parameters b and pm being defined by eq. 4 and 5. The dynamic viscosity q was replaced by the kinematic viscosity u using u=q / p .

The second term in eq. 3 is negligible for short time t and, consequently, low liquid uptake p. The solution for this limiting case is the Washbum equation (eq. 6). The physicochemicalparameters of the liquid and the porous body may be grouped to a system parameter w (eq. 7). This liquid uptake coefficientw is a measure for the rate of imbibition in the system liquid/porous body. It has been shown that the predictions of eq. 7 regarding the dependance ofthe liquid uptake coefficient w on the physicochemical parameters u and u are experimentally observed (ref. 6) . This may be considered as an indication, that the the capillary bundle model is an appropriate model for aporous body.

99

1

rpp2acos6

w = (

2u

(7)

Inspection of eq. 6 shows that it is not possible to determine the contact angle 8 without knowing the geometrical parameter r. This property of the equation was stressed in the Introduction. Since the Washburn equation is the solution for short time t, eq. 6 cannot be used to describe the liquid imbibition for t-m; the Washburn equation predicts p-00 for 1-00. This physical senselessprediction has been the subject ofmuch discussionwhich ignored the limiting character ofeq. 6 (ref. 10). The correct solution of eq. 3 for long time t is eq. 8. Inspection of this equation shows that p - p w for Consequently, the parameter pw is the final liquid uptake ofthe porous body after infinite time when

t-00.

the liquid has come to rest.

t

=

-1 b [p+p,ln

[1-2-]

If the In-term of eq. 8 is expanded into a first order series, the Washburn equation (eq. 6 ) is the result proving the connection between the liquid uptake coefficientw and the parameters b and pw (eq. 9).

w

=

(9)

[2bpm]1'2

The correct solution ofthe imbibition equation (eq. 8) opens the way to the simultaneous determination of the contact angle 0 and the geometrical parameter r. Eq. 8 may be fitted by standard non-linear regression

techniques if enough data points can be provided. The fit parameters b and pm allow the computation of 6 and r.

t

=

"

-b

p + p +p,ln O

[

pz2J]

I--

- to

Since we cannot start measuring exactly at t - 0 and p=O, we actually use eq. 8 with a minor modification (eq. 10). The parameters to and po serve to compensate the time offset at the start of the measuring process. It should by noted, that we now use t and p to designate our experimental coordinate system, i. e., t designates the time from the start of data sampling, not the time from the first contact between the liquid and the porous body. An alternative approach was proposed by Hilbig and Girlich (ref. 7). They used a second order series

expansion ofeq. 8 which leads to the linear regression equation shown in eq. 11with our notation. Despite its simplicity, the approach ofHilbig and Girlich does not appear to have found much recognition yet.

EXPERIMENTAL Toluene was of analytical grade and used without further purification. Water was deionized by an ionexchanger. The silicone oils (dimethylpolysiloxaneswith trimethylsilyl-endgroups) being of technical grade are manufactured by Wacker-Chemie GmbH, Munich (FRG).

100

Sintered glass frits were used as model I

porous bodies. 1500 g of lead free soda glass

I gloss frit

spheres (Dragonit 25, Dragon-Werk, FRG) with average diameter 45 - 70 pm were poured

sample support

into an alumina mould (160 x 130 x 90 mm3). The mould was covered with an alumina plate which fitted exactly into the mould. In a

liquid

___ electronic balance

--

computer

-

&& Apparatus for the imbibition measurements

chamber furnace the mould was heated to 640 'C with a heating rate of 3.5 Wmin, held for 120 min, and cooled to room temperature with a cooling rate of 10 'C/min. The samples with

constant

cross

section

(120x30x30mm3) were cut from the obtained body with a diamond circular saw. They were carefully cleaned with chromic acid, water and acetone. The glass fits were dried in a vacuum drying oven at 110 'C/50 mbar for 20 h before they were used for imbibition experiments. The apparatus for the measurement ofthe liquid imbibition into the glass fits has been described in detail elsewhere (ref. 6). A schematic sketch is shown in Fig. 1.Usually, the data acquisition frequencywas 1- 2 data

points per second. This means, that a typical experiment which lasts for about 10 - 15 min until the glass frit is saturated by the liquid, consists of cu. 400 data points. The data acquisition frequency was lowered in experiments with high viscosity liquids having a low imbibition rate. RESULTS AND DISCUSSION

Fit Procedure Tests have shown, that optimal performance of the fit may be achieved by a three step technique using standard linear and non-linear regression algorithms (ref. 11): Step 1: Linear regression of the Washburn equation (eq. 6) for the time range 10 s I 100 s of the imbibition measurement. The result ofthis step is the liquid uptake coeficient w. Step 2: Non-linear regression (Levenberg-Marquardt method) of the correct solution (eq. 10)

holding to and poconstant at 0. In order to fit the data by a non-linear regression, estimates ofthe parameters

b and pw have to be supplied. The estimate for the parameter b is computed by means of eq. 9 assuming an arbitrary value for the final liquid uptake pm. Our tests have shown, that the convergence of the non-linear fit is not deteriorated by a rather poor estimate of pw. We actually multiply the value of the liquid uptake at the by a factor oftwo or three and use this value as an estimate for pw. stop ofthe measurement pstop Step 3:

Non-linear regression (Levenberg-Marquardt method) ofthe correct solution (eq. 10)with all

were computed in step 2 and the estimates for to and poare parameters to vary. The estimates for b and pLm supposed to be 0.

101

Tests have shown that it is not possible to combine steps 2 and 3 into a single non-linear regression fit. The convergence ofthis four parameter fit is very poor; in many cases, the fit did not converge at all. Steps 2 and 3 utilize all the measured data points with t 10 s, since the very first data points should be rejected. The determination of the porosity p deserves special mention. This parameter

30

entered the theory of the imbibition process in

cN- 7

E

3 Y

eq. 2 as a proportionality factor connecting the 20

height h of the liquid in the porous body with

i

the liquid uptake per unit area p. This

0)

1 0

c

n

m ._

derivation makes clear that the porosity to be

10

considered here is defined as the ratio between

.-

U 3 1

the volume of the imbibed liquid and the 0

100

200

300

400

5

1

Time t [s]

geometrical volume of the porous body being the cross section ofthe body multiplied with the penetration height of the liquid. If the

Measured and fitted data

imbibition process is followed until the porous body is saturated with the liquid, the plot of p vs. f shows a point, where the slope of the curve

suddenly decreases. This point with the coordinates (tst/psat)is called the saturation point of the porous body. The porosity p may be computed from the saturation liquid uptake psatund the height of the porous body by an appropriate transformation of eq. 2. Alternatively, any combination of p and h may be used for this purpose. Inspection of Fig. 2 reveals that the applicability of the Washburn equation (eq. 6) is limited to data points with 10 s t c 100 s. The correct solution of the imbibition equation (eq. 10) fits the measured data (

points perfectly. Measured Contact Anales Table 1shows some values for the equivalent radius rand the contact angle 6'.

We used three groups ofliquids to test our approach for the determination of 6'. The first liquid was water being a high surface tension liquid (0 = 72 mN/m), while toluene and the silicone oils are low surface tension liquids (U= 28 mN/m (ref. 12) and c = 18 mN/m, respectively). The silicone oils AK 10, AK 50 and AK 300 are poly(dimethylsiloxanes) with trimethylsilyl-endgroups. They had viscosities at 25 "C of v = 7 mm2/s, Y = 35 mm2/s, and V

= 250 mm2/s, respectively.

All these liquids are wetting liquids for glass, i. e., the equilibrium contact angle on a smooth glass surface is eeq= 0 (ref. 13). It is evident, that the measured contact angles are far apart from this equilibrium contact angle eeq.They are essentially identical for all tested liquids. Discussion Our approach to the determination of contact angles between the capillary surface of porous bodies and liquid penetrating the capillaries makes it possible to measure the contact angles without any assumption on

102

TABLE 1 Measured values (av. = average for the respectiveliquid) Liquid

W

[kg/m2min’n]

I

P

Water Water Water

r

0.25 0.27 0.26

4.3 9.5 1.0

Water (av.) Toluene Toluene Toluene Toluene Toluene Toluene Toluene

10.7 9.99 11.7 11.9 10.3 10.0 9.81

110 144 27 1 408 124 118 107

0.27 0.26 0.27 0.31 0.26 0.22 0.25

3.9

3.3 2.7 2.1 3.6 3.9 3.8

Toluene (av.) SiliconeAK 10 SiliconeAK 50 SiliconeAK 3 00 Silicone (av.)

2.19 1.14 0.626

1

41.0 126 54.8

cos 0

0.24 0.24 0.23

6.5 3.4 7.5

0

“I

[PI

&mZ]

0.33 0.21 0.24

71 78 76

0.261t0.06

754

0.30 0.34 0.51 0.52 0.32 0.39 0.30

73 70 59 58 71 67 73

0.38k0.10

67dO

0.31 0.49 0.46

72 60 63

0.42*0.10

654

the wetting behaviour of a reference liquid. It is essential that enough data points are supplied for the nonlinear fit and that the time range of the experiment spans far beyond the scope ofthe Washburn equation (eq. 6).

Simulation tests have shown, that the ratio between the liquid uptake pstop at the stop of the experiment

, be larger than ca. 0.1 for the non-linear fit to converge with sufficient and the final liquid uptake l ~should precision. This limitation is imposed by the optimization procedure of the non-linear regression. If the ratio pstop/pw is smaller than ca. 0.1, the Washburn equation describes the data points well. This means from the

mathematical standpoint, that the non-linear fit will not converge. In this case the liquid uptake coefficientw can solely be determined. The contact angles measured by the described method are much higher than the equilibrium contact angles of the respective liquids on smooth glass surfaces. This result parallels results ofZografi et af. (refs. 15, 16,17), who showed, that contact angles ofat least partly wetting liquids measured by the imbibition method

are generally higher than the respective equilibrium values. They concluded that those contact angles cannot be expected to be physically correct in the sence ofintrinsic equilibrium contact angles. The advancing meniscus of a liquid raising in a capillary has to find a compromise between two forces: the gravitational force which tends to flatten the meniscus, and the capillary force which tends to adjust the contact angle between the liquid and the capillary walls. It is reasonable to assume, that the observed contact angle has avalue between these two extrema, i. e., the contact angle 0 ofawetting liquid should be larger than the equilibrium contact angle 8- but smaller than 90 *. Inspection ofTable 1reveals that the measured values of 0 indeed fulfill this assumption.

103 It would be expected that the contact angle 0 measured by the imbibition method should become similar to the equilibrium contact angle eeq, ifthe superficialvelocity ofthe liquid meniscus decreases (ref. 14). This may be achieved by using liquids with high viscosity since the liquid uptake coefficient w is proportional to the inverse square root ofthe viscosity (c.f: eq. 7) (ref. 6) and w itselfis proportional to the superficialvelocity (c.

f: eq. 3). Though the comparison between the measured liquid uptake coefficients w for toluene and the silicone oils shows, that the superficialvelocity is changed by a factor of about 20, the observed contact angles

0 are still essentially identical. The experiments with the silicone oils prove that it is not possible to achieve quasi-equilibriumconditions by decreasing the superficialvelocity of the raising liquid meniscus. A further point deserves special discussion. It is obvious that the contact angle measured by the imbibition technique is an average contact angle, i. e., the measured value of 0 is an average for all the capillaries in the porous body having different orientation. It may be argued that this fact jeopardizes the interpretation of the contact angles measured by our technique at all, but the same argument would be valid for the conventional imbibition measurements using the Washburn equation. As far as we know, this point has never been discussed in depth. CONCLUSION Our experiments show that it is possible to determine the contact angle 0 with one sample of a porous body and one liquid without making any assumptions about the contact angle of a reference liquid. Our data indicate that the contact angles 0 ofwater, toluene and silicone oils towards the capillary walls of glass frits are much higher than the respective equilibrium contact angles. The measured contact angles obviously are non-equilibrium (advancing) contact angles and should not be discussed in terms of equilibrium surface energies. At this moment, we do not have a tentative explanation about the finding, that the measured contact angles are essentially identical for all the liquids tested. The results of our study make the conventional surface characterization of porous media (e. g. powder plugs) by measuring the contact angles of a series of liquids with different surface tensions by the imbibition method doubtlid, since the assumption of a completely wetting reference liquid ( 0 = 0 -) may not be justified. Furthermore, our data show, that the measured contact angles have no relevance to equilibrium surface energies, at least on high energy surfaceswetted by the liquids used for the imbibition experiments. ACKNOWLEDGMENTS The preparation ofthe glass frits by Dr. B. Pachaly, Wacker-Chemie GmbH, is gratefully acknowledged. Thanks for technical assistance is due to M. Brummer. REFERENCES

1 2 3 4

5 6 7

Neumann, A. W., Good, R. J.; Sud Colloid Sci. (R. J. Good, R. J. Stromberg, ed.; Plenum: New York) 1979,11,31 Heertjes, P. M., Kossen, N. W. F.; Powder Technol.1967,1(1), 33 White, L. R.; J. Colloid InterfaceSci. 1982,90(2), 536 Washbum, E. W.;Phys. Rev. 1921,17(3), 273 Weber, E., Neumann, A. W.; Giesserei 1969,56(21), 628 Demlehner, U.;Farbe Lack 1989,95(10), 708 Hilbig, G., Girlich, N.; Bauphysik 1984,6(6),214

104

8 9 10 11 12 13 14 15 16 17

Hilbig, G.; Bauphysik1986,8(4), 111 Schindler, B., Sell, P. J.; Chem.-hg.-Tech. 1973,45(9-lo),583 Hoffmann, D., Niesel, K ; A m . Cerum. SOC.Bull. 1988,67(8),1418 Press, W. H., Flannery, B. P., Teukolsky, S . A., Vetterling, W. T.; Numerical Recipes; Cambridge University Press: Cambridge 1986 Adamson, A. W.; Physical Chemistry of Surfaces;4th ed.; J. Wiley 62 Sons: New York 1982; p. 40 Lit. 12, p. 349 Rose, W., Heins, R. W.; J. Colloid Sci. 1962,17,39 Yang,Y. W., Zografi, G.; J. Pharm. Sci. 1986,75(7),719 Yang, Y.-W., Zografi, G., Miller, E. E.; J. CoZZoid Interface Sci. 1988,122(1),24 Yang,Y.-W., Zografi, G., Miller, E. E.; J. Colloid Interface Sci. 1988,122(1),35

F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids II 0 1991 Elsevier Science Publishers B.V., Amsterdam

105

THE MAIN PRINCIPLES OF MODELLING OF POROUS SOLIDS. MODELS OF SYSTEMS WITH NEEDLE-LIKE PARTICLES A. P

. KARNAUKHOV

Institute of Catalysis, Novosibirsk 630090 (USSR) SUMMARY As the result of analysis of literature and development of some new ideas the main principles of porous solids modelling are presented. Two models of the systems with needle-like particles are discribed. Special attention is paid t o the problem of network modelling. INTRODUCTION Porous solids of various origins are of various and complex morphology (ref. I ) . Their structure is corpuscular (ensembles of particles) o r spongy (labyrinth of shannels and cavities). Modelling of these complex systems is necessary for theoretical description and interpretation of their geometrical, sorption, diffusion, mechanical, thermal and electrical properties (ref. 2). Model determination The model of a porous solid is the system of particles or pores approximately reflecting its basic properties; the most important requirement is the geometrical similarity. The model is more simple than a porous solid. The degree of simplification depends on the aims of investigation and the possibilities of an investigator. The simplest models are the systems or the regularly arranged particles o r the pores o f a simple geometrical form and equal size. F o r corpuscular structures these are the models which consist of the regularly arranged globules, round disks, round rods, polyhedrons. F o r spongy structures these are the models of cylinder or inkbottle pores. More complex are the models of irregularly arranged particles o r pores of various sizes. Agreement between the model and the object A real porous solid is substituted by an approximately equivalent model. Equivalence may vary in different properties: geometrical, sorption, physical, etc. To have a model fitted to an ob-

106

ject, the exact identity in any property and an approximate correspondence in all others are postulated. This may be illustrated by evolution of simulation for such a typically globular system as silica gel. In the simplest model 1 of the uniform capillaries (see Fig. I ) , an assumption of the identity of the pore volume V and the surface area A in a sample and a model, was accepted and the pore diameter in model was calculated. It is close to an average diameter in the sample. In a more complex model 2 of capillaries of various sizes, the identity of sorption or mercury intrusion isotherms was taken and thus the pore size distribution was calculated. In the simplest uniform globular model 3 (ref. 3 ) the identity of V and A was assumed and thus coordination number n, diameter of globules D, sizes of necks dn = 2.8 V/A, and voids d were calculated. In the next three globular models 4, 5, 6 (ref. 3) approximate or exact identity of sorption isotherms was accepted. Texture parameters of these models are somewhat different from those for the sample due to the ignorence of interconnections of pores. In the network model 7 of spherical voids and cylindrical necks (refs. 4,5), the identity of sorption isotherms was assumed and the necks' and voids' distributions were determined. Geometrical and physical properties of the sample and the model as well as the distribution of voids are significantly different from each other due to the opposite sign of the curvature of a surface in the sample and in the model. Typical element of model From the very start, the modelling of porous systems was connected with choice of the typical element of a model: the cylindrical capillary, conic pore, inkbottle pore, slit- and wedgeshaped pores. From the contemporary point of view, these models are more suitable to studying the spongy structures. In case of the corpuscular systems it is useful to distinguish the elementpore as the space between particles. In this case, an elementary pore is obtained by cutting the neighbouring particles by planes in the directions, dependent on the geometry of a system. For the globular models 3 , 4 , 6 (see Fig. I ) , secant planes p8SS through the globules centres and points of their contact. As a result, from the models 3,4 regular polyhedrons are cut, and

107

Fig. 1. Evolution of the model of silica gel texture. V,, As -- pore volume and surface area of the sample, a -- adsorption on iQ; v , -- pore volume an surface area of the model, -- adsorption on n -- coordination number of globules packing, dN/dn -- distribution of the number of globules over the coordination number, dNn/dn -distribution of the number of necks over their sizes, z -- coordination of a lattice,/,,N Ntot -- cumulative fraction of necks. The solid curve -- experimental isotherm; the dotted curve -isotherm for the model. D, d, dn, -- diameters of $obule, Pore Y neck, void.

9

3;

v, =Y, As=Am

approxiinate lden-

continuouS

Identity

-'igm 1

108

from the model 6 -- irregular polyhedrons (Fig 2) are cut with elementary pores inside. Fig. 3 illustrates one of the possible elementary pores for the platelet structures, a n d Figures 5 and 8 in last sect.-- the elementary pores for the needle-like structures.

Fig. 2. Models of the elementary pores for the irregular packings of globules. Fig. 3 . Model of the elementary pore for the platelet structures.

Interconnection between the model's elements In the previous classical modelling, the elements mentioned above were supposed to be independent. At present, it is obvious that this assumption leads to a distortion in description of various processes occurring in porous solids, such as desorption of sorbate, intrusion of mercury, filtration, molecular-sieve adsorption. For this reason, modelling of the primary elements may be considered as the first step, which is necessary though insufficient. The second step must be the modelling of interconnection between the elements. At present, it is conducted by the network models, and processes in them -- by percolation theory (refs.4-7). However, so far it was made only for comb5nation of the sphe-

109

rical voids and round windows. Strictly speaking, these network models are appropriate for description of spongy structures only. Their application to the globular systems may lead to mistakes in interpretation o f the adsorption branch as independent capillary condensation in voids due to convex curvature of void surface. As it was shown by Karnaukhov and Kiselev (ref. 8 ) , the capillary condensation in these systems, starting at places of globules' contacts, leads to merging of a condensate in the necks of pores and its following spontaneous propagation to the pore void. F o r this reason, the next development of the problem of modelling seems to be in creation of the network models, in which the elements may be of the other various types of pores. Different degree of elements disordering should be considered in them. F o r instance, in the platelet systems there may be an orientated packing of elements according totheir basis planes, and an irregular one in every layer, in the needle-like systems -- the orientated packing in bundles, and the irregular distribution of the bundles themselves, etc. It is possible that application of various models from those where the elements are completely independent (the models of montmorillonite, ?-Al2O3) to those, in which they are completely interconnected (the models o f porous glasses, xerogels) will allow to explain the origin of not only the type of H2 capillary condensation hysteresis, but other types as well. It may be good to use the irregular network models with the alternating coordination of the lattice (ref. 5 ) , the two-dimensional analogue of which is the lattice given in Fig. 4. Distribution of the coordination numbers in this lattice may be found by independent physical or computer simulation (refs. 9,lO). Ffg. 4. Scheme of the twodimensional irregular network model.

110

Inversion rule Porous solids are the two-phase system: gas o r liquid phase and solid phase. Accroding to inversion rule (refs. l , l l ) , the sum of volume fractions of solid and pores is equal to one: -?+E

= I

.

(1 1

This rule means that the detailed geometry of solid part determines the detailed geometry of porous part and vice versa. The rule of inversion may be efficiently applied to modelling. Due to it, studying of the pores structure may be substituted by studying of the solid’s structure. The particular porous solid may be modelled in one of these systems. Corpuscular solids are more simple and exact to be modelled by the system of particles, the spongy ones -- by the system of pores. The rule of inversion makes it possible to establish the relation between the parameters of particles and those of pores in corpuscular structures (ref. 1) on the basis of equality of the surface of pores and the surface of particles. This equality presents the expression for the pore diameter: K = A V p ? D , (2) dP KPr where K Kpr are the form factors for pores and for particles, P’ V -- volume of pores, density of solid, D -- size of parP ticles. This expression directly points to the fact that the more is the size of particles and the more loose is their packing (deter mining the volume of pores) the more the size of pores is.

p--

Models of systems of the needle-like particles and fibres The morphology of these materials may be divided into two groups. In the first one needles and fibres are orientated along the particle axis (e.g., the needles of C(-Fe2O3, tubular crystals of chrysotile asbestos, fibrous polymers, fibrous carbon, etc.), in the other one there is random packing of particles (e.g., in boehmite, x - A l 2 O 3 , gels of tungsten oxide, zirconium oxide, in many clay minerals, in paper, and filters). According to this two models may be presented. The first one is the model of longitudinal packing of round

111

rods. For three regular packings of these rods with the coordination numbers six ( & = 9.25%), four ( 6 = 21.5%) and three ( & = 39.5%) it is possible to cut three elementary pores (see Fig. 5) and to construct an interpolation curves (solid lines) which are the porosity and pore size versus n (Fig. 6). The diameter of rods is determined from micrographs or from the surface area, quasicoordination number -- from porosity.

n.= 6 (100-

€)%

80

n= 4 60

rn 2

n=3

4

6

Fig. 5 . Models of the elementary pores for the longitudinal regular packings of round rods. Fig. 6. Interpolation curve of the dependence of porosity and relative size of pores d/D on the coordination number for the regular longitudinal packings o f round rods. D is the diameter of the rods, d is the diameter of the circumference inscribed in a pore (ref. 12). 1 and 2 are the experimental values for the cuts of cords and packings of steel rods.

Fig. 6 demonstrates an excellent agreement of theoretical (points 3) and experimental (points 1,2) dependence 6 on n. Experimental values are obtained by study of cord fibres' cuts and buttends.of steel rods' bundles (ref. 12). The maximum difference between pore diameters, determined by mercury penitration and by model was 19%. The model of the longitudinally packed r o d s is an ideal example of the pores independent of each other. The percolation effects should not take place for it. For this reason, traditional

112

methods of capillary condensation and of the mercury porosimetry may be applied to it. In case of occasionally distributed needles one can use a model of the cross-sectionally round rods. In this model their rods are packed in layers, so that their axes are perpendicular in adjacent layers. In every layer the distance between the rods may vary, which leads to changing of the volume of pores and porosity. The parameters of the model are the diameter of rods D and the distance between the axes of rods C expressed in fractions of D. C is calculated from the value of porosity by the curve given in Fig. 7 . The minimum value of porosity Emin = 0.215 corresponds to the dense packing of rods in the layer ( C = 1) . The model of the elementary pore for the packing C = 2, E = 0.6 is given in Fig. 8 .

40

3

2

3

4

5

6

7

Fig. 7. Dependence of the porosity on the distance X between the axes of round rods. There is a relative distance C = X/D on the abscissa axis. Fig. 8. Model of the elementary pore for a regular cross-sectional packing of round rods with C, equal to 2 . The large experimentally measured value of porosity f o r the systems o f the needle-like particles serves as the basis f o r application o f the described model. For the occasional packing of steel rods (ref. 1) the value = 0.61 was obtained, which corresponds to C = 2.0 for the model. In ref. 13 for the needle-

I

113

like structure of ferrous oxide (phase of goethite), the value = 0.64 was obtained (C = 2.2). The model of y-A1203 ( A = 210 m2/g, 6 = 0 . 8 7 ) , studied in (ref. In?), has the parameters of D = 5.7 nm, C = 5.5. The discussed model is one of the least studied. There is no theory of the capillary condensation and mercury intrusion for it. For this reason it is difficult to calculate pore sizes from isotherms of sorption and intrusion by these methods. For this model the percolation effects should be the most prominent, and for it to be revealed it is necessary to construct the correspondent net-work models, because the usual models of spherical voids and round windows are not appropriate in this case. REFERENCES 1 2

3 4 5 6 7 8

9 10 11 12

13 14

A.P. Karnaukhov, in S.J. Gregg and K.S.W. Sing (Eds.), Characterisation of Porous Solids, SCI, London, 1979, p. 301. A.P. Karnaukhov, in Physical and Chemical Principles of Synthesis of Oxide Catalysts, Nauka, Novosibirsk, 1978, p. 231 (in Russ.). A.P. Karnaukhov, Kinet. Katal. 1 2 (1971) 1025, 1235 (in Russ.) C . C . Wall, R.J.C. Brown , J. Coll. Interface Sci. 8 2 ( 1 9 S l ) 141. V.P. Zhdanov, V.B. Fenelonov and D.K. Efremov, ibid. 120 (1987) 218; D.K. Efremov and V.B. Fenelonov, Kinet. Catal. Lett. 40 (1989) 177. A.V. Neimark, Dokl. AN SSSR 273 (1983) 384 (in Russ.). G. Mason, in K.K. Unger, J. Rouquerol, K.S. Sing and €1. Kral (Eds.) Characterisation of Porous Solids, Elsevier, Amsterdam, 1988, p . 323. A.P. Karnaukhov and A.V. Kiselev. Zh. Phis. Khim. 3 .1 (1957) . . . . 2635 (in Russ.). R.V. Zagrafskaya, A.P. Karnaukhov and V.B. Fenelonov, Kinet. Katal. 16 (1975) 1583. R.I. Ayukaev, V.K. Kivran and M.E. Aerov, Dokl. AN SSSR 218 (1974) 66 (in Russ.). L.V. Radushkevich, in hl.Tvl. Dubinin and V.V. Serpinskii (Eds.) Base Problems of Phys. Adsorption, Nauka, Moscow, 1970 , p. 270 (in Russ.). S.F. Grebennikov and V.I. Konovalov, in M.M. Dubinin and V.V. Serpinskii (Eds.) Adsorption and Porosity, Nauka, Moscow, 1976, p. 6 3 (in Russ.). K.A. Dadayan, R.V. Zagrafskaya, A.P. Karnaukhov and V.B. Fenelonov, Kinet. Katal. 1 8 (1977) 1517 (in Russ.). V.A. Dzisko, T.S. Vinnikova, L.M. Kefely and I . A . Ryzhak, Kinet. Katal. 7 (1966) 859 (in Russ.).

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F. Rodriguez-Reinosoet al. (Editors),Characterization of Porous Solids 11 0 1991 Elsevier Science Publishers B.V., Amsterdam

115

ADSORPTION-DESORPTION HYSTERESIS IN POROUS NETWORKS D.K.EFREMOV and V.B.FENELONOV Institute of catalysis, Novosibirsk, USSR.

SUMMARY As a result of computer experiments with model porous networks, the factors ( other than pore shape and size distribution ) determining the form of the adsorption-desorption hysteresis loop have been elucidated.

INTRODUCTION At present, quantitative information about pore structures of catalysts and adsorbents with pore sizes ranging from 1.5 to 50 nm is usually obtained from analysis of isotherms of adsorption and desorption in the region of a capillary-condensation hysteresis. It is often assumed that the form of the hysteresis loop is determinated primarily by the pore shape and their Size distribution [ 1,2 I . The objective of this work was to elucidate factors (other than pore shape and size distribution) determininig the form of hysteresis loops. MODEL POROUS SOLIDS This work have been carried out by the method of numerical adsorption experiments on model porous network, a mesoporous fragment of wich is shown in Fig. 1. This model porous space consists of spheroidal cavities ( voids ) and cylindrical necks between these voids. Such a model has allowed us to correctly evaluate volumes of all arising configurations of the adsorbate under different relative pressures of sorbate vapours, P/p,. Generation of the model pore space in computer memory was initiated by introducing density function of radius distribution of spheroids, f ( r ) , which was determined for size region ( A,B ) (see Fig.1 ) and which satisfied the condition : B

J f(r) dr = 1 A

116 0

PORE RADIUS. (A1 Fig. 1 . Density distribution functions f and g of model porous spaces, a fragment of which is shown in the upper part of figure.

Further the subroutine generating random numbers uniformly distributed over the interval ( 0 , l ) was transformed to obtain random numbers over the interval ( A , B ) with the distribution density f ( r ) . The radii so obtained were successively memorized in cells of a three-dimensional numerical N*N*N-array with even coordinates. Then the values of radii of cylinders that conneoted spheroids were introduced into the cells of the same array having two even and one odd coordinates. To obtain a desirable type of distribution of cylinder radii, a random procedure was used. This procedure satisfied the following requirements: (I) radii of all cylinders lie within the segment ( C , D ) , where C < O . 5 * A and D < 0 . 5 * B ; (11) radius of each cylinder does not exceed half radius of the smallest of two connected spheroids : (111) the distance between the centers of neighbouring connected spheroids is equal to 2 * ( B + D ), which precludes the possibility of '*overlapping**of spherical menisci after

117

irreversible condensation in the connecting cylinder. To pass from a simple cubic lattice with a constant coordination number (connectivity) equally 6 to a randomized lattice with average coordination number Z < 6 we have used a random procedure, which substitutes zero for part of cylinder radii in such a way that isolated pore clusters a r e not formed. Density distribution functions used for generating spheroid and cylinder radii in all cases considered below, are shown in Fig.1. In all cases a model porous solid was assumed to have macropores with surface area A,,, which were not filled in model experiments even at a limiting value of P/ Po = 0.99. The contribution of multimolecular adsorption A,,** was added to the adsorbate volume in mesopores at each P o o . In a number of cases the existence of micropores with volume V, filled at very low P o o was assumed. Then the V, value was added to the current volume of the adsorbate. In numerical experiments, changes of the form of isoterms in the region of hysteresis loops were studied as function of: (1) Size of lattice N (where [(N-1)/2 l 3 is amount of spheroidal voids ) , ( 2 ) Connectivity of the lattice (average coordination number)

z, (3) Proportion of the volume of micropores, V, ,in the total pore volume V, ( parameter V,/Vo ), ( 4 ) Proportion of the maoropore surface area, Be,, of the total surface area ,Ao ( parameter A,,/Ao 1. ADSORPTION EXPERIMENT

First, the adsorption and capillary condensation of nitrogen at

77 K was modelling. It was assumed that prior to irreversible capillary condensation the surface of a porous solid is uniformly covered with an adsorption film with the thickness t = 0.354

*

1/3

(

5 / b(P/P0)

)

(here and below all linear ciimensions are given in n m ) . For the calculation of adsorbate configurations at the junctions of spheroids and cylinders,spherical and cylindrical rings with the thickness t were "pasted together" by suitable toroidal-shaped sectors with the sectional radius t. In accord with Kelvin equation it was assumed that cylindrical pores with

118

the radius rc are filled with the condensate if

rc -

t


CMC) in the evaporation experiments. The evaporation rates of SDS-drop [3.1 10-6g/s] and CTAB-drop [2.3 10-6g/s]and pure water [1.9 10-6g/s]were found to be different, due to the above described differences in contact angle and radii. However, the CTAB-drop was found to evaporate with a constant rate while the SDS-drop evaporated with a decreasing rate. This shows that the radius of the CTAB-glass interface remains also constant during evaporation. It is larger than the radius of the water-glass interface but smaller than the radius of the SDSglass interface. The less spreading of CTAB compared to SDS may be explained by a mutual attraction between the glass surface (due to a negative charge) and CTAB (which is a positively charged detergent). This is not the case for SDS which is a negatively charged detergent. The same charge for a glass surface and SDS-drop causes the radius of the SDS-Glass interface not to remain constant as was the case for CTAB-Glass. B.3. EvaDoration of liquids from porous media. Measurements of the rates of evaporations of liquid drops placed on a porous solid surface were conducted using a small cylinder of polystyrene (Height = 10.5 nun, Diameter = 6.6 mm) which contained the solid powder or small glass spheres, so as to fill up to ca. 4 the volume of a cylinder (Fig. 4 ) . The cylinder was placed in a chamber with controlled temperature and humidity. Thereafter a given volume of the liquid was poured into the cylinder. The weight of the liquid was measured with a sensitivity of k 5 pg. The rates of evaporation of n-hexane from glass spheres with diameter of 0.1 nun or 0.5 mm, respectively, were investigated. The data in Fig. 5 show that n-hexane evaporates with different rates in the two cases, and also that the evaporation shows clearly three different stages (marked as rate 1, rate 2 and rate 3 in Fig.

157

5). The first rate (rate 1) is approximately constant and corresponds to the evaporation of n-hexane molecules of the bulk liquid. The n-hexane molecules which are present in the pores between the glass spheres evaporate with a constant rate (rate 2) but the magnitude is lower than rate 1. The remaining n-hexane molecules which are adsorbed on the surface of the glass spheres evaporate with a decreasing rate (rate 3).

Fig. 4 .

The evaporation of liquid from porus medium.

By using linear regression, the value of the first rate is found to be ca. 5.6 g/sec and 5.0 g/sec for n-hexane/glass spheres with diameter of 0.1 mm and 0.5 mm, respectively. The value of the second rate for both sizes of glass sphere is found to be the same, i.e. 3.0 1 0 - ~g/sec. In order to determine the dependence of the evaporation rate On solid particles with different composition and pore volume, we have used fine solid powders, e.g. SVc45 (a-alumina standard, total pore volume Vp = 0.037 cm3/g), SVCSO (alumina carrier, Vp = 0.312 cm3/g), SVC52 (kieselguhr, Vp = 0 . 0 0 9 cm3/g) and SVC71 (graphite, Vp = 0.0608 cm3/g). These powders and their data have been provided by Haldor Topspre A / S . The data for the evaporation of n-hexane from these powders VS. time are given in Fig. 5 . These data show that n-hexane in these liquid/powder systems also evaporated at three different rates. The first rate (rate 1) and the second rate (rate 2) are constant and were estimated by using a linear regression:

158

rate 1: Y = A 1 + B1 * X rate 2 : Y = A2 + B 2 * X where X is time (sec), Y is weight of liquid, A 1 and A2 are constants and B1 and B2 are slopes of plot (=rate of evaporation (g/sec)) The magnitudes of A l l B 1 , A2, and B2 for different systems are given in Table 1.

.

0.1

0.08

E

Glass (0 .5 mm -

Glass (0.1 mrn

0.04

0.02

0 0

Fig. 5.

1000

2000

3000

4000

5000

6000

Evaporation of n-Hexane from porous media.

The results from Table 1 show that the values of rate 1 and rate 2 for all systems do not deviate very much from each other. It is seen that n-hexane molecules in bulk liquid evaporate three times faster than n-hexane molecules in the pores between particles. The most interesting observation was made for the evaporation rate which involves the adsorbed layers of liquid molecules which are in the pores of the solid material. It was found that n-hexane in the particles which have a high pore volume (SVC50) evaporated at a lower rate than from low pore volume particles (SVC45 or SVC52 or SVC71).

159

TABLE 1 The first and second rate for different n-Hexane/Powders system.

I n-Hexane/ powder svc45 SVC50 svc52 svc71

Rate 1 Y = A1 + Bl*X A1

B1

Rate 2 Y = A2 + B2*X A2

B2

R-Squared

(*I 0.11360 0.11186 0.11165 0.11059

-9.1E-5 0.09035

-2.6E-5

0.99988 0.99831

0.09920

-3.3E-5

0.99996 0.99852

0.09397

-2.7E-5

0.99989 0.99983

0.09742

-2.9E-5

0.99979 0.99968

-1.OE-4 -8.7E-5 -8.5E-05

CONCLUSION

The surface area of solids was determined from the heat of immersion method using calorimetry. These data agreed with the BET method. These data are of use for describing the evaporation of liquids from solid surfaces (both the rates and the heat of evaporation). The evaporation of sessile drops of water (resting on glass surface) and n-octane (on teflon) was found to be a stationary process. In both cases, when the size of evaporating drop decreases, only the contact angle decreases while the radius of liquid-solid interface remains constant during evaporation. Furthermore, the rate of evaporation, in these cases, was found to be linearly proportional to the radius of liquid-solid interface. Sessile drop of water, SDS-, and CTAB-solution when placed on a glass surface, were found to evaporate into the air with different rates. A CTAB-droplet will evaporate at a faster rate than a waterdroplet but it evaporates at a slower rate than a SDS-droplet. Both water- and CTAB-droplets evaporate with a constant rate, while the SDS-droplet evaporates with a decreasing rate. This suggests that there is a different effect between the two detergents: negative detergent (SDS) and positive detergent CTAB onto glass surface.

160

The liquid in a cylinder which contained small particles such as glass spheres or solid powders will evaporate at three different rates. The first rate is the evaporation rate of liquid molecules in the bulk liquid, the second one is the evaporation rate of liquid molecules which are present in the pores between particles and the third one is for the liquid molecules which are present in the pore volume of particles. In general, both the first and second rate are constant but the third rate is a decreasing rate. Although the first and second rate for most systems are about the same, the third evaporation rate of n-hexane will be slower in particles which have a high total pore volume. This may be due to the possibility that more volume of liquid penetrates into the pores and then it takes a longer time to evaporate. This suggests that one can estimate the pore volume of the porous solid from the latter. ACKNOWLEDGEMENTS This work was supported by BRITE contract [No. RI lB-0290-Cl. REFERENCES 1 Chattoraj, D.K. & Birdi, K.S., Adsorption & the Gibbs Surface Excess, Plenum Press, New York, 1984. 2 (a) Birdi, K.S., Vu, D.T. and Winter A., J. Phys. Chem. 1989, 93, 3702. (b) Birdi, K.S. & Vu, D.T., Mechanisms of Oil Recovery, Report, 1988, Danish Ministry of Energy, Copenhagen. 3 Birdi, K.S., Lipid & biopolymer Monolayers at Liquid Interfaces, 1989, Plenum Press, New York.

F. Rodriguez-Reinoso et al. (Editors), Characterization of Porous Solids II 0 1991 Elsevier Science Publishers B.V., Amsterdam

161

A NEW APPARATUS FOR CONTINUOUS ADSORPTION. APPLICATION TO THE CHARACTERIZATION OF MICROPOROUS SOLIDS H. AJOT, J.F. JOLY, F. RAATZ and C. RUSSMANN INSTITUTFRANCAIS DU PETROLE, 1et 4 avenue de Bois Preau, BP311,92506Rueil Malmaison (France).

SUMMARY A new apparatus for continuous adsorption is described. This apparatus is based on anew technique which uses proportional valves with an upstream pressure regulation. The decrease of upstream pressure is programmed at about 1 torr/min, leading to constant flow rates in the range of 0.17 to 0.2 ml(STP)/rnin independent of the downstream pressure. Complete nitrogen adsorption-desorption isotherms can be recorded with an automatic procedure. The main advantages of this new apparatus are: simplicity, accuracy and a wide field of applications, including the study of microporous solids. INTRODUCTION Gas adsorption is the standard technique to study the textural properties of porous solids (ref. 1). The classical technique is based on incremental additions of gas providing adiscret set of points along the isotherm. This technique can be referred as a “discret” technique. It appears to be limited and time consumming when high accuracy is required. This is especially true in the case of microporous solids. To overcome this intrinsec limitation, “continuous” adsorption techniques have been developed. In these techniques the adsorbate is admitted to the sample tube at a slow flow rate. As it is critical to maintain, at any given time, the adsorption equilibrium, very low adsorbate flow rates must be used. Volumetric and gravimemc apparatus have been developed in order to obtain a continuous adsorbate addition. Two main volumetric techniques can be distinguished, the use of i) narrow restrictions such as capillaries (refs. 2,3) and orifices in metal foils (ref. 4), and ii) sonic flow restrictions (refs. 5,6). Constant flow rates cannot be obtained using capillaries and orifices, even for downstream pressures lower than 100 mbars. Thus, complete adsorption-desorption isotherms cannot be easely obtained. In contrast, constant flow rates can be obtained with sonic flow restrictions, in the entire range of desired downstream pressures (up to 1 bar without experimental difficulties) by using high upstream pressures (up to 10 bars) (ref. 7). Gravimetric techniques as described in ref. 5, lead to complete adsorption-desorption isotherms without downstream pressure limitations (a needle valve is used). We have developed a new apparatus leading to the acquisition of complete adsorption-desorption isotherms. In this apparatus the adsorbate is admitted to the sample tube at a slow constant flow rate

162

using a proportional valve and an upstream pressure regulator (in the desorption mode the adsorbate is removed from the sample tube according to the same principle). The flow rate is thus independent

from the downstream pressure. This new concept has been protected by a patent. APPARATUS AND PROCEDURE ApyratuS A schematic of the apparatus is presented in figure 1. The adsorbate, usually nitrogen, is admitted to the sample tube at a slow flow rate (typical value: 0.17 ml(STP)/min) through a proportional valve. The decrease of the upstream pressure is typically programmed to 1 torr/min. Two proportional MKS valves are used, one for the adsorption, one for the desorption. During desorption, the difference between upstream and downstream pressures has to be in the range of 76 to 228 torrs to insure a constant flow rate. Both adsorption and desorption branches of the isotherms are depicted with theoritically an infinite number of points (practically loo0 points are recorded).

Fig. 1. Schematic of the apparatus. V10 and V11: proportional valves; C1, C2 and C3: pressure gauges; R1: adsorbate container; R2: calibration volume; S.T.: sample tube; V: vacuum line. V1 to V9: valves.

163

Procedure The sample is first ou.tgassed down to torr using a turbomolecular pump, with a specific temperature programme depending on the nature of the studied sample. The sample is then isolated from the vacuum system. A dewar flask containing liquid nitrogen is placed around the sample tube, the level of nitrogen is kept constant by periodically replenishing the liquid lost by evaporation. The dead volume is determined by helium, the measurment is automaticaly conducted by the use of a computer. Helium is withdrawn from the apparatus, the sample is outgassed under vacuum until the vacuum is close to lO.'torr. The initial upstream pressure is of about 1290 torrs, the pressure regulator is programmed so that the decrease of pressure is close to 1 torr/min. Nitrogen is thus slowly admitted at a slow constant flow rate in the range of 0.15-0.20ml(STP)/min through the proportional valve to the sample tube. The nitrogen admission is stopped when the partial pressure in the sample tube is close to 1, the adsorption branch is thus described with a high accuracy. To record the desorption branch, the upstream pressure is lowered to lO.'torr, and nitrogen is evacuated from the sample tube at a slow constant flow rate in the range of 0.15-0.20 ml(STP)/min. During the adsorption procedure, the sample tube can be isolated, it is thus possible to check that the equilibrium is reached at any given time. Other adsorbates than nitrogen can be used in the same way. Isotherm acauisition Volumes of nitrogen container and of the sample tube are known with a high accuracy. By recording simultaneously upstream and downstream pressures, the quantity of adsorbed nitrogen is calculated, the isotherms are obtained by plotting it as a function of partial pressure P/Po. RESULTS This new continuous adsorption technique has been used to determine the textural properties of a mesoporous solid ($alumina) and of microporous solids (zeolites). Results have been compared to those obtained with the "discrete" technique. For the experiments, nitrogen is used as adsorbate. 1.f-aIumina d-alumina (Rhone Poulenc product) has been outgassed at 723K under vacuum, lo6torr. The adsorption branch has been determined at 77K with nitrogen at constant flow rate of 0.17 ml(STP)/min, 967 points are recorded. T h e desorption branch is obtained by evacuation of nitrogen at a constant flow rate of 0.17 ml(STP)/min, 930 points are recorded. The complete nitrogen isotherm is reported in figure 2. The calculated B.E.T. surface area is 257 m'/g (252 m'/g using the "discrete" technique). The agreement between the two techniques is very satisfactory.

2. NaY zeolife torr). After Nay, provided by Union Carbide, has been outgassed at 773K under vacuum cooling the sample tube at 77K,the complete nitrogen isotherm is recorded and is reported in figure 3.

164

Fig. 2. Nitrogen isotherm at 77K of #alumina.

Fig. 3. Nitrogen isotherm at 77K of Nay.

165

The adsorption branch is obtained using a constant flow rate of 0.17 ml(STP)/min, 967 points are recorded. To record the desorption branch the same flow rate is used, 930 points are then recorded. The calculated B.E.T. surface area is 871 m2/g (900 m2/g indicated by Union Carbide). It should be noticed that the Union Carbide value has been obtained using a dynamic apparatus ("one point" B.E.T.). 3. ApDlication to H-zeolites with different structures H-Beta, H-mordenite and H-MFI zeolites have been prepared from as-synthesized zeolites using classical modification procedures: ionic exchanges in NH,NO, solutions followed by calcination under air at 823K. The main physicochemical characterists of the three solids are given in table I. TABLE 1 Physicochemical characteristics of H-zeolites

I

zeolites

I

Si/Al total

I

% DX

I

% Na

I

H-BETA

H-MFI

0.013

Dubinin volume, B.E.T. and t surface areas of these zeolites are determined using the continuous nitrogen adsorption at 77K with flow rate values close to 0.2 ml(STP)/min. The values obtained are summarized in the table 11.

TABLE 2 Dubinin volume, B.E.T. and t-surface areas of H-zeolites determined using continuous nitrogen adsorption

I

zeolites

I

H-MFI

I

I

0.204 0.193

S BETm2/g

1

692

0.280

H-BETA rHMORD.

V Dubinin cm3(liq)/g

I

361 441

St m2/g

I

37

I

10

I

164

Values found for Dubinin volume, B.E.T. and t surface areas reported in table I1 are in good agreement with that generally reported for such zeolites.

166

The isotherm of H-Beta is reported in figure 4 and exhibits an hyterisis loop indicating that mesopores are present, the closer point of the hyterisis loop is found to be close to P/Po=O.42. Catastrophic desorption of mesopores is seen as generally found for dealuminated HY zeolites (ref. 8), one can discuss about the origin of this phenomenon. It is certainly due to mesopores, evidenced in transmission electron microscopy, which are not directly connected to the exterior of the crystals. The formation of these mesopores is probahly related to the presence of faults in the stacking sequence of polytypes as mentioned in ref. 9.

Fig. 4. Nitrogen isotherm at 77K of H-Beta.

CONCLUSION We have developed a new continuous adsorption technique. This technique is different from those already described in the literature since it does not employ any mass flow controllers, capillaries, orifices in metal foils or sonic flow system. It is based on the use of proportional valves (one for the adsorption, one for the desorption) with upstream pressure regulation (or downstream regulation in the desorption mode). The programmed decrease of the upstream pressure is around 1 torr/min with typical flow rates of 0.17-0.20 ml(STP)/min. The main advantages of this new apparatus are:

167

1. It's simplicity, 2. Flow rates low enough as to ensure a thermodynamic equilibrium at any given time, 3. Controlled and constant flow rate, independent of the downstream pressure, 4. Complete adsorption-desorption isotherms can be recorded, 5. Wide field of applications including microporous solids, since high accuracy is obtained in the very low pressure range.

ACKNOWLEGMENTS We would like to sincerely acknowledge Mr GARNER and MAFWY REFERENCES 1. S.J. Gregg and K.S.W. Sing in "Adsorption, Surface area and Porosity", Academic Press Inc., second edition, 1982. 2. K.R.Lange, 1. Colloid. Sci., 18 (1963), pp. 65-72. 3. E.G. Schlosser, Chemie Ing. Techn, 31 (1959), 799. 4. P.S. Northrop, R.C Flagan and G.R. Gavalas, Langmuir, 3 (1987), pp. 300-302. 5. J. Rouquerol, F. Rouquerol, Y. Grillet and R.J. Ward, Proceeding of the IUPAC Symposium (COPS I) Bad Soden, April 26-29, 1987, Studies in Surface Science and Catalysis, Elsevier, Amsterdam, 1988, vol. 39, pp 67-76. 6. Y. Grillet, F. Rouquerol and 1. Rouquerol, J. Chim. Phys., 74 (1977), pp. 179-182. 7. J. Rouquerol, personal communication. 8. J. Lynch, F. Raatz and P. Dufresne, Zeolites, vol. 7 (1987), pp. 333-340. 9. H. Ajot, P. Caullet, J.F. Joly, J. Lynch andF. Raatz, Preprints of the COPS IIIUPAC Symposium, Alicante 6 9 May 1990, pp. 62-64.

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F. Rodriguez-Reinosoet al. (Editors), Characterizationof Porous Solids II 1991 Elsevier Science Publishers B.V., Amsterdam

169

A NEW MERCURY INTRUSION-RETRACTION SIMULATOR USED AS A MEANS FOR THE CHARACEREATION OF POROUS MATERIALS

CHRISTOS D. TSAKIROGLOU and ALKIVIADES C. PAYATAKES Department of Chemical Engineering, University of Patras, and ICE/HT-FORTH, GR 261 10 Patras, Greece

SUMMARY Information about the pore structure of porous solids is embedded in mercury intrusionretraction curves in highly convoluted form. Any attempt to derive a "pore-size distribution" must inevitably depend on postulates concerning the pore shapes and the pore network skeleton. For an important class of porous materials the pore space can be represented as a matrix of chambers interconnected through narrow throats. Information about the chamber size distribution and the network skeleton can be obtained from serial tomography. Information about the throat size distribution can, then, be obtained by deconvolving the intrusion-retraction curves. To this end, a reliable mercury intrusion-retraction simulator must be available. Such a simulator for three dimensional chamber-and-throat networks is developed here. This simulator takes into account the mechanisms with which mercury menisci move in pores and stop at entrances to throats or (in certain cases) chambers. It also takes into account the mechanism of snap-off, which leads to the disconnection and entrapment of mercury. The simulator is used to study the effects of the main geometrical, topological and statistical network parameters on the capillary pressure curves. INTRODUCTION Mercury porosimetry produces a set of capillary pressure curves which contain information about structural characteristics of porous media in highly convoluted form. The conventional method of analysis (refs. 1-3) is based on the tube-bundle model and ignores important characteristics of porous media, such as the existence of chambers and throats and the high interconnectivity of the pores. Several researchers have tried to interpret mercury porosimeay data of unconsolidated porous materials (such as sandpacks, soil etc) by assuming that the pore space is similar to that in a packing of uniform spheres (refs. 4-9). Pore network models have also been used to study the effects of geometrical, topological and statistical parameters of porous media on mercury capillary pressure curves. In these models the pore space is represented by a network of nodes and bonds in which shape and size are assigned either only to the bonds or both to the nodes and the bonds (ref. 10). In this way the porous medium can be considered as a network of interconnected capillaries of different sizes (refs. 11-13), or as a network of large pores (chambers) interconnected through narrow constrictions (throats), (refs. 14-19). Optical studies of certain sedimentary rocks (mostly sandstones) indicate that chamber-and-throat network models can be used to represent their pore space (refs. 20-23). Experimental studies in planar chamber-and-throat networks etched in glass plates have provided information about the mechanisms of mercury intrusion and retraction, and about the

170

effects of the wettability of the air/mercury/solid system and the geometrical, topological and statistical properties of the networks (refs. 24-29). In recent years it has been recognized that a more accurate method of pore analysis should consist of an appropriatecombination of techniques of which mercury porosimeay is but one of the components (refs. 18,30,31). First, serial sectioning analysis of pore casts (refs. 32-35) can be used to determine the chamber-size distribution, the correlation between the sizes of adjacent chambers, and information pertaining to the interconnectivity of the network (e.g. specific genus and coordination number). Then, the capillary pressure curves can be used to determine the throatsize distribution, and the correlation between the sizes of contiguous throats and chambers. In order to deconvolve these curves a reliable simulator of intrusion and retraction of mercury in evacuated chamber-and-throatnetworks must be developed. In (ref. 37) and in the present work a new simulator of mercury intrusion into and retraction from a three-dimensional chamber-and-throat network is developed. The capillary resistance encountered at entrances to chambers under certain conditions during mercury intrusion, and the snap-off in throats during mercury retraction are taken into account. The effects of geometrical, topological and statistical parameters and of the intrusion and retraction contact angles on the form of capillary pressure curves are studied. Comparisons between the actual throat and chamber size distributions and the measured "pore size distributions"(by the convetional method of analysis) are also made.

PORE NETWOFX MODEL Here the skeleton of the pore network is considered as a cubic lattice. Other networks, including random ones, can also be used. Large pores (chambers) are placed at the nodes and long, narrow pores (throats) at the branches, thus creating a 3-D chamber-and-throatnetwork. The diameters of chambers and throats are randomly chosen from preselected distributions (e.g. Gaussian, Lognormal, etc) and they are assigned at random to the nodes and the bonds of the network (a different procedure is followed for correlated networks, as described below). The distance between the centres of two adjacent chambers (length of periodicity) is adjusted so that the porosity of the network matches that ot the prototype. A porosity value of &=0.20 was considered for all the networks in the present work. A more detailed description of the chamber-and-throat network construction is given in (refs. 36,37).

SIMULATION OF MERCURY INTRUSION AND RETRACTION 1) Simulation of mercury intrusion Once the pore network has been constructed (see above) mercury menisci are placed at the entrances to all boundary throats and the external pressure is set at an initial value which is smaller than the capillary pressure of the smallest throat, so that no mercury enters into the network. Then, the pressure is increased by a small step AP and the effect of this change on the positions of the mercury menisci is examined. First, all menisci posed at entrances to throats are examined. If P,,sP,, where P , is the capillary pressure required for a throat to be filled by mercury (ref. 37),

171

the throat is filled and the meniscus is placed at the entrance of the downstream chamber. Each time two branches of mercury meet, they are assumed to coalesce instantly. Second, all menisci posed at entrances to chambers are examined. If the external pressure exceeds the minimum capillary resistance of entry into the chamber (ref. 37), the chamber is filled with mercury and new menisci are placed at the entrances to all contiguous throats. At the end of this scanning, all menisci newly placed at entrances to throats and chambers are scanned for stability and so on. The procedure is continued until no more unstable menisci can be found. Next, the pressure is increased by another step and the procedure is iterated until all the network becomes filled with mercury. 2) p n When the network is completely filled with mercury, the external pressure is decreased by a small step AP and the network is scanned in search of sites where flow events can take place under the existing conditions, The following types of flow events may occur. a) A throat full of mercury connects two chambers also occupied by mercury and has the required length for a collar to be developed. If PexlPts,where Pt, is the critical capillary pressure for snapoff in a throat (ref. 37), then snap-off takes place, the throat is emptied and two new mercury menisci are formed at its ends. b) A throat is occupied by mercury and at one of its ends there exists an empty chamber. If PexQti, where Pti is the capillary pressure for piston-type retraction (refs. 26,37), the throat is emptied and a meniscus is placed at the entrance to the other adjacent chamber. c) A chamber filled with mercury is connected with at least one empty throat. If P,/at> exceeds the critical aspect ratio E=Pti/Pt, (refs. 26-27,37) snap-off intensifies and a large amount of mercury progressively loses its continuity and it is trapped in the network. If the ratio / is comparable to the critical aspect ratio E, snap-off in throats and emptying of chambers occur in the same pressure range and this results in higher retraction efficiency. Comparison between the actual TSD and CSD,on one hand and the pore size distributions derived by the differentiation of the intrusion (PSDI) and retraction (PSD2) curves, on the other, is made in Fig.lb,c,d .

100

/ = 2.5

80 4-

-TSD CSD

5 6 0 % 40

i

f

20 /

50

100

CSD

............. PSDl

,: ;.

: :

I

-,

0

f

NETWORK S I Z E . 20XPOX20

b

.," _

150 P.#&

200

250

MO

::

Fig. 1. (a) Simulated capillary pressure curves for networks with the same lognormal CSD =l6.0 pm, (=40.0 pm, 0,=15.0) and three different lognormal TSDs : (I) (--) 0,=8.0, (11) (-.. -) =13.0 pm, 0,=5.0, (111) (- -) =lO.O pm, 0,=5.0. (b), (c), (d) Comparison between the actual TSD and CSD and the pore size distributions (by number) obtained by differentiating the intrusion (PSD1) and retraction (PSD2) curves, according to the tube bundle model. The relative frequencies of PSDl and PSD2 refer to number of pores, and they are obtained using the conventional method, which assumes that all pores are non-communicatingcylinders of equal length but of varying diameter. As it can be seen PSDl is comparable only to the TSD, being narrower than TSD in both directions of larger and smaller sizes. This is explained by the fact that

173

large throats are shadowed by smaller ones, and small throats of negligible volume are filled in the last stages of the process (see also refs. 16-17). PSD2 lies between the TSD and CSD curves, as mercury retraction is controlled by the emptying of chambers and snap-off in throats. PSD2 moves closer to the TSD, as the ratio / increases, because then it is mainly throats that are emptied by snapoff while an even larger amount of mercury is trapped in chambers. The mean coordination number is a measure of the connectivity of a pore network. Simulated capillary pressure curves for networks with the same Gaussian CSD and TSD, but with different mean coordination number (=6,5,4,3), are given in Fig. 2a. As the mean coordination number decreases the accessibility of the interior pores to the boundary of the network decreases. Hence, a given saturation value is obtained at higher pressures during intrusion and at lower pressures during retraction so that the hysteresis between capillary pressure curves widens and the residual mercury saturation increases. As the mean coordination number decreases, PSDl moves to smaller sizes because the shadowing of large throats increases (Fig.2b), whereas no important change occurs to PSD2 (Fig.2~).

037

I

TSD PSDl (c,=6.0)

025-

0

0

,=I

50

150 ZOO P. k h

!OO

250

300

350

,

-

i-\

0.1

.....

TSD CSD PSDZ (c,=6.0) PSDZ ( ~ ~ 4 . 0 ) PSD? (c,=3.0)

....... :

NETWDRK SIZE : 20 X 20 X 20

OD6 0134

O

B

2

J

J

) U 0.P

)

5

0

"0

50

100

!50 P.kFa

200

250

30

Fig. 2. (a) Effect of the mean coordination number, , on simulated capillary pressure curves for a network with Gauusian TSD (43>=10.0 m, 0,=3.0) and CSD (=30.0pm, cs =7.5). (b) Comparison between the actual kSD andlthe pore size distributions PSDl's o b t h e d by differentiating the above intrusion curves. (c) Comparison between the actual TSD, CSD and the pore size distributions PSD2's obtained by differentiating the above retraction curves. (d) Effect of the intrusion contact angle, 01, and of the retraction contact angle, OR, on simulated capillary pressure curves for a network with Gauusian TSD (=10.0 pm, 0,=3.0) and CSD (=30.0 pm. 0,=7.5).

174

Simulated capillary pressure curves for a network 20x20~20obtained by using various intrusion and retraction contact angles are given in Fig. 2d. It seems that the form and the degree of hysteresis of intrusion and retraction pressure curves are strongly affected by the values of the contact angles. Simulated capillary pressure curves for networks with the same CSD and two different bimodal TSD’s having the same and (T, values are shown in Fig. 3a. Since intrusion is controlled mainly by the large throats, the intrusion curve widens and extends to a higher pressure range as the fraction of large throats decreases. In these networks, which have high ratio /d),>, mercury retraction is controlled by snap-off events, and as the frequency of narrow throats increases, snap-off occurs over a wider pressure range with the result that the retraction curve widens and the residual mercury saturation increases. As it can be seen in Fig.3b,c, the large sizes of throats and chambers are not reflected in PSDl and PSD2 because of the shadowing effect during intrusion, and the entrapment of mercury in a large number of them during retraction (/=4.0).

20

0

6

TSD (c = 0.8) CSD

...........PSDl 4

f

50

b

I00

150 200 P.kFa

‘1 4

E

250

C

300

3 0

STSD D (c = 02)

...........PSDl PSDZ

C

....

2

0 t

Fig. 3. (a) Simulated capillary pressure curves for networks with the same lognormal CSD (=40.0 pm, 0,=15.0) and two different bimodal TSD’s (=10.0 pm, 0,=5.0) . Parameters of the component lognormal size distributionsused as input data for the TSD’s: (1) -( ) =12.0pm,0,1=3.0, =2.0 pm, ot2=3.0, c=O.8 (11) (.----) =l8.Opm, 0,,=6.O, =KO m, (T 1.5, c=0.2 (b), (c) Companson between the actual TS8 and C!$D and%: pore size distributions (by number) obtained by differentiating the above intrusion (PSD1) and retraction (PSD2) curves, according to the tube bundle model value can be seen in Fig. 4a. The effect of the width of bimodal TSD’s having the same a,>

175

The intrusion curve moves to lower pressure ranges as the frequency of wide throats increases. Since mercury retains its continuity to the external mercury sink through large throats (which become disconnected by snap-off at lower pressures) the possibility of mercury retraction from chambers increases, and the residual mercury saturation decreases as the frequency of wide throats increases. In these cases where the fractions of large and small sizes of throats are comparable, neither very large sizes nor very small ones are reflected in PSDl (Fig.4b,c,d). It must be noted that the shape of PSD2 is affected by the shape of TSD as snap-off in throats intensifies during mercury retraction ((/=4.0).

4-

20

1

b

= 05)

.j.

..

-z:

,

,

~

..i '

50

-

!OO

6- -TSD

150

200

P ILFa

(C

= 0.4)

:.

........... CSD PSDl 4-

(C

.........

),:/

0 0

r

TSD

CSD ........... PSDl

PSD2

250

300

EO

C

::

... ... .. ..

Fig. 4. (a) Simulated capillary pressure curves for networks with the same lognormal CSD (=40.0 pm, o =15.0) and three different bimodal TSD's. Parameters of the component lognormal size distributions used as input data for the TSD's: (I) (-) =18.0 pm, ot,=8.0, =2.0pm, oQ=2.83, c=OS (=10.0 pm, o,=10.0) (11) (-. -) =15.0pm, o,,=4.0, =6.67pm, oQ=1.8, c=0.4 (=10.0 pm, 0,=5.0) (111) (- -) =13.0pm,ot1=4.0,=5.5 pm, o,=2.18, c=0.6 (=lO.O pm, vt=5.0) (b), (c), (d) Comparison between the actual TSD and 6SD and the pore size distnbunons (by number) obtained by differentiating the above intrusion (PSD 1) and retraction (PSD2) curves, according to the tube bundle model

EFFECTS OF C-t AND

SIZE-CORRELATIONS Some characteristics of experimental capillary pressure curves, especially the width of the pressure range, have been interpreted by constructing pore networks where the sizes of the throats are not randomly arranged,but are correlated to the sizes of adjacent chambers (refs. 14,18,19,38). Actually, at least two types of correlated networks can be considered depending on the arrangement of the sizes of throats and chambers in the network. C-c

176

a) Networks with chamber-to-throat size correlation (c-t correlation) The sizes of the chambers themselves are arranged completely at random, but each chamber casts a "vote" on the size of its adjacent throats according to the relation

where s is a dimensionlessparameter. The vote value for each throat is defined as the average of the votes of the two adjacent chambers. The sizes of the throats are ranked in descending order and they are assigned to the bonds of the network according to the results of the voting (ref. 36). For s=O there is no c-t correlation.For s=l (used here) there is a significantc-t correlation. b) Networks with chamber-to chamber size and chamber-to-throat size correlation (c-c and c-t correlation) The sizes of chambers are ranked in ascending order and they are partitioned in classes of equal width. A few sizes are randomly chosen from the set of the available sizes as seeds, and they are randomly assigned to chambers of the network. For each of these seed chambers the following procedure is followed. If the seed chamber belongs to class I, the sizes of its immediate neighbors are also chosen from class I. If this class becomes empty, then sizes from classes 1-1 and 1+1 are chosen, and so on. Each chamber that is assigned a size in this way is treated from that point on as -~

10-

8f

6-

UNCORRELATED NETWORK

............. ____

TSD CSD PSDl PSD2

4-

::

ii ;;

... ...

4 6-

4f

C-t

C-t

CORRELATED

NETWORK

-.I-.

TSD CSD PSDl PSD2

C

:i ii

:: :

4 ' c-c

CORRELATED

3 NETWORK 1 2 1 0

Fig. 5. (a) Effect of the degree of correlation between chamber-sizes and throat-sizes on simulated capillary pressure curves for networks with lognormal CSD (=40.0pm, oc=15.0) and TSD (=13.0 pm, 0,=5.0, ). (b), (c), (d) Comparison between the actual TSD and CSD and the pore size distributions (by number) obtained by differentiatingthe above intrusion (PSD1) and retraction (PSDZ) curvesusing the tube bundle model.

177

a new seed chamber. The procedure is iterated until all the available sizes become assigned to the chambers of the network. The arrangement of the throats follows the rules described above in (a). Comparison between the capillary pressure curves of an uncorrelated and two correlated networks with the same TSD and CSD is made in Fig. 5a. As the degree of correlation becomes stronger the intrusion curve widens in both directions. The retraction curve is affected mainly in the portion near the end; the residual mercury saturation decreases as the correlation increases. As the degree of correlation increases, PSDl widens (Fig.Sb,c,d), following the increase of the width of the intrusion curve. Especially in the case of significant c-c&c-t correlation (FigSd), PSDl becomes multimodal, as mercury fills small subnetworks of different throat sizes at progressively higher pressures. As the degree of correlation increases, PSD2 approaches the CSD, and it widens (Fig.Sb,c,d) as the fraction of the chambers which are emptied increases. In the case of c-c&c-t correlation (FigSd) PSD2 becomes bimodal because chambers belonging to clusters of similar throat and chamber sizes are emptied at once in the last stages of the process. CONCLUSIONS - DISCUSSION A new theoretical simulator of mercury intrusion in and retraction from three-dimensional chamber-and-throat networks is developed. Stepwise porosimetry is modelled as a sequence of flow events occurring at each new external pressure value. The main conclusions resulting from the study of the effects of geometrical, topological and statistical parameters on the capillary pressure curves are listed below. * The intrusion curve is conmlled mainly by the TSD and moves to higher pressure ranges as the TSD moves to smaller sizes (unimodal distributions), or as the fraction of the wide throats decreases (bimodal distributions). * The form of the retraction curve is the result of two competing processes, namely snap-off in throats and emptying of chambers. As snap-off intensifies with increasing / ratio the quantity of trapped mercury also increases. * As the mean coordination number decreases the intrusion and retraction curves widen, the degree of hysteresis increases and the residual mercury saturation increases. * The capillary pressure curves are strongly affected by the values of the intrusion and retraction contact angles. Exact determination of these parameters is needed in order for adequate information about the pore structure to be extracted. * Correlations between the sizes of neighboring chambers and between the sizes of chambers and adjacent throats affect the form of capillary pressure curves strongly. As the degree of correlation increases, the intrusion curve widens and the residual mercury saturation decreases. * The pore size distribution obtained by differentiation of the intrusion curve (PSDI) is narrower than the TSD in both directions. It moves to smaller sizes as the mean coordination number decreases, and it widens as the degree of correlation increases (in the cases studied). * The pore size distribution obtained by differentiation of the retraction curve (PSD2) lies between the TSD and CSD and it moves closer to the TSD as the ratio / increases. For large ratios / the shape of PSD2 is affected by the shape of TSD as snap-off intensifies during mercury retraction. PSD2 becomes wider and moves closer to CSD, as the degree of

178

correlation increases. The simulator was developed as a part of a generalized method for the deconvolution of capillary pressure curves in order to obtain the equivalent capillary throat diameter distribution and to determine the throat-to-chamber size correlation. To this end information about the chamber-size distribution, the mean coordination number, and the chamber-to-chambersize correlation must be available from serial tomography. ACKNOWLEDGEMENTS This work was supported by EC, Contract No. TH 15.73/85, and by the Institute of Chemical Engineering and High Temperature Chemical Processes. REFERENCES 1 E.W. Washburn, Phys. Rev., 17 (1921) 273-283. 2 L.C. Ritterand H.L. Drake, Ind. Eng. Chem., 17 (1945) 782-786. 3 H.L. Drake and L.C. Ritter, Ind. Eng. Chem., 17 (1945) 787-791. 4 S. Kruyer, Trans. Faraday Soc., 54 (1958) 1758-1767. 5 L.K. Frevel and L.J. Kressley, Anal. Chem., 35 (1963) 1492-1502. 6 J.C. Melrose, Soc. Pet. Eng. J., 5 (1965) 259-271. 7 R.P. Mayer and R.A. Stowe, J. Colloid Sci., 20 (1965) 893-911. 8 R.P. Mayer and R.A. Stowe, J. Phys. Chem., 70 (1966) 3867-3873. 9 D.M. Smith and D.L. Sterner, J. Colloid Interface Sci., 111 (1986) 160-168. 10 F.A.L. Dullien, Porous Media; Fluid Transport and Pore Structure, Academic Press, New York, 1979. 11 I. Fatt, Trans. AIME, 207 (1956) 144-159. 12 I. Chatzis and F.A.L. Dullien, J. Can. Pet..Tech., 16 (1977) 97-108. 13 G.P. Androutsopoulos and R. Mann, Chem. Eng. Sci., 34 (1979) 1203-1212. 14 I. Chatzis and F.A.L. Dullien, Int. Chem. Eng., 25 (1985) 47-66. 15 G.R. Lapidus, A.M. Lane, K.M. Ng and W.C. Conner, Chem. Eng. Commun., 38 (1985) 33-56. 16 W.C. Conner, A.M. Lane, K.M. Ng and M. Goldblat, J. Catal., 83 (1983) 336-345. 17 W.C. Conner and A.M. Lane, J. Catal., 89 (1984) 217-225. 18 Y. Li, W.G. Laidlaw and N.C. Wardlaw, Adv. Colloid Interface Sci., 26 (1986) 1-68. 19 C.E. Diaz, I. Chatzis and F.A.L. Dullien, Transp. Porous Media, 2 (1987) 215-240. 20 F.A.L. Dullien and P.N. Mehta, Powder Technol., 5 (1971/72) 179-193. 21 F.A.L. Dullien and G.K. Dhawan, J. Colloid Interface Sci., 47 (1974) 337-349. 22 N.C. Wardlaw and J.P. Cassan, Bull. Can. Pet. Geol., 26 (1978) 572-585. 23 N.C. Wardlaw and J.P. Cassan, Bull. Can. Pet. Geol., 27 (1979) 117-138. 24 N.C. Wardlaw and M. McKellar, Powder Technol., 29 (1981) 127-143. 25 I. Chatzis and F.A.L. Dullien, Powder Technol., 29 (1981) 117-125. 26 Y. Li and N.C. Wardlaw, J. Colloid Interface Sci., 109 (1986) 461-472. 27 Y. Li and N.C. Wardlaw, J. Colloid Interface Sci., 109 (1986) 473-486. 28 N.C. Wardlaw and Y. Li, Transp. Porous Media, 3 (1988) 17-34. 29 C.D. Tsakiroglou and A.C. Payatakes, AIChE 1988 Annual Meeting, paper No 102L, Washington, D.C., Nov. 27-Dec. 2, 1988. 30 A.C. Payatakes and M.M. Dias, Rev. Chem. Eng., 2 (1984) 85-174. 31 M. Yanuka, F.A.L. Dullien and D.E. Elrick, J. Colloid Interface Sci., 112 (1986) 24-41. 32 R.T. DeHoff, E.H. Aigeltinger and K.R. Craig, J. Microsc., 95 (1972) 69-91. 33 M. Yanuka, F.A.L.Dullien and D.E. Elrick, J. Microsc., 135 (1984) 159-168. 34 I.F. MacDonald, P. Kaufman and F.A.L. Dullien, J. Microsc., 144 (1986) 277-296. 35 I.F. MacDonald, P. Kaufman and F.A.L. Dullien, J. Microsc., 144 (1986) 297-316. 36 G.N. Constantinides and A.C. Payatakes, Chem. Eng. Commun., 81 (1989) 55-81. 37 C.D. Tsakiroglou and A.C. Payatakes, J. Colloid Interface Sci., 137 (1990) 315-339. 38 N.C. Wardlaw, Y. Li and D. Forbes, Transp. Porous Media, 2 (1987) 597-614.

F. Rodriguez-Reinosoet al. (Editors),Characterization of Porous Solids II 0 1991 Elsevier Science Publishers B.V., Amsterdam

179

FILM SURFACE AREA MEASUREMENTS FOR MICROPOROSITY AND SURFACE ROUGHNESS ANALYSIS Gregory P. Johnstonl,Douglas M. Smithl, Alan J. Hurd2, Peter Heifer3 1 UNM/NSFCENTER FOR MICRO-ENGINEEREDCERAMICS,University of New Mexico Albuquerque, NM 87131 USA 2 Division 1153, Sandia National Laboratories, Albuquerque, NM 87185 USA 3 Department of Physics, University of Missouri, Columbia, MO 65211 USA ABSTRACT From measurements of the change in nitrogen surface area as a function of the quantity of vapor preadsorbed on a solid powder or porous solid, surface/pore structural parameters may be obtained. The approach is demonstrated for water vapor adsorbed on various fumed silica powders, Vycor phase-separated glass, and several silica gels for surface roughness and micropore size distribution. INTRODUCI'ION AND BACKGROUND In principle, measurements of the surface area with varying coverage of a

preadsorbed vapor (film surface areas) yields additional information concerning surface and pore structure. The basic principle is that one measures the surface area of a dry porous solid with nitrogen adsorption, equilibrates the sample with a vapor at higher temperature, rapidly cools the sample, and remeasures the surface area via nitrogen adsorption. The surface area decrease (or increase) with increasing film content when combined with an appropriate physical model should contain structure information. Properties which can be probed include coordination number in particle compacts, surface roughness, and micropore pore size distributions. Karasz and co-workers [l]first reported the use of nitrogen and argon adsorption on water preadsorbed on a solid surface as a structure probe. Wade [2,3] adsorbed water on silica and alumina and measured the N2 surface area as a function of water coverage. The reduction in surface area was used to extract the coordination number (i.e., average number of particle contacts per particle) for samples pelleted at different pressures. Coordination numbers obtained from these film surface area measurements and Wade's model of water adsorption/condensation resulted in coordination

180

numbers which were 30 to 60% larger than that expected from the porosity. Smith and co-workers [4,5]used a more complete model of the adsorption and toroidal condensation processes in conjunction with both Wade's data and film surface area measurements on packings of monodisperse silica spheres and obtained coordination numbers in reasonable agreement with porosity-derived values. In addition to coordination number, film surface area measurements have been

used to obtain qualitative information concerning surface roughness [6]. This process is illustrated in Figure 1 for which the surface available for surface area measurement of a rough surface is smoothed with increasing film thickness. This idea could also be extended as a pore size distribution probe. In other words, as the thickness of a film approachs the pore size, the surface area of the pore would rapidly decrease to zero. Although Figure 1 illustrates the film as a smooth layer of constant thickness, we do not mean to imply this is actually the case except for films of many monolayers. Instead, this is a conceptual model of the statistical film thickness.

Figure 1 Decrease of surface area on a rough surface as a function of increasing film thickness.

181

THEORETICAL BACKGROUND

For a fractal surface, the reduction in surface area is related to the volume (or

where V is the volume of film preadsorbed, Z is the N2 surface area, Zo is the N2 surface area on the dry solid, and Ds is the surface fractal dimension. Thus, a log-log plot of Z/Zo versus V should be linear and have a slope which is a function of Ds. For pore structure analysis, the pore size distribution ( E D ) may be obtained from Z(V) by following:

dv

1)

r(V) = l / Z ( V ) dV, assigns a value of r to every measured value of Z(V).

2)

Denote Z(V(r))as z(r), where V(r) is the inverse function of r(V)

3)

dV/dr (r) = - r dE/dr (r) where dV/dr (r) is the pore size distribution.

(2)

The complete proof for (2) is given elsewhere [7]. Several special cases of (2) may be considered. For a flat surface: Z(V) = S (a constant) which implies: dV/dr (r) = 0

(3)

For a fractal surface: Z(V) = C V

(2-Ds)’(3DS)

where C is a constant. This implies:

(4)

EXPERIMENTAL

For surface roughness studies, fumed silica of different roughness (Cab-0-Sil grades L90, MS7, HS5, EH5) was employed. These had been previously characterized with SAXS and molecular tiling experiments [6]and Ds was found to vary as L90 (2.02.1), MS7 (2.1-2.3),HS5 (2.2-2.3),and EH5(2.5). For pore structure analysis, two xerogels

were prepared using either a two-step acidtatalyzed tetraethylorthosilicate(TEOS) reaction system (designated as A2) which results in microporosity or a two-step basecatalyzed TEOS system which results in a broader PSD with pores ranging up to 10 nm [8]. In addition, a commercial sample of Vycor phase-separated glass was employed.

Surface area and pore size analysis was conducted using N2 at 77 K.

182

After sample outgassing at 383 K for three hours under vacuum, film surface areas were obtained by equilibrating the samples with water vapor at 293 K and the desired relative pressure and measuring uptake (volumetrically or gravimetrically). The samples were then rapidly cooled to 77 K and a conventional BET nitrogen surface area experiment (5 points, 0.05cP/Po 102 compared with that of the outgassed gel. This feature is vividly illustrated in Figure 3f, which shows the scattering from a gel sample saturated with water having zero scattering length density (8% v/v D20), after exposure at the same p/po. Here the scattering curve is virtually identical to that o f the outgassed gel (cf. Figure 3 a ) . Changes in the SANS of silica gel S2 after exposure to water vapour are shown in Figure 4. Here the primary particle size of the sol forming the gel is considerably smaller (,I 12 nm) and more polydispersed. Consequently for the outgassed gel (Figure 4a) the maximum in the interference peak occurs at a lower Q of 0.057 A-’, corresponding to an interparticle separation of 11 nm. The less pronounced maximum compared with the S4 gel, can be ascribed to partial coalescence of the contacting particles after the outgassing treatment at 423K.

241

10 -i L

-

In

I

. E v

’

G

:

W

lo-’

Fig. 4. SANS of silica gel S2 equilibrated with water at p/po: (a), 0; (b), 0.08; (c), 0.43; (d), 0.97; (e), 0.97. Water compositions (D,O % ‘/v) are 61% for (b)-(d) and 8% for ( e ) respectively. Broken line shows Q - 4 power law.

0.08) causes a significant Exposure to a low water vapour pressure (p/po change in the interference peak (4b) in contrast to the S4 gel. This difference can be ascribed to the smaller size of the sol particles forming the gel. Since the uptake will be close to a monolayer at this pressure, the thickness of the adsorbed film will result in a more pronounced ‘neck’ at the points o f particle contact in the S2 gel. The effect on the scattering will thus be somewhat akin to that which arises from particle coalescence already noted. Beyond the interference maximum there is no perceptible difference in I(Q) in the Porod region. At a p/p, of 0.43 (4c) the scattering is unchanged but at a p/po of 0,97 (4d), where saturation occurs there is a dramatic reduction in I(Q), as previously noted with the S4 gel. At the corresponding pressure where the gel is saturated with water of zero scattering length density ( 4 e ) the scattering is identical to that of the outgassed gel indicating that the surface and structure o f the gel is unchanged on saturation with water. The processes of adsorption and capillary condensation of vapours in regular packings of monodispersed spherical particles have been described theoretically

242

I

LL

In

0’7

t

I

I

II

0

Fig. 5. Dependence of relative surface area of adsorbed water film, SF/S,, on p/po, for a sphere packing with n = 8. Sphere diameters are (a) 100; (b) 200; and ( c ) 300 8, respectively.

101

I

I

I

I

1

\I

Fig. 6. SANS o f ceria gel C1 equilibrated with water at p/po: (a), 0; (b), 0.43 and (c), 0.97. Water compositions (0,O % ‘/v) are 75% for ( b ) and 8% for (c) respectively. Broken line shows Q-4 power law.

243

by several workers (refs. 6-9). In general three processes occur as the vapour pressure is increased. These include (a) multilayer adsorption on the sphere surfaces, (b) the gradual filling of the capillary condensate around the points of contact between spheres and (c) condensation in the cavities between spheres. It has been shown that the area of the surface film only becomes appreciably less than that of the solid when the sphere size is small (diameter < 15 nm) and n, the particle co-ordination number, is large. Such effects are 2, then only important when the p/po is approaching the point when spontaneous capillary condensation occurs. This feature is illustrated in Figure 5 which shows the ratio of adsorbed water film to solid area, SF/So, for n = 8 and for sphere diameters, 0, which are in a range relevant to the oxide gels here. The relative insensitivity of SF/So to p/po arises because the loss in interfacial area due to the growth of the meniscus at the points of contact, is offset by the contribution of the meniscus itself. Such behaviour is in accord with the SANS results described for the S4 and S2 gels. The foregoing model is somewhat idealised and the analysis, assuming w e l defined multilayer and capillary condensation processes, may become invalid when the pore size of the sphere packings approaches the micropore range. In this respect the SANS results for the ceria gel (Figure 6) provide important insight into the water sorption process. Here the particle size of the sol (% 7 nm) is sufficiently small to give a microporous gel showing type I isotherm behaviour. The outgassed gel (6a) shows a maximum in the interference between % 0.09 and 0.10 A - l corresponding to an interparticle separation of 2, 6 to 7 nm. This feature is less pronounced and broad indicating more extensive particle coalescence than with the silica gels. However on saturation of the gel with water (75% v/v 020) at p/po = 0.43 (6b) there is still, perhaps surprisingly, considerable scattering. Thus the interference feature is suppressed, as observed previously with the silica gels, and the intensity in the Porod region is reduced by a factor of 2, 2. The scattering from the gel saturated with water of zero scattering length density (6c) i s again virtually identical to the outgassed sample. The marked scattering observed when the gel i s saturated with 75% v/v D20 clearly shows that this is not a contrast match composition, despite having been previously established with the ceria sols. This suggests that the effective density of the sorbed water in the pores is less than the bulk density. This lower effective density may arise from differences in the ordering of water molecules when confined in the ceria micropores compared with that imposed by H-bonding in the bulk liquid. Such effects of pore geometry have indeed recently been discussed by Sing et a1 (ref. 10) to explain inhibition of water uptake in the molecular sieve silicalite, compared with that of l e s s ordered molecular liquids such as nitrogen. Indeed other evidence

244

based on incoherent inelastic and quasielastic neutron scattering indicates that the H-bond structure and diffusion of water in the microporous ceria gel differs markedly from that reported with mesoporous silicas (ref. 11). These general conclusions on the mechanisms of sorption in micropores are based on the limited SANS measurements with the ceria gel. Evidently there is scope for further investigations, particularly with microporous solids with different pore geometry, such a slits, which may be compared more readily with recent theoretical simulations of sorbate structure (ref. 12). ACKNOWLEDGEMENTS The work described was undertaken as part of the Underlying Research Programme of the UKAEA. The experimental assistance of Mr. B.O. Booth and Mr. M . Scanlon in the preparation of gel samples used in SANS measurements is gratefully acknowledged. REFERENCES 1 B . O . Booth and J.D.F. Ramsay, in: J.M. Haynes and P. Rossi-Doria (Eds.), Principles and Applications of Pore Structural Characterisation, J.W. Arrowsmith Ltd., Bristol, 1985, p. 97. 2 A. Guinier and G. Fournet. in: Small Anale - Scatterinq- of X-rays. - . Wiley. -. New York, 1955. 3. J.D.F Ramsay, in: K.K. Unger, J. Rouquerol and K.S.W. Sing (Eds.), Characterization o f Porous Solids. Elsevier. Amsterdam. 1988,. .P. 23. 4 J.D.F. Ramsay, Chem. SOC. Rev., 15 (1986) 335. 5 J.D.F. Ramsay and B.O. Booth, J. Chem. SOC., Faraday Trans. I, 79 (1983) 173. 6 B.G. Aristov, A.P. Karnaukhov and A . V . Kiselev, Russ. J. Phys. Chem., 36 (1962) 1159. 7 D. Dollimore and G.R. Heal, J. Colloid Interface Sci., 42 (1973) 233. 8 W.H. Wade, J. Phys. Chem., 69 (1965) 332. 9 D.M. Smith and N.E. Olague, J. Phys. Chem., 91 (1987) 4066. 10 M . B . Kenny and K.S.W. Sing, Chem. & Ind., 39 (1990). 11 J.D.F. Ramsay and C. Poinsignon, Langmuir, 3 (1987) 320. 12 B.K. Peterson, J.P.R.B. Walton and K.E. Gubbins, J. Chem. SOC., Faraday Trans. 11, 82 (1986) 1789.

F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids II 0 1991 Elsevier Science Publishers B.V., Amsterdam

245

SMALL ANGLE AND ULTRA-SMALL ANGLE SCATTERING TECHNIQUES FOR CHARACTERIZATION OF POROUS MATERIALS

J.C.Dore and A.N.North Physics Laboratory, University of Kent, Canterbury, CT2 7NR, UK

SUMMARY Small-angle X-ray (SAXS) and small angle neutron (SANS) scatterin can be used to study the properties of porous materials over a range of 10f100nm. Experimental methods using reactor neutrons and synchrotron radiation are described and current methods of analysis reviewed. New developments which extend the range of the measurements down to low scattering vectors (- 10-5A-1)are presented and the application to various systems critically examined. Spatial features covering a range of log, to 2~ can be investigated and are illustrated by reference to work on materials of varying pore size, pore shape, surface texture and composition. Recent work using the principle of "contrast-matching'' to study multi-phase systems such as liquids in pores (partial-filling) is briefly described and the basic features of neutron and X-ray methods are critically compared. The complementary nature of the two measurements is emphasised and linked to likely future developments of the technique.

INTRODUCTION The structural features of porous solids may be of many different forms depending on the size, shape, connectivity and surface texture of the materials from which they are formed. Furthermore, the basic characteristics may be ordered as in the case of zeolites, or partially disordered in the case of structures formed through sol-gel or spinodal decomposition processes. A full mathematical representation of this complex spatial distribution is rarely possible and it is necessary to make approximations in order to extract information on comparative properties for real materials from a limited set of experimental measurements. Conventional methods such as gas adsorption (surface area, pore size) and electron microscopy (direct imaging in two dimensions) are already well established. In recent years the techniques of small-angle scattering have played in increasing role as an alternative means of investigation. Recent improvements in beam intensities and instrumentation for neutron and X-ray techniques have greatly enhanced the value of these methods. Since the scattering profile results from coherent interference effects it represents a direct observation of the spatial distribution of scattering centres in the sample and is not subject to any approximations. The data is an effective

246

average over the irradiated area and is therefore complementary to the image techniques of electron microscopy. This short review provides an update of some recent developments, particularly in the area of ultra-low small angle scattering (USAS),and gives consideration to possible extensions into new methods of studying the structural features of porous materials using both X-ray and neutron techniques.

THEORETICAL FORMALISM The basic theory of small-angle scattering has been reviewed elsewhere [1,21 and only a short digest of fundamental principles will be reproduced here. The intensity of coherent scattering from an assembly of scatterers may be written as

where a(Q) is the scattering amplitude and Q is the elastic scattering vector which has a magnitude:-

4n 0 Q = -sin2

x

for a scattering angle 0 with incident radiation of wavelength, h. At high Q-values (2 1A-1)the pattern exhibits diffraction effects characteristic of the atomic arrangement but at low Q-values the intensity will depend on large-scale inhomogeneities in the sample. The mean coherent scattering amplitude p(r) represents an effective average over the scatterers for a region larger than the atomic dimensions and the intensity can then be formally written as:-

and for an isotropic material becomes:-

where p(r) represents the spatial distribution. Comparative values of p(r) for X-rays and neutrons are different as shown in Table 1.

241

TABLE 1:

Some typical values of scattering length densities, p.

Material

I

H20 D20 CCh, c7D16 c7D16 Si02 CBr4

I

Neutrons -0.56 6.34 6.30 -0.48 6.28 4.09 4.73

I

] } I

X-rays 9.3 13.0 7.9 26.0 26.0

For an idealised two component system of an amorphous nature with no preferred orientation the intensity simplifies to

where (Ap) is the contrast difference, F(Q) is a form-factor for the individual "particles" in the assembly and S(Q) is a structure factor representing the distribution of particle centres. For porous materials prepared by the sol-gel process, and conveniently modelled by an aggregation of hard spheres, the form-factor corresponds to the scattering by an isolated sphere and the first peak in the structure factor results from interparticle correlations that are usually linked to the mean separation of the centres. The geometrical structure of the pore network in real materials is clearly of a more complex nature but it is usual to make the assumption that the effective form-factor can be averaged over a distribution, N(R) of pore sizes such that:-

If assumptions are made about the pore shape, which is usually assumed to be spherical, it is possible to extract information on N(R). Alternative assumptions can be made about the spatial distribution of mass in the aggregate and one which has attracted much recent attention is that based on a fractal formalism. [3,4] I n this case the intensity has a very simple form:-

248

where DM is the fractal dimensionality. This power law cannot apply over all length scales in a real system and at larger Qrange will be sensitive to correla-tions in the surface texture. The relationship becomes:-

where Ds is a surface fractal and eventually, aT an asymptotic limit, reaches the Porod regime, where:-

All of these concepts play a role in the interpretation of SAS data as shown in the following examples.

INSTRUMENTATION Most conventional small angle scattering methods with X-ray or neutrons use an incident monochromatic beam and a multi-detector as shown schematically in Fig.1. The presence of a beam stop to prevent the primary beam entering the detector provides a lower limit to the Q-values accessible for study. Since the scattering formalism scales as a function of QR, this gives a cut-off in the size range that can be 2.10-3A-1 means that structural investigated; a typical value of Qmin inhomogeneities with a scale > 2000A cannot be studied. The SAXS and SANS method is therefore suitable for studies of microporous media but is less useful for the higher range of mesoporous systems.

-

Fig.1: Schematic layout for a conventional SAS measurement. All research reactors have S A N S facilities and typical examples are the D11 and D17 instruments at ILL, Grenoble [5] and the PACE, instrument on the Orph6e reactor at CEN, Saclay [6] which use area multidetectors. X-ray facilities can use a Kratky camera with a laboratory-based generator but the use of dedicated instruments on a

249

synchrotron gives a huge gain in intensity. Typical examples are the SAXS instruments on lines 2.1 and 8.2 of the Synchrotron Radiation Source at the Daresbury Lab. [A An extension of the range to lower Q-values for X-ray studies can now be achieved by using an alternative technique based on the Bonse-Hart camera. The basic layout is shown in Fig.2 where a single channel cut crystal is used to give a well oriented monochromatic X-ray beam from four Bragg reflections and a similar arrangement is used to determine the intensity of the scattered beam. The tight collimation of this arrangement enables measurements to be made at very small scattering such that Qmin is reduced to 2.10-5 A-1 corresponding to an effective length scale up to 2p. The full evaluation of the data requires a deconvolution analysis particularly when the scattering intensity is a rapidly varying function of Q. Although the principles of the method have been known for many years, it is only recently that the full advantages have become apparent [8] through the use of synchrotron radiation sources (e.g. USAXS on line 2.2 at the Daresbury Lab). Corresponding methods are under development for neutrons [9] using longer wavelengths (1lo& but the instrumentation is still at a relatively early stage.

-

-

Fig.2 Schematic layout for a conventional USAS measurement It is useful to comment briefly on the comparison of X-ray and neutron techniques since the measurements for a two-component system such as a porous material should give identical results using either radiation probe. For cases where the pores are void, the contrast Ap is high and a full SAS intensity profile can usually be determined to satisfactory precision within 10 minutes using modern facilities. One problem which can arise in neutron studies is the subtraction of the flat incoherent contribution which can be quite large in the case of hydrogenous materials This disadvantage is partially offset by the possibility of using isotopic substitution to vary the Ap-value in a systematic way and this technique is very powerful when the pores are filled with a liquid medium. The incoherent scattering and background poses a smaller problem in SAXS studies and the higher intrinsic intensity of the main beam means that the I(Q) profile can be determined over a more extended Q-

250

range and with better Qresolution. However, there is no means of varying the A p value unless anoma-lous scattering techniques are adopted and these have not yet been tried. It now seems clear that SAXS, S A N S and USAXS can be used in a complementary manner to give information that would not be obtained from a single method. [lo] This factor will be illustrated in the varied examples of the following section. LLUSTRATIVE EXAMPLES The relative merits of the SAS technique can be illustrated by reference to some of the current collaborative studies undertaken by the UKC Scattering Group.

Silica and Alumina svstems. Porous silica may be routinely manufactured with a high surface area and pore volume but the preparation and treatment leads to a wide range of different characteristics. The standard method uses a sol-gel technique leading to an aggregated structure which is usually dried and heat treated. This process leads to a material with a high surface area and reasonably monodisperse pore size according to gas adsorption measurements. A typical example of a SAXS measurement (Aldrich silica; nominal 60 A pore size) and a fitted pore distribution is shown in Fig.3.a. An alternative method based on a leaching process for a two component glass in which one water-soluble component may be removed to give a spinodal glass leads to a quite different pore structure as shown by the data given in Fig.3b for a specially prepared research material (Schott glass). Current analysis of the available data suggests that neither system can be readily described by either a fractal or a simple pore distribution function but further analysis is in progress.

o-vahle

a I A-l

Fig.3: S A N S studies of porous silica samples a) commercial gel system (Aldrich); b) leached glass (Schott) The heat treatment of materials can lead to significant changes in the pore structure. The data for a finely divided research glass of small pore size [ll]which has

251

been heated to different temperatures is shown in Fig.4. The main effect is to reduce the pore volume, as expected, but the data also show a second contribution to the scattered intensity at low Q-values which becomes the dominant feature for the high temperature material The presence of this scattering is not fully understood but could arise from particle size or surface texture effects. This example shows that some care will often be required to interpret unusual features in the measured profile but that this could also reveal previouslv-unknown factors, in th characterisation of the material. Sintered Silica A : 366 ' C 6 : 406 OC

C : 760 O C D : 1025 O C

i 0.1

0.2

Fig.4: Sintenng effects in porous silica arising from heat treatment at various temperatures In some speaalised cases the pore structures are known to be anisotropic. This occurs in porous fibres and can be studied by measurements in which the sample orientation is varied to give conditions in which the Q-vector is either parallel or perpendicular to the fibre axis. An example is given by Stacey [12] for S A N S studies of alumina and Fig5a shows a similar measurement made with X-rays; Fig.5b shows an example for a naturally-occurring silica fibre taken from the skeletal structure of a sea animal [ l l ] where the anisotropy is more pronounced. It can be seen that the scattering intensity is dramatically altered by changes in the sample orientation. Suitable analytic methods are now being developed to extract information on the alignment properties of the pores based on partially-oriented cylindrical voids. Geoloeical materials Sedimentary rocks are often porous and can be studied by SAS techniques. Early work by Mldner, Hall and co-workers 1131 has shown that these structures can be represented by a fractal formalism. We have extended some of their work by using a combination of SAXS and USAXS techniques. The results are given in Fig.6. The (U)SAXS intensity shows a power law scattering with an exponent of -3.49 suggesting a surface fractal dimensionality of Ds= 2.51 whereas the S A N S value is Ds= 2.61.

252

Alumina Fibres

(la)

Channel Number

Fig.5: Anisotropic scattering for a) synthetic alumina fibres [12]; b) natural bio-silica from a sea animal [ll] It would be expected that the extension to lower Q-values would reveal a decrease in the slope corresponding to the change over to a mass fractal on a larger length scale. Surprisingly, the USAXS data exhibit a continuation of the same relationship and the I(Q) plot is therefore dominated by surface effects. Mildner et a1 [13] show that a comparison of neutron and X-ray data, which give different slopes is probably linked to the occluded pockets of oil in the interfacial regions and the information could be of importance for oil-recovery. Further work on geological specimensisisplanned. planned. -,specimens 1 Bakken Shale

USAX$

:I

...\**A

LoQclta)l -

2 4--

0 ,

\ \ , I

I

I

I

1

I

I

I

I

Fig.6: SAXS, USAXS and S A N S measurement son Bakken shale (geological) showing a surface fractal characteristic over six decades of I(Q).

253

Liauids in m r e materials The pore material may be the host for other distributed matter in a solid or liquid form. The modified behaviour of liquids in constrained geometry is currently attracting much attention [141. If the pores are filled with the liquid the only change to the scattering is due to the changed magnitude of A p . The use of hydrogen/deuterium mixtures in SANS studies is particularly important since it is often possible to contrast match the liquid to the substrate. This phenomenon is illustrated in Fig.7 for H20/D20 water in porous silica. The match point is achieved for 64% D20 (mole fraction) and confirms that all pores are open to the general network. If the pore filling is restricted it is possible to investigate the effects of capillary condensation as shown by Ramsay [15]. Other work has been reported by Li et a1 [16] in which a quantitative analysis has been carried out, based on the assumption of a fractal distribution with a spinodal structure factor. This group also point out that the process of drying at high temperature can lead to surface cracking and a dramatic increase in the scattering intensity. Similar work by the UKC group I171 is not yet published. There is clearly much scope for more extended work in this field on differing absorbants and absorbents under varying conditions.

Fig.7: Contrast-matching of water in porous silica by variation of isotopic composition in (H20/D20) mixtures

SUMMARY AND PROJECTION OF FUTURE WORK The opportunities for the use of SAS and USAS techniques have become attractive in recent years but relatively little work has yet been done. The high intensities of modern X-ray and neutron facilities can be exploited in various ways,

254

making use of a Q-range suitable for the particular problem under investigation. Several specific developments deserve mention in this context:routine measurement of pore distribution functions and changes i) due to sintering or any other external variable; direct observation of capillary condensation and study of spatial ii) distribution of fluids; iii) anisotropic studies in oriented samples such as fibres and layered materials. iv) timeresolved I(Q) measurements to study pore-filling processes, liquid flow or displacement by viscous fingering; study of complex interfaces and surface texture by complementary v) measurements with both X-rays and neutrons; The development of the scattering method will, in some cases, require an extension of the existing theoretical framework for interpretation of the measurements. It will also enable checks to be made on the simplifying assumptions inherent in the interpretation of the data obtained from other less direct means of investigation. The next few years should see a dramatic increase in the use of this technique for a wide range of materials considered at this meeting and it is to be expected that substantial developments will have been achieved for presentation at

COPS m. ACKNOWLEDGEMENTS We wish to thank various people who have contributed to this work through provision of facilities, computational knowledge or specific samples; they include Josb Teixeira (LLB), Wim Bras (SRS), John Harries (SRS), Martyn Stacey (ICI), Peter Hall (Schlumberger), Peter Langer (Schott Glass), Carole Perry (Brunel University) and others. ANN would like to thank the SERC for financial support that made this work possible.

255

REFERENCES 1. 0.Glatter & O.Kratky, 'Small angle X-ray scattering', Academic (Pub) 1984. 2. A.Kostorz, p.227, in 'Treatise on Materials Science and Technoloy', Vo1.15, Neutron Scattering, Academic (pub), 1979. 3. H.Bale & P.W.Schmidt, Phys.Rev.Lett., 1984, 53,596 4. J.Teixeira, in H.E.Stanley & N.Ostrowski (eds) 'OnGrowth and Form' Martinus Nijhoff (pub) 1986, p145. 5. D11 and D17 instruments: 'Neutron Research Facilities at the ILL High Flux Reactor', B.Maier (ed). 6. PACE and PAXE instruments, Orphke Reactor,Lab.Leon Brillouin, C.E.N., Saclay A.N.North et al., Nuc.Inst. & Methods, 1988,834,188. 7. 8. A.N.North, J.C.Dore, A.RMackie, A.M.Howe and J.Harries, Nuc.Inst. & Methods, in press (1990). 9. C.Zeyen & E.Davis, private communication. 10. A.North, in M.C.Fairbanks, A.N.North and R.J.Newport (eds). 'Neutron and X-ray Scattering: Complementary Techniques', Adam Hilger (pub), 1989.~.181. 11. S a m s e provided by C.Perry, Brunel University. 12. M.Stacey, this meeting D.F.R.Mildner, R.Rezvani, P.L.Hal1 and R.L.Borst, Appl.Phys.Letts., 13. 1986,48,1314. 14. J.Ramsay, this meeting. 15. J.-C. Li, M.J.Benham, L.D.Howe and D.K.Ross, p.155, in M.C.Fairbanks, A.N.North and R.J.Newport (eds), 'Neutron and X-ray Scattering: Complementary Techniques [as ref.101. 16. J.C.Dore and A.N.North, unpublished data.

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F. Rodriguez-Reinosoet al. (Editors), Characterization ofPorous Solids I1 0 1991 Elsevier Science Publishers B.V., Amsterdam

257

GEL-PRECIPITATED OXIDE GELS WITH CONTROLLED POROSITY - DETERMINATION OF STRUCTURE BY SMALL ANGLE NEUTRON SCATTERING AND ADSORPTION

ISOTHERM MEASUREMENTS. J. D. F. Ramsay, P. J. Russell and S. W. Swanton Colloid Chemistry Section, AEA Industrial Technology, Harwell Laboratory, Didcot, Oxfordshire, OX1 1 ORA, United Kingdom. SUMMARY In the gel precipitation process hydrous oxide gels in a polymer matrix are formed by precipitation (eg. as spheres, fibres etc.) by controlled neutralisation of a metal salt solution (eg. Th(IV), AI(III), Zr(IV), Ti(1V) etc.) containing a water soluble polymer (eg. polyacrylamide). On immediate precipitation such gels are markedly porous (c-0.90).Surface and porous properties of the dried gel may be controlled and are determined by the method of dehydration. The displacement of water by a partially miscible solvent (butanol) results in little shrinkage whereas drying in air results in a marked contraction of the gel structure. The surface and porous properties of dry gels have been characterised by nitrogen adsorption isotherm measurements and the evolution of the structure from wet to dry gels has been studied by small angle neutron scattering (SANS). Using a model mixed oxide system containing zirconia and titania, which are similar chemically but have a large difference in scattering length density, the properties of the inorganic oxide phases (size, surface area, homogeneity) and the polymer have been studied by SANS by the contrast variation technique. INTRODUCTION The process known as gel precipitation was developed at Harwell as a route to mixed oxide ceramic nuclear fuel (ref. 1). The process, which is outlined in the flow-diagram of Fig.1, differs from conventional sol-gel routes to oxide ceramics by the incorporation of a high molecular weight water soluble polymer (eg. polyacrylamide, polyvinyl alcohol). The role of the polymer is very important in the precipitation process. Firstly it allows considerable control in the shape (spheres, fibres) of the gel which is produced on precipitation of the aqueous metal salt solution (eg. Th(IV), U(VI), AI(III), Zr(IV), Ti(1V) etc.) in the external basic medium. Secondly it has a marked effect on the porosity of the gel. Thus on immediate precipitation the gel formed is markedly porous (porosity, 00.90). The surface and porous properties of dried gels are determined and may be controlled by the method of dehydration. Thus displacement of water with a partially miscible solvent (such as as a short chain alcohol) results in little shrinkage of the gel whereas drying by evaporation in air leads to a marked contraction of the gel structure. Our technical interest in gel precipitation stems from the potential to produce porous oxide adsorbents with controlled pore structure. Furthermore mixed oxide gels can be produced with high homogeneity.

258

METAL SALT SOLUTION

POLYMER SOLUTION

Droplet formation

I

Precipitation in conc. NH,

I

Washing (water)

Solvent displacement

DRY GEL SPHERES

Dry in air

DRY GEL SPHERES low porosity

Debonding

I POROUS CERAMIC SPHERES 1 I S int er ing

I DENSE

CERAMICS

I

Fig.]. Chemical flow diagram for the gel-precipitation route to single- and mixed-metal oxide microspheres of controlled porosity. The process has seen considerable technical development but more limited study of the basic mechanisms involved. Little is known about the development of the structure during the early, wet stages of the process and in particular the role and interactions of the polymer. This problem is being addressed by the application of small angle neutron scattering (SANS). SANS is particularly suitable because the penetrating power of neutrons makes it possible to study gel microstructure in the wet state. In addition using contrast variation techniques (refs. 2-4) it is possible to study the structure of the individual components in the gel (eg. polymer and oxide phases) and to examine the homogeneity of mixed oxide gels. We report here SANS measurements made at Harwell on zirconia, titania and mixed zirconia/titania gel systems formed in the presence of polyacrylamide. Zr(1V) and Ti(IV) are similar chemically but their oxides have appreciable differences in scattering length density. Measurements have been made on wet (undried) gels and gels that have been dehydrated directly

259 in air and by organic solvent displacement. Contrast variation experiments have been made by exchanging wet gels and rewetted dried gels with appropriate H,O/D,O

mixtures. These

experiments have been complemented by measurements of gas adsorption isotherms from dehydrated gels. THEORY OF SMALL ANGLE SCATTTERING Small angle scattering arises from variations in scattering length density, p , which arise over distances d,,

(d,,,

- A/28) in the range 1-100 nm such as may arise in dispersions of colloidal

particles and porous solids for example. The fundamental equation relating the small angle scattering intensity as a function of the scattering vector, Q, (where Q

=

4 r sin $/A, and 28 is the

scattering angle) to the structure of the scattering inhomogeneities for a statistically isotropic system is (ref. 5)

where K is an experimental constant. q2 is the mean square fluctuation in scattering density and the function -y(r) contains all the information from the effects of the form (size, shape) of the heterogeneities and their mutual arrangement. Although separation of this information is difficult, precise interpretations can be obtained from -y(r), in particular for two-phase systems such as porous media. For a two-phase system with sharp interphase boundaries

where

v2 is given by

4, and 9, are the respective volume fractions of the two phases with scattering length

densities p, and p z , and (p,-p,) is the contrast. For the gel systems considered here certain generalisations can be made regarding the dependence of I(Q) on Q. Thus for aggregated systems which have fractal properties it can be shown that I(Q) scales with an exponent corresponding to the fractal dimension, D, (refs. 6-8) namely UQ)

- Q-D

(3)

The value of the exponent relates to the mechanism of formation of the aggregates and the range over which the power scaling occurs to the size or extent of the cluster. Thus for the process of diffusion limited aggregation (DLA), D has a value of 2.5. Such a scaling effect relates to the mass fractal dimension and arises for a dimension in reciprocal space (Q) between the size of the cluster, a,, and the primary particles, a2 (see Fig.2). At higher Q it can be shown that for a

260

/

Range of fractal self similarity

log

Region”

+:-

Q

Fig.2. Schematic representation of a particle aggregate (a) having a range of self-similarity between approximately al and a2. The form of the scattering is depicted in (b).

two-phase system with sharp interphase boundaries the scattering in the limit of high Q is dependent on the surface area, S, of the system and obeys a Q-4 power law:

This

Q-4

scaling of the intensity at high Q is described as the Porod law region and arises when

Q p 4 , where r refers to the half dimension of the scattering inhomogeneity eg. a pore. EXPERIMENTAL Materials Gel-precipitated spheres were produced by the method outlined schematically in Fig.1. Feed solutions were prepared by mixing equivalent volumes of 4% polyacrylamide solution in formamide/water with aqueous solutions of zirconium nitrate and or titanium chloride (total metal concentration 0.8 mol dm-’). Feed droplets (-1 mm diameter) were produced by pumping the feed solution through a vibrating jet as shown in the photograph, Fig.3a. The droplets gelled (retaining their integrity as individual spheres) and metal hydrous oxide precipitation occurred on immersion in concentrated ammonia solution. The gel spheres were washed repeatedly with water (or ammonia solution in the case of titania) to remove salt. Batches of wet gel were divided into three, one portion being retained and another dried by evaporation in air. The third was

261

Fig.3. Photographs showing (a) rapid drop formation from a vibrating jet, and (b) the resultant oxide gel spheres after dehydration. [Courtesy of Harwell Laboratory]

dehydrated by solvent displacement: the aqueous phase was exchanged repeatedly with butanol and the solvent was removed by subsequent evaporation in air. The uniform size and highly regular spherical shape of dried gel spheres are illustrated in Fig.3b. Samples of the gel spheres (either wet or dry) were transferred to silica cuvettes (path length 1 mm) for SANS measurements. For contrast variation studies the dry gels were rewetted with H,O/D,O mixtures of the required composition and the supernatant aqueous phases of the wet

and rewetted samples were exchanged with the appropriate H,O/D,O mixture repeatedly to attain the required isotopic composition. Small annle neutron scattering Measurements were made at a wavelength, A, of 6 A using the multidetector SANS spectrometer installed in the PLUTO reactor at Harwell Laboratory (ref. 9). Data were analysed using standard programs to normalise for detector efficiency, and correct for sample self-absorption and background contributions.

262

Adsorotion isotherm measurements Nitrogen adsorption isotherms at 77 K were measured volumetrically using a Digisorb 2600 (Micromeritics Instrument Corporation). Dried gel samples were outgassed at ambient temperature for approximately 16 hours. Specific surface areas, SBET,and pore volumes, Vp, were calculated in the standard manner. Mean pore radii, rp, were derived from the desorption branches of the isotherms from the maxima of pore size distributions computed on the basis of the Kelvin equation, using a cylindrical pore model as previously (refs. 10-12).

RESULTS AND DISCUSSION Adsorotion isotherms The method of dehydration has a marked effect on the surface and porous properties of the dried gels. This is illustrated by the nitrogen adsorption isotherms in Fig.4 for zirconia gels which have been dried in air (a) and by solvent displacement (b). The isotherm for the solvent displacement dried gel is almost Type I1 in character which is typical of structures composed of an assembly of particles with a very open packing (ref. 10). This feature is demonstrated by the very high uptake at saturation, which corresponds to a considerable porosi:y (00.90) in the gel and the large pore size (see Table 1). In contrast the isotherm for the air dried gel is Type IV in character, and has features which indicate a gel with a considerably reduced porosity where the size of the pores are approaching the micropore range (52 nm). This is illustrated by the marked reduction in the uptake at saturation and the shift of the hysterisis loop to much lower pressures. Indeed the restricted size of the hysterisis loop shows that the isotherm is almost reversible and therefore approaching Type I behaviour

-

which is typical of a volume filling process in a microporous

solid. Such behaviour is an indication that marked shrinkage has occurred leading to a highly compact assembly of very small particles The marked differences in specific surface area,,,,,S Vp and rp depending on the method of dehydration are listed in Table 1.

TABLE I Surface and porous properties of zirconia gels dehydrated by different routes from nitrogen adsorption isotherms. ~~

Drying method

SBE,/m2 g-'

Mean pore radius/nm

~

~

Pore volume/cms g-'

Air dried

130

52

0.09

Solvent displacement dried

320

22

1.76

~~

263

100~00

I

I

I

I

I 0.02

I

1

I

0.05

0.10

0.2

10.00

1.00

0.10

0.01

'0

m 0.25

0.5

0

I

1.0

0.75

Fig.4. (Above left) Nitrogen adsorption isotherms at 77 K for zirconia gels. (a) Gel dehydrated by evaporation in air. (b) Gel dried after water displacement with butanol. Open and closed symbols represent adsorption and desorption respectively. Fig.5. (Above right) SANS from zirconia gels. (a) 'Wet' gel in water, 0 , (b) butanol displacement dried gel reimmersed in water, 0 , and (c) gel dried in air then reimmersed in water, 0. N.B. Data normalised for equivalent zirconia concentration.

As an example of the scattering data obtained, Fig.5 compares the scattering from dried zirconia gels after evaporative and solvent displacement drying reimmersed in water with that measured from the original wet gel. The scattering curves have been normalised to take account of different sample transmission and metal concentrations. At low Q the scattering from the wet gel (0)

shows a power law scaling of I

Q

Q-"'';

such behaviour is typical of a fractal aggregate

system. Similar scattering behaviour is shown by the rewetted solvent displacement dried gel

(0)

indicating that there is little microstructural change occuring during solvent displacement drying.

In contrast the marked macroscopic contraction of the wet gel on drying in air

(0) is

accompanied

by a significant reduction in scattering intensity and a change in the shape of the scattering curve indicating a considerable microstructural change. Also at higher Q (>lo-'

A-') the scattering

264 5.0

.'

L.0

3.0

2.0

k

1.0 0-0 -1.0 -2.0 -3.c

Fig.6. SANS contrast variation results for solvent displacement dried gels of (a) titania, (b) an equimolar mixture of titania and zirconia and (c) zirconia. Intensity corresponds to Q/A-' of 2.5~10'~. eventually tends towards Q-4 behaviour

- suggesting

that the structure is composed of very small

primary units ( ~ 3 0A). The scattering in Fig.5 indicates a reduction in surface area to about 40% of that of the wet gel on air drying. This reduction in surface area is consistent with the changes in,,,S

measured by nitrogen adsorption listed in Table 1 .

Contrast variation studies Other investigations (eg. XRD, EXAFS) indicate that the structure of the oxide phase is amorphous. This is of interest in the context of mixed oxide systems for the preparation of homogeneous gels and the homogeneity of gels at the microscopic level is being investigated by SANS using the contrast variation technique. This is illustrated in Fig.6. for experiments using

solvent displacement dried titania and zirconia gels and an equimolar mixed titania-zirconia gel immersed in H20/D20 mixtures. Fig.6. shows the square root of the intensity measured at a fixed scattering angle plotted against the isotopic composition of the aqueous phase. For each gel system the plots are reasonably linear over the range of contrasts (except for the zirconia system close to

its contrast match point as discussed below) and we note that the mixed oxide gel has a scattering length which is intermediate between that of the single component gels which indicates that the gels are homogeneous and can be regarded as two-phase systems (ie. solid and pores) over the scale length, d,,

s 20 A,

measured. This can also be concluded from the SANS behaviour (not

shown here) of the mixed oxide which shows similar shape throughout the range of contrasts.

265

We note that the contribution to the scattering from the polymer component of the gels is weak compared to that from the oxide component. Only in the case of the zirconia gels close to the match point of zirconia (-95% D,O), which is also of greatest contrast to the scattering length density of the polymer, would we expect a significant contribution to the total scattering from the polymer. It is this which causes the anomalously high intensities close to the match point of the zirconia gels. ACKNOWLEDGEMENT This work was undertaken as part of the Underlying Research Programme of the UKAEA. We would like to thank Mr S. J. Wilkinson for experimental assistance with the SANS measurements. REFERENCES 1. 2. 3 4. 5. 6. 7. 8. 9. 10. 11. 12.

B. Stringer, P.J. Russell, B.W. Davies and K.A. Danso, Radiochimica Acta, 36 (1984) 31. J.D.F. Ramsay, Chem. SOC.Rev., 15 (1986) 335. J.D.F. Ramsay, R.G. Avery and L. Benest, Faraday Discuss. Chem. SOC., 76 (1983) 53. J.D.F. Ramsay and R. G. Avery, this meeting. A. Guinier and G. Fournet, Small angle scattering of X-rays, Wiley, New York, 1955. T.A. Witten and L.M. Sander, Phys. Rev. B, 27 (1983) 5686. P. Meakin, Phys. Rev. A, 27 (1985) 1495. S.R. Forrest and T. Witten, J. Phys. A, Math. Nucl. Gen., 12 (1979) 109. D.I. Page, Atomic Energy Res. Estab. Rep. AERE-R9878, 1980 R.G. Avery and J.D.F. Ramsay, J. Colloid Interface Sci., 42 (1973) 597. J.D.F. Ramsay and B.O.Booth, J. Chem. SOC.Faraday Trans. I., 79 (1983) 173. B.O. Booth and J.D.F. Ramsay in: J.M. Haynes and P. Rossi-Doria (Editors), Principles and applications of pore structural characterisation, J.W. Arrowsmith, Bristol, 1985, p.97.

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F. Rodriguez-Reinosoet al. (Editors),Characterization of Porous Solids I1 0 1991 Elsevier Science Publishers B.V., Amsterdam

267

SMALL-ANGLE NEUTRON SCATTERING STUDY OF FUMED SILICA POWDER COMPACTION ALAN J. HURD1v2, GREGORY P. JOHNSTONZ, and DOUGLAS M. SMITHZ lSandia National Laboratories, Albuquerque, New Mexico 87185-5800 (USA), 2Center for MicroEngineered Ceramics, University of New Mexico, Albuquerque, New Mexico 87131 (USA) ABSTRACT In a previous study of fumed silica by mercury porosimetry (ref. l), we established an inverse dependence of the powder compressibility n on applied pressure P, heralded by power-law differential volume vs pressure curves. Independent small-angle neutron scattering (SANS) measurements, undertaken to establish microstructure, indicated a decreasing zero-angle intensity, I(q+O), with increasing sample compression. Preliminary analysis suggested that I(q+O) is proportional to the compressibility n . Since it is well known that I(q-+O) is proportional to n for systems in thermodynamic equilibrium, our results implied an analogous relation for systems in mechanical equilibrium. However, the preliminary study was incomplete, lacking scattering data for a wide range of compactions. In this paper, we have tested this relationship, in the low pressure regime, by correlating the scattered neutron intensity from samples in various degrees of compaction. We find that, while the intensity does decrease with increasing compaction (after removing the effects due merely to greater sample density) as expected according to the compressibility analogy, the dependence is not the same as that found by mercury porosimetry. Lightly compressed fumed silica has been studied as a percolating system by several groups (refs. 2-4); our results pertain to states of greater compaction. INTRODUCTION Previous studies (refs. 1.2) of fumed silica compaction have established an empirical "equation of state" between powder pore volume and applied pressure,

The compressibility, which is defined as

&

P

-

1 -

dV ~

V

dP

1

dV

V

dP

= -A

(2)

is therefore inversely proportional to pressure. Here V, the total volume of the powder, is comprised of compressible pore volume V, silica volume V,:

V=V,,+V,.

and incompressible

The scattered intensity at zero angle I(q+O)

might be expected to be proportional to

n

by analogy to thermalized systems.

In fact, preliminary scattering studies on compacted fumed silica powders demonstrated that I(0) decreases with increasing compression. we attempt to test the relationship

In this paper

268

which, if true, would imply a straightforward statistical mechanics for powder behavior. Thus, it should be possible to understand the empirical equation of state in Eq. (1) on a statistical basis.

Our study was motivated by interest

in the pore space surrounding the fractal powders as they are forced together. To illustrate what we mean by a statistical understanding of the state of the powder, we refer the reader to Edwards and Oakeshott (ref. 5).

If the

particles are sufficiently numerous and the local construction rules welldefined, then the macroscopic properties of the powder should be predictable and interesting.

The essential idea is that all configurations consistent

with mechanical stability are equally probable, but that for the overwhelming majority of these states the measurable properties are essentially the same. Thus, we should be able to predict, for example, the volume of a heap of sand. Unfortunately, it is necessary to understand the role of energy in our powder system in order to develop a calculus for the pressure-volume equation of state and the suppression of density fluctuations; we hope to provide these insights with future experiments.

The present study is a first step toward

that goal. Fumed silica is "glass soot" made by burning silicates in flames.

It is

known to be mass-fractal particles, i.e. submicron-sizeaggregates composed of random, weakly branched strings of 100 A silica spheres, with a great deal of internal porosity. Since the limiting small-angle intensity can be related quite generally to the fluctuations in the sample, I(0)

a

2

4 N > =

(4)

the relationship being tested here is the proportionality

I

v

'a

? ci

2



(5)

ap

The probability W(N,V,A,. . . ) of having N particles in a given total volume V must be sharply peaked at for large N.

W depends on some number of

extensive parameters A , . . . , which remain unspecified in our discussion of powders; for now we assume that a single function A suffices to encapsulate

269 our ignorance.

By expanding W in the neighborhood of its peak at N 4 > , we

can express the width, or fluctuation in N, in terms of the curvature in A.

W(N,V,A,. . . ) = W()

+

1 2 a2A (N-) - I 2 aN2 N-+>+

' '

(By stability arguments, the linear term in the expansion must be zero and the sign of the A-curvature must be negative.)

Thus, the Gaussian width-squared

is 2/(a2A/aN2) and is equal to 2. But adding particles to a constant volume is equivalent to compressing a sample of constant mass; hence, it is actually the variation in A with volume that matters. -(aA/aV),

In thermodynamic systems, A is the (Helmholtz) free energy and

is the pressure, so

a2A

2

----..- 2 aN2

v2 N~

ap -

av

(thermodynamic systems). (7)

Thus, in thermodynamic systems, Eq. ( 5 )

follows directly from the key

relation between free energy and pressure.

For powder compaction, it must

again be an energy argument, but we have yet to identify the fate of the mechanical energy put into the system. EXPERIMENT Eight samples of Cab-0-Sil (grade EH-5, Cabot Corporation) fumed silica were prepared in closed aluminum cells with 3 mm path length.

The cell was an

aluminum cylinder, 1 . 2 6 cm inside diameter, with 1 mm thick aluminum windows pressed into each end.

Densities ranged from 0,038 g/cc to 1 . 2 g/cc; the

loose powder density (see below) is even less than that of sn aerogel. Small-angle neutron scattering was performed at the Manuel Lujan Los Alamos Neutron Scattering Center (LANSCE). 0.05

The useful wave vector range was

< q < 0.16 A-1 after correction for scattering from an empty cell. The

high sample densities (1.2 g/cc) were done at the Missouri University Research Reactor (MUM). ANALYSIS Figure 1 shows the measured sample density as a function of l/a, where a is a compression factor defined by a-V/V, with V the compressed sample volume and V, the volume o f loose powder that was compacted. By least-squares fitting to p=po/a, we found po=0.0296 g/cc (loose powder density).

270

Q

9 0

2.0

0.0

4.0

80

60

1 /.

Figure 1.- Densities of compressed fumed silica samples. In the very low pressure regime, we noticed that the scattering curves all had the same form but different amplitudes.

Each curve was divided by

p

and

by sample thickness to correct for the effects of scattering mass; this brought the very low pressure curves into coincidence, proving that very little structural difference existed between these samples; the higher density samples did, however, exhibit deviations at low q as seen in Figure 2 .

We

compared the total scattered intensity between curves by dividing each curve by a "reference curve" f(q)

in order to leave only amplitude information.

f(q) was formed by simply averaging the six lowest density curves and is shown in Figure 2 with two other representative curves. Finally, the lowest-q intensity datum from each normalized curve was taken as our approximate I(0)

.

(rather than attempt a dangerous extrapolation to

0) and plotted in Figure 3 . The abscissae are VP., where V, is the pore q volume (calculated from the density) and V, is the silica volume (calculated from the mass). For low densities (V,/V, > lo), the intensity was found to be constant when normalized in the above manner indicating no significant interparticle interference accessible to the

SANS.

At higher densities,

however, I ( 0 ) was found to drop as particles packed closer together and scattered more coherently.

271

0.001

0.01

0.1

9 Figure 2.- Scattering curves of compressed fumed silica. scattering curve f(q) p-0.306

for very low density

g/cc; (c) p=1.00 g/cc.

samples p C 0 . 0 9

(a) Average g/cc;

The denser samples scatter less intensity at

small angles.

0

1

(b)

10

100

VdVS

Figure 3.- Approximate zero-angle intensity vs. normalized pore volume.

272 [We note that the large-q data in the raw scattering curves do not quite approach a Porod asymptote (slope of -4), as noted previously (ref. 6), indicating a somewhat rough primary particle surface.

Since the curves

coincide at large q (after correcting for scattering mass),

the interfacial

area is unchanged with compaction except at the highest densities, when it decreases.

We infer that chains in the aggregate do not break to form new

surface area (or, if they do, an equal amount of surface area is annihilated simultaneously).] Using n

a

1/P from Eqs. (1) and (2). we would expect

I(O)

a

P-'

a

v3

P

Instead we observe (for V,/V, 9 9 . 9 9 % , Air Products Ltd.), and the carbon dioxide was of 9 9 . 7 5 % purity (Distillers M.G. Ltd.). Characterisation Neopentane was chosen in addition to nitrogen to assess the effect of molecular diameter on the nature and extent of adsorption on the chars studied (ref.

7).

Nitrogen adsorption isotherms were determined at 77K using a Carlo Erba

Sorptomatic 1800 and an Omnisorp 100, the latter being used for measurements at very low relative pressures. Neopentane isotherms were measured at 273K using a

CI Robal vacuum microbalance, while a quartz spring McBain-Bakr type vacuum microbalance was used to measure water sorption isotherms at 298K.

The

neopentane used was of 9 9 . 0 % purity (Argo International Ltd.) while the deionised water was subjected to repeated freeze/thaw cycles under vacuum to remove dissolved air, before use. 250*C to a residual pressure o f
nl

(1)

Where W is the volume o f adsorbates adsorbed in micropores at temperature T and relative pressure P/Po; Wo is the limiting volume of the adsorption space, A(=RT ln(Po/P)) is the adsorption potential, n, p , and Eo are specific parameters of the system under investigation. The DR equation is one form of the DA equation with n = 2 . Analyses of numerous adsorption experiments have shown that the DR equation is useful to describe phenomenologically vapor adsorption on activated carbons. However, deviations from linear DR plots are frequently encountered. The deviation is mainly ascribed to some heterogeneity in the micropore structure. Dubinin and Stoeckli [ 4 ] proposed the DR equation having two terms which

430

originate from two independent structures. Marsh [5] and Master and McEnaney[6] discussed the relationship between the deviation from the ideal DR equation and the micropore structure of carbonous materials. McEnaney[7] has tried to describe the micropore filling in terms of general formula. Jaroniec and Choma[8] have proposed new mathematical expression for the micropore filling in micropores of energetic heterogeneity. On the other hand, Sing et a1[9-11] have proposed two-stage mechanism o f the micropore filling on the basis of ds-and calorimetric analyses for abundant adsorption data; two elementary processes are a significantly enhanced 'primary' process that occurs at lower P/Po and a 'secondary' or 'cooperative' process at higher P/Po. The micropore filling mechanisms by carbonous materials, however, are not sufficiently established yet. Activated carbon fibers (ACF'S) are highly microporous with small external surface areas and very little mesoporosity[l2-141. ACF's have been extensively investigated from both fundamental and practical aspects. The detailed adsorption isotherm of N2 on ACF should provide an important key to the micropore filling mechanism. In the preceding papers[l5,16], the adsorption isotherms of N2 on ACF'S were statically measured with the aid o f a computercontrolled gravimetric apparatus; the detailed DR plot indicated a multi-stage micropore filling (MSMF) mechanism including monolayer adsorption on the pore wall of supermicropores. The quadrupole of N2 interacts with the carbon surface; the quadrupole produces the herringbone pattern o f the N2 molecules adsorbed on the graphitized carbon black in the submonolayer[l7,18]. Adsorption isotherms of N2 on ACF's have two steps below 0.01 of P/Po which should be associated with the submonolayer phase transition. As Ar without the quadrupole has the molecular size and polarizability similar to N2, N2 and Ar adsorption isotherms are frequently compared with each other to assess the true microporosity[7,10,20]. Hence the analysis of Ar adsorption isotherms on ACF'S should give a further evidence for the MSMF mechanism. In this paper the adsorption isotherms of N2 and Ar on ACF'S will be compared and the micropore filling mechanism in the ACF system will be discussed.

EXPERIHENTAL

Cellulose(CEL, Toyobo KF1500)-, pitch(PIT,Osaka gas A10)-, and polyacrylonitrile(PAN, Tohorayon FE200)-based ACF'S have been used in this study. Nonporous carbon black(NPC, Mitsubishi Kasei 32 [21]) was also used for comparison. The adsorption isotherms of N2 and Ar were statically measured by an automatic gravimetric apparatus at 77 K. The detailed description of this apparatus has been reported[15]. We obtained adsorption isotherms of more than

431

70 measuring points over about 20 h by this apparatus. The samples were pre-evacuated at 383 K and 1 mPa for 2 h. Gases of more than 99.99 % purity were dried by slow passage through a cold trap. X-ray diffraction of the ground sample was measured by an automatic X-ray diffractometer (Rigaku Denki 2028). High resolution electron micrographs were taken on a JEM-200FX instrument operated at 200 kV. The ACF sliced at a right angle to the fibrous direction in 50-60 nm thickness was observed.

RESULTS AND DISCUSSION Characterization of ACF X-ray powder diffraction patterns of ACF samples have two broad peaks at 28= 25' and 28= 43 O . which are reflections from the (002) planes and from the (001) and (101) planes, respectively. The interlayer distance from the 002 planes was 0.35-0.36 nm for all nm, corresponding to ACF's. The 002 crystallite size was 0.7-0.9 ca. 2-3 times of the interlayer distance. The details on X-ray diffraction study were already reported in the preceding papers[15,17]. Also the detailed description of the microporosity from the N2 adsorption isotherms previously appeared. The micropore volumes Wt and WOLfrom the t- and ds-plots, respectively are described here[ Wt in mlg": CEL; 0.590, PAN; 0.354, and PIT; CEL; 0.606, PAN; 0.344, and PIT; 0.3241. 0.330. WOrin mlg": Figure 1 shows electron micrographs of ACF samples. It is not to easy to conclude the microporosity from the micrographs[23,24]. The micrographs of these ACF samples with greater magnification are relatively homogeneous with microporosity due to distorted slits, ca. 1 nm in width; these pores are separated by walls of about three graphite-like layers in thickness, coinciding with the X-ray diffraction data. Meanwhile the low magnification micrograph of CEL shows greater heterogeneity, which probably originates from the mesoporosity. Other PIT and PAN do not have such images on the low magnification micrograph due to the mesoporosity.

DR plots €or N2 adsorption isotherms micropore

filling

and

multi-stage

mechanism

The DR plots of N2 adsorption isotherms are composed of three or four lines with different slopes, as shown in Fig. 2.15 The inflection points appear near 0.004, 0.05, and 0.3 of P/Po. These linear sections are denoted L-, M-, H-, and S-regions in the order of the P/Po increase. The broad X-ray diffraction patterns and the high resolution electron microscopic observation show that ACF's consist of micrographites. The micropores of ACF'S may be assumed to stem from defaults of the graphitic layers upon activation; the

432

F i g . 1. E l e c t r o n m i c r o g r a p h s of ACF'S. (c): P I T

and ( d ) : PAN.

( a ) and (b) : CEL,

433

micropore size is approximated by integral multiples of the graphitic layer's thickness (0.34-0.35 nm). We can express the micropore size in terms of 0.3 0.05 0.004 P/P, the width of an adsorbed N2 molecule, since the width of an N2 molecule (0.34 nm) is nearly equal to the interlayer distance of the graphitic structure. The micropore(MP) analysis[25] for the t-plot indicated qualitatively the presence of the two-four N2 l"* ( P , / P )

X]g--fg

layer-sized micropores which come from defaults of two-four :$. graphitic layers; we can associate the micropore size estimated by the MP analysis w i t h each region of the (4 (b) detailed DR plot according to the multi-stage micropore filling(MSMF) mechanism. In A detailed DR plot and the MSMF mechanism[l51, N2 Fig. 2 molecules are filled in the schematic model for the multibilayer-sized micropores at stage micropore filling for N2 t h e L r e g i o n , t h e y a r e adsorption on ACF. (a) cooperative monolayerly adsorbed on the filling on the monolayerly covered micropore-walls at the M- supermicropores, (b) monolayer region, they are adsorbed in adsorption on supermicropores and t h e m o n o l a y e r covered(c)pore f i l l i n g i n the N2 micro por es a t the H- region bilayer-sized ultramicropores (this process corresponds to the cooperative micropore filling proposed by Sing et al[9-111, and then they are adsorbed on the external surface in the S-region, as illustrated in Fig. 2. The MSMF mechanism includes the primary and cooperative pore filling mechanism by Sing et a1[9-111 and each stage of the MSMF mechanism can be explicitly determined, while the two-stage mechanism by Sing et a1 does not show a clear boundary between two elementary processes. The analysis of the detailed DR plot can distinguish each elementary process in the micropore filling by different o E o value. Here B E o value is associated with the isosteric heat of adsorption, qst, B=l/e at the fractional filling of l/e, as expressed by eq. 2[25].

IF

(C)

-

.

qst,e=l/e

=

PEo

+ A% (&:

heat o f vaporization)

(2)

In the preceding study[l5], it was shown that the qst value corresponding to each elementary process agrees with the literature

434

value. In later section, it will be examined whether the M S M F mechanism can be applied to the Ar adsorption data. DA and DR plots for Ar adsorption isotherms Figure 3 shows the adsorption I isotherms of Ar. Here we use E the solid phase vapor pressure of 27.4 kPa at 77 K as the saturated vapor pressure of Ar. All isotherms are of Type I, 6 being almost identical to those of N2. The uptake of Ar at the low pressure region is more 400 gradual than that of N2, which should be attributed to the absence of the quadrupole in the A r - A C F s y s t e m . T h e s e Ar Y adsorption isotherms were a n a l y z e d by the D R plots. Figure 4 shows the DR plot of the Ar adsorption on CEL. The 0 DR plot is not linear but there 0 0.2 0.4 0.6 0.8 1.0 are three concave regions P/P, against the abscissa; the DR equation does not express the Ar adsorption. Ar does not form Fig. 3. Adsorption isotherms Of the liquid-like adsorbed layer Ar on ACF's at 77 K * upon adsorption of Ar at 77 K, but should form the solid-like phase on the surface. The DA e q u a t i o n of n = 3 may be applicable to such a 6.8 system[3,27]. Figure 5 shows the DA(n=3) plots for the Ar adsorption isotherms on ACF'S at 77 K. The DA plot has three sections as well as the DR plot for the N2 adsorption isotherm. It bends upwards at two points w i t h i n c r e a s i n g P / P o ; the inflection point is different from each other. The DA plots for PIT and PAN have steep rises Fig.4. DR plot f o r the just near the ordinate. We may designate these linear sections Ar adsorption isotherm on in the DA plots L-, M-, and HCEL. regions in the order of the P/Po

1

2

7

435

increase as well as the case of the DR plots for N2. Probably the steep r i s e near the ordinate in the DA plot for Ar corresponds to the S region(multi1ayer adsorption on the external surface) in 7 the DR plot for N2; it is 2 difficult to determine the 3 bending point of the S-region from the H-region in the Ar adsorption.

7

.

0

1

7

7.0

h

.

6.5

6.5

v

Comparison analyses

of and

Ar and

N2

6.0 6.0

5.5

I

I

I

0

I

50

100

150

5.5

ln3(p0/p)

multi-stage

micropore filling mechanism. Fig. 5. DA(n=3) plots for the T h e coordinates of the Ar adsorption isotherms inflection points of the DA plot for Ar and DR plot for on ACF'S. N2 and oEo values from the slopes are compared in Table 1. H e r e t h e a m o u n t o f adsorption,W, is more important than the P/Po value in the inflection point for comparison of the Ar and N2 a n a l y s e s ; t h e a m o u n t of adsorption W for Ar in mlg-' 5 % 4 is calculated with the liquid density value(l.40 gml-l) at ; 4.0 8 7 K. The W value of the 'a inflection point in the DA 3.5 plot for Ar agrees with that ; * in the DR plot for N2 within 3.0 20 % d e v i a t i o n . If we compare the W value o f the inflection point expressed in 0 50 100 150 the ratio against each W o value, the agreement is ln3(po/p) improved to 10 % deviation at maximum. Therefore, the Ar adsorption can be explained by Fig.6. DA(n=3) plot for the Ar the MSMF mechanism. The adsorption isotherm of adsorption isotherm on NPC. Ar on NPC is also expressed by the DA(n=3) equation, as shown

5

436

$4

$4

4 0

w rn Y

a

4

0

e

II

m

W

d a, 5 52

V Q N

$4

z 0 rn

rcl Y

a

0 4

a,

a

rcl

5 0

cn

c 0

M

a, LI

. o. m.

m r . m

m

. om.o m-.

m

0

0

0

0

-

0

N

o

0

u

a

a

0

0

0

m

-

”9‘s.

0

*.-lo

*

. . . O

0

m

. m. - .

a c u m

o

p

0

N

. .

0

-3

i t m

N

m i t

a

? ? ” m

0

l

u

. m. o.

u -

r

. .

m a r -

a

00 I n -

0

m . 3

0

i t 4 0 0

m

e u

rl

0

0

0

a

0

0

. .

m

“.?1 0

0

. . 0

a

e

0

o

0

0

. . .

m

4

0

437

in Fig. 6. The DA plot is composed of a long line and a steep rise, which corresponds to the monolayer adsorption and the multilayer adsorption, respectively. As the DA equation is based on the potential theory, the monolayer adsorption may be expressed by the DA equation even in the nonporous system[28]. The slope of this linear region gives .BEo of 5.4 kJmol-l. The BEo value for Ar on ACF in the same region may be compared with that on NPC. Table 1 lists also the BEo value for each linear sections. The B E o values of Ar on ACF'S for the L- and M-regions are greater than the BEo value for the monolayer formation on NPC by more than 1.8 kJmol-l and 0.1-0.6 kJmol-', respectively. These differences should be caused by the enhancement by the micropore field. Consequently, Ar is adsorbed by the micropore filling in the Ar bilayer-sized pores (L-region) at first and then Ar forms the monolayer on the pore-walls of the three and/or four Ar layer-sized pores (M-region), accompanying the cooperative filling of Ar in the H-region. Thus, analyses of adsorption data o f Ar without quadrupole support the MSMF mechanism. That is, the importance of the introduction of elementary processes into the micropore filling proposed by Sing et a1[9-111 has been shown and their two-stage mechanism has been extended to three-stage mechanism with the monolayer adsorption on the micropore walls by analyses of the d e t a i l e d N 2 a n d Ar a d s o r p t i o n i s o t h e r m s . A l t h o u g h the micrographitic structures and the micropores change with gas adsorption by in situ X-ray diffraction and in situ small angle Xray scattering[21,29], this study neglects such a dynamic effect of microporous carbons. In future, the dynamic micropore structure should be taken into account in the micropore filling mechanism and also calorimetric study will be needed.

ACKNOWLEDGEMENTS This work was partly supported by a Grant in Aid for Fundamental Scientific Research from the Ministry o f Education of Japan. Special thanks are due to Dr. T. Okada for observation of ACF samples with a high resolution transmission electron microscopy.

REFERENCES 1 2 3

4

K.S.W.Sing, Carbon, 27 (1989) 5. H.F. Stoeckli, Carbon, 28 (1990) 1. M.M. Dubinin, in P.L. Walker Jr. (Editor), Chemistry and Physics of Carbon, Marcel Dekker, New York (1966) pp.51. M.M.Dubinin & H.F. Stoeckli, J. Colloid Interface Sci., 75 (1980) 34.

438

5 6

H. Marsh, Carbon, 25 (1987) 49. K.J.Master & B. McEnaney, J . Colloid Interface Sci., 95 (1983) 340. 7 B. McEnaney, Carbon, 26 (1988) 267. 8 M.Jaroniec & J. Choma, in P.L. Walker Jr. (Editor), Chemistry and Physics of Carbon, Marcel Dekker, New York (1989) pp.197. 9 D. Atkinson, A.I. McLeod & K.S.W. Sing, J. Chim. Phys., 81(1984) 791. 10 D. Atkinson, P.J.Carrott, Y.Grillet, J. Rouquerol & K.S.W. Sing, in A.I. Liapis(Editor), Fundamentals of Adsorption, Engineering Foundation, New York (1987) pp.89. 11 P.J.Carrott & K.S.W.Sing, in K.K. Unger, J.Rouquero1, K.S.G. Sing & H . Kral (Editors), Characterization of Porous Solids, Elsevier,Ansterdam (1988) pp.77. 12 Y. Komatsubara, S.Ida, H. Fujitsu & I. Mochida, Fuel, 63 (1984) 1738. 13 J.J.Freeman, F.G.R.Gimblett, R.A.Roberts & K.S.W. Sing, Carbon, 25 (1987) 559. 14 K.Kaneko, N. Kosugi & H. Kuroda, J.Chem.Soc. Faraday Trans., 85 (1989) 869. 15 K.Kakei, S.Ozeki, T.Suzuki & K.Kaneko, J.Chem.Soc. Faraday Trans., 86 (1990) 371. 16 K.Kaneko, T. Suzuki & K.Kakei, Tanso, (1989) 288. 17 J. Rouquerol, S. Partyka & F. Rouquerol, J.Chem.Soc. Faraday Trans. I, 73 (1977) 306. 18 W.A. Steele, A.V.Vernov & D.J. Tildesley, Carbon, 25 (1987) 7. 19 K.Kaneko, T.Suzuki & K.Kakei, Langmuir, 5 (1989) 879. 20 D.A. Wickens, Carbon, 28 (1990) 97. 21 S. Hagiwara, K.Tsutsumi & H . Takahashi, Carbon, 16 (1978) 89. 22 T. Suzuki & K.Kaneko, Carbon, 26 (1988) 745. 23 R.W.Inness, J.R. Fryer & H.F. Stoeckli, Carbon, 28 (1989) 71. 24 M.Huttepain & A. Oberlin, Carbon, 28 (1990) 103. 25 R.S.Mikhai.1, S. Brunauer & E. E. Boder, J. Colloid Interface Sci., 26, 45 (1968). 26 K.Kawazoe, V.A. Astakhov & Y. Eguchi, Kagaku Kogaku, 35 (1971) 1006. 27 T.Kawai, Rep. of Eng. Inst. of Kanagawa Univ., No.1 (1971) 38. 28 S.J. Gregg & K.S.W.Sing, Adsorption, Surface Area and Porosity, Academic press, London (1982) pp.222. 29 K.Kaneko, Y. Fujiwara & K. Nishikawa, J.Colloid Interface Sci. 127 (1989) 298.

F. Rodriguez-Reinoso et al. (Editors), Characterization of Porous Solids II

439

0 1991 Elsevier Science Publishers B.V., Amsterdam

POROUS

N.T.

STRUCTURE

A.M.

KARTEL,

Division

of

Ukrainian

OF

SYNTHETIC

ACTIVE

and V.V.

STRELKO

WZY

sorption.

institute

of

Academy

of

Sciences.

CARBONS

General

Kiev

and

inorganic

Chemistry.

(USSR),

ABSTRACT Synthetic active carbons produced f r o m some types o f porous polymers or resins belong t o a new class o f carbon adsorbents which exhibit a unique combination o f physicochemical properties. Spherical-granule nitrogen-containing carbon SCN and pure carbon scs have been developed, which possess (according t o benzene vapour adsorption d a t a ) easily c o n t r o l l a b l e porous structure. The methods o f synthesis developed make it possible t o develop t h e micropore volume o f such carbons t o 0.6-0.9 cm3/g. The medium micropore-size can b e varied over a wide range f r o m narrow micropores nm). Adsorption-Weight analysis (halfwidth 0.3 nm) t o supermicropores (0.9-t.4 d a t a indicate a developed mesoporous s t r u c t u r e (volume 0.5-1.4 Cm3/g, specific mesopore surface area 100-500 m2/g). It has been shown by mercury porosimetry t h a t SCN and SCS carbons are characterized by a narrow mesopore volume distribution ( t h e main peak lies in t h e region 12-54 nm) and a small macropore volume development (0.1-0.2 cm3/g). The pecularities o f t h e porous s t r u c t u r e o f synthetic carbons are controlled by t h e prolonged and, in some cases, molecular-sieve nature o f their sorption f r o m solutions, which is o f prime importance f o r solving a number o f problems for s o r p t i o n technologies and medicine.

INTRODUCTION Synthetic porous

active

copolymers

subsequent

and

vapour-gas

properties pore

carbons

including

are

a

new

spherical activation.

increased

type

of

granulated The

carbon

resins

sorbents

mechanic81 s t r e n g t h

as

sorbent

by

prepared

their

DYrolysis

obtained well

have

as

a

from and

improved

highly

specific

structure.

The

structure-sorption

generally

determine

important carbons

its

characteristics and

SCN

VIZ

divinilbenzene

characteristics

of

practical

application,

of

porous

the

SCS

co-polymers,

any

adsorptive

material

will

this

paper

present

the

so

structure

from

obtained respectively

of

two

WIII

types

vinylpyridine

(ref.

and

of

synthetic

Styrene

with

t,?).

METHODS

For

the

degree o f studied were

by

present burn-off

study,

conventional

determined

by

SCN

and

SCS

have been selected. methods.

mercury

carbon

speciments

with

The porous structure o f

Macro-

porosimetry

and (Pore

mesopore Sizer

a

distribution

R9300,

progressive

t h e carbons was by

Micromeritics

radii Inc.,

The threshold radius was 3 nm (limiting pressure - 2500 kg/cmz). Apparent ( 8 ) and t r u e (d) densities were determined pycnometrically

USA).

mercury and benzene respectively. have

been

and water

obtained vapour

quartz

wlth

Specific

from

Data on t h e carbon micro-

adYorption-desorption

isotherm3

using

and mesostructures

of

benzene,

methanol

a t 20% using a t h e r m o s t a t t e d vacuum adsorption unit supplied

spring

balance.

Mesopore

volume

distributions

radii

by

surface values were computed f r o m t h e desorption isotherm

and

bT617ChW.

The microstructure o f t h e carbons was also determined by application o f microp@rous zone model developed the

sorption

isotherms

2,4-dibromphenol) evaluation

from

(ref.

of

by

Dubinin ( r e f .

ti.

low-soluble

water

SOIUtiOnS

organic

also

was

3).

the

method based on

A

substances

(pW6-Chlorantlrne,

used

a

for

microstructure

4).

RESULTS TYprC.31 porograms o f are shown in Figure volume

distribution

the

follows

As

1.

by

synthetic

radii,

the

carbons

from

the

obtained

mercury

by

porosimetry

respective d i f f e r e n t i a l

macropores (r>100 nm)

are

curves o f

actually

completely

absent in t h e SCN and SCS carbons and t h e Predominant mesoporous sizes are 35 and

nm,

12

respectively.

Location o f factors: content

of

obtained in

t h e most

degree

of

probable peak f o r

polymer

pore-former.

cross-linking

The

pore

volume

f r o m styrene-divinylbenzene

Figure

t h e mesopores depends on numerous

(divinylbenzene distribution

matrices

content), radii o f

by

defferent

Of

nature

types

the

isotherms

for

benzene,

methanol

and

water

vapour

t.he SCN and SCS carbons specimens w i t h d i f f e r e n t degrees o f burn-off Figure

The

3.

results

mesoporous

content

substantial

mesoporosity

6re

reacting those

are

considerably

pycnometric

at of

lower

calculate

the

the

structural

width

and

-

occurring.

than

total

the

their

(V,=1/6 -1/d). i.e.

adsorption variance

the

t h e theory

presented in

giving

information

on

its

the

(ED),

micropores

pores

adsorption

specific

adsorption

of

Table

halfwidth

In

Table

2

mesopores

obtained

from

isotherms,

one

of

as

of

well

as

micropores

the

distribution

micropore volume 1.

activation

of

surface

volume

Volume

are shown

(Vs=Vn,+Vnc), however,

Dubinin-Radushkevich

parameters constituting t h e s t r u c t u r e o f and

mesopore

limiting

the

of

on

insignificant

futher

volumes

values

Using benzene and

under

The

total

values

energy

of

constituting

obtained are

is

but

rel6tively

a

60% whereas

to

development

fundamental equations f o r values

demonstrate

micropores

parameters.

(X),

( W)

up

micropore volumes

characterictic

micropores

obt6ined

burn-offs

measurements

may (Wg),

carbons

are presented

2.

AdSorption-desorpt1on in

6nd

slit-like over

their

and

Dubinin-StoecKli

filling

(ref.

the

slrt-like

3).

The

micropore

t h e carbon adsorbent microporous zones

re-structure

during

progressive

activation

are

441

ddV zr

2

35 nm

1

Fig.

Pore

1.

r,nm

1000

100

s i z e d i ~ t r i b u t i o nf o r s y n t h e t i c carbons SCN ( 1 , 2 )

and scs ( 3 , 4 )

w ~ t hburn-offs: 40% 11.3) and 75% 12.4).

56 nm

10 F i g . 2.

100 I 0

Pore s i z e d i s t r i b u t i o n f o r

100

100

I0

synthetic

carbons

100 r,nm

10

prepared

s t y r e n e - d i v i n y l b e n z e n e copolymers w l t h v a r i o u s c r o s s - i inkage c o n t e n t : ( a ) 10/80%; ( 5 ) 30/130%; ( c ) 30/160%; (d) 40/180%.

from

and

p o r e -former

442 Q.,

C

40%

SCN: 20

r

L

1c

0.5

0.5

I

0.5

SCS: 40%

I(

0.5 Fig.

3.

0.5

0.5

A d s o r p t i o n i s o t h e r m o f benzene ( a ) , methanol (b) and water vapour

on s y n t h e t i c a c t i v e carbons SCN and SCS w i t h v a r i o u s b u r n - o f f s .

(c)

443 TABLE 1 Porous s t r u c t u r e o f s y n t h e t i c a c t i v e carbons ~~

Parameter

Burn-off,

X

SCN-1M

SCN-2H

SCN-1K

SCS-1

SCS-2

SCS-3

40

60

75

40

60

75

Pore vo~ume, c d / g

- total

0.75

0.93

1.59

0.53

0.86

1-15

- i n t r u d e d by Hg

0.41

0.46

0.95

0.34

0.52

0.71

- macropore

0.02

0.03

0.09

0.08

0.11

0.12

- s o r p t i o n (by benzene)

0.45

0.65

0.97

0.44

0.10

0.93

- micropore

0.36

0.48

0.61

0.19

0.34

0.44

t o t a l (by Ar)

420

560

1320

540

880

1380

mesopore (by benzene)

36

74

199

66

88

200

0.485

S p e c i f i c s u r f a c e area,

-

d/g

D u b i n i n - S t o e c K I i e q u a t i o n parameters

- w,,

cd/g

0.375

0.520

0.650

0.189

0.356

-

KJ/mole

27.3

18.5

14.9

33.1

18.5

14.2

0.418

0.681

0.859

0.298

0.559

0.706

Eg,

- m i c r o p o r e h a l f w i d t h , nm

TABLE 2 Structural

parameters

o f S y n t h e t i c a c t i v e carbons a c c o r d i n g t o

m i c r o p o r e zone (MZ)model

Parameter

SCN-1M

SCN-2M

T o t a l MZ volume, cn?/g

0.860

MZ f a c e s i z e , nm

96

Mesopore h a l f w i d t h , nm

SCN-1K

SCS-1

SCS-2

SCS-3

0.978

1.090

0.766

0.866

0.963

53

22

47

39

10

2.2

1.8

2.1

3.4

3.1

2.8

T o t a l MZ q u a n t i t y , Nw10-'6

0.10

0.66

10.4

0.76

1.4

13.5

l 5 0 l a t e d m i c r o p o r e volume, n d

1.24

4.15

8.0

0.64

2.46

4.58

S i z e o f c r y s t a l l i t e face, nm

1.61

2.33

2.81

1.48

2.07

2.45

Crystallite Quantity i n i s o l a t e d MZ

171070

8920

320

31500

5980

385

Micropore Q u a n t i t y in i s o l a t e d MZ

294440

17530

730

38960

9740

710

Geometrical s u r f a c e area o f micropore, d/g

861

705

710

634

637

623

444 shown.

Isotherms o f acetylene black in

Figure

tsalswbed ?TWn Waxer

p-&XlltKMki%ng

5CM EWkWS

b+'

$OWt?QflS

t h e AeltbOll - Abhck coordinates are presented

plotted f o r

4.

DISC 11S S l O N According

to

mercury

mesoporous b u t sorbents. by

These

conflicting

independent

methods,

macropores

that

volume o f

the

classified

be

higher The

above

as

t h e radius o f polymer

are

that

a

evaluating by

volume,

structure

since

is

described

cOpOlymW

mesoporous

the

porous

specific

structure Shape

of

Then, t h e whole

their

filling

up

would

occur

at

typical

investigations we

content

benzene

t h e most

have

copolymers

(divinylbenzene (alkyl

of

characteristic

the

a method o f

typical

the

synthetic

the

most

resins, Locat.ion o f

CWbOtiS

probable size

channels would be determined by t h e properties o f

a

divinylbenzene

%3ttlfiy o f

as

characterized

they are macroporous

macropores by t h e mercury porosimetry method would

Thus

gore-formers

by

interpreted

be

cross-linking

and

be

and

and

demonstrated

obtained

matrix

type.

carbons

5).

macroporous

the

carbone

should

mesopores

(ref.

for

Styrene

results,

"latent"

the

mesopore from

synthetic

isotherms would Suggest

could be reached via t h e more narrow mesopores.

pressures

obtained

porosimetry,

benzene vapour

of

of

been

for

the

conducting With

dif fering

by

5-60%),

amount

their

paraffin,

60-160%,

varying b o t h t h e

value

and

process

definitive commercial

degree

of

nature

of

oils,

etc.)

t o t a l and sorption volumes o f

Drobable radius f o r

pores

t h e t r a n s p o r t pores f r o m 3 up t o

nm as shown in Figure 2.

210

CharacteriStiCS

of

the

synthetic

progressive increase in macroincreases. Water well

Shifts

Vapour 85

When

the

position

associated with

the

SCN

desorption

linear

the

of

water

carbons

chemically-bound

t h e degree o f conforms burn-out

to of

Intercrystallite burning their

widening o f

burn-off a

micropores share

of

section

at

vapour

the

low

are

inflection

burn-off of

relative

pressure

of

benzene

adsorption P/Po

the

nitrogen atoms the

radii.

present

micropore

Crystallite

resulting

in

contributing

is approaching

1,

but

an more

the

one

values.

is above 4 0 % and, If s t i l l hlgher carbon

degree o f

branch

a

demonstrate

1

the

in

the

the as and

is

note

the

probably

sorbent.

model (Table

2)

the crystallites when

a half-width o f a slit

enlargement

improved

may

arrangement

significantly,

volume,

may

This

zone

t h e s l i t s and enlargement o f

supermicropore

amorphous

values

isotherms

Analysing t h e carbon characteristics f r o m one may n o t e t h e

Table

also confirmation o f t h e above f a c t .

isotherms

for

convexity

the

towards

initial

adsorption are

studying t h e

of

isotherm

in an

decrease

8

methanol v m o u r

isotherm

in

adsorption

in

carbons

and mesopore volumes as

however,

viz

at

indicate of

the

60-75%

makes up only

a

445

0.4

0.2 /

/ I

/

/ I

I I

I

I I

Fig.

4.

SYnthetlc

AdsOrptlOn actlve

lsotherm

carbons

of wlth

SCN

p-chloranlllne varlous

from

aqueous

burn-offs

and

actlve

carbons

solutlon

carbon

black.

TABLE 3 Mlcropore by

structure

adsorption

of

parameters dlssolved

Parameter

synthetic

2,4-d1bromphenol

Symbol

SCN-1M

SCN-2M

SCN-1K

SCN-2K

Vtn;

0.27

0.32

0.31

0.26

V,

0,27

0.43

0.53

0.4b

v,,~

0.09

0.16

0.30

0.36

superml c r o p o r e

Vsml.1

0

0.11

0.22

0.20

mnolayer f I I led supermlcropore

V s m ~ 2 0.09

0.05

0.06

0.la

120

340

1160

Pore volume,

cm3/g

- micropore - volume f l i i e d m l c r o p o r e - t o t a 1 superml c r o p o r e - volume f i l l e d

-

of

parachloran~lme and

S D e c if ic surf ace area o f monolayer f I I l e d pore, mz/g

s1

55

on

446 half

the

total

Vaiuco,

of

conflicting

processes,

shrinkage within

micropores micropore

and

the

their

distributions adSOrptiOn their

adsorption

on

are filled

of

by

the

VOlUmeS of

determined

by

the

is

the

to

a

due

black.

microporous

true

micro-

While from

According

volume

mechanism

monolayer

to

to

structure

area

solutions

the

alters

supermicropore

in

of

studies

wider

the

comparison (ref.

micropores and a

and

the

Therefore

isotherms

earlier

true

a

mass.

and

the

of

4,6)

part

of

supermicropores

formation.

t h e Pores being filled as

effect

surface

studying

up t h e

the

equation

micropores

are filling

up by t h e mechanism o f

Specific

sum

geometric

substances

carbon

a

loss in carbon

a

detect

organic

express

the

of

the

to

substances

supermicropores

of

because

possible

low-Soluble

organic

surfaces

narrowing

Pecularities were

of

low-soluble narrow

i.e.

extension

40-75% burning range

insignificantly.

with

volume.

geometric

up by a volume

mechanism may be

follows:

8

a,

where

conforming pores which Avogadro When

a

sorption

may

volumes

where

of

whose

and

the

under

two

precipitation

substances

molecules

micropores

are

with Diane,

oriented

a

following

may

calculated

the

monolayer

*- s o r p t i v e e.g.

a

concentration

of

J

over

in t h e

be

surface

determined

IS

balanced

specific

dissolved substance

be calculated

of

value

soiution,S,is

saturated

number, W -monolayer

value

The

adsorption

are adsorbing a

2,4-d1bromphenol

sq

limiting

sorption

molar

volume.

para-chloraniline

surface

N-

formation,

and

nonuniformly

the

way:

the

by

reduction

method,

e.g.:

(rcb -values o f substances adsorbed a t t h e carbon and t h e black a,,#= vmL - volume o f the true micropores; s,b -

a t similar concentrations; specific

surface

of

between monolayer

vs,,,il

carbon

black.

S, , VmL and Vsmi values

The computed

and

(being filled up in a volume way) and

manner) are represented

reaching values comparable with

in Table

Vmi,

3.

the

studies on SCN and

distribution

vsmiz

It follows

; the

supermicropores a t 60-75% burn-off makes up over 2/3 Results o f

the

proportion

of

the

(filling

up

latter in

a

f r o m t h e data obtained of

the

volume-filling

Vsmi

scs synthetic carbons porous structure by

447 independent methods a r e r e p o r t e d i n our Papers ( r e f . 1, 2 , 7) total

data

allows

the

formation

of

in

detail.

The

t h e p o r e s o f d i f f e r e n t t y p e s and t h e i r

S u r f a c e deVelOPment, dependent on a c t i v a t i o n degree t o be o b s e r v e d

and

are

a

b a s i s t o conclude t h e f o l l o w i n g :

1.

SCN

and

Synthetic

SCS

a r e distinctive f o r t h e c o n s i d e r d b l e

carbons

development o f s u p e r m i c r o - and mesopores. T h e i r volume c o u l d be even

higher

carbons.

than

the

SorDtion

volume

o f the maJority o f comercia1 active

The g i v e n s o r b e n t s possess " l a t e n t "

mesoporous necessary,

comp~lrable or

macropores

accessible

via

the

whose e f f e c t i v e r a d i a a r e 35 nm (SCN) and 12 nm (SCS). i f

channels

t h e s i z e c o u l d be v a r i e d f r o m 3

up

to

210

nm

depending

on

the

i n i t i a l polymer s o u r c e s . 2.

Supermicropores

ones t h a t

filling

supermicropores

up

whose

For o r g a n i c substances, capacity

not

oniy

for

of by

the the

f i 1 1 ing

above s o r b e n t s a r e s u b d i v i d e d i n t o t h e n a r r o w volume

filling

mechanism,

and

t h e s y n t h e t i c carbons t h e r e f o r e have

a

biological

Widened

high

sorpt!on

low b u t a l s o f o r t h e m i d d l e and h i g h m i e c u i a r w e i g h t

m a t e r i a l s w h l c n 1 5 o f g r e a t s i g n i f i c a n c e f o r p u r i f y i n g a number specifically

the

i s p r imar i l y o c c u r r i n g by monoiayer f o r m a t i o n .

iiquids.

The

of

solutions,

w e i i developed s t r u c t u r e o f t h e l a r g e

s u p e r m i c r o - and mesopores Should l e a d t o h i g h k i n e t i c r a t e s o f s o r p t i o n on

s yn t h e t i c car bons

the

.

RE F E RE NCE S 1 V . V . S t r e l k o , T.G. Plachenov, N.T. K a r t e l e t a l . , P e c u l i a r i t i e s o f 5trUCtUt-e o f s p h e r i c g r a n u l e n i t r o g e n - c o n t a i n i n g s y n t h e t i c carbons p r e p a r e d f r o m r e s i n s , i n : Carbon a d s o r b e n t and t h e i r i n d u s t r i a l a p p l i c a t i o n s (Russ.), Nauka, Moscow, 1983, pp. 172-185. 2 V . V . S t r e l k o , Y . F , K o r o v i n , N.T. K a r t e l and A . M . P U Z Y , S t r u c t u r e - s o r p t i o n c h a r a c t e r i s t i c s o f a new s y n t h e t i c CarbOIlS SCS t y p e , U k r a i n i a n Chem. J. (Russ.), 50 (11) (1984) 1157-1162. 3 M.M. Dubinin, Micropore s t r u c t u r e o f carbon adsorbents. Report 1 . C 6 m n c h a r a c t e r i s t i c o f m i c r o - and s u p e r m i c r o p o r e s f o r s l i t - l i K e mOdel, P r o c e e d i n g o f USSR Acad. SCI., ser. chem. ( R u s s . ) , 8 (1979) 1691-1696. 4 A . M . Koganovsky, T . M . Levchenko, V . A . ~ iichenko, r ~ d s o r p t i o n o f resolved substances ( R u s s . ) , Naukova Dumka, K l e v , 1977. 5 0. K a d l e c , A . Varhanikova, A . Z u k a l , S t r u c t u r e o f p o r e s o f a c t i v e carbons p r e p a r e d by water-vapour and z i n c - d i c h l o r i d e a c t i v a t i o n , Carbon, 6 (4) (1970) 321-331. A . V . Mamchenko and A . M . K6qanOVSkY, A d s o r p t i o n o f r ? w l v e d 6 T. I . Yakimlva, substances i n super- and n a r r o w m i c r o p o r e s o f a c t i v e cartjons, J . Phys. Chem. (RUSS.), 5 4 (3) (1980) 741-743. 7 S . L . Medvedev, A . V . Mamchenko, N.T. K a r t e l and T . I . Yakimova, E s t i m a t i o n o f m i c r o p o r e s t r u c t u r e o f a c t i v e c a r b o n SCN t y p e aCC6rding w i t h a d s o r p t i o n o f r e s o l v e d substances d a t a , U k r a i n i a n Chem. J . ( R u s s . ) , 53 (6) (1967) 581-584.

This Page Intentionally Left Blank

F. Rodriguez-Reinosoet al. (Editors),Characterization of Porous Solids IZ 0 1991 Elsevier Science Publishers B.V.,Amsterdam

EVALUATION OF MICROPOROSITY IN ACTIVATED CARBONS WITH HIGH ASH (Cr203)CONTENT M.A. Martinez-SAnchez', J.M. Martin-Martinez', A.C. Orgiles- Barcelo', F. Rodriguez-Keinoso2 and M.J. Selles-Perez2. 'INESCOP. Asociacion de Investigacion de las lndustrias del Calzado y Conexas. Elda. Alicante. Spain. 'Departamento de Quimica InorgAnica e Ingenieria Quimica. Universidad d e Alicmte. Alicante. Spain.

INTRODUCTION Activated carbons are adsorbents with a wide pore size distribution and consequently the precise determination of their porous structure is a rather difficult task. Since activated carbons are essentially microporous, most work devoted to their characterization is centred around the determination of t h e microporosity. Several methods have been extensively used to analyze the adsorption isotherms of nitrogen and other adsorptives. The micropore volume filling theory of Dubinin has been successfully used but there are well-known problems when the micropore size distribution is heterogeneous (refs. 1,2). The n-nonane preadsorption technique has also been used in the last few years but it provides information only on narrow microporosity and t h e results are conditioned by interconnectivity network of t h e porosity (refs. 3,4). The t- and &-plot methods have also been widely applied using

different non-porous reference materials, the selection of which may be critical (refs. 5,6). The main objetive of the work described here is to evaluate the microporosity in

;I

series of activated carbons with increasing burn-off and

ash (Cr203) content using the isotherms on non-porous carbon and Cr'O, samples ;IS references in the a-plot method and the comparison with results obtained from the Dubinin theory and n-nonane preadsorption.

44Y

450

EXPERIMENTAL

Series P of activated carbons was prepared by carbonization in N, ( 1 123K) of chromium-tanned leather waste followed by activation in CO,

(1098K) for different periods of time to cover the 7-70% burn-off range (burn-off is included in the nomenclature of the samples). Adsorption of N,

(77K), CO, (27310 and n-butane (273K) and preadsorption of n-nonane were determined in conventional gravimetric systems in order to characterize the carbons.

The non-porous reference carbon was prepared by heat treating in Ar (2100K, 30 min.) an activated carbon prepared from olive stones; BET

surface area was 7.3 m2/g and the value for the C constant was 158. The N, adsorption isotherm for this carbon is shown in Fig. l(a). ‘The isotherm is in excellent agreement with the one proposed by Rodriguez-Keinoso et al

(ref. 7) and in good concordance for the relative pressure range 0.1-0.8 with

one published by Sing et al (ref. 8). Three different types of non-porous reference material for Cr,O, were selected: two from the literature, B2(280)110 and B3(880)2 (ref. 9) and the ashes obtained from sample P-70 (more of 90% of which is Cr,O,). The N, adsorption isotherms for the three samples are included in Fig. l(b), together with some relevant data. There is an acceptable agreement only in isotherms for t h e ashes and B3(880)2), specially up to a relative pressure of

0.8. RESULTS AND DISCUSSION

The N2 adsorption isotherms for carbons of series P given in Fig. 2 show the development of micro- and mesoporosity from P-7 to P-58 and a

decrease in adsorptive capacity thereafter. Table 1 shows that there is an important increase in ash content with increasing burn-off so that only a 31%

of

sample

P-70

is

carbon.

The

application

of

the

Dubinin-Radushkevich (DK) equation to the adsorption data of the N,

(77K), CO, (27310 and n-C,H,, (27310 for all carbons leads to the micropore volume (V,) values listed in Table 1. There is an increase in V,

451

up to 58% burn-off decreasing thereafter. On the other hand, increasing burn-off modifies the pore structure of carbons; thus, carbon P-7 has a narrow and uniform microporosity since V, (N,)

=

V, (CO,) and such a

Fig. 1. N, (77K) adsorption isotherms on a) Carbon Ap; b) different Cr,O, samples.

hD

10

Z

8

\ 4

E

v

F I 4

0

0

0.4

0.8

Fig. 2. N, (77K) adsorption isotherms of series P. b)P7 (X)P25 @P39 @P58 (o)P70.

(0)P64

452

porosity is not enterely accessible to n-butane. Increasing burn-off produces a widening of t h e microporosity - V, (n-butane)

- V,

(N2) > V, (CO,) - the

limiting case being P-64 since the difference decreases for P-70. TABLE 1

Micropore volumes (V,,, cm3/g) from DK equation CARBON

ash (%)

N,(77K)

C0,(273K)

n-C4H,,,(273K)

0.24 0.27 0.27 0.23 0.20 0.14

0.25

P7 P25 P39 P58 P64 P70

I

0.35 0.33 0.22

0.21 0.31 0.34 0.37 0.33 0.2s

Fig. 3 includes the a-plots for the adsorption of N, (77K) using the Ap non-porous carbon as reference material. The shapes of the plots indicate the widening of microporosity with burn-off and t h e plots for carbons with medium burn-off exhibit a clear deviation at large values of

the meaning

a 14 12 10 h

3

8

i f 5

v

c 4 2

u

I I

I

I! 1/

k 2 3

Fig. 3. N, (77K) a plots for carbons of series P. [Reference: Carbon Ap.] (O)P7 @P25 @)P39 @PSS @P64 (.)P70.

453

of which (i.e, the meaning of the pore volume deduced from its extrapolation) is not well established. The V, values (Table 2) deduced by extrapolation of t h e straight portion of t h e plots to

a =

0, follows the same

evolution deduced from the DR equation but they are slightly lower (up to 10%) in carbons of medium burn-off. The external surface areas deduced

from the corresponding slopes increases with burn- off up to P-58 remaining almost constant thereafter. Since the ash content of t h e samples increases

with burn-off (see Table 1 ) one could question the validity of using a reference material entirely made of carbon as stated in t h e IUPAC recornendations (ref. 10). TABLE 2 CY

method applied to carbons of series P

non-porous Ap I

non-porous B2(280)110

CARBON

V,,(cm”g)

0.25 0.28 0.32 P5 8 P64 P70

0.32 0.30 0.21

S,(rn2/g)

V,,(cm3/g)

4 71 91 I42 I44 134

S,(m2/g)

0.25

3

0.32

80

0.22

108

The reduced isotherms of the different reference materials (Fig. l(b)) show that carbon Ap is relatively coincident with the other three materials only up to a relative pressure of 0.4; sample B3(880)2 and the ashes are

rather coincident up to a relative pressure of 0.75 and both differ from the isotherm for B2(280)110. Fig. 4 includes the

CY

plots for carbons P-7, P-39

and P-70, using the three Cr,O, reference materials. For carbon P-7 the a-plots are similar and lead to the same value of V, (0.25 cm3/g) and S, (2-3 m2/g). The a plots for samples P-39 and P-70 are rather curved, especially

if t h e ashes o r B3(880)2 are used as reference material, t h u s making difficult the evaluation of V, and S,. One could expect the ashes to be the

454

2L OO

2

1

3

0

1

2

3

a

U

12

10 h

M

2 % &

-

E C

6 ' a A

4

2

0

2

1

3

U

Fig. 4. N, (77K) cx plots for carbons of series P. a) Reference: Cr,O, (ashes). b) Reference: B2(280)110. c) Reference: B3(880)2. @)P7 0) P39 QP70.

455

most adequate material if the chemical nature of the samples were the main factor in using the a-plot method (ref. 10) but the results of Fig. 4 show that this is not the case for the test samples (series P) used in this work. This means that the similarity in chemical nature of reference and test samples

is not the only factor to be considered. On the other hand, the reference

B2(280)110 seems to define less curved a-plots although there are two possible straight portions that can be drawn as in the a-plots of Fig. 3. The results given in Table 2 indicate that t h e results are, surprisingly, in very good agreement with those obtained using the carbon Ap as reference material. Preadsorption of n-nonane may help to evaluate t h e applicability of t h e a-plot method. Table 3 includes the data for samples P-39, P-58 and P-70, selected because their wide micropore size distribution. The V,' values (given by the difference at P/P,=0.80 between the isotherms without and with n-nonane adsorbed) are very similar to those given in Table 2 for CO, (27310, these values giving then the volume of narrow micropores. T h e relatively lower values of V, (volume of n-nonane retained by the samples) for P39 and P53 are indicative of porosity interconectivity typical of carbons with medium burn-off as shown elsewhere (ref. 1 I). The application of the a-plot method to the N, (77K) isotherms after n-nonane preadsorption - only Ap and B2(289)110 reference materials give non-curved plots - is shown in Fig. 5 and the corresponding values of V, and S, are included in Table 3. The plots are almost parallel to these for the

original carbons (Fig. 3 ) , indicating that the n-nonane preadsorption only affects to t h e narrow microporosity. Again, it is surprising that t h e two reference materials lead to similar values of micropore volume outside t h e narrow microporosity. The results of Table 3 clearly differentiate the

narrow (V,') and wide (V,") microporosity of the carbons. It is importan to note the similarity of V,'and V, (CO,) confirming the validity of adsorption of CO, at 273K to evaluate the narrow microporosity of activated carbons

(ref. 11). Series P, however, show a general behaviour which is not exactly coincident with other series of carbons previously studied (refs. 12-14) in the

456

TABLE 3 Results from n-nonane peadsorption. Volumes, (cm'/g); Surfaces, (m2/g) non-porous Ap 'ARBON

P39 P58 P70

0.24

0.29

0.23 0.13

0.25

0.03 0.08

0.14

0.08

a

85 120 109

1

non-porous B2(280)110

0.04 0.09 0.09

64 98 91

a

Fig. 5. N, (77K) a plots of some carbons of series P with preadsorbed nonane. a) Reference: Ap. b) Reference: B2(280)110. @)Pp39 QP58 QP70.

457

sense that the -method

usually yields somewhat larger values of micropore

volume than the DR equation for carbons with medium - to - high burn-off;

the results given here show a 10% larger values for t h e DR equation. Whether this is due to the uncertainty in the selection of the reference material is still a problem to be solved. I t is clear however that these results for series P show that the role of the reference material in the a-method is not as clear iis expected. Further work on samples of mixed chemical nature is needed.

REFERENCES 1

2 3

4

5 6 7 8 9 10

II 12 13

14

F. Rodriguez-Reinoso and A. I-inares-Solano. "Chemistry and Physic of Carbon". 1 (1989). Marcel Dekker. New York. J. Garrido, A. Linares-Solano, J.M. Martin-Martinez, M. Molina-Sabio, F. Rodriguez-Reinoso and K. Torregrosa; Langmuir 3, 76 (1987). A. Linares-Solano, J.D. Lopez-Gonzblez, J.M. Martin-Martinez, and F. Rodriguez-Reinoso; Ads. Sci. 'I'echnol. 1,123 (1984). F. Rodriguez-Reinoso, J.M. Martin-Martinez, M. Molina-Sabio, R. Torregrosa and J. Garrido; J . Colloid. Interf. Sci. 106,305 (19%). (1. Pierce; J. Phys. Chem. 72, 3673 (1968). S.J. Gregg and K.W.S. Sing. "Adsorption, Surface Area and Porosity". 2nd ed. Academic Press. London (1982). F. Rodriguez-Reinoso, J.M. Martin-Martinez, C. Prado- Burguete and B. Mc Enaney; J. Phys. Chem. 91,515 (1987). P.J.M. Carrott, R.A. Roberts and K.S.W. Sing; Carbon 25, 769 (1987). F.S. Baker, J.D. Carruthers, R.E. Day, K.S.W. Sing and L.J. Stryker. Disscusion Faraday Society 52, 173 (1971). Reporting Physisorption Data for Gas/Solid Systems. Pure Appl. Chem. 57, 603 (1985). F. Rodriguez-Reinoso. Pure Appl. Chem. 61,1859 (1989). J. Garrido, A. Linares-Solano, J.M. Martin-Martinez, M . Molina-Sabio, F. Rodriguez-Reinoso and K. Torregrosa; J. Chem. Soc. Faraday 108 (1987). Transactions I, €3, P. Gonzlilez-Vilchez, A. L,inares-Solano, J.D. Ldpez-Gonzlilez and F. Rodriguez-Reinoso; Carbon l7,44 (1979). J. Garrido, J.M. Martin-Martinez, M. Molina-Sabio, F. Rodriguez-Reinoso and R. Torregrosa; Carbon 24, 469 (1986).

a,

This Page Intentionally Left Blank

F. Rodriguez-Reinosoet al. (Editors), Characterization of Porow Solids ZI 1991 Elsevier Science Publishers B.V.. Amsterdam

459

INFLUENCE OF COAL OXIDATION ON COKE POROSITY

J.J. Pis, R. Menendez, J.J. Lorenzana, A.J. Perez, H. Marsh' and E. Romerol lnstituto Nacional del Carbbn, CSIC, Aptdo 73, Oviedo 33080, Spain. Northern Carbon Research Laboratories, Dept. of Chemistry, University of Newcastle upon Tyne, Newcastle upon Tyne, NEI 7RU, U.K.

SUMMARY This paper studies the effects of low temperature pre-oxidation on cokes from three bituminous coals of different, rank. The development of porosity was quantified by microscopy analysis and mercury porosimetry and results compared and evaluated in terms of coal rheological behaviour during heating and the mechanical properties of resultant cokes.

INTRODUCTION Several studies, using different approaches (refs. 1-7) are reported of coal oxidation. As yet, no unified approach exists to study coal oxidation and its effects on subsequent coal processing. The mechanism of oxidation is complex and appears to differ for temperatures below and above 70°/800C (refs. 8-11). Martin (ref. 10) suggested the formation of peroxides at the lower temperatures, whereas at the higher temperatures the initial formation of peroxides is followed by their decomposition and subsequent formation of carboxylic acids. The majority of studies of coal oxidation relate to coal carbonization. Coal oxidation is known to be detrimental to the coking properties of coals (ref. 12). The introduction of oxygen-functional groups into coal produces loss of mobile hydrogen and formation of cross-linkages within the coal, either during oxidation or during the pyrolysis of coal. These changes are responsible for loss of fluidity and consequently for changes in resultant coke structure and properties. Crelling (ref. 13) quantified effects of additions of weathered coals during co-carbonizations with fresh coals. A decrease in coke stability and an increase in coke reactivity and breeze content were observed as the proportion of weathered coal in the blend was increased. An increase of reactivity and a decrease of strength was also observed by Pis U .(ref. 14) in cokes from low temperature oxidised coals. Pre-

u.

u.

460

oxidation inhibits the development of anisotropy via a fluid phase, so increasing amounts of isotropic carbon (coke) (ref. 15, 16) or decreasing the size of the optical texture of the coke (ref. 17). Metallurgical coke strength is mainly controlled by the porosity contained within its structure (ref. 18). Decreases in coke strength caused by coal oxidation could be due to modifications of the porosity of coke. Optical microscopy linked to an image analysis system describes macroporosity in cokes (ref. 19). A limitation of the image analysis method is that the information obtained usually relates to a twodimensional image of the object. However, with controlled progressive polishing to remove known depths of the specimen, image analysis can give a three-dimensional assessment of porosity (20). Mercury porosimetry is a convenient method to characterise macropores in cokes, covering a wide range of mesoporosity and approaching the microporosity, 7.5 pm to 3.75 nm (at a pressure of 200 MPa). There are, however, several serious limitations (ref. 21), to mercury porosimetry. There is mercury contamination, advancing or retreating of mercury over the solid surface, and a measurement of pore entrance radii which may be smaller than the main body of the pore. This work describes the development of porosity in metallurgical cokes obtained from three series of coals with different extents of preoxidation. Mercury porosimetry and an optical microscope allied to an image analyser were used to measure porosity of cokes and results are compared. EXPERIMENTAL Three bituminous coals, of decreasing rank, with volatile matter content 17.8 to 32.2 wt.% were used. The most important characteristics of the parent coals are given in Table 1 and indicate that the Turon coal has the maximum fluidity. The three coals were ground to c 1 mm. The ground coals were placed in trays and oxidised in an oven, in air, at 140°C up to 24 h (Gregory 8 h). To carbonize the coals, 400 g of fresh and oxidised coal was placed in stainless steel cylinders (1 1.5 cm high, 9 cm internal diameter) within an electrical furnace and heated at 5 K min-l to a final heat treatment temperature of 1000°C. Strength and reactivity data of resultant cokes are published (ref. 14).

461

TABLE 1 Petrographic and chemical analysis of coals used Coals Chemical analvsis. wt.%. fdry) Volatile matter Ash Carbon Hydrogen Sulphur (N+O) (diff.) Plastic D roDert ies Arnu dilatation (Yo) Gieseler fluidity (ddpm) Petroaraohic Analvsis. % vol Vitrinite Exinite Semi-fusinite Fusinite

Alpheus

17.8 7.1 84.3 4.2 0.7 3.7 81 71 86.0 0.0 5.7 8.3

Turon

Gregory

26.7 9.5 79.4 4.8 0.9 5.4

32.2 8.2 77.3 5.0 0.6 8.9

161 2754 89.2 2.7 1.9 6.2

62 178 76.3

5.0 5.9 12.8

For image analysis, cokes from the three coals each with different extents of oxidation were mounted in blocks, polished and surfaces examined using a Vickers M41 microscope. The extents of porosity were determined by using an Optomax V image-analysis (I.A.) system. Using the "feature-analysis'' method the computer software of the I.A. system recognised differences in grey levels of a screen-image of porosity of the specimen. The computer is programmed to give several porosity features, such as total porosity, size distributions and shape, the number of pores examined, their mean area, perimeter, diameter, shape (form factor) and percentage of porosity, as a percentage of the total area, were obtained. Approximately 20 fields in each of the two blocks were examined providing a data base from about 40 fields of view. Resolution is limited to about 5 pm diameter. Coke porosity was also studied by mercury porosimetry; true For the (helium) and apparent (mercury) densities were measured. determination of the helium density a Micromeritics Autopicnometer 1320 was used. Apparent density to mercury was determined in a Carlo Erba Macropores Unit 120.

462

RESULTS AND DISCUSSION Figure 1 shows .the variation of coke porosity obtained by microscopic image analysis with oxidation time for the three series of cokes.

60

-

. 50 -

~I’-o

i$

Alpheus

.= 40%

v)

20

a

v /*

y

30 -

I ! 0

Turon

1

I

I

5

10

15

Oxidation time, h

Fig. 1. Variation of coke porosity determined by image analysis with oxidation time of parent coal. Cokes from Alpheus and Turon, of highest rank and highest vitrinite content, do not show a significant change; there is a slight decrease in porosity (38 to 32%) in the intermediate stages of oxidation (between 1 and 9 h) for Turon cokes, in agreement with results from mercury porosimetry (Figure 5). Cokes from Gregory coal, of lowest rank and minimum vitrinite content give a pronounced increase in porosity, 41% (fresh coal) to 63% (8 h oxidised coal). Figure 2 shows the variation of the mean perimeter of pores in the cokes with pre-oxidation time. Cokes from Alpheus coal develop a slightly smaller sized porosity. The size of the pores in Turon cokes does not change appreciably. For Gregory cokes the mean perimeter of pores increases from 540 pm (fresh coal) up to 660 pm (6 h oxidation).

463

TABLE 2 Abrasion indices of the cokes from oxidised coals (ref. 14). time oxidation (h) 0 1 2 3 6 8 12 18 24

.

Alpheus 5.8 5.8

Turon 5.3 6.0 5.9 6.1 6.4 7.1 12.3 42.3 70.3

6.1 7.0 7.5 9.9 28.7

/

700-

Gregory 6.7 6.3 6.7 6.6 26.4 38.6

Gregory

L

0) L

0)

E 'i 60 0 W

Q

A

c

0 W

4/

/ A

0

500-

0 Turdn

o - - * I

Alpheus 1

1

1

Fig. 2 Variation of pore size with oxidation time of parent coal from image analysis. A coke quality criterion is strength. Comparison of porosity determined by image analysis (Figure 1) with the coke strength (Table 2) shows increasing an abrasion index (decreasing strength) with increasing percentage porosity and pore size. Alpheus and Turon are the more resistant to oxidation; after 10 h strength has not significantly changed, being coincident with the evolution of total porosity (I.A.). Gregory cokes

464

undergo a dramatic increase in abrasion index at the same point.

This is in

agreement with the concept that large pores mainly control coke strength (ref. 19). Variation of porosity, studied by mercury porosimetry, of the three series of cokes, is shown in Figure 3. An increase in coke porosity is observed in the cokes from oxidised samples of Alpheus, Tur6n and Gregory coals, the largest being for Alpheus and Gregory coals. For Gregory coal the increase in porosity is very significant. In fact, for Turon coal a decrease in porosity is observed in the first stages of coal preoxidation, and after this a slight enhancement in porosity is produced.

0

5

10

15

Oxidation time, h

Fig. 3. Variation of coke porosity with oxidation time of parent coal, from mercury po rosimetry data. Figure 4 shows the cumulative pore volume distribution with pore diameter of Alpheus cokes, produced from pre-oxidised coal samples. Cumulative pore volumes of cokes from oxidised coal are larger than those of cokes from the fresh coal. A very similar evolution is observed for cokes from oxidised samples of Gregory coal (data not reproduced). The drastic reduction in plastic properties of coals, which occurs as a result of oxidation, seems to be the principal cause of this increase (ref. 22).

465

However, for cokes from preoxidised Turon coal, the situation is different (Figure 5). The sample preoxidised for 2 hours has a smaller cumulative pore volume than that from fresh coal. With 24 h of coal preoxidation the trend is reversed and cumulative pore volumes of cokes are now larger than those of cokes from the fresh coal. The Tur6n coal has the highest dilation when fresh, (Table l ) , the other two coals exhibiting lower dilations 8 and 62% respectively. The decrease in porosity of cokes from pre-oxidised Turon coal is similar to that observed by BCRA (ref. 23). The high volatile bituminous coals with a total dilatation between 115 and 280% were oxidised at 100°C until a dilatation of about 65% was reached. The largest decrease in porosity (determined by microscopy) was observed in coal with the highest value of dilatation. These conditions are close to those given in the initial stages of Tur6n. It could be inferred that in coals with high dilatation values (high values of plastic properties), a slight oxidation involves a reduction in macroporosity, perhaps due to a partial collapse of pores as a consequence of both swelling in the plastic stage and a decrease in the permeability of the plastic layers. The two techniques for pore analysis in cokes, Le. image analysis based on optical microscopy, and mercury porosimetry are complementary to each other. The limiting resolution of the optical microscope, in terms of the pixel density of the computer screen is about 5 pm. Pores with diameters of -5-200 pn are identified. Mercury porosirnetry provides information in the range of - 4 to 7500 nm (7.5 pm). It is reported by Patrick U .(ref. 19) that coke strength correlates well with porosity (5200 pm diameter). This study confirms the results of Patrick &A. The mercury porosimetry data indicate that significant changes also occur in porosities of diameter >7.5 pm, and this aspect has not been discussed significantly, before. Whether or not these changes simply parallel the changes in larger porosities, or possibly have an important role,within themselves, in crack generation and propagation when coke is stressed in the on-going study.

466

-9 9

0.1

0.09

7

, "

0.08

5

v

0.07

w

3

0.06

2

0.05

2

0.04

2w

0.0s

1 +

0.02

22

0.01

3

0

0

0.4

0,8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

log R (nm) Fig. 4. Cumulative pore volumes of cokes from preoxidised samples of Alpheus coal using mercury porosimetry.

7-

0.09

j

24 h

0

w [r

g ,,,

0.04

0.03

> F

0.02

3

0.01

a 1

I

s o

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

log R (nm) Fig. 5. Changes of cumulative pore volume of cokes from preoxidised samples of Turon coals using mercury.

467

CONCLUSIONS Coal oxidation produces an increase in porosity in resultant cokes for i) all three coals, when studied by mercury porosimeter, pores 50 nm. This classification is based upon adsorption criteria. In micropores adsorption is enhanced as a result of the overlap of dispersion forces from proximate pore walls. In mesopores adsorption occurs as on free surfaces until capillary condensation takes place as a result of interactions between adsorbate molecules on opposite pore walls. In macropores condensation takes place as in mesopores, but at relative pressures SO

close to unity that effects on isotherms are virtually impossible to detect. Thus, while

macropores are important in providing routes for adsorptives to gain access to mesopores and micropores, they effectively do not influence isotherms so that their structure cannot directly be investigated from adsorption measurements. Techniques for studying macropore structure in carbons such as porosimetry, gas transport and microscopy have been reviewed in ref. 2. There are many well-established methods available for estimating mesopore sizes in activated carbons, and other porous adsorbents, from adsorption isotherms using models for capillary condensation (ref. 3). Such methods are used routinely, both in the laboratory and in industry, and, in recent years, they have been incorporated into the software of commercial, automated, adsorption instruments, for example Omicron Technology Corporation's Omnisorp

477

478

systems and the Sorptomatic series instruments manufactured by Car10 Erba. It would be a highly desirable development in the characterisation of porous solids if reliable methods could also be devised for routine use in estimating micropore sizes. This paper is a review of methods for estimating micropore sizes from a single experimental adsorption isotherm. Laborious ways for probing micropore structure involving analyses of isotherms of adsorptives of different molecular size and shape are not directly considered. Standard analyses of adsorption isotherms for non-microporous solids usually involve models for adsorption on free surfaces, such as the Brunauer-Emmett-Teller (BET) equation (ref. 4), and models for capillary condensation such as the Kelvin equation (ref. 5). However these analyses are limited when applied to microporous adsorbents such as activated carbons. Adsorption on these solids at low relative pressures (p/ po = x less than about 0.4) predominantly involves the filling of micropores in which there is enhanced adsorption, rather than the formation of multilayers and subsequent capillary condensation. It is for this reason that the MP method (ref. 6) for determining micropore size distributions using a development of the BET model has failed to gain wide acceptance. Methods for determining micropore structure based on adsorption isotherm data, which offer the potential to be developed into programmes for routine characterisations, are reviewed in this paper. These methods involve analyses of a single isotherm based on the Dubinin-Radushkevich equation (ref. 7), a development of the potential theory of adsorption (ref. 8). Techniques for obtaining both single parameter estimates of micropore size and micropore size distributions are described. The estimation of micropore size distributions using intermolecular potentials in model micropores is also considered.

SEPARATION OF EQUILIBRIUM MICROPORE ISOTHERMS In the first stage of determination of micropore structure, adsorption measurements should be tested to ensure that the adsorption system is in equilibrium. This prevents including in analyses non-equilibrium adsorption data which in activated carbons result mainly from the effects of thermally activated entry into micropores via narrow entrances (refs. 9, 10). Once the system is in equilibrium, micropore isotherms may be separated from total isotherms, which may include adsorption on non-microporous surfaces, using techniques such as preadsorption (ref. 1 l), isotherm subtraction (ref. 12), t-plots (ref. 13) and as-plots (ref. 14). A comparative study of these methods for activated carbons with different extents of activation was made in ref. 15.

479

SINGLE PARAMETER ESTIMATION OF MICROPORE SIZE The Dubinin-Radushkevich @R) equation may be written as

v = V,

A 2 exp ( - -) PEO

where V is the volume of micropores filled at relative pressure x, V, is the total micropore volume, A = RT ln(l/x) is the adsorption potential or differential molar work of adsorption (R is the gas constant, T is absolute temperature),

p is the affinity or similarity coefficient

which depends on the adsorptive and E, is a characteristic energy which depends on the microporous structure of the adsorbent. It has been suggested (ref. 16) that the DR equation represents adsorption in homogeneous microporous solids, that is in these solids E, is a constant for all micropores. For microporous carbons an empirical, inverse correlation has been found (ref. 17) between E, estimated from adsorption data using the DR equation, and R,, the average Guinier radius of gyration, measured using small-angle x-ray scattering (SAXS) methods, which may be written as

E, =

14.68 (+-0.16)

I kJ moil

(2)

Rg

A single micropore size may be estimated from Rg assuming a simple pore shape, for example

R

g

b2

w2

2

12

=(-+-)

0.5

(3)

for a disc-shaped pore of width w and with two circular walls of radius b. Similar inverse correlations have been observed between E, and average micropore size less than about 1 nm estimated from gas-solid chromatography experiments (ref. 18) and using molecular probes and immersion calorimetry (ref. 19), for example

E ,= -

K W

(4)

480

where w is the width of the micropore determined from molecular probe studies and K is a weak function of E,.

In ref. 20 SAXS and molecular probe data were correlated with the

empirical expression

w = 6.64 - 1.79 lnEo

(5)

as shown in Fig. 1. In ref. 21 eqns. (2-5) were further analysed in terms of a disc-shaped model pore.

3.2 2.8

I

-

2.0 1.6 1.2

-

0.4 0.8

-

0.0

,

.

-

I

I

.

I

.

I

.

I

.

I

*

\

-

\

2.4

3

.

@@%

-

"'"\

OO.

-

\.

b. 0 Molecular probe data SAXS data I

.

I

.

I

.

I

.

I

,

\ : I

,

I

.

,

.

,

Fig. 1. Correlation of micropore width, w, in activated carbons with Dubinin's characteristic energy, E,, (eqn. 5 ) using data from small-angle x-ray scattering (SAXS) and molecular probes (after ref. 20). It is clear that eqns. (2-5) provide simple means of obtaining single parameter estimates of micropore size from a DR isotherm. However a number of criticisms can be made. First, concerning SAXS measurements, the poor grouping of some SAXS data (refs. 22,23) and the lack of a Guinier limit for some carbons (ref. 24) limit the statistical reliability and the extent of applicability of eqn. (2), as was acknowledged by its authors. Second, concerning molecular probe data, correlations such as eqns. (4) and ( 5 ) relate E, to micropore size using dimensions of the probe molecule. Such correlations do not take into account the compressibility of the

481

adsorptive molecule in the force fields between micropore walls. For example, it was estimated in ref. 25 that a correction of about 0.1 nm must be made for the compressibility of argon and xenon in micropores; thus, failure to correct for compressibility of the adsorptive molecule may result in a substantial overestimate of micropore size. Another criticism stems from the assumption that the DR equation is homogeneous and that therefore all of the carbons used to establish the correlations in eqns. (2-5) are also homogeneous as regards micropore sizes. This is certainly not the case; evidence for structural heterogeneity in activated carbons, that is micropores of different sizes, has been obtained from electron microscopy and molecular probe studies (refs. 26-28). Recently, in ref. 29, it has been suggested that for some activated carbons the DR equation results in a good fit to micropore adsorption data, even though molecular probe experiments indicate that the carbons are structurally heterogeneous. A further criticism of the methods for single parameter estimates of micropore size is that the DR equation frequently does not result in a good fit to equilibrium, microporous adsorption data. To represent such data the Dubinin-Astakhov @A) equation (ref. 30) has been proposed. This may be written as

v = V,

>"

A exp ( - PEO

where the DA exponent n 2 1 is an adjustable parameter which may be estimated from adsorption data; thus, the DR equation, eqn. (l), is the special case of the DA equation, eqn. ( 6 ) ,for n = 2. While fits to data are frequently better using the DA equation - which to some extent is statistically inevitable, since the DA equation has an extra adjustable parameter no physical significance for the exponent n has yet been determined, although values of n > 2

are found for adsorption in carbons with narrow micropores and n < 2 for wide-pore carbons. An alternative generalisation of the DR equation which gives improved fits to data, (see ref. 16), accounts for non-identical micropores (heterogeneity) by including a distribution function for Eo. Thus, if it is assumed that E, is correlated with pore size, as discussed above, then Stoeckli's generalised DR equation has some physical significance, unlike the DA equation. The generalised DR (GDR) equation is discussed further in the next section as a basis of estimating micropore size distributions.

482

ESTIMATION OF MICROPORE SIZE DISTRIBUTIONS The generalised Dubinin-Radushkevich eauation The GDR equation may be written as

V =

J

V, exp ( -

0

A >z f(Eo) dE,

PEO

where f(E,) is the probability density function (pdf) of E,, such that

f(E,) 2 0

non-negativity

(84

-

I 0

f(E,) dE, = 1

normalisation to unity

A simple treatment which anticipated the GDR (ref. 31) effectively assumed that f(EJ is the

sum of two Dirac &functions, that is there are two classes of micropore each with a different total volume and E,. The isotherm equation in ref. 3 1 may be written as

where the subscripts 1 and 2 refer to the two classes of micropore. Later, in ref. 32, f(Eo) was related to the normal distribution which gives the following isotherm equation

V = Voexp ( - B, y ) exp ( -

y2

T)

1 - erf(u) 1 2

where B, is proportional to the mean squared value of E,, y and u are functions of B,, A, A and P, A is the standard deviation of the distribution of B, and erf(.) is the error function. The application of these two approaches to activated carbons was considered in ref. 33. Recently (ref. 34) different model functions for f(E,) were considered, and applied to a

483

number of different carbon adsorbents. For example one isotherm equation for heterogeneous microporous adsorption (ref. 34) may be written as

where q and m are parameters of a gamma-type distribution for B, [the same B, as in eqn. (lo)]. There are severe statistical difficulties in estimating f(Eo) from the GDR because it is a linear, one-dimensional Fredholm integral equation of the first kind (ref. 3 3 , in which the total micropore isotherm is the driving term, the DR equation, eqn. (l), is the kernel and the energy distribution, f(E,), is the unknown function which is sought. Equations of this kind are illposed or improperly- or incorrectly- posed which means here that many different energy distributions will, on substitution in the GDR, give similar total isotherms. Therefore fidelity of the model to the data does not in itself validate an estimate of the energy function. The problems of ill-posedness for equations of the same form as the GDR were discussed in ref. 36. The simplest and most widely used way to 'solve' equations similar to the GDR is to assume that the unknown function is defined by a mathematical formula, which is selected to allow direct integration to give an analytic function for the total isotherm. The parameters of the isotherm are then estimated, for example by regression analysis, and substituted back into the formula for the unknown function to define a 'solution'. Eqn. (10) is used in this way; the method in ref. 31 and many of those discussed in ref. 34 also use this approach. However, it should be noted that, almost exclusively, the assumed form of the energy function is selected for the mathematical convenience of being able directly to integrate the GDR. Ill-posedness still remains in that different functions f(E,) will give similar isotherms. It is a matter of discretion as to which of the range of possible parametric energy distributions is finally chosen to represent heterogeneity, since any pdf on the interval [0, -) may be given as an estimate of f(Eo), provided that the model total isotherm fits the data, say to within experimental error. Estimation of micropore size distributions from the eeneralised Dubinin-Radushkevich eauation If a monotonically decreasing function, E, = h(z), between E, and micropore size z is known or assumed then from f(E,) the pdf of z, g(z), is given by

484

g(z) =

I

f[h(z)]

This function, which satisfies constraints equivalent to eqns. (8a, 8b) for f(E,), characterises the structural heterogeneity of the microporous adsorbent (at absolute temperature T, with respect to the adsorptive X and adsorbent Y). The domain of g(z) will be limited by the size of the smallest micropores in Y which molecules of X can enter, zmin,and the largest pores in which micropore filling occurs, zma. This imples that in addition to the constraints on f(E0) in eqns. (8a, 8b), the domain of f(E,) will also be constrained to some finite range [h(z,,,),

h(zmin)]. This is both a useful additional constraint on the choice of functions for

f(E& selected for analytical solutions of eqn. (7) and a useful test for numerical solutions. Thus for a given estimate of f(E,) the method for obtaining micropore size distributions involves: (i) the determination of a relationship between E, and pore size z, E, = h(z), and (ii) the calculation of the micropore size distribution g(z) from f(E,,) using eqn. (12). The first of these steps is the more important; the second is a simple mathematical wnsformation. A relationship equivalent to eqn. (2) has been used recently to estimate pore size

distributions in activated carbons (ref. 37), see Fig. 2.

0

1

2

3 w/nm

4

5

6

Fig. 2. Some examples of distributions of the width, w, of slit-shaped micropores in activated carbons for benzene adsorption at 293 K (after ref. 37).

485

Clearly the criticisms above of the use of eqn. (2) for obtaining single parameter estimates are also applicable to its use in obtaining pore size distributions. In particular, if the DR equation is not homogeneous, then it should not be used as the kernel of the GDR equation, eqn. (7), since E, does not correspond to a single-valued adsorption energy in pores of uniform size and therefore the relationship E, = h(z) is not valid. The probable bias in micropore size distributions estimated using methods which involve this inconsistency needs to be explored.

GENERAL DISCUSSION Here wider consideration is given to models of adsorption and structure in activated, microporous carbons. This general discussion leads to suggestions for future work in this area. Methods based upon the Dubinin-Radushkevich equation

An assumption which is made in both single parameter and distribution estimates of micropore size is that there is a single energy factor, E, from the DR equation, which is associated with each micropore. This much simplifies the probable physical nature of micropores in activated carbons, which involves: (i) spacial variations in adsorption energy, due to different degrees of adsorption energy enhancement across the pore width (important in wide pores), and to different pore shapes [for example in wedge-shaped pores (ref. 38)l and (ii) the inherent energetic heterogeneity of carbon surfaces, due to surface defects, heteroatoms, etc. Thus for a single micropore E,, or more precisely E = PE,, represents some measure of the energy of interaction between the adsorptive and the adsorbate. These simplifications are compounded when relationships, which have been criticised here, are estimated between E, and pore size, z. The generalised adsorption isotherm (GAI) for heterogeneous, microporous solids (ref. 36) may be written as

c

where N(p), the total isotherm (the driving term), is the total amount adsorbed at p, n(p, E), the local isotherm (the kernel), is the amount adsorbed at p in micropores charactensed by an

486

energy E, and F(E) (the unknown function which is sought) is the pdf of E. Thus the GDR is a special case of the GAI where amounts adsorbed are expressed by volume and the local isotherm is the DR equation (so that

E=

E,).

The GAI gives the DR equation when a

Langmuir kernel is approximated by a step-function (the condensation approximation) and it is assumed that the energy function is a Rayleigh distribution of the molar isosterk heat of adsorption q. This interpretation, in which the DR equation is heterogeneous, may explain its success in representing adsorption on a wide range of solids (ref. 39). Deviations from the DR equation represented by the DA equation, may also be accounted for by the condensation approximation, but with different forms of F(E). As for the DR methods reviewed here, in principle pore size distributions may be estimated from the GAI for a selected local isotherm if a function

E = G(z)

relating

E

to pore size z is

known or assumed. The present authors have used the Langmuir isotherm (ref. 40)and the n-layers BET equation (ref. 41). together with suitable distribution functions for the heat of adsorption q, to represent adsorption in activated carbons. In a wider context many different combinations of local isotherm and energy distribution functions in the GAI have been applied to carbons and other microporous adsorbents (ref. 34). However, no analyses have yet been

published to relate heats of adsorption, or other characteristic adsorption energies, to pore size, other than those reviewed here which are based on the DR equation and methods based upon intermolecular potentials discussed below. Further work in this area is much needed.

A different and promising approach to estimating micropore sizes is based on intermolecular potentials. Using Lennard-Jones intermolecular potential functions, relations between the potential Q in model micropores of width w or radius r and the location of a single molecule in the pore were derived (ref. 25). The minimum potential Qo(z) was noted to decrease with increasing pore size z = w or r, eventually reaching the value of the minimum for a free surface, $,(-).

as expected from qualitative considerations of the superposition of

dispersion forces from proximate pore walls. It was shown in ref. 42 for many different activated carbons that E = PE, from the DR equation was proportional to the difference between the heat of adsorption in micropores at low surface coverage, qmi,and the heat of adsorption on a (nonporous) graphitised carbon black, 9,. From this correlation, assuming that qmi/qg= Qo(z)/Qo(-), a model, inverse correlation between E, and z for the adsorption of argon in micropores was derived (ref. 20) based upon the 10:4 intermolecular potential

487

function for slit-shaped pores obtained in ref. 25, see Fig. 3. In principle it would be possible to calculate similar correlations for different adsorptives, and for different pore shapes, which could be used to transform distributions of E, from the GDR into pore size distributions. While this has not yet been done, the advantage of this approach compared with that involving correlations between E, and pore size from SAXS or molecular probe data is that a value of E, is related to a single pore size. A further extension of this approach would be to explore correlations between energy parameters of different local isotherms, for example the heat of adsorption in the Langmuir equation, with model potential functions.

36 .

-

32

-

28

-

24

-

8

20-

9

-

I

I

I

I

I

I

&

' 16 mo 12

-

8 4 -

0

Fig. 3. Variation of Dubinin's characteristic energy, E,, for argon adsorption in carbons with the width, w, of model, slit-shaped micropores (after ref. 20). The calculations in ref. 25 for model micropores only consider interactions between a single adsorptive molecule and the walls of the model micropore. They do not account for interactions between adsorptive molecules and so cannot model the process of micropore filling. Recently (ref. 43) results from molecular modelling studies were reported for the adsorption of nitrogen on porous carbons in which both adsorptive-adsorbent and interadsorptive interactions were considered. Using an approximate theory of inhomogeneous fluids known as mean-field theory, a function p(p, w) was derived (ref. 43) which relates the

488

density p of nitrogen in pores to pressure and pore width. This function was subsequently used as the kernel in the GAI, eqn. (13), and parametric estimates of pore width dismbutions were obtained. A significant aspect of this work is that it applies to adsorption both in micropores and in mesopores. Another important observation is that adsorption in a single micropore is not a smoothly increasing function of pressure; rather, for a pore of width W, a steep rise in amount adsorbed occurs at a critical pressure which is related to w. Although this recent molecular modelling approach in the estimation of pore sizes (ref. 43) is an improvement on any of the other pore size estimation methods considered in this paper, a notable shortcoming is the extensive computations required to derive the density function p(p, w), which are beyond the capability of current microcomputers attached to commercial adsorption equipment. Also, the micropore size distributions presented in ref. 43 have a lower limit of 1.3 nm which is determined by the lowest relative pressure, x =

at which

experimental measurements were made. To obtain meaningful size distributions for smaller micropores using this method will require precise measurements of adsorption isotherms at very low relative pressures (in principle this is a general requirement of any method for obtaining micropore size distributions from adsorption data). Also, for general applicability, density functions for different adsorptive-adsorbent-temperature systems would need to be determined and, in addition, the sensitivity of the method to the form of the integrated adsorptive-adsorbent potential (which involves factors such as pore shape and pore wall thickness) needs to be explored.

CONCLUSIONS The estimation of mesopore size distributions from a single adsorption isotherm is a widely accepted technique. Because understanding of adsorption in micropores is much poorer than adsorption in wider pores, methods for estimating micropore sizes from a single adsorption isotherm have not been widely accepted. Single parameter estimates of micropore size based upon correlations between the Dubinin's characteristic energy, E,, and measures of pore size using small angle x-ray scattering and molecular probe studies have been reviewed. Although these methods are easy to use, they are subject to a number of criticisms, central among these being the assumption that the DR equation is homogeneous, that is it applies to adsorption in pores of uniform size. There is much evidence that activated carbons are heterogeneous microporous solids and this can be accounted for by using the Ceneralised DubininRadushkevich (GDR) equation to obtain a micropore size distribution. A problem with this

489

approach is that the GDR equation is ill-posed, which means that many different pore size distributions can give similar fits to adsorption data. A different and promising method for estimating micropore sizes is based on intermolecular potentials. This approach has the advantage of being based upon sound physicochemical principles and can avoid the empiricism of methods based on the DR equation. However, at present considerable computing power is required to obtain pore size distributions using this method.

REFERENCES 1

2 3 4 5 6 7. 8 9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24 25 26 27

K. S. W. Sing, D. H. Everett, R. A. W. Haul, L. Moscou, R. A. Pierotti, J. Rouquerol andT. Siemieniewska, Pure Appl. Chem., 57 (1985) 603. B. McEnaney and T. J. Mays, in: H. Marsh (Ed.), Introduction to Carbon Science, Butterworths, London, 1989, pp. 153-196. S. J. Gregg and K. S. W. Sing, Adsorption, Surface Area and Porosity, 2nd edn., Academic Press, London, 1982. S. Brunauer, P. H. Emmett and E. Teller, J. Amer. Chem. SOC.,60 (1938) 309. A. Zsigmondy, Z. Anorg. Chem., 71 (1911) 356. R. Sh. Mikhail, S. Brunauer and E. E. Bodor, J. Colloid Interface Sci., 26 (1968) 45. M. M. Dubinin and L. V. Radushkevich, Proc. Acad. Sci. USSR, 55 (1947) 331. M. Polanyi, Verb. Deutch. Physik. Ges., 16 (1914) 1012. F. A. P. Maggs, Research, 6 (1953) 513. P. Zwietering and D. W. van Krevelin, Fuel, 33 (1954) 331. S. J. Gregg and J. F. Langford, Trans. Faraday Soc., 65 (1969) 1394. S. Ali and B. McEnaney, J. Colloid Interface Sci., 107 (1985) 355. B. C. Lippens and J. H. de Boer, J. Catal., 4 (1965) 319. K. S. W. Sing, Chem. Ind., (1968) 1528. J. M. Martin-Martinez, F. Rodn'guez-Reinoso, M. Molina-Sabio and B. McEnaney, Carbon, 24 (1986) 255. H. F. Stoeckli, J. Ph. Houriet, A. Perret and U. Huber, in: S. J. Gregg, K. S . W. Sing and H. F. Stoeckli (Eds.), Characterisation of Porous Solids, Society of Chemical Industry, London, 1978, pp. 31-39. M. M. Dubinin and H. F. Stoeckli, J. Colloid Interface Sci., 75 (1980) 34. H. F. Stoeckli, Chimia, 28 (1974) 727. H. F. Stoeckli and F. Kraehenbuehl, Carbon, 22 (1986) 297. B. McEnaney, Carbon, 25 (1987) 69. M. M. Dubinin, Carbon, 26 (1988) 97. M. M. Dubinin and G. M. Plavnik, Carbon, 2 (1964) 261. M. M. Dubinin and G. M. Plavnik, Carbon, 6 (1968) 183. A. Janosi and H. F. Stoeckli, Carbon , 7 (1979) 465. D H. Everett and J. C. Powl, Chem. SOC.,Faraday Trans. 1,72 (1976) 619. J. R. Fryer, Carbon, 19 (1981) 431. H. F. Stoeckli, A. Lavanchy and F. Kraehenbuehl, in: J. Rouquerol and K. S. W. Sing (Eds.), Adsorption at the Gas-Solid Interface, Elsevier, Amsterdam, 1982, pp.201-209.

490

28 29 30 31 32 33 34 35 36

37 38 39 40 41 42 43

R. W. Innes, J. R. Fryer and H. F. Stoeckli, Carbon, 27 (1989) 71. H. F. Stoeckli, Carbon, 27 (1989) 962. M. M. Dubinin and V. A. Astakhov, Adv. Chem. Ser., No. 102 (1971) 69. T. I. Izotova and M. M. Dubinin, Zh. Fiz. Khim., 39 (1965) 2796. H. F. Stoeckli, J. Colloid Interface Sci., 59 (1977) 184. M. M. Dubinin, in: S. J. Gregg, K. S. W. Sing and H F Stoeckli (Eds.), Characterisation of Porous Solids, Society of Chemical Industry, London, 1978, pp. 1-11. M. Jaroniec and R. Madey, Physical Adsorption on Heterogeneous Solids, Elsevier, Amsterdam, 1988. G. F. Miller, in: L. M. Delves and J. Walsh (Eds.), Numerical Solution of Integral Equations, Clarendon Press, Oxford, 1974, pp. 175-188.. B. McEnaney and T. J. Mays, in: K. K. Unger, J. Rouquerol, K. S. W. Sing and H. Kral (Eds.), Characterisation of Porous Solids, Elsevier, Amsterdam, 1989, pp. 151-161. M. Jaroniec, R. Madey, J. Choma, B. McEnaney and T. J. Mays, Carbon, 27 (1988) 77. D. A. Wickens, Carbon, 28 (1990) 97. B. McEnaney, Carbon, 26 (1988) 267. B. McEnaney, T. J. Mays and P. D. Causton, Langmuir, 3 (1987) 695. T. J. Mays and B. McEnaney, in: Proc. 18th Biennial Conference on Carbon, Worcester Polytechnic Institute, Worcester, MA, U. S. A. , 1987, pp. 88-89. H. F. Stoeckli and D. Morel, Chimia, 34 (1980) 502. N. A. Seaton, J. P. R. B. Walton and N. Quirke, Carbon, 27 (1989) 853.

F. Rodriguez-Reinoso et al. (Editors), Characterization of Porous Solids I1 0 1991 Elsevier Science Publishers B.V., Amsterdam

A Comparative Using Benzene

491

Study of t h e Porous S t r u c t u r e of A c t i v e Carbons and Water Adsorption, Immersion Calorimetry and Liquid Chromatography

R.H.Raaeke; P.Bruckner C 8 n t r 3.1 I fi s t i t u t e o f F 11 y si c a 1 C e m i s t r y U 1 1 9 9 B e r l i n . Germany

ABSTRACT Some m e t h o d s f o r p o r e s t r u c t u r e a n a l y s i s h a v e b e e n p r e s e n t e d : T h e a d s o r p t i o n o f b e n z e n e and t h e e v a l u a t i o n of isotherms through t . h s Dubiinin - R a d u s h k e v i c h e q u a t i o n , t h e e s t i m a t i o n o f immersiijin h e a t s i n benzene, t h e a d s o r p t i o n of w a t e r a t r e l a t i v e p r e s s u r e s of h=C).6 a n d 1 . O , t h e s i z e e x c l u s i o n l i q u i d c h r o m a t o g r a p h y w i t h t r a c e r s o f ( d i f f e r e n t m o l e c u l a r d i a m e t e r s and t h e one - p c i n t . adsorption o f n i t r o g e n . S i x a c t i v e c a r t o n s are i n c l u d e d i n t h e i n v e s t i g a t i o n s . I t is n o t p o s s i b l e t o o h t a i n r e l i a b l e v a l u e s w i t h t h e s i m p l e w a t e r a d s o r p t i o n m e t h o d . The r e s u l t s o b t a i n e d w i t h s ~ t h e r m e t h o d s a r e compared w i t h p e r f o r m a n c e s o f adsorpt.ion of p h e n o l from aqueous s o l u t i o n s as o b t a i n e d from m e a s u r i n g e q c i i i b r i a and column d y n a m i c s . I t is shown, t h a t t h e r a n k o f the r e s u l t s of p u r e s t r u c t u r e a n a l y s i s i s t h e same as f r o m t h y dynamic e x p e r i m e n t s .

THE PROBLEH The p o r o u s s t r u c t u r e o f a c t i v e c a r b c l n s i s t.he d e f i n i n g f a c t o r of t h e i r a d s o r p t i o n p e r f o r m a n c e : The p o r e d i a m e t e r d i s t r i h u t i o n d e t e r m i n e s t h e a d s o r p t i o n elnergy a n d t h e r e f o r e , t h e slope of adsorpt.iiln i s o t h e r m , whereas i n mainly microporous c a r b o n s t h e m i c r o p o r e volume l i m i t s t h e a d s o r p t i o n c a p a c i t y a t t h e h i g h e r end of the a d s o r p t i v e cconcentration. Furthermore, the chemical ~::ijmpositori o f t h e c a r b o n s u r f a c e i n f iuences ttie s e l e ~ t i v i t y ot adsorption, e.$. t h e c o m p e t i t i o n of t h e w a t e r a d s o r p t i o n w!lrn w o r k i n g i n s q u e o u s s o l u t i o n . However, h e r e o n l y t h e s t r u c t u r - a 1 cRrGoris a r e t a k e n i n t o a c c o u n t . p r o p e r t i e s of F o r s j t u d y i n g t h e s t r u c t u r e o f c a r b i ~ n ss e v e r a l c o n m e r c i a l equipn l z n t s h a v e treer: d e v e l o p e d , e . g . f o r t h e BET measuren1ent.s w i t ; - I n i t r o g e n 2 t 77 K , t h e m e r c u r y p o r o s i m e t . r y e t c . However, in the f o l l c i w i n p w e s h a l l p r e s e n t some m e t h o d s b a s e d o n t h e o r e t . i c a l snrl e x p e r i m e n t r l f i n d i n g s which are convenient, f o r i n v r s t i g a t i n g t h e c o n n e c t i o n between t h e c a r b o n s t r u c t u r e and the adsorption p e r f o r m a n c e : A d s o r p t i o n o f b e n z e n e and e v a l u a t i o n of isotherms t h r o u g h t h e D u b i n i n - K a d u s h k e v i c l h e q u a t i o n /l,,’! t h e e s t i m a . t i o n o f immersion h e a t s i n benzene / Z / , t h e o r p t i o n of water at r e l a t i v e p r e s s i i r e s o f h = 13.6 a n d 1 . 0 the zize exclusion 1i q u i d chromatography w i t h t r a c e r s of d i f f e r e n t molecular diameters / 4 / and t h e o n e - p o i n t a d s o r p t . i c n o f n i t r o g e n / s / . ~

492

THE THEORETICAL BACKGROUND OF HETHODS

1. : T h e p h y s i c a l a d s o r p t i o n o f b e n z e n e O n 9 t i v e carbon f r o n l t h e g a s p h a s e i s a s s u m e d t o o c c u r a s VOlume f i l l ng o f t h e m i c r o p o r e s and a l a y e r - b y - l a y e r c o v e r a g e of t h e masopare s u r f a c e .rklePefcr!re t,fIe ~ . ~ l l : . ~3.ii,l ~ ~ - 8.dst:~ lt. i I-! t.ti r 81 i :c Y I I p ~ I:! e x t r a c t e d f r o m t h e t o t a l a d s o r b e d amount a < ! ~ j :

/6/.

I

a m i

= a -

* 9s

S,e

(l?.

D u b i n i n e t a l . e v a l u a t e d t h e amount Q a a d s o r b e d p e r u n i t s u r f a c e area from t h e benzene i s o t h e r m measured frJr t h e n o n p o r o u s reference adsorbent / 7 / . we, however e s t i m a t e d t h e s p e c i f i c s u r f a c e 3 r e a Sme o f t h e m e s o p o r e s f r o m t h e a d s c r p t i o n i s o t h e r m s t u d i e d / 8 / . I n c a l c u l a t i o n s of t h e meso p o re s i z e d i s t r i b u t i o n a n d t h e s p e c i f i c s u r f a c e a r e a Sme i t h a s b e e n a s s u m e d t h a t t h e p a r a l l e l - s i d e d s l i t s 3 r e r i g i d and t h e s i z e d i s t r i b u t i o n d o e s not e x t e n d c o n t i n u o u s l y f r o m t h e m e s o p o r e i n t o b o t h t h e m a c r o p o r e the a n d m i c r o p o r e r a n g e . We h a v e u s e d t h e d e s o r p t i o n b r a i n c h of h y s t e r e s i s l o o p o f t h e i s o t h e r m f o r t h e c o m p u t a t i o n . The p r o c e d u re of B . F . R o b e r t s /9/ h a s been a p p l i e d . I n t h i s c o m p u t a t i o n , is a r i g o r o u s a p p l i c a t i o n of t h e c o n c e p t o f s i m u l t a n e o u s which c a p i l l a r y c c n d e n s a t i o n and m u l t i l a y e r a d s o r p t i o n , t h e adsorbed v o l u m e i s f i r s t e x p r e s s e d a s a f u n c t i o n o f p o r e s i z e ; t h e n it. i s c o n v e r t e d t o p o r e v o l u m e . A s t a n d a r d t - c u r v e /lo;/, which r e p r e s e n t s t h e b e n z e n e a d s o r p t i o n or1t.o n o n p o r o u s c a r b o n b l a c k s , has been used f o r c o r r e c t i o n f o r m u l t i l a y e r t h i c k n e s s .

We h a v e f i t t e d t h e a d s o r p t i o n d a t a t o t h e D u b i n i n - R a d u s h k e v i c h - e q u a t i o n /'ll/', u s i n g t h e n o n l i n e a r L e v e n b e r g - M a r q u a r d t method ,/12/: ~ N I I

=i WO/ B Eo

with

+ e x p ( -E

Vmol

(

1

=

k

=

x

= =

1


i . e . [condensed a d s o r p t i v e o f n o r m a l l i q u i d d e n s i t y . T h i s c a n n o t kie t r u e when t h e p o r e s a r e o f m o l e c u l a r d i m e n s i o n s . F u r t h e r m o r e , i.t is n e c e s s a r y t o i n t r o d u c e t h e c o r r e c t i o n f o r a d s o r p t i o n in mesopores f o r o b t a i n i n g t h e real v a l u e s of t h e micropore parameters . T h a t ' s why t h i s p r o b l e m n e e d s f u r t h e r s t u d y . : The s i z e e x c l u s i o n c h r o m a t o g r a p h i c m e a s u r e m e n t s w i t h t r a c e r s of d i f f e r e n t m o l e c u l a r d i a m e t e r s g i v e i n f o r m a t i o n on t h e d i f f e r e n t i a l p o r o s i t y , i . e . on t h e p o r e d i a m e t e r d i s t r i b u t i o n / 4 / . T h e e v a l u a t i o n of t h e r e t e n t i o n times t R , i y i e l d s t h e p o r e volume , a v a i l a b l e t o t h e r e s p e c t i v e tracer i:

4.

Pi

t R . 1

=

(

1

t

m

*

x i t h H = column l e n g t h .

pi * i K i w

+ 1)

)

*

H / w

linear velocity,

void r a t i o i n c n l u n i n m . ani! Kx = a d s o r p t i o n c o n s t a n t of i (Henry c o n s t a n t ) .

i7),

m= packed t o equilibrium

Wa u s e d a c e t o n e a s c a r r i e r a n d t h e t r a c e r s b e n z e n e , e t h y l b e n z e n e , ! i r x y ? b e n z e n e a n d d e c y l b e n z e n e r t h e i r d i a m e t e r s were t a k e n f rom H a l a s z a n d V o B t e l ./18,/.A f t e r c a l i b r a t i o n w i t h t e x t u r e d a t a o b t a i n e d by b e n z e n e a d s o r p t i o n o n t o c a r b o n TVAX a n a v e r a g e d e q u i l i b r i u m c o n s t a n t Ki is e s t i m a t e d f o r e a c h of t h e t r a c e r s i . TVAX h a s b e e n u s e d a s a t y p i c a l c a r b o n w i t h a n a v e r a g e d e v e l o p e d m i c r o p o r o u s a n d m e s o p o r o u s s t r u c t u r e . The r e s u l t s f o r 5 c a r b o n s are shown i n F i g . 1 . 5. : A very convenient t o o l f o r rapidly characterizing adsorbents i s t h e one - p o i n t a-dsorption of n i t r o g e n / 5 / . However, in m i c r o p o r e s t h e a d s o r p t i o n d o e s n o t occur by monolayer completing b u t t h r o u g h voliume f i l l i n g . T h e r e f o r e , n o a b s o l u t e v a l u e s b u t a r a n k of a d s o r p t i o n c a p a c i t y may b e o b t . a i n e d .

495

Comparison of methods for investigation of pore structure

micropore volume I

I

0-0

F i g . 1.

LC;

I

+a

t

I

I

I

I

.?

1

benzenp ads. .o-owater ads,o-*NN?l-ptjo+imm. calor. i benzene

496 Phonolisotherms at

B"C ( f i t t e d

with the Redlrh-kterson-Eq.)

10 '

F i g . 2.

CONCLUSIONS performances of phenol a d s o r p t i o n from aqueous s o l u t i o n s as o b t a i n e d f r o m m e a s u r i n g e q i l i b r i a /19/ and column d y n a m i c s /ZO/ 3re compared w i t h t h e r e s u l t s of p o r e s t r u c t u r e a n a l y s i s . The f o l l o w i n g r a n k of t h e performances h a s been o b t a i n e d from dynamic > . per ime n t;s ( c a l c u l a t e d an w e i g h t b a s i s , s e e F i g . 2 and Table 3 ) :

'Yhe

5-

F i l t r s s o r b 4013

',

EHT 1323

TVAX

AC 3

Hydraffin 71

f i . v s c a r b o n s a r e i n c l u d e d c o n s i s t e n t l y i n al: investigatian-. I n 'l'ahle 3 , t i 5 0 j i s t h e h a l f t i m e o f t h e p h e n o l tlre3iitiirclugr! c u r v e , b i s t h e bed d e n s i t y and t < 5 U j / G are t h e r r e c t e d f o r differences i n d e n s i t y b r e a k t l i r o i ~ g hh a l f t i m e s , The b r e a k t h r o u g h h a l f times a r e taken a s a measure f o r t h e adsorptioi-t equilibrium constants.

9nly

Tf3BLE 3 :

Dynamic pl7ertol a d s o r p t i o n efflcipncy of

carbqn;

497

F i g . 3.

t'( h

fron! p h e n o l i s a t h e r m m e a s u r e m e n t s i F i g . 3 ) i s t h e s3n:e as from d y n a m i c e x p e r i m e n t s . WRK i s a w a t e r g u r i f i c a t i o r ! c a r b o c made from h i g h t e m p e r a t u r e l i g n i t e coke,, w h i c h !]as t h e l o w e s t ad-,.,4rpLion c a p a c i t y i n a c c o r d m c e w i t h i t s h i g h pheriol n u m b e r . Dynamic measurenien?s h a v e r i o t h e r r . p e r f o r m e d w i t ! i W2E. A?l

methods of c h a r a c t e r i z i n g t h e psrouz s t r u c t u r e mierep-re vg3lumes and c i f i c s u r f a c e areas), w i t h tire e x c e p t ior? o f the w a t e r a d s c r p t i o n a t r e l a t . i v e p r e s s u r e s o f h = O . S a n d 1 .U, g i v e t h e same t r e n d s b u t . n o t e q u a l r e s u l t s . T!je simplest methods f o r , w i t h s m a l l e s t . expense i n t i m e aind s u r f a c e area e s t i m a t i o n s q u i p m e r t t , a r e the i m m e r s i o n c a l o r i m e t r y w i t h b e n z e n e .r!d t h e one -. p o i n t a d s o r p t i o n o f n i t r o g e n a t 77 K . 2 0 t h m e t h o d s g i v e t k e same t e n d e i n c i e s f o r all c a r b o n s , In c o c p a r i s o n t u t h e s e m e t h o d s , t h e time e f f o r t f o r b e n z e n e adscrl:t i o n measureme:-:t and 1i q u i d c h r o m a t o g r a p h y 1s m u c h h i g h e r , H o w e v e r . t h e r e s u l t s o f t h e I s t % c ? : met.hods h s v r a l s o t h e t e n d e n c i e s b u t f a i l tc. z g r e r a b s o l u t e ly. We t h i n k t h a t d i f f e r e n t a s s n m p t i o n s u n d e r l y i n g the several methods l e s d t o t h e s e d e v i a t . i o n s , e . g . t h e cummorily u s e 1 1 r i W i d : s l i t - p o r e iiiodel may n o t b e f u l f i l l e d i n e v e r y c a s e . 8~

I

b e s t cavbon i n phenol adsorpt.iun performsnce is F i l t : a s o r h f o i i . i w e d b y BIiT a n d AG 3 , w h e i - e a s Hy 71 a n d WPK ( f r o n ; t h e i i i l i b r i u n i i s o t h e r m f o r t h e p h e n o l f r o m a q u e o c s s o l u t . i c ~ n , 5:ee e 3.t. t h e l o w e r e n d range . F i l t r a s o r b !;as t h e ! a ~ . g e , s t vc:lume wo and 3 ~!i.c-diump o r e w i d t h d . OI-~ t ] i e oc,i)er hand, WKK a n d Hy 71 h a v e s m a l l e r p o r e v ~ l u r n e . A d d i t i o n a i ? y , . WfiK h a s a very large r n i c : r o p o r e w i d t h #:see F i g . 1:. 11-1 s j y n a l ~ l i c m e a s u r e m e n t s T V A X h a s a p p a r e n t l y a s m a 1 . l r ~ p e r f c ; r m a r I c e a:: My 1'' ? - ) L i t . t h i s i s d u e t u its l o w b e d d e n s i t y . w h e r e a s t.he cc!rrec.ted for d e 1 i s i t . y p e r f o r m a n c e ( T a b l e 3 ) i s c o m p a r a b l e w i t h t h e HHT sam;.le. 'l'tie

400

I t is e v i - l e n t , t h a t t h e r a n k c f t h e r e s u l t s c;f p o r e s t ~ - ~ ~ : t u r - e a n a l y s i s , e x c e p t t h o s e o b t a i n e d from t h e w a t e r a d s o r p t i o n method, is t h e same 8 9 f r o m . d y n a m i c e x p e r i m e n t s . 'I'iie p r e s e n t s t u d y s h 0 k . r ~ t h e u s e f u l n e s s o f t h e d e s c r i b e d m e t h o d s for i n v e s t i g a t . i n g t h e c o n n e c t i o n b e t w e e n p o r e s t r u c t u r e a n d a d s o r p t i o n perft2rnlarlg;..j.

498

ACKNOWLEDGEMENT i w i s h t o t h a n k my c o w o r k e r s D r . G . B u n k c , i ~ h e X i . ~ l n gC. h . ( - ; h e n , i n g , E , ~ h i ~ -a nj d ~ ~ r s f. i . J u n g f o r t h e i r c o n t r i b u t i o n s .

REFERENCES 1 2 3

4

5 6 7

8 9

10

11

M.M. D u b i n i n . H.F. S t o e c k l i , J _ . C o l l . I n t e r f a c e b- c!1., 7.5 (l!380) 34. K . H . R a d e k e , Carbon, 22 i 1 9 8 4 j 473 G . A . A n d r e e v a , N . S . P o l y a k o v , M.M. D u b i n i n , K.M. N i k o l a e v , E . A . U s t i n o v , I z v . A . N . USSR. s e r . c h h. (1981) 2188 G. B u n k e , D . G e l b i n , O e m . E m . S c i . 40 ( i 9 8 5 j 2079 R . H a u l , G . Duembgen, chat^ Ina. T e c.b. 3% ( 1 3 6 0 ) 343 S . J . G r e g g , K . S . W . S i n g , B d s o r w t i o n . S u r f a c e Area a n d Forositv. 2nd A c a d e m i c P r e s s , L o n d o n . 1982 M . M . Q u b i n i n , Carbon, 23 ( 1 9 8 5 ) 373 F . B i l l i g , F . B r i i c k n e r , GroRmann. 8.. L e p p i n . M . , S c h m i d t , D . , Seltmann, U . , Thiede, E . , Tern-. i n p r e s s B . F . R o b e r t s , J . C o l l . I n t e r f a c e S c i , , 23 ( 1 9 6 7 ) 2G6 V. F o n e c , Z . K n o r , S . C e r n y , &&-o.n on cv ' R u t t e r w o r t h s , p . 5 5 8 , London ( 1 9 7 4 ) M . M . D u b i n i n , i n D . A . C a d e n h e a d ( E d i t o r j , -5s in d Membrane--SciencE, V o l . 5 , p p . 1 - 7 0 . Academic Fress, New Y o r k , ( 1975) W. H . P r e s s , B . F . F l a n n e r y . S . A . T e u k o l s k y , W. T . Vetterling, cipes. Cambridge U n i v e r s i t y F r e s s , C a m b r i d g e ( 1 9 8 8 ) p p . 5 2 5 -528 H . F . S t o e c k l i , L z v . A . N . USSR. s e r . c ( 1 9 8 1 ) 62 F . E . B a r t e l l , R . M . S u g g i t t . J . Phy.s. Chela_,, 58 ( 1 9 5 4 ) 3 6 L . R o b e r t , U.S o c . U.F r w., ( 1 9 6 7 ) 1 4 7 F . B r i i c k n e r , R . S . V a r t a p e t j a n , Chem. T e c h n , , i n p r e s s L . G u r v i t s c h . J . PhS O C .fiu.s.s-> 47 ( 1 9 1 5 ) 805 J . Halasz, P . V o g t e l , A n g c w - L - E S L l , 19 ( 1 9 8 0 ) 24 A. S e i d e l , E . T z s c h e u t s c h l e r , K . H. Radeke, D . G e l b i n , C h e 0 . E n s 3LLL, 40 119851) 215 G . R e s c h k e , K . H. f i a d e k e , E . G e l b i n , Ckiem. En ,b, S c i . , 4 0 (1986) 549

a.

u.

-

12 13 14 15 16 I7

18 19 20

3

m.

.?

F. Rodriguez-Reinoso et al. (Editors),Characterization of Pororrs Solids ZI 0 1991 Elsevier Science Publishers B.V., Amsterdam

499

MERCURY POROSIMETRY OF POROUS GLASS AND ACTIVE CARBON PRELOAUED

WITH N-DECANE OR WATER

H. Lentz and Y. Zhou*) Universitat-GH Siegen. Fachbereich 8. Postfach 101240. D-5900 Siegen (FRG)

ABSTRACT The possibilities of high-pressure mercury porosimetry for the investigation of preloaded porous solids a r e demonstrated using a mesoporous glass and a micro-porous active carbon preloaded with n-decane or with water. The volume of pores partially loaded with a non-interacting liquid decreases linearily with t h e increasing preload. Special interactions e.g. in t h e system porous glass and water a r e indicated a s a deviation of such regular behavior. If t h e pore radius i s calculated at a constant contact angle, t h e radius will formally increase with increasing preload. Hence a smaller contact angle has to be assumed for t h e solid preloaded with liquid in o r d e r to explain t h i s paradoxical result.

INTRODUCTION

Porous solids have been investigated with completely empty pores or - in o r d e r to s t u d y t h e s t a t e of t h e filling liquids

-

with completely filled pores.

However, in practice t h e r e a r e numerous examples of partly-filled

porous solids.

An investigation of these systems may also contribute t o a n understanding of t h e properties of adsorbed phases. The facilities of high-pressure mercury porosimetry for t h e investigation of preloaded porous solids will be demonstrated using mesoporous glass and rnicroporous activated carbon preloaded with n-decane o r with water (ref. 1). APPARATUS The a p p a r a t u s used w a s a non-commercial porosimeter which enabled u s to make accurate measurements between 0.4 and 2000 bar corresponding to a pore radius between 2

.

10'

and 3.6 nm. The porosimeter consists of a steel cylinder

and a piston forced into t h e cylinder by a r a m (ref. 2 ) . The p r e s s u r e and ttie volume change were measured accurately by a s t r a i n gauge and b y the displacement of t h e piston respectively. Up to a p r e s s u r e of 5 bar t h e mercury was forced into t h e porosimeter by a n air pump and t h e amount of mercury was determined accurately by a balance (ref. 3). Fig. 1 shows schematically t h e

*)

present address: Dr. Zhou, Yaping Si-Ji-Zun / 13-3-201 Tianjin University Tianjin / China

500

--------- 1 Vacuum

,

r--I

L_ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _J

Fiq. 1. Mercury porosimeter (Schematic), u p p e r part: p r e s s u r e from 0.4 to 5 bar, bottom part: p r e s s u r e u p t o 2000 bar 1 ) High-pressure vessel, 2 ) Piston, 3 ) Ram, 4 ) Support of ram, 5 ) Displacement indicator, 6 ) Strain gauge, 7 ) Electronic for strain gauge, 8) X-T-recorder, 9 ) Valve, 10) Balance, 11) Mercury storage vessel, 12) PVC-tubes, 13) Bourdongauge, 14) Vacuum meter, 15) Valve, 16) Needle valve, 1 7 ) Safety valve.

a p p a r a t u s in some detail. The measured p r e s s u r e P w a s used to calculate the pore radius r by t h e Washburn equation (ref. 4 )

The values taken for t h e surface tension and t h e contact angle were 0.48 Nm-I and 1400 respectively. The reproducibility of t h e measurements i s f 0.5 %. An estimation of the accuracy is difficult. However, t h e comparison with o t h e r methods indicates

2 5 % for t h e total pore volume and f 12 % f o r t h e pore radius.

For sorption measurements a volumetric method w a s used. In a thermostated constant volume of nearly 300 cm3 the mole numbers of different gas fillings have been determined by a n accurate piezo resistive p r e s s u r e gauge. POROUS MATERI.4LS The porous materials used were characterized b y adsorption and desorption measurements with nitrogen in a constant-volume-apparatus

and b y titrat.ion

(MotLlau-Fisher (ref. 5 ) ) with t h e same liquids as used later f o r the preloading u p to the complete filling of the pores.

501

0.8

1

1.2

1.6

1,4

13 [g r

Fig. 2. Pore size distribution of mesoporous glass 1: Sorption 2: Porosinietrv The mesoporous glass (CPG-10 240 A from Fluka) should have a pore volume of 960 mm"g-1

(Fluka); we measured 986 mm3g-l

(porosimeter u p t o 2000 b a r ) ,

990 rnr11~g-l (final sorption at P/Po = 0,98), 1040 mm3g-l

(titration with

n-decane). The pore radius should be 12.1 nm a n d w a s measured t o be 17.1 nm (porosimeter, 0 = 140°) and 15.5 nm (desorption 6,7) as demonstrated in Fig, 2. The surface a r e s should be 88.1 m2g-I

( B E T ) , 121 m2g-I

and w a s measured t o be 98.3 m2g-1

(Dubinin-Kaganer) and 116 m2g-l (porosimeter (ref. 8 ) ) .

The active carbon (Chevron) h a s a total pore volume (ref. 4 ) of 1150 mmsg-1 (n-decane or benzene) or 940 mm3gg-l (water). The porosimeter can measure 690 mm3g-l and the sorption of nitrogen (refs. 9, 10) results in 710 mm3g-1. The pore radii rarige between 0.38 and 8 nm with a peak a t 0.4 rim as calculated

from nitrogen adsorption (Y).The surface a r e a b y g s s adsorption measurements i s

502

1750

37

n1Lq-I

(Dublnin-Kaganer) a n d t h e s u r f a c e wetted by mercury (ref. 8 )

IS

mLg-1.

4000

-

n -..

m

G

5

3000

L

01

? 9 a 2000

1000

-I

10

10'

102

103

105

10' rlnm)

Fig. 3. Pore size distribution of activated c a r b o n 1: Sorption 2: Porosimetry PRELOADING The porous solids have been preloaded with liquid b y esposing t h e material t o t h e v a p o r of t h e boiling liquid o r by wetting t h e material i n t h e liquid a n d removing t h e liquid partially by heating i n a d r y chamber. Both methods dive t h e same results. The f i r s t one was mainly used for small amounts of preload a n d t h e partly-drying-method

w a s used f o r high preloads.

R E S U L T S AND DISCUSSION a ) Mesoporous glass

Fig. 4 s h o w s a plot of t h e experimental points of t h e pore volume as function of t h e n-decane load f o r mercury intrusion in the mesoporous glass. The e s t r u s i o n ( n o t shown i n Fig. 4 ) shows a h y s t e r e s i s in p r e s s u r e b u t releases t h e i n t r u d e d mercury almost CGmpktely.

503

160[

I40C 1701 1 ooc

BOO

600

400

/ 200

0 10‘

1O2

10’

JOY

los r (nml

Fig. 4. Pore size distribution of mesoporous glass with different contents of n-decane 0: 0; 1: 0.083; 2: 0.200; 3: 0.308; 4: 0.520; 5: 0.734 g n-decane/g glass. The pore volume as determined from t h e dashed line in Fig. 4 is indicated by open circles resulting in t h e s t r a i g h t line 1 in Fig. 5. The points measured by extrusion (indicated by c r o s s e s ) deviate only a little from t h e intrusion points. The volume of pores partially loaded with n-decane decreases linearily with the increasing preload and can be calculated from t h e m a s s and t h e density of the liquid a s demonstrated by the dashed line 2 in Fig. 5. The shift in the s t e p s in Fig. 4 corresponds t o a n increasing

pore r a d i u s

calculated a t constant contact angle with increasing preload ( s . Fig. 6). To explain this unrealistic result a change in t h e contact angle has to be assumed. The s t e p of c u r v e 1 in Fig. 4 will be in congruence with t h e s t e p of c u r v e 0 if the contact angle for t h e preloaded glass i s 135O instead of 140°. All f u r t h e r curves of Fig. 4 can then be interpreted as a successive filling of t h e pores. A detailed interpretation of t h e results i s only possible, if better information of the contact angle o r at least i t s change is available.

504 120 0 1100

500

-

~

LOO 300

~

-200

0

0,l

0.2

0.3

0,L

0,s

0.6

0.7

0,8 0,Y

1,0

1J

(g n-decane/gCPGl

Fig'. 5. Pore volume of mesoporous glass as function of t h e c o n t e n t of n-decarle 1: I n t r u s i o n ( 0 ) 2: Calculated from P,V,T-data, x extrusion

(g n-decane/gCPG)

Fig. 6 . Pore r a d i u s of mesoporous glass as function of t h e c o n t e n t of n-decane ( 0 = 140 OC)

505 If water is used as a preload of t h e nresoporous glass, t h e main features of t h e r e s u l t s of t h e non-interacting liquid n-decane remain. However, t h e pore volume d e c r e a s e s u p t o 0.1 g water p e r g mesoporous glass only a little (Fig. 7). This behaviour c a n probably be explained by a t i g h t e r packing of the f i r s t 2 or

3 molecular layers. Also t h e extrusion c u r v e ( 3 in Fig. 71 d i f f e r s widely from the intrusion c u r v e ( 1 in Fig. 7 ) f o r t h e porous glass p a r t l y loaded with water, t h u s

a relatively high amount of mercury is not released from t h e glass - wat,ei. system. b ) Microporous Active Carbon The r e s u l t s f o r preloaded activated carbon will b e described in sonre detail elsewhere (ref. 11) a n d c a n h e r e be summarised only shortly. The measured r e s u l t s of t h e pore volume occupied by m e r c u r j from 0.4 t o

2000 b a r as a function of t h e amount of loaded liquid

c a n naively be compared

with t h e difference between t h e pore volume a n d t h e volume occupied b y t h e

0

0.1

0.2

02

0.4

5.5

0.6

0,7

0.8

0.9

1.0

1.1

1.2

( g water / g CPG

I

Fig. 7. Pore volume of mesoporous glass as function of t h e water content. 1: Intrusion 2: Calculation from P,V,T-data 3: Extrusion

506

:oo

\

'

\ \ \ \

n

n7

V,L

n~ ",-

nh ",V

n R ",-

in t,"

1.,L.

I.,?

1. 6 I-

(g waterlg carbon I

0

0.2

0,4

0,6

0,8

1to

12

(gn-decane/g carbon1 Fig. 8. Pore volume (0.4-2000 b a r ) of microporous activated c a r b o n as function of t h e water ( 0 ) or n-decane (x) content. Total pore volume: water; n-decane 1: I n t r u s i o n 2: Calculated from P,V,T-data

507

liquid a t this temperature and a p r e s s u r e of 2000 bar (Fig. 8). There is a large deviation due to the fact t h a t t h e total pore x*olume of the microporous actix7ated carbon i s larger than t h e pore volume determined by mercury u p to 2000 bar.

A preload with n-decane and with water leads to similar results. Thus t h e r e is no indication of special interaction between liquid and solid phase.

Obviously the liquid occupies f i r s t t h e small pores outside the measuring range of the porosimeter. I n the pore range covered by t h e instrument t h e hehaviour is regular and can be predicted. ACKNOWLEDGEMENT

We thank the Deutsche Forschungsgemeinschaft and t h e Fonds d e r Chemischeri Industrie for financial support. REFERENCES 1 1'. Zhou, Thesis, Siegen, 1989. 2 G. Holzel and H. Lentz, High-Temp.-High Pres., 12 (1980) 113-116. 3 K. Becker, H. Lentz, E. Hinze, G. Nover and G. Will, Ber. Bunsenges. Phys. Chem., 90 (1986) 833-838. 4 E. W. Washburn, Phys. Rev., 17 (1921) 273-283. 5 A.Y. Mottlau and N.E. Fisher, Anal. Chem., 34 (1962) 714-715. 6 A. Wheeler, in: Catalysis 2: Fundamental Priciples, Reinhold, New York, 1959. 105-165. 7 S.J. Gregg and K.S.W. Sing, @sorption, Surface Area and Porosity, 2nd. Ed., Academic Press, London, 1982. 8 H.M. Rootare and C.F. Prenzlow, J. Phys. Chem., 7 1 (1967) 2733-2736. 9 S. Brunauer, R . S L Mikhail and E.E. Bodor, J. Colloid Interface Sci, 24 (1967) 451-463. 10 S. Brunauer, Z. Phys. Chem. N.F., 64 (1969) 54-63. 11 Y. Zhou and H. Lentz, in preparation for "Carhon".

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F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids I1 0 1991 Elsevier Science Publishers B.V., Amsterdam

SORPTION OF HYDROCARBONS IN SILICALITE-1 AND NaY ZEOLITES

J.A. Hampson, R.V. Jasra and L.V.C. Rees Physical Chemistry Laboratories Imperial College of Science and Technology and Medicine London SW2 2AY INTRODUCTION The separation of binary gas mixtures by pressure swing adsorption (PSA) is becoming more widely used as a clean, efficient method in its own right, but as energy becomes more expensive it will become even more widely used for economic reasons. In the design of a PSA system it is essential to use an adsorbent which has optimum performance, both equilibrium and kinetic, for the specific binary mixtures to be separated. Zeolites could be excellent adsorbents for many PSA systems as they are so easily modified to produce the required performance characteristics. The cations in the zeolite channels, for example, can be easily exchanged to increase/decrease the electric fields present in the channels: the Si/Al ratio of the zeolite can be readily changed to give increased/decreased cation densities in the channels: the zeolite framework can be chosen to give the optimum channel dimensions to provide the required adsorbent/adsorbate intraction energies. However, the literature contains little information on the effects of such modifications on the adsorption of binary mixtures. The results to be reported in this contribution are part of a large programme designed to establish the preferred zeolite surfaces for the separation of n-hydrocarbons from branched hydrocarbons and their unsaturated counterparts. These studies are, of course, also of fundamental significance in the study of adsorbent/adsorbate interactions. EXPERIMENTAL The adsorbents used in this study were silicalite-l (l), the pure silica analogue of ZSM-5 (2), containing only trace quantities of aluminium and NaY zeolite with the unit cell formula of Na,,[ (A10,)56(SiOz),36] 260H,O The adsorbates usedwere ethane, propane, ethene and propene supplied by ARGO International with purities of at least 9 9 % . The sub-atmospheric sorption data have been obtained using an isosteric method originally developed by Bulow et a1 ( 3 ) . The apparatus used in the present studies is fully described by Graham et a1 (4). The high pressure sorption data were collected using a Sartorius electronic high-pressure ultra-microbalance, model S3D-P. RESULTS AND DISCUSSION The isosteres for ethane, ethene and propane sorbed in NaY are shown in Figures 1, 2 and 3 respectively. The linearity of The isosteres is excellent over the temperature range covered, 1.e. 15-5OoC, and they could be extrapolated over a wider temperature range with confidence. The isotherms calculated from these isosteres at 25OC are given in Figure 4 and the heats of

509

510 12

Fig. 1. Ethane/Na-Y isosteres. Sorbate loadings (in mmol/g): (1) 0.0947; (2) 0.1639 (3) 0.3038; (4) 0.4238; (5) 0.5239; (6) 0.6062 (7) 0.6984; (8) 0.8867; (9) 1.0500; (10) 1.2980 Po = 1 Pa

11

10

9

\ a

-

8

z

7

6

5

311

3 3

3:2 10311

3 4

K-I

8

Fig.2. Ethene/Na-Y isosteres. Sorbate loadings (in mrnol/g): (1) 0.0256; (2) 0.0612; (3) 0.0972; (4)0.1366; (5) 0.1967; (6) 0.2701; (7) 0.3697; (8) 0.4580; (9) 0.5448 Po = 1 Pa

7

6

-a

, a

z

5

4

3 1

3.3

3 2

103/T

3 4

K-'

Fig.3 Propane/Na-Y isosteres. Sorbate loadings (in rnmol/g): (1) 0.3106; (2) 0.3524; (3) 0.3939; (4) 0.4362 (5) 0.5025; (6) 0.5865; (7) 0.7186; (8) 0.7878; (9) 0.9098: (10) 0.9842 Po = 1 Pa

8

I

as a -

z

7

6

3:1

3.2 I03/T

3.3 K-'

3.4

511 3

JI 2

+.

Propane

#.

Ethene

*.

Ethane

rn

n

0 E \

m 01

:

1

U

0 10

0

20

36

50

40

P r e s s u r e / kPa

Fig. 4. Sorption isotherms in Na-Y at 25°C

40

38

34

--

32

3

30

E 0

\

=.

I

28

s,

Propane

I.

Ethene

if.

Ethane

26

24

22

20 0

I

2

c o v e r a g e / mmolg-'

Fig.5. Isosteric heats of sorption in Na-Y

6

512

adsorption obtained from the slopes of the isosteres are shown in Figure 5. Because of the high quality of the isosteric data the isotherms in Figure 4 are accurately defined. As expected the sorption of propane is much greater than that of ethane at 25°C. The initial slopes of these isotherms are linear within the experimental error of the data. It is interesting to note that the ethene isotherm at 25°C is almost coincident with the propane isotherm at lower equilibrium pressures indicating a balance in the sorption potential of a double-bond and a CH, group. However, the heats of adsorption in Figure 5 show significant differences between the sorption energies of ethene and propane. Both ethane and propane show heats of adsorption in Figure 5 which increase with increasing loadings due to sorbate-sorbate interactions over the range of 0-5 molecules per supercage covered in these measurements. This increase is only -2 kJ mol-’

for ethane but is -9 kJ mol-‘ for propane. The smaller ethane molecule seems to be able to detect some heterogeneity in the sorption sites of the NaY supercages at very low loadings (

U 0

0.2 0.1

J 0

0.0

C

1

2

3

4

5

6

7

8

1

0

10

20

30

40

50

Pressure / kPa

Fig.6. Sorption of hydrocarbons in Na-Y and Silicalite-1 at 25°C

40

36

Ethane/Propane !i0/50

34

Coverage / mmolg-'

Fig.7. Isosteric heats of sorption in Silicalite-I

6

514

shown in Figure 7. The heat of sorption of ethane and propane in silicalite-1 is -7 kJ mol-' greater than in NaY at low loadings. The heat of sorption of ethane in silicalite-1 stays sensibly constant with coverage up to 1 mmolg-' (i.e. 1.5 molecules per intersection) and thus differs from the small, gradual increase found with the sorption of ethane in NaY (see Figure 5). It is easier for sorbate-sorbate interactions to occur in the large supercages of NaY compared with the much smaller cavities at the intersections in the channel network of silicalite-1. In silicalite-1 the heat of sorption seems to decrease slightly on increasing the loading from 1.5 to 2.5 molecules per intersection. The sorption of ethane, ethene, propane and propene has been determined in silicalite-1 at pressures up to 25 atmospheres and temperatures between 0% and 70'C. The differences in the sorption behaviour of these sorbates can be seen in the 25% isotherms presented in Figures 8(a-d) . All of these isotherms are quite rectangular in shape with maximum loadings of -2 mmolg-'at 25OC (i.e. -3 molecules per intersection). Figures 8a and 8b show the enhanced sorption potential of propane and propene over ethane and ethene respectively at lower coverages but at higher loadings the silicalite-1 channels and intersections can accommodate a slightly larger number of the smaller sorbate species. Figure 8c shows that the sorption of ethane and ethene is v'ery similar at lower coverages but at higher coverages, higher equilibrium pressures there is a small enhancement in the sorption of the smaller, unsaturated ethene molecules. A similar behaviour is shown in Figure 8d in the sorption of propane and propene but there is a much smaller enhancement in the amount of the smaller unsaturated propene sorbed over the saturated, larger propane at higher equilibrium pressures. Finally, the sorption of an ethane/propane mixture in silicalite-1 was studied in the isosteric system. From the resulting isosteres the isotherm at 25'C was calculated for a constant sorbed phase composition of 49.35 mole % ethane and 50.65 mole % propane. This isotherm may be compared with the corresponding pure ethane and propane isotherms in silicalite-1 in Figure 9 and can be readily seen to be intermediate in behaviour to these two pure component isotherms. While determining these mixture isosteres the composition of the gas phase was determined with the on-line mass-spectrometer at temperatures between 25 and 50% and at four different loadings of the sorbed phase of the same composition as given above. The gas phase compositions are given in Figure 10. The separation = X,Y,/X,Y,, where X,, X, and Y,, YE are the mole factor, Q fractions of propane and ethane in the sorbed and gas phases respectively can be calculated from the data given in Figure 10. For a mole fraction YE of 0.895 for ethane in the gas phase a separation factor a, of 8.75 is obtained while for Y of 0.87 Q is 6.87. These experiments indicate that silicalike-1 is an excellent adsorbent for the separation of ethane/propane mixtures over the temperature range 25 to 5OoC.

515

+

* 0

Ethane Propane

1 ,

o Ethene

U

I

# Propene

'ressure/kPa

+ Ethane

o Ethene Pressure/ kPa

-

-

m

P . W

m m

,

L W

0 >

*

Propane # Propene 0

C.T--. $00 200

300

do

-500

Pressure/kPa

Fig.8 High pressure sorption isotherms in Silicalite-l at 25°C

516 2

+

Ethane

o

Propane/Ethane

x

Propane

1

50/50

-

0

10

I

20

30

Pressure / CPa

Fig.9 Sorption isotherms in Silicalite-1 at 25°C

0.30 m D

c a m O1

0.63

c 4

=, r 0

2

0.88

u

c)

LL

r

0.87

0.86,

30 Temperature

40 OC

Fig.10. Mole fraction of ethane in gas phase as a function of temperature. Sorbed phase 50 mol% ethanelpropane sorbed in Silicalite- 1

517

At 25OC Figure 10 shows that the separation factor is nearly independent of loading in the range covered by the experiments varying only between 8.30 and 8.75. The isotherm at 25OC in Figure 9 for the mixture is only slightly curved up to loadings of -50% of that found at high pressures (see Figure 8a). In a PSA separation of such a mixture operating, say, between 1 atmosphere and vacuum Figure 8a shows that the propane isotherm is too rectangular at 25OC for an ideal PSA separation process. However, Figure 10 shows that the separation factors decrease only slightly with increasing coverage from 7.5 to 6.9 at 5OoC. These separation factors are still perfectly adequate for PSA separations and at this higher temperature the propane isotherm is now less rectangular and more suitable for the PSA method. CONCLUSIONS The preliminary results presented in this paper indicate that silicalite-1 could be used for the separation of ethane/propane mixtures, although the temperature may need to be raised to 5OoC to give more ideal performance. The results obtained also suggest that ethene/propene mixtures could also be separated in a similar manner with silicalite-1. NaY zeolite seems, also, to be capable of giving excellent separations of the above mixtures and would seem to be the better sorbent for the separation of ethane/ethene and propane/propene mixtures. REFERENCES 1.

E.M. Flanigen, J.M. Bennett, R.W. Grose, J.P. Cohen, R.L. Patton, R.M. Kirchner and J.V. Smith, Nature 271, 512 (1978)

2.

G.T. Kokotailo, S.L. Lawton, D.H. Olson and W.M. Meier, Nature, 272, 437 (1978).

3.

M. Bulow and P. Lorenz, "Fundamentals of Adsorption 11" (Ed. by A. Liapus) Engineering Foundation, New York, USA 1987, p.119.

4.

P. Graham, A.D. Hughes and L.V.C. Rees, Gas Sep. Purif. 3 , 56 (1989).

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F. Rodriguez-Reinosoet al. (Editors),Characterization of Porous Solids II 0 1991 Elsevier Science Publishers B.V., Amsterdam

519

HOW CAN AN ADSORPTION SYSTEM SHOW PHASE TRANSITION A case study on the adsorption of p-xylene in ZSM-5 Dongfeng Pan' , Alfons B. Mersmann Departmenl B of Chemical Engineering, Technical University of Munich POB 20 24 20, D-8000 Miinchen, FRG.

ABSTRACTS The intermediate plateau and the hysteresis loop of p-xylene/ZSM-5 isotherm are explained by using recent crystallographical results of adsorbate-loaded crystals. Two adsorption mechanisms - the occupation of low energy adsorption sites and the crystal lattice mediated interaction between the adsorbate molecules - are found to be responsible for the phenomena. Based on these considerations, qualitative model calculations are carried out and the results agree with their experimental counterparts. INTRODUCTION For physical adsorption systems which are concerned in this study, there are two classical answers to the title question: Capillary condensation and strong adsorbate-adsorbate attraction. The first case is often encountered in macroporous materials. The transition pressure lies near the saturation region; the second case is well known from low temperature adsorption experiments, where -wlkT is large, w, k , T being adsorbate-adsorbate interaction energy, Boltzmann constant and temperature, respectively. Their isotherms have the characteristical S-shape. The common background of these systems is that the adsorbent does not change its structure. Recent crystallographical investigations on adsorbate-loaded zeolite crystals [I ,2,3] indicate that a third answer is possible:

The adsorbate induced structural changes of the adsorbents induces in turn a phase transition of the adsorbate phase. This implies that the most basic postulate of the physical adsorption adsorbents

-

-

the inertness of

is not valid in some cases, especially in connection with high silicious ZSM-5 or

silicalite, where the electrostatic effects are small because few exchangable cations are present. Author to w h o m correspondence should be addressed.

520

Two most extensively investigated adsorption systems with a phase transition are N*/ZSM5 [4,5] and p-xylene/ZSM-5 [3,6,7]. Because no crystallographical details concerning the adsorbate loaded ZShI-5 crystals are available for the first case, this study is concentrated on the second case. The Ar/ZSM-5 [5] and benzene/ZSM-5 [9,8] also show the similar isotherm behavior.

STRUCTURE CHANGES OF ZSM-5 CRYSTALS The as-synthesized ZSM-5 crystal lattice consists of staggered layers [lo], possesing an orthorhombic structure. After calcination and at temperature below critical point of about

340K, the crystals assume a monoclinic phase [ l l ] . At the beginning of the adsorption, the p-xylene molecules first occupy the intersections between straight and sinusoidal channels [ 121. The reason is purely geometrical: Comparing to other places in the channel system, the intersection is just large enough to contain one p-xylene molecule (Kinetic diameter of p-xylene: 5.S5w [13]), providing a strong attractive interaction between adsorbent and adsorbate. At a p-xylene loading between 3 and 4 molecules per unit cell, the crystal lattice again undergoes a structure change, accompanied by deforming the rather cyclic pore shape of the sinusoidal channels to a more elliptical one [3]: from 5.891"ix 5.35A to 6.37Ax 4.76A. This transition is induced by the occupation of some sinusoidal channels. These sites have a higher potential energy for they are so close to the adsorbent atoms that the repulsive interaction takes place. Therefore the occupation probability is small according to the Boltzmann exponential factor. Because of geometrical reasons - the p-xylene molecule is flat, preferring a slit like pore - the occupied channel sections will be stretched to form a flat shape. Through the layer structure the stretching is propagated to the 4 neighboring channel sections [3]. From the energetical point of view the ZSM-5 crystal has some metastable phase which can be reached by changing the temperature or the adsorbate loading. The prerequisite of the deformation is that the two phase are energetically close enough to each other. The new pore structure provides now a better accommodation for the adsorbate molecules. In other words, the potential energy of these adsorption sites is lowered after a neighboring site of the same type is occupied. The more the neighboring sites are occupied, the larger the deformation will be, reducing more and more the original repulsion between atoms of the crystal and the adsorbate molecules. The lowering of the potential energy is assumed to be approximately proportional to the number of sites occupied. In an effective sense the energy difference before and after the occupation of the neighbors can be interpreted as a result of a long range inleraction between the adsorbate molecules. Therefore it can be called as a crystal lattice mediated interaction.

MODEL The crystallographical findings described above indicate two mechanisms which play the most importante role in the p-xylene adsorption on ZSM-5: The adsorption of p-xylene in the channel intersections and

521 0

the adsorbate induced structural changes, which in turn affect the adsorption.

For simplicity the first mechanism is modelled by the partition function of Langmuir lattice gas

where NI is the number of molecules adsorbed, q1 the partition function of an isolated admolecule, M1 the number of sites of first kind. The second mechanism is modelled by the quasi-chemical approximation for a twodimensional lattice gas with the nearest neighbor interaction energy w. As mentioned in the foregoing section,

u)

is used in an effective sense. The partition function Q2(Nz)is well

known in the literatures [14].

If the two mechanisms are not coupled, which means no interaction between the adsorbate molecules occupying different types of adsorption sites, the partition function of the entire system is given by:

C

Q(N) =

Qi(Ni)Qz(Nz)

(2)

NI +Nz =N

N being the total number of adsorbed molecules. Using standard procedures in statistical thermodynamics [14], one obtains

where p is the chemical potential of the lattice gas. It is related to gas pressure by p = po

+ kT l n p

(4)

Since the numbers of sites of type 1 and 2 are equal according t o the structure analysis, there is

N Ni -=(-+-)/2 M All

N2 M2

or

O=-

Qi

+ 02 2

(5)

From equation (3) it follows

K1 P = 1-82

K a p=

81

p-1+202

02( p + 1 - 202)

(7)

with

p

=

41 - 402(1 -

- exp(-w/kT))

This is the model isotherm. p, K1,IC, are the gas pressure, the Henry-constant of sites 1 and 2, respectively. The similarity of this model with two-patch models is evident. Only the physical background is different. Also the derivation of this model can be easily extended t o cases where

522

the coupling term C(Nl, N,) of the two adsorption mechanisms is known. In this case the partition function of the whole system can be written as

Q(W= C

Qi(Ni)Qz(Nz)C(N1,Nz)

N I +Nz =N

Therefore the isotherm is given by the following equations: PO

+

ln p = - a l n ~ ~ -( ~ ~ )

aNi

kT

(9)

aN1

P O + l n p = -alnQz(Nz) - alnC(Nl,Nz)

kT

aNz N = NI

aN2

+ Nz

Using Bragg-Williams approximation [14], the coupling term takes the form

(12)

InC(N1, N,) = -wABNlN2

Such corrections are of interests for quantitative fittings. But it is not importante for this qualitative study. RESULTS AND DISCUSSION Figure 1 shows some calculation results with different values of the model parameters. The model calculation with the parameter value w/kT = -2,

K1

= 100, I(Z = 1 reproduces

the most importante characteristics of the experimental p-xylene isotherm in figure 2 [6]:The intermediate plateau and the hysteresis loop. The finite slope at phase transition point is due to non-idealities of the crystals used in the experiments, which can be treated by the method of Dash and Puff [15]. Since phase transitions are cooperative phenomena, the “cooperation information

”

(In

this case, the information is the existence of neighboring adsorbate molecules) is transported by the interaction energy w. For small eu, entropy effects dominate, distorting the information. Therefore no phase transition occurs for w = -1. The difference of potential energies between the two types of sites Awl2 is reflected in the quotient I(l/I(zl which is given by K1

- = exp(-AwlZ/kT

I mmol/g o c c u r s as i t was s t a t e d

531

above, with n e a t r e l e a s e equal t o conuensation n e a t b u t e x c e e a i n g i t by 2-3 kJ/mol.

(44 kJ/rnol)

E'urtner a a s o r p t i o n a o e s n o t a t

a l l d i f f e r from a a s o r p t i o n h e a t on c a t i o n - f r e e s i l i c a - s i m i l a r s t r u c t u r e o f z e o l i t e NaZSid-5. D i f f e r e n t i a l h e a t s of a d s o r p t i o n of o t h e r p o l a r molecules ( G O 2 , CH OH, C H OH) a l s o h a v e s t e p form.

3

2 5

I

1

2

3

a,?

F i g . 4. D i P f e r e n t i a l h e a t s of m e t h a n o l v a p o r a a s o r p t i o n oti s i l i c a l i t e (a) arid 1uaZSai-5 (b) a t 300 K. Above e n t r o p y o f a a s o r p t i o n i n J/mol K. I n i t i a l h i g h v a l u e s o f a l c o i l o l a d s o r p t i o n h e a t ( F i g . 4) c o r r e s p o n d t o i n t e r a c t i o n w i t h 0.5 mmol/c of ITa c a t i o i i s . Adsorpt i o n c a p a c i t y o f t h e second s e c t i o n w i t h t h e h e a t p l a t e a u b e i n g

a t t h e l e v e l of '/) kJ/mol, i s a l s o 0.5 inmol/g, i.e. t h e second m o l e c u l e o f a l c o h o l i s aadcd t o i n i t i a l coniplex. Exterit of' t h e t h i r d and t h e f o u r t h s e c t i o n s corresponcl Lo a u a i t i o r i oi' t h e t h i r d a n a t h e S o u r t h a l c o h o l m o l e c u l e s t o t h e p r e v i o u s colnplex; anu i r i t h i s case they ciirectly i n t e r a c t with c e n t r a l cation. Such t e t r a t h e a r a l s o r b t i o n complex c a n be formed o n l y i n t h e i n t e r s e c t i o n s of two t y p e s o f c h a n n e l s i n t h e s t r u c t u r e 01% pentas i l e z e o l i t e s . The Iirst alcohol m o l e c u l e d r s p l a c e s Iu'a c a i i o r i from e q u i l i b r i u m p o s i t i o n 111a l a t t i c e ( t h i s i s s u p p o r t e u by l i n e a r d r o p o f h e a t on t h e whole s e c t i o r i OP f i l l i t i g from 0 t o 0. I, mmol/e) and l o c a l i z e s i t O I I f a v o u r a b l e p o s i t i o n e d o x i g e n atoms o f a l a t t i c e 111 t h e p o i n t s o f chanriels i a t e r s e c t i o n . 111 t h i s c a s e m e t h y l and e s p e c i a l l y e t h y l g r o u p s p a r t i a l l y e n t e r s t r a i g h t chatinel o€ z e o l i t e . The second a l c o h o l m o l e c u l e i s a d ded t o l o c a l i z e d complex Srorn t h e o p p o s i t e s i d e as w e l l as w i t h a l k y l r a d i c a l p a r t i a l l y i n a s t r a i g h t charinel. To form s u c h a

532

l i n e a r complex ( w i t h o u t displacement from t h e p l a c e oi’ l o c a l i x a t i o n ) a l c o h o l m o l e c u l e b e s n o t have any s t e r i c d i f f i c u l t i e s and n e a t curve at t h e s e c t i o n o f 0.5-1.0 mmol/g i s c o n s t a n t . To add t h e t h i r d molecule of a l c o h o l from t h e s i d e of s t i l l f r e e z i g zag channel new displacement of l i n e a r complex t a k e s p l a c e and a d s o r p t i o n h e a t a t t h i s s e c t i o n of 1.0 t o 1.5 mmol/g drops l i n e a r l y . And a t l a s t , t h e f o u r t h molecule i s connected t o complex w i t h o u t any d i f f i c u l t y and w i t h c o n s t a n t h e a t a t t h e s e c t i o r i o f 1.5-2.0 rmnol/g. When a l l c a t i o n s of N a a r e i n v o l v e d i n t o complex f o r m a t i o n , f u r t h e r a d s o r p t i o n of a l c o h o l s similar t o t h a t 011 s i l i c a l i t e (Fig.4) i s accomponied w i t h s l i g h t i n c r e a s e i n a d s o r p t i o n h e a t , aciiievirig r a t h e r low iiiaxirflwu w i t h t h e f o l l o w i n g s h a r p drop t o c o n d e n s a t i o n h e a t i n t h e r e g i o n o f s o r p t i o n completion. Entropy aiagrams i n accordance w i t h f o u r - s t e p c h a r a c t e r o f ads o r p t i o n h e a t c u r v e s have polyextremal form and minimum o f ent ropy curve c o r r e s p o n d s t o each s t e p on a h e a t curve. Adsorption of C02 on IUaZSlii-5 (Fig. 5) i s s u b s t a n t i a l l y g r e a t e r t h a n on s i l i c a l i t e , b u t i n the i n i t i a l r e g i o n of f i l l i i i g of 0.0-0.1 mmol/g a d s o r p t i o n h e a t s on NaZShi-5 and on s i l i c a l i t e a r e similar and r a t h e r h i g h , i . e . a t t h i s s e c t i o n of f i l l i n g energy of i n t e r a c t i o n w i t h 013-groups which i s g r e a t e r t h a n t h a t o f i n t e r a c t i o n w i t h Na c a t i o n i s m a n i f i s t e d (while i n t h e c a s e w i t h alcohol the s i t u a t i o n i s contrary).

40 30

Pig.5.

D i f f e r e n t i a l h e a t s o f carbon d i o x i d e a d s o r p t i o n on s i l i c a l i t e ( a ) and IVaZSivi-5 ( b ) a t j00 K. Above - e n t r o p y o f a d s o r p t i o n i n J / m o l K.

533

uveragy energy of f o r m a t i o n o f lia+-CO2 a a s o r p t i o n complex i n NaZSl4-5 z e o l i t e ( e x t r a p o l a t i o n t o z e r o f i l l i n g ) makes up 50.0 k J / mol. I n t h i s c a s e l i n e a r drop of t h e h e a t evideiices, as i t w a s a u r i n g a l c o h o l a d s o r p t i o r i , about displaceilient of Na c a t i o n froiil i t s e q u i l i b r i u m p o s i t i o n i n a l a t t i c e . A f t e r s t e p w i s e berid a t f i l l i n g o f 0.5 miol/i;: tile h e a t curve a g a i n drop l i n e a r l y from 40 t o 30 kJ/mol t o f i l l i n g of 1 .O mniol/~;, i.e. s t o i c h i o m e t r i c mechanism of complex forrilation w i t h exchange c a t i o n s i s observed i n cormon w i t h t h e c a s e w i t h a l c o h o l . fiowever, h e r e t h e energy of complex f o r m a t i o n i s s u c h t h a t r e l a t i v e weak i n t e r a c t i o n v i i t k i cat i o i i a n u r e l a t i v e l y s t r o n g i n t e r a c t i o n w i t h l a t t i c e does n o t a l low l a r g e l i n e a r complex OcO-iva+-OCO t o move i i i a s t r u i d i i t chaiiiiel o f b e o l i t e . “iiat i s why t h e l a s t s t a g e of f i l l i n g o f 1.0-1.5 i u i i o ~ / g corresporius t o a u s o r p t i o r i oil c a t i o i i - f r e e s e c t i o i i o ~ ? z s s c t e s t r u c t u r e , w h i l e a d s o r p t i o t i iieat v a l u e s i n t h i s r e g i o i i c o i n s i a e w i t h a u s o r p t i o n iieat l e v e l oil s i l i c a l i t e . Tile d e u s i t y of inolecules arrailgemeiit of v a r i o u s n a t u r e an6 geometry i n p e n t a s i l z e o i i t e s v a r i e s . For example, n.alkaries i n s i l i c a l i t e a r e a r r a n g e u v e r y dense (erici t o e n d ) and occupy all acisor*ptiori s p a c e ( 9 ) . 1G.alcohols f i l l 0.U of s o r p t i o n volume o f t h e i r c h a n n e l s w h i l e beiizerie o n l y 0.b of t h e volume. Thus, i n one c a s e i n t e r m o l e c u l a r i n t e r a c t i o n o f a l c o h o l s w i t h each o t h e r through hycirogen bonds p r e v e n t t h e i r c l o s e packing i n t h e chaiin e l s w h i l e i n t h e o t h e r c a s e (when benzene i s a d s o r b e d ) rnolecul a r conformation p r e v e n t i t from p e n e t r a t i o n i n t o inore narrow zig-zag channels. Adsorption o f a p o l a r m o l e c u l e s of hydrocarbons i s t h e most s e i i s i t i v e t o c a v i t i e s s i z e , t h e s i z e o f c h a n n e l s and. v a r i o u s tlwinuowslli n z e o l i t e s . For example, u i f f e r e n t i a l h e a t s o f n.alkanes a d s o r p t i o n on z e o l i t e s a t z e r o f i l l i n g ( o b t a i n e d by e x t r a p o l a t i o n o f l i n e a r l y i n c r e a s i n g s e c t i o n of t h e h e a t curve t o z e r o f i l l i n g ) i s i n c r e a s i n g l i n e a r l y w i t h t h e Lrowth o f t h e number of carbon atoms i n n.alkane m o l e c u l e , aria f o r s i l i c a l i t e t h i s dependence i s e x p r e s s e d by r e g r e s s i o n 11.6+10.0 n kJ/mol, where 111111 i s t h e l i m b e r of carbon atoms i n molecule. For n . a l c o h o l s a d s o r p t i o n h e a t on s i l i c a l i t e l i n e a r dependence i s d i f f e r e u t : 34.0 + 9.0 n. For t h e a l c o h o l s f r e e menber of r e g r e s s i o n which r e p r e s e n t s w a t e r ‘molecule a d s o r p t i o n energy i s much Less t h a n w a t e r vapor c o n d e n s a t i o n h e a t . T h i s f a c t e x p l a i n s h y d r o p h o b i c i t y o f s i l i c a l i t e (9).

534

From s i m p l e t h e o r e t i c a l p r e m i s e s i t i s c l e a r t h a t t h e n a r rower i s t h e s o r p t i o n s p a c e t h e g r e a t e r i s t h e e n e r g y of d i s p e r s i o n i n t e r a c t i o n of a p o l a r m o l e c u l e arid i t i s a peak one f o r s u c h p o r e s i n which m o l e c u l e i s c l o s e l y a t t a c h e d t o t h e w a l l s . The c h a n n e l s i n hydrogen form of n a t u r a l s e o l i t e - c l i n o p t i l o l i t e (H-CL) i s l i k e l y t o be c l o s e l y a t t a c h e d t o n.alkane m o l e c u l e s (10). H-CL c h a n n e l s a r e s o narrow t h a t n.alkane m o l e c u l e s w i t h n = 2 do n o t p e n e t r a t e t h e r e o r p e n e t r a t e w i t h g r e a t d i f f i c u l t y ( w i t h h i g h a c t i v a t i o n e n e r g y a n d v e r y slow). Ethane a d s o r p t i o n h e a t on H-CL a t zeyo f i l l i n g made up 40.0 kJ/mol (10). Taking i n t o a c c o u n t t h e f a c t t h a t for most o f z e o l i t e s w i t h open porous s t r u c t u r e s r e g r e s s i o n f r e e members of n . a l k a n e s a d s o r p t i o n h e a t iilakes up 7.0 kJ/mol ( 1 ) arid f o r t h e most narrow o n e s t h i s v a l u e can n o t exceed 12 kJ/mol ( f o r s i l i c a l i t e , as i t w a s g i v e n above, qo= 11.6 kJ/moi) we o b t a i n h e a t i n c r e m e n t p e r CH2-group f o r H-

KL which i s 14.0 kJ/mol.

On t h e same b a s i s , i f we t a k e qo= 10 kJ/mol for KL z e o l i t e ( c h a n n e l d i a m e t e r b e i n g 0.71 nm) t h e n i n crement p e r CI12-group w i i l make up -9.5 kJ/mol. The o b t a i n app r o x i m a t e v a l u e s o f h e a t i n c r e m e n t p e r CH2-group - 14.0, 10.0

and 9.5 kJ/mol f o r t h r e e dimensions ( d i a m e t e r s ) o f c h a n n e l s aver a g e c r o s s - s e c t i o n s (0.4,o.G and 0 . 7 ) c o r r e c t l y r e f l e c t a p r i o r i r e g u l a r i t y i n t h e growth of a d s o r p t i o n i n t e r a c t i o n e n e r g y w i t h d e c r e a s i n g i n p o r e s s i z e . However, t h i s r e g u l a r i t y i s q u a l i t a t i v e o f h a l f q u a n t i t a t i v e as a r e t h e r e s u l t s of c a l c u l a t i o n s o f t h i s k i n d f o r c o r r e s p o n d i n g models.

H&yARj&cj!s I . A.A. I s i r i k j a n . I n : A d s o r p t i o n arid a d s o r b e n t s . Nauka. Moscow. 198'7, 41-53. 2. lLM.Dubiriin, A . A . I s i r i k j a n , A.I.Sarakhov, V.V. S e r p i n s k i . Izv. &I USSH. Chem.(1968), No 8 , 1690-1699; (1969) No 1 1 , 2 3 5 5 - 6 0 . 3 . K.S.&hmedov, G.U.Kakhniatkariev, Ivi.Ivl.Dubinin and A . s , I s i r i k j a n . Izv. A& USSR. Chem. (1987), N o 8 , 1717-1721. 4. Ibi.Ui.Iktbinin,A.A.Isirikjan.G.U.Kalchmatkariev a n a V.V.Serpinski. I s v . Ai\i USSR. Cliem.(IY'/2), No 6 , 1269-1276 ; (1973), IT0 4 , 934y j 6 . 5. u . a . I s i r i k j a n . I n : C a l o r i m e t r y i n a u s o r p t i o n and c a t a l y sis. S O AN USSR. N o v o s i b i r s k (1 389), 21 7-214. 6. M.I.Dubinin, G.U.Hakhmatkariev and i i . A . I s i r i k j a n . I z v . f i l i USSH. Chern. (1984 ), iVo 1 2 , 207r[-2ij7tj. 7 . G.U.fiakhmatkariev,B.A.A.IsirikJan. Izv. AN USSK. Ciiern. ( 1 9 8 8 ) , No 1 1 . 224442245. 8. ~ ~ . ~ . D u b i r i i n , A . 8 . I s i r i k j a n ,I$. 1.Hegent , W. Sciirirner., H. S t a c h , H. T m r i , U. Lohse. I z v . Al! USSIi.Chern. ( 1 9 8 4 ) , 80 9. 1931-1938. 9. E.X.Flaiiigen, J,id.Bennet e t al. N a t u r e 271 (19'(8).512. 10, M.M.Dubiriin,E.Ch.Anaktschiari, A.A.Isirikjan. I z v . AN USSR. Chern. (1 9 8 7 ) , No IT .2631-2632. 1 1 . W.Ychrinier, ii.Stach e t al. Z.Phys.Chemie ( L e i p z i g ) 261 ( 6 ) ( 1 9801. 1 129-1 1 38.

F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids I1 0 1991 Elsevier Science Publishers B.V., Amsterdam

535

Sorption of argon and nitrogen on network types of zeolites and aluminophosphates

H. Reichert', U. Mullerl, K.K. Ungerl, Y. Grillet2, F. Rouquero12, J. Rouquerol2, J.P. Coulomb3 1Institut fur Anorganische Chemie und Analytische Chemie, Johannes Gutenberg-Universit, Joh. -Joachim-Becher-Weg 24, D-6500 Mainz, F.R.G. 2Centre de Thermodynamique et de Microcalorimetrie du C.N.R.S., 26 Rue du 141e R.I.A., F-13003 Marseille, France 3Departement de Pysique du C.R.N.S. F- 13003 Marseille-Luminy , France

Abstract Synthetic zeolites and aluminophosphates comprising 10- and 12- membered ring openings, unidimensional and network type of pore systems (MFI, MEL, E N , LTA, AEL, AFI and FAU) were used as model adsorbents to examine the impact of micropore structure on the sorption properties. Argon and nitrogen were employed as adsorptives. Adsorption measurements were carried out on gravimetric and volumetric sorption devices and also monitored by microcalorimetry. From the low coverage regime of the isotherm Henry's constants and isosteric heats of adsorption were derived. Both quantities allowed the discrimination between 10- and 12- membered ring systems. Unidimensional 10- and 12membered ring zeolites and aluminophosphates gave Type I isotherms for argon and nitrogen. Stepped isotherms were observed for argon and nitrogen on network types of molecular sieves. On MFI type zeolites with nitrogen a distinct hysteresis was observed between p/po = 0.1 and 0.15, as reported earlier. In-situ measurements of the system Silicalite I / nitrogen at 77 K by neutron diffraction experiments indicated discontinous changes in the diffraction pattern of both MFI and nitrogen upon increasing adsorbate coverage. Introduction Crystalline microporous solids such as synthetic zeolites and aluminophosphates have gained remarkable interest as adsorbents to study adsorption phenomena in microporous systems. These types of molecular sieves possess a well-defined, regular pore structure of molecular dimensions, comprising from unidimensional channels to three-dimensional networks [1-51. In our laboratory we have focussed on the synthesis of large and uniform crystals of ZSM-5, Silicalite-I, ZSM-48, A1P04-5 and AlPO,-ll was thoroughly investigated. Large crystals of microporous solids with negligible external surface area are essential to assess the intrinsic adsorption properties. Isotherms of nitrogen and argon were measured at 77-87 K at two distinct ranges: (i) The high coverage range at a reduced adsorption temperature of 0.5 < T/T, < 0.7 (T, is the critical temperature of the bulk adsorptive) is where the final micropore filling occurs and adsorbate-adsorbate interactions dominate.

536

(ii) The low coverage range at a reduced adsorption temperature of 1.8 < T/T, < 3.1 is where only adsorbent-adsorbate interactions take place. The objective of the study was to manifest the phenomena which gives rise to the deviations from Type-I-isotherms usually observed on microporous solids. Experimental The samples were prepared by optimization of synthesis procedures described in the Literature (see Table 1). The samples were calcined at 823 K. Prior to all adsorption measurements the samples were outgassed for 12 hours at 473 K and with a vacuum of mbar. The products were characterised by scanning electron microscopy, X-ray diffraction, thermal analysis and electron microprobe analysis. Additionally, the HZSM-5-crystals were analysed by IR and 2%-MAS-NMR spectroscopy. High resolution adsorption isotherms were recorded by a dynamic volumetric device (Omnisorp 360, Omicron Corp. U.S.A.). Investigations into the low coverage range were determined gravimetrically with a relative sensitivity of 106 (ultramicrobalance 4433, Sartorius, F.R.G.). The continous calorimetric measurements were performed on a reversible isothermal microcalorimeter of Tian-Calvet type (C.N.R.S. Thermodynamique et Microcalorimetrie, Marseille, France) [7]. Neutron powder diffraction data were collected at 77.4 K on a 2-axis diffractometer (D1B at ILL, Grenoble, France) at a constant wavelength of 2.525 A.

TABLE 1.: Molecular sieves used for this study Sample

Structure

Silicalite-I HZSM-5 ZSM-48 AIP04- 11 A1P04-5 A1PO4-17

MFI MFI (FER) AEL AFI ERI

Pore opening (-membered ring) 10 10 10 10 12 8

Literature 1, 2, 5, 6 1, 2, 5, 6 4 3 3, 5 3, 8

Results and Discussion In the low coverage range, at temperatures of 303 K to 373 K, coverages of less than one molecule of adsorbate per unit cell were observed (see Fig. 1). Which thus reflects pure adsorbate-adsorbent interactions. The slopes of these linear isotherms yielded the Henry constants KH. The heats of adsorption values were calculated according to the equation KH =KH ' .exp(-AH/RT) from the linear regression of the experimental data at different temperatures (see Fig. 2). In Table 2, the results from these measurements are shown.

537

Figure 1 Adsorption of nitrogen at low coverages on MFI type zeolites

PRESSURE

I

[mbar of Nitrogen]

1 7

Figure 2 Van't Hoff-Plots for MFI and AFI type structures for nitrogen

Nitrogen Van't Hoff-Plots

r.llM I

I

" "

3.0 -

-4

.73

"'

3.4

'

"

'

" "

I'

"

3.6

"

3.8

40-3

1/T

:

"

TABLE 2.: Isosteric Heats of adsorption Adsorbent

Structure

H-ZSM-5 MFI Silicalite-I MFI Silicalite-I MFI ZSM-48 PER) ~ 1 ~ 11 0 ~ - AEL AlP04-5 AFI

Adsorbate

AH[kJ/mol]

Nitrogen Nitrogen Argon Nitrogen Nitrogen Nitrogen

14.9k0.9 15.0k1.3 16.0k0.9

13.0k0.6 12.6+ 1.3 7.7k1.3

No difference was observed in the heats of adsorption between HZSM-5 (Si/Al= 1OOO) and the corresponding aluminium free structure Silicalite-I. Experiments with argon as an adsorptive also showed no significant difference in the heats of adsorption on the MFIstructures. On comparing the network-type MFI-structure with the unidimensional 10membered ring channel structure ZSM-48 no significant differences were either seen. However, significant diffierences in the heats of adsorption were found between the 12-membered ring channel structure A1P04-5 and the 10 membered ring channel structure AlP0,-1 1. Thus,

538

adsorption measurements in the Henry's-law region provide a useful tool to identify the size of micropores.

I 7

6-1 0

Figure 3 microcalorimetric measurements on EN-type of molecular sieve

Adsorption on AIP04-17

, , , ,

,

,

, ,

, , . ,

5

, ,

, , , .

,,

, ,,.

, , , ,

a

15

, , , , I

20

UPTAKE [rnolecules/unitcell]

The final micropore filling on network types of molecular sieves was studied in the high coverage range at 77 K. As previously observed on MFI-,MEL- and LTA-type network zeolites, nitrogen on A1P04-17 was found to exhibit a non-uniform behaviour. Microcalorimetric studies clearly indicated the onset of additional exothermic interactions at an uptake of approximately six molecules per unit cell (see Fig 3). This corresponds to a cooperative filling process after adsorption on the six adsorption potential minima in the structure [8]. The nonuniform behaviour of the heat curves cannot be seen on the adsorption isotherms which show pure Langmuir type behaviour (see Fig. 4). 20

Nitrogen

Figure 4 adsorption isotherms on ERI-type of molecular sieve

oa 0

E

Y

0

010

I " " l ~ " ' I ~ " I " " I ' " ~ I ' " ' I " ' ' l

0.2

04

0.6

RELATIVE PRESSURE [p/po]

As demonstrated on large and uniform crystals of MFI-Type zeolites the steps in the heat curves perfectly correspond to steps in the adsorption isotherm (see Fig. 5). As the large crystals were crushed with a pestle and mortar the steps in the isotherm were consequently flattened and the hyteresis (at p/pO = 0.1 to 0.15) was depressed. (see Fig. 6).

539

Figure 5 nitrogen isotherm and isosteric heat of adsorption on large MFI crystals at 77 K

Adswption of Nitrcpn on Slicdite-l

,I,, ~

, ,,

,,,, l

, , , , r

,, , , n

,

;"

,?, , , . ,

20

"

,,,,

~Y)

, , ,,

, 40 I

I

UPTAKE [molecukr/uritcdl]

Nitrogen Isotherm MFl/77 K

32 7

monodisperse

crushed crystals

20

o.w

OM

0.10

0.1s

Figure 6 isotherms on large, uniform and on crushed crystals of SiliditeI

'1'"'I"~'I'"'T""T""I

om

0.25

03

Rebtlvo Presswe p/pO

One can conclude that stepped isotherms and low pressure hysteresis loops may only be observed on monodispersed and large crystals of network types of molecular sieves. The hysteresis loop was examined in detail by scanning the region between the adsorption and the desorption branch of the hysteresis. The points between the two branches were stable for many hours, thus, the low pressure hysteresis is controlled by equilibrium properties and not by kinetical effects. Previous studies provided clear evidence that the stepped isotherms of argon and nitrogen on MFI-crystals can be rationally explained by lccalised adsorptive molecules at the channel walls and intersections [lo]. At higher loadings the step in the region of the hysteresis was proposed to be a result of solidification of the adsorbate. To obtain more evidence for this hypothesis in-situ neutron scattering experiments were performed on the system Silidite/Nz at 77 K at different pressures following the hysteresis loop (see Fig. 8-10 and Table 3).

540

Figure 7 scanning between adsorption and desorption branch of the hysteresis loop on Silicalite-I

.... ..... . &. ........ I+

r

;-

. ........:

I

:-

(i.

....................................... an

0.U

0.U

am

am

020

PfLATM PRESUlRE [p/po]

TABLE 3: Points on the isotherm used for neutron scattering Point

A B C D

relative pressure P/P0 0.07-10-3 0.081 0.321 0.127 11,

coverage N2/unit cell 18.4 23.5 30.1 29.6

branch adsorption adsorption adsorption desorption Figure 8 neutron diffraction patterns of N2/Silicalite-I at 77K at theangles 18"s20 5 97" uncovered MFI to point A

Although the data cannot yet be totally interpreted, the following explanation can be given. The diffractogram of the unloaded zeolite that shows some doublets change to singlets when the crystals have adsorbed nitrogen (see Fig 8). This indicates a transition from the monoclinic phase to the orthorhombic phase of the MFI-structure. This change was reported earlier for benzene and xylene and for higher temperatures 113-153. With further uptake of nitrogen the diffraction pattern changes distinctly (at 20=1.8 to 2.2) with peaks emerging (see Fig. 9).

541

Figure 9 neutron diffraction patterns of N*/Silicalite-I at 77K at the angles 18" 5 2 8 I 97" point A to C

By comparing the difference in the spectra at points B-C to the spectra of the solid hexagonal 5-Nitrogen phase, analogous peaks are seen (see Fig. 10). Differences at desorption to point D were not discovered. Thus evidence for a transition of the adsorbed nitrogen to a solid like phase was found. 1,5 1,25 -

3-N2(3D Solid)

Figure 10 diffraction pattern of a) solid 5-nitrogen and

(101)

1-

0,75

(002)

03 -

0,25. 0

j \

b) difference spectra of point B-C on the system Silicalite-I/N;! at 77 K

1

1.2

1,4

1,6

1,8

2

2,2

2,4

542

Conclusion To conclude, one can first point out the usefulness of the low-coverage isosteric heats of adsorption of nitrogen: they indicate a clear difference in behaviour between the 10-membered ring systems (MEL) and the 12-membered ring molecular sieves (AFI, MFI) with a 2-fold decrease in isosteric heat values. Finally, neutron diffraction experiments clearly confirm our previous conclusions drawn from the shape of the adsorption isotherms and from the microcalorimetric studies [16]: the step at at about p/po=O. 12 on the N2 adsorption isotherms is due to a fluid solid transition of the adsorbate. Also, as m n as nitrogen is adsorbed, the zeolite structure progressively undergoes a change from monoclinic to orthorhombic structure. +

Acknowledgements We would like to thank the Deutsche Forschungsgemeinschaft for their financial support. References U. Miiller, K.K. Unger, Z. Kristallogr., 182 (1988) 190. 1 U. Miiller, K.K. Unger, Zeolites, 8 (1988), 154. 2 S.T. Wilson, B.M. Lok, E.M. Flanigan, US Pat. 4,385,994 (1983). 3 E.W. Valyosik, US Pat. 4,585,747 (1986). 4 D.M. Bibby, N.B. Milestone, L.P. Aldridge, Nature, 285 (1980), 30-31. 5 6 U. Miiller et al., A.C.S. Symp. Series, 398 (1989), 346-359. 7 J. Rouquerol et al., J. Chem. S o c . , Faraday Trans. I, 73 (1977), 306 8 U. Miiller et al, in E.F. Vansant and R. Dewolfs (Us.), Gas Separation Technology, (1989), Elsevier, Amsterdam, 255 9 U. Miiller, Ph.D. thesis, Joh.-Gutenberg Universitiit Maim (1990). U. Miiller et al., Studies in Surface Science and Catalysis, Elsevier, Amsterdam, 46, 10 (1989),477 11 U. Miiller et al.,Proc. 3rd Int. Conf. "Fundamentals of Adsorption" Sonthofen, F.R.G. May 7-12, 1989, in press. 12 D. Pan et al.,"How can adsorption system show hysteresis", this procedmgs elsewere. C.A. Fyfe et al., Studies in Surface Science and Catalysis, Elsevier, Amsterdam, 46 13 (1989), 827-842. 14 B. F. Mentzen, Studies in Surface Science and Catalysis, Elsevier, Amsterdam, 46 (1989), 477-494. R.E. Richards, L.V.C. Rees, Zeolites, 8 (1988), 35-39. 15 U. Miiller et al., Fresenius Z. Anal. Chem. (1989) 333, 433 16

F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids II

543

0 1991 Elsevier Science Publishers B.V., Amsterdam

POROSITY OF SILICAS: COMPARISON OF NITROGEN ADSORPTION AND MERCURY PENETRATION D.R. Milburn, B.D. Adkins, and B.H. Davis Center for Applied Energy Research, 3572 Iron Works Pike, Lexington, KY 4051 1

INTRODUCTION Nitrogen adsorption and mercury penetration are two of the most common methods for obtaining information about the porosity of solids. Unfortunately, experimental realities limit the region where the two methods are both applicable to pore sizes of

m.10 - 30 nm.

To date there have been few studies that compare data

generated by the two techniques in this pore size range. Both nitrogen adsorption and mercury penetration provide a direct measure of pore size distribution and pore volume. However, these direct measures do not permit a determination of the morphology of the materials from pressure-volume relationships. DeBoer (ref. 1) was among the first to relate the shape of the nitrogen adsorption/desorption isotherms and the location and shape of the hysteresis loop to the type of pores associated with the material. Much attention has been paid to better define the relation between morphology of the pores of a material and the adsorption/desorption isotherms (ref. 2). Much less attention has been paid to the relationship of morphology to mercury penetration data (ref. 3). Most investigators, including Lowell and Shields (4-6) interpret the mercury penetration data assuming that all pores are nonintersecting and attribute the hysteresis to a change in the contact angle, 8, of mercury and the solid. Conner and coworkers (refs. 7,8)have recently utilized a porehhroat network model to obtain information about the morphology of materials from mercury penetration data. The void/solid structure is viewed as an interconnected network so that adsorption/desorption and retraction/intrusion can be associated with the openings and constrictions within the void network. These latter investigators analyzed the data as if the materials consisted of agglomerated microspheres. The measured ratio of the most probable radii of intrusion to those of retraction seemed to be characteristic of the void structure and pore shape. Conner et at. (ref. 8) developed a heuristic diagram for the classification of void/solid morphologies from a

544

plot of void fraction versus the radius ratio (Rextrusion/Rintrusion). These authors also made the interesting observation that intrusion and retraction porosimetry curves obtained for silica spheres essentially coincide so that a hysteresis loop is not obtained; this is probably the first time this observation has been reported except for nonporous macrosphere (G. 2 mm) silicas. The model developed by Conner et al. (ref. 7) that is based upon packing of spheres is of interest. We have found that a model based upon a simple cubic packing of nonporous spheres returns the best agreement among surface area, pore volume and average pore size data for nitrogen adsorption/desorption measurements with numerous metal oxide samples (ref. 9). It is of special interest to compare the data obtained from the two techniques with common materials to learn whether a model based on packings of spheres applies equally well. The Shell 980 series of silicas provides materials with three pore diameters

(ca.

15,30 and 60 nm) and for each of these, three pore volumes (ca. 1.I, 1.3,and 1.5 cm3g-’) are available. These materials would appear to provide a unique opportunity to compare porosity data obtained with two common experimental techniques:

mercury porosimetry and nitrogen adsorption. At the same time, the study would afford data to compare nitrogen adsorption to mercury depressurization and nitrogen desorption to mercury penetration.

EXPERlMENTAL Nitrogen adsorption-desorption isotherms were obtained with a Quantachrome Autosorb 6 instrument. Prior to analysis, samples were outgassed for several hours at about 10” torr and 200°C. Surface areas are calculated from the linear form of the BET equation. The model utilized for pore size distribution calculations is a packed particle model, assuming each primary spherical particle is in contact with six neighboring spheres. The primary particles agglomerate into larger, nearly spherical clusters ranging from B. 1.5 to 3.0 mrn diameter. This model was used to relate the neck opening in a face of the unit cell found by particle packing; corrections were made for an absorbed layer and for condensation at contact points (for more detail refer to reference 9). Mercury penetration curves were generated from pressure-volume measurements from 0 to 60,000 psia using a Quantachrome Autoscan 60 instrument. The surface areas are calculated using the Rootare-Prenzlow equation (ref. 10).

545

RESULTS AND DISCUSSION The absence of hysteresis for mercury penetration and depressurization curves was reported earlier for Shell S980 series silica samples, and this has been used as evidence for a network void structure theory (ref. 8). More recently these measurements have been repeated with portions of the same Shell S980 samples. These workers observed hysteresis in the second measurements but do not know what caused the incorrect data to be plotted in their earlier work (ref. 11).

............................................................ - ___---Extrusion

/

p

.-

..

I

I

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

I I

I Intrusion I I I I I I I I

Shell Silica Spheres

S980 D2.2

Figure 1.

_-

1

ibo

1000

ioboo

Pressure. (psia)

-

............... ........ *' 0.80--

i

.


; t r a d i t i o n a l method as d e s c r i b e d elsewhere ( r e f . 9, 10). Adsorption e x c e s s v a l u e s r l f o r polymers were c a l c u l a t e d by t h e d i f f e r e n c e ( 0 C ) o f t h e s o l u t i o n concentrat i o n s b e f o r e and a f t e r a d s o r p t i o n measurements.

-

where m ti v e l y

.

and

ma

- masses

o f s o l u t i o n and a d s o r b e n t , respec-

RESULTS AND DISCUSSION Ad s o r p t i o n is0 therms

f-A

Y

I

I

8-A

mg g-'

F i g u r e 1 shows t h e a d s o r p t i o n i s o t h e r m s o f PEG and DX i n aqueous s o l u t i o n s on mesoporouse carbon s o r b e n t CS-2 (Carboraff i n e ) . The c o i n c i d e n c e o f a d s o r p t i o n i s o t h e r m s f o r PEG 20000 and DX T 20 can be noted. Bone a d s o r p t i o n i s o t h e r m s a r e char a c t e r i z e d by s h a r p maximum. It can bee s e e n from Fig. 1 t h a t increase with t h e a d s o r p t i o n v a l u e s € o r PEG on t h i s sample growth o f m o l e c u l a r weight (from ?EG 300 till PEG 60001, b u t t h e n t h e a d s o r p t i o n amounts d e c r e a s e w i t h t h e f u r t h e r growth i n PIIq v a l u e s . The r e s u l t s i n d i c a t e t h e d i f f e r e n t a c c e s s i b i l i t y o f mesopore s u r f a c e f o r t h e polymer macromolecules a d s o r p t i o n .

578

Iwlolecular weight dependences f o r polymer a d s o r p t i o n The r e l a t i o n s h i p between t h e maximum a d s o r p t i o n v a l u e and t h e a v e r a g e m o l e c u l a r weight Mw a l l o w s i n some c a s e s t o e s t i m a t e t h e mean s t a t i s t i c a l t h i c k n e s s of adsorbed polymer lgye r . If adsorbed macromolecular c o i l s s t r a i g h t e n e d o u t i n t h e f i e l d o f a d s o r p t i o n f o r c e s , it c o u l d be expected t h a t t h e deU pendence nmax v s M, is v e r y s l i g h t . Such dependence w a s f o und for PEG a d s o r p t i o n i n w a t e r s o l u t i o n on g r a p h i t i z e d carbon b l a c k ( r e f . 4.). U The dependences nmax v s PIw were o b t a i n e d f o r t h e p o l y s t y r e n e a d s o r p t i o n i n d i l u t e s o l u t i o n s o n porous s i l i c a and carbon s o r b e n t s ( F i g . 2). It i s e v i d e n t t h a t t h e p o s i t i o n s o f curve ma-

Fig. 2. P l a t e a u a d s o r p t i o n o f o l y s t y r e n e as f u n c t i o n o f moleCS-1 (27, ‘2-80 ( 3 ) , CX-2 (4). c u l a r m a n s . KCK-2 (I), xima and t h e i r s h a p e s depend b a s i c a l l y on t h e p o r e s t r u c t u r e par a m e t e r (i. e. p o r e volume d i s t r i b u t i o n ) . The low Lroping b r a n c h s nf c’ii’ves a r e r e s p o n s i b l e for t h e macromolecule p e n e t r a t i o n i n t o a d s o r b e n t p o r e s and a l l o w s t o e v a l u a t e t h e f r a c t i o n o f i n t e r n a l p o r e s u r f a c e accessible f o r t h e macromolecular c o i l s . The maxima p o s i t i o n s a r e c h a r a c t e r i s t i c s f o r t h e mesopores i n a d s o r b e n t sample, which a r e e n t i r e l y a c c e s s i b l e f o r macromolecular c o i l s w i t h t h e g i v e n diameter o r less.

579

Hydrodynamic diameter D of f l e x i b l e c h a i n macromolecule i n d i l u t e s o l u t i o n can be c a l c u l a t e d by u s i n g Flory-Fox e q u a t i o n (ref. 12)

-

Flory parameter, equal where [ q 1 - i n t r i n s i c v i s c o s i t y and @ t o 2.6 lo2' l/mole ( r e f . 12). The D-values f o r p o l y s t y r e n e macr o m o l e c u l a r c o i l s i n CC14 s o l u t i o n s were c a l c u l a t e d by t a k i n g i n t o account t h e Mark-Howink e q u a t i o n p a r a m e t e r s k = 2.75 10-4 and a = 0.69 r e s p e c t i v e l y ( r e f . 13). For PEG i n w a t e r s o l u t i ons k = 1.25 lo-' and a = 0.78; for DX i n water s o l u t i o n s k = 9.78 and a = 0.5 ( r e f . 14). We presume t h a t macromol e c u l a r c o i l s w i t h hydrodynamic d i a m e t e r D can p e n e t r a t e i n t o p o r e s which have openings i n t o c a v i t y more o r same d i a m e t e r ( d >, D). The dependences o f s u r f a c e coverage f o r d i f f e r e n t macromolecules on t h e i r c o i l s i z e s can be c a l c u l a t e d f o r t h e adsorbents with various pore s t r u c t u r e s .

Pore d i s t r i b u t i o n s A s t h e r e i s a r e l a t i o n s h i p between t h e macromolecular c o i l s s i z e and t h e p o r e opening diameters, it i s p o s s i b l e t o c a l c u l a t e t h e dependence o f a c c e s s i b l e p o r e volume V on p o r e diame t e r s d. For t h e model o f c y l i n d e r p o r e shape we used t h e f o l l o wing e q u a t i o n

and d are e x p r e s s e d i n m2 g-' and nm, r e s p e c t i v e l y . Fig. 3 shows t h e com2arison o f t h e p o r e volume d i s t r i b u t i o n s c a l c u l a t e d by macromolecular and mercury p o r o s i m e t r y methods for two macroporous s i l i c a samples C-80 and CX-2. Porograms found by irercury p o r o s i m e t r y were o b t a i n e d i n Karnaukhov l a b a t I n s t i t u t e o f C a t a l y s i s ( N o v o s i b i r s k , USSR). T h i s f i g u r e d e m o n s t r a t e s satisf a c t o r y agreement between t h e maxima p o s i t i o n s o f t h e s e d i s t r i butions. Table 2 g i v e s t h e numerical v a l u e s o f p o r e s t r u c t u r e 1 charact e r i s t i c s f o r s i l i c a samples and carbon s o r b e n t s . Values o f d and V were c a l c u l a t e d from t h e c u r v e s o f d i f f e r e n t i a l p o r e volume d i s t r i b u t i o n by t h e g r a p h i c i n t e g r a t i o n . The comparison if

A

580

o f c o r r e s p o n d i n g v a l u e s shows a l s o good agreements i n some cases.

n 0.4

I

I

1

I

d, nm

120

80

40

Pig. 3 . Comparison o f p o r e d i s t r i b u t i o n i n C-80 (1, 2) and CX-2 (3, 4) measured by polymer- (1, 3) o r Hg-porosimetry (2, 4)

TABLE 2 V and d

-

-

v a l u e s for s i l i c a and carbon s o r b e n t s . 1 polymer porosimetry, 2 c a p i l l a r y condensation, 3 mercury porosimetry

-

-

--__-

I .

Kch-2

1

CS-2

C-&3

’>

‘_

i

3

-

1

Cb-3

2

‘1

3

CONCLUSION Macromo l e c u l a r po ros imet ry shows t h e new p o s s i b i l i t i e s for t h e s t u d y o f meso- and macroporous s o l i d s t r u c t u r e (ref. 15). Tfowever, t h i s method r e q u i r e s many polymer s t a n d a r d s w i t h nar-

581

row m o l e c u l a r weight d i s t r i b u t i o n s and t h e o p t i m i z e d c o n d i t i o n s

for t h e predominant a d s o r p t i o n o f f l e x i b l e macromolecules i n s o l v e n t , molecules o f which a r e adsorbed weakly. Accoding t o u s f u r t h e r experiments are need f o r t h e development o f macromolec u l a r p o r o s i m e t r y method. ACKNOWLEDGEMENT I n t h i s work we used many R i s e l e v ’ s i d e a s . F33FEHEn’CES 1 2

3 4

5

6

7 8

S.J. Gregg and K.S.W. S i n g , Adsorption, S u r f a c e Area and P o r o s i t y , 2 nd. Ed., Academic ?ress, London, 1982. A.V. Kiselev, I n t e r m o l e c u l a r I n t e r a c t i o n s i n Adsorption and Chromatography, Vysshaya Shicola, Noscow, 1986. E.K. Bogacheva, A.V. K i s e l e v , Yu.S. N i k i t i n and Yu.A. E l t e kov, Zh. Fiz. Khim., 39 (1965) 1777. Yu.A. Eltekov, Pure and Appl. Chem., 61 (1989) 1987. Yu.S. N i k i t i n , i n I . V . B e r e z i n ( E d i t o r ) , Immobilized Enzimes, p. 68, DIGU, i~~oscow (1976). S.P. Ztdanov, A.V. K i s e l e v , A.S. N a s a n s k i i and Yu.A. E l t e kov, Koll. Zh., 39 (1977) 354. N.A. E l t e k o v a , D. Berek and I. Novak, Zh. 7 i z . Khim., 63

(1989) 2675.

M.M. Dubinin, L.I. Kataeva and h.S. Polyakov, Izv. Acad. Nauk SSSR, S e r . Khim., (1986) 719. 9 M.M. Dubinin, L.I. Kataeva, N.S. Polyakov and V.F. Surovik i n , Izv. Acad. Nauk SSSR, S e r . Khim., (1987) 1453. I 0 N.A.Eltekova a n d Yu.A. E l t e k o v , Zh. Fiz. Khim., 60 (1986)

2272.

H r n e i r , and E.J. Xornmelzvaal, Bcta. H y d r o c h h Hydrobiol., 6 (1978) 153. 1%P. F l o r y , S t a t i s t i c a l Mechanics of Chain Molecules, C o r n e l l , I t h a c a , N. Y., (1969). 13 A.V. K i s e l e v , A.S. N a s a n s k i i and Yu.k. Eltekov, Koll. Zh., 7 1 J. Chudoba, R.

37 (1975) 556.

1 4 Yu.A. E l t e k o v , N.M. S t r a k h o v a , I. Kalal, I. Peska and I. Stemberg, J. Polym. S c i . , Polym. Symp,, 68 (1980) 247. I 5 N.A. E l t e k o v a and Yu.A. E l t e k o v , USSR. P a t . , 1500914 (1980).

This Page Intentionally Left Blank

F. Rodriguez-Reinosoet al. (Editors), Characterization of Porous Solids ZI 0 1991 Elsevier Science Publishers B.V., Amsterdam

583

FORMATION OF SECONDARY PORES IN ZEOLITES DURING DEALUMINATION: INFLUENCE OF THE CRYSTALLOGRAPHIC STRUCTURE AND OF THE SVAI RATIO H. AJOT', J.F. JOLY', J. LYNCH', F. RAATZ' and P. CAULLET* 'INSTITUT FRANCAIS DU PETROLE, 1 et 4 avenue de Bois M a u , 92506 Rueil Malmaison Cedex, France 2ENSCM~,3 rue A. Werner, 68093 Mulhouse Cedex, France SUMMARY The parameters affecting the genesis of mesopores in zeolites during dealumination have been investigated The formation of mesopores is essentially controlled by the structural defects density. Structural defects correspond to: i) framework vacancies, ii) crystalllographic defects andiii) trivalent elements incorporatedin the framework. At least two parameters control the structural defects density: the initial Si/Al ratio and the synthesis conditions. INTRODUCTION Dealumination of zeolites with low initial SVA1ratios leads to materials with new textural properties. The creation of extensive secondary porous network has been observed in dealuminated zeolites with low initial SVAl ratios, such as Y (refs.1-4), omega (ref. 5). offretite (ref. 6), mordenite (ref. 7) and CSZ-1 (ref. 8) structures. Two main parameters seem to affect the formation of mesopores in zeolites during dealumination: the crystallographic structure and the SUA1ratio, in addition the synthesis conditions have certainly to be considered as well. In order to determine the effect of each of these parameters, different zeolites with different initial Si/Al ratios were submitted to classical dealumination treatments. The effect of the initial SVAl ratio was studied with mordenite (Si/A1=5 and 10) and Y zeolite (Si/A1=2.7 and 7). The effect of the synthesis conditions was studied in the case of Beta zeolite synthesized in alkaline and fluoride medium. The specific effect of the crystallographic structure will be deduced from the two first approaches and from literature data. EXPERIMENTAL Starting from two Toyo Soda mordenites NaMI(Si/Al=5) and NaM2 (Si/AI=IO), dealuminated mordenites DeHMl and DeHM2 were prepared by steaming of low sodium forms NH.,Ml and NH.,M2 respectively, at 1073K (4 hours) followed by acid leaching in 3N HNO, at 373K (2 hours). A low sodium NH,Y form, obtained by repetitive ammonium exchanges of NaY (LZY-52 Union Carbide) was submitted to (NI-I,,)+3F6treatment leading to DeHY 1 with a framework Si/A1 ratio close to 7 (total SVAl ratio: 5.4). In a second step, DeHYl was submitted to steaming treatment at 1073K leading to DeHY2. DeHY2 has been acid leached in 1.5N HNO, solution leading to DeHY3.

584

Beta1 zeolite was synthesized using the classical alkaline medium synthesis method. The HBeta form was then obtained by calcination under air at 823K followed by two successive NH,NO, exchanges leading to the low sodium form HBetal. HBetal was submitted to a direct acid leaching treatment in 0.5N HNO, solution at 373K during 2 hours, leading to DeHBetal. Beta2 zeolite has been synthesized in the fluoride medium by J.L. GUTH and his team (ref. 10). A 823K calcination leads directly to the H form HBeta2. DeHBeta2 was then obtained by steaming at 1023K, 4 hours, followed by acid leaching in 3N HNO, solution, 2 hours at 373K. The main physicochemical charecteristics of dealuminated samples are summarized in table 1. TABLE 1 Physicochemical characteristics of dealuminated zeolites.

I

reference

aonm

Si/Al,

DeHMl

---

> 110

DeHYl DeHY2 DeHY3

2.445 2.427 2.426

7

DeHBetal DeHBeta2

---

Si/Al total 110

DX% 98

BETS m2/g 468

5 5 12 29 1lo

87 107 111

628 470 559

---

573 338

I

I I

---

41

62

-----

---

Nitrogen adsorption The nitrogen adsorption-desorptionisotherms were recorded at 77K with a#SORB apparatus (licence IFP). The samples were pretreated at 723K during 12 hours under vacuum (lo-’ torr) before isotherm acquisition. Electron microscopy The internal porosity of zeolites was investigated by observation of ultrathin sections of grains embedded in resin, using a Jeol. 120CX transmission microscope (TEM). To avoid artefacts many grains in different orientations were observed enabeling a global analysis. RESULTS . .. . 1. p (i) Nitrogen adsorption The complete nitrogen isotherms of DeHMl and DeHM2 are reported in figure 1 and are characterized by an hysterisis loop with a lower closer point at about P/po=O.42. This indicates that, as

585

0.4 cn

.6 0.3 v

%

0.2

E 3

-6 0.1

>

O.P 1 0.2 0.4 0.6 0.8 . 1 Partial pressure

"8!0

012 0:4 016 0:8 Partial pressure

1 0

Fig. 1. Complete nitrogen isotherms at 77K of A) DeHM1, B) DeHM2, C) DeHBetal and D) DeHBeta2.

Fig. 2. Microtome sections of dealuminated mordenites: a) NH4M1, b) DeHM1, c) NH,M2 and d) DeHM2.

586

in the case of dealuminated HY (ref. 3), the mesopores are not directly connected to the exterior of the crystals leading to catastrophic desorption of mesopores. The hysterisis is more developed in DeHMl indicating a more developed secondary porous network than in DeHM2. (ii) Electron microscopy Figure 2 depicts characteristic mipgraphs of m M 1 , DeHM1, NHJ42 and DeHM2 samples. As expected the starting materials show no evidence of mesopores, individual grains exhibiting uniform contrast. Mesoporescan be directly seen in DeHM 1 as low density regions. These mesopores are approximately equiaxed with average diameter about 5 nm and appear randomly distributed throughoutthe grain sections.No evidence for direct connection of the mesopores to the grain surface is observed. In D e w sample, mesopores are only rarely observed and on a small number of grains.

Kx Electron microscopy Figure 3 depicts micrographs of DeHY 1, DeHY2 andDeHY3samples. As previouslymentionned in the literature (ref. 9), the (NH.,),SiF6 treatment leads to mesopores close to the exterior of the crystals due to the fact that dealuminationof the bulk crystal is limited using this technique. These mesopores have diameters ranging from 10 to 25 nm. Steaming at 1073K leads to the apperance of mesopores randomly distributed throughout the crystals sections. Their average diameter, about 30 nm, is much larger than that previously described for steamed W Y (refs. 1-4). Nodules of 4 nm to 6 nm diameter are present in steamed samples. In addition, when the zeolite grains of DeHY2 are oriented so that (111) type lattice fringes are visible, the pores are seen to be straight-edged with faces perpendicular to the (111) direction.

..

2. (Beta z&& .) (i) Nitrogen adsorption Completenitrogen isotherms of DeHBetal and DeHBeta2 are reported in figure 1. The isotherm of DeHBetal exhibitsan hysterisisloop indicatingthat despite high initial Si/Al ratio (10)mesopores have been created during dealumination. Their formationis certainlydue to the presenceof a high density of defects in the structure,clearly visible in high resolution micrographs as an apparent distorsion of the lattice planes (figure 4). These mesopores seem not to be connected to the exterior of the crystals as indicated by the catastrophic desorption at PPo about 0.42. In contrast, the isotherm of DeHBeta2 exhibits a slight hysterisis loop. (ii) Electron microscopy Migrographs of ultra-microtome sections of DeHBetal and DeHBeta2 are shown in figure 4. DeHBetal exhibits a very dense network of small (< 4 nm diameter) pores fquently superposedin the micrograph due to the relatively large (> 50 nm) section thickness. In the case of DeHBeta2 the mesopores are of particular type. They are cylinders running along directions perpendicular to the c-axis. Viewed end on these pores are seen to traverse the solid (at least over a length equivalent to the section thickness), providing a direct connection to the exterior of the crystals.

587

Fig. 3. Microtome sections of dealuminatedHY zeolites: a) DeHY 1, b) DeHY2, c) DeHY3 and d) DeHY3 (high magnification).

Fig. 4. Microtome sections of Beta zeolites: a) metal (high magnification), b) DeHBetal, c) DeHBeta2 section perpendicularto c-axis and d) DeHBeta2 in a plane containing c axis.

588

DISCUSSION The combined use of nitrogen adsorption and CI'EM analysis leads to a coherent description of the formation of secondary pores in zeolites duringdealumination by classical techniques (steam and acid leaching treatments). Effect of the- i In the case of mordenite, the effect of the initial Si/Al ratio on mesopores formation during

dealurnination is clear. Dealurnination of mordenite with WA1ratioof 5 leads to mesopores formation. When the initial Si/Al ratio is greater than 10 very few mesopom are created even during severe dealumination. In the case of HY with initial framework Si/Al ratio close to 7, mesopores are created during dealurnination. These mesopores are larger (diameters up to 30 nm) than expected and exhibit a particular shape. This could be related to a particular distribution of framework aluminium atoms after the (NH&SiF6 treatment during which only 60% of the initial aluminium have been removed (specific aluminium atoms may have been extracted). It thus appears that if the initial Si/Al ratio is a parameter controlling the genesis of mesopores in zeolites during dealurnination, the initial crystallographic distribution of aluminium has also to be considered. .. Effect of the 7 The specific effect of the synthesis conditions (alkaline or fluoride medium) has been studied in the case of Beta zeolite which present the particularity to be composed of at least two polytypes (refs. 11,12).

The case of Beta zeolite appears particularly since mesopores have been created during dealumination despite relatively high Si/A1 ratios (10 and 17). Considering alkaline medium synthesized Beta zeolite, mesopores are seen as cavities with average diameter of 4 nm. Mesopore generation could be related to the density of structural defects present in this zeolite. The case of Beta zeolite synthesized in fluoride medium is similar since the genesis of mesopores could also be explained by the presence of structural defects. But as the mesopores are seen to be cylinders running along particular directions, we can suppose that these structural defects are oriented in specific directions too. The exact nature of these defects is uncertain but they are most likely related to the presence of polytype stacking since they exhibit specific crystallographic orientations. The density and perhaps the nature of such structural defects can be strongly influenced by the synthesis conditions. One may suspect the defects to be either locally high concentrations of aluminium or faults in polytype stacking sequences leading to a high disorder.

To rationalize the influence of each of the parameters (initial Si/Al ratio, synthesis conditions) on the formation of mesopoms during dealumination, we propose the following scheme: During dealumination, apart from framework dealumination, formation of aluminium rich nodules occurs. These nodules will lead to mesopores after acid leaching treatment providing that the framework Si/Al ratio is high enough so as not to be damaged by the acid leaching. The aluminium rich nodules arise from local framework destructions due to high local density of vacancies created

589

by aluminium extraction or already present in the as-synthesized zeolite. The initial Si/Al ratio appears logically to be one of the most important parameters for mesopores formation since it controls the framework aluminium density, thus the density of potential vacancies (A1 atoms). Post synthesis modifications ("secondary synthesis") can also lead to particular framework aluminium distributions and thus to particular vacancies distributions. In addition to existing or potential framework vacancies, slructural defects may also be present in as-synthesized zeolites (ex. Beta zeolite). Structural defects also lead to mesopores formation during dealumination. If such defects are characterized by specific orientations, the mesopores created can present similar orientations (this is the case for dealuminated fluoride medium synthesized Beta). The term "structural defects" could also be generalized by considering that it could refer to: i) framework vacancies, ii) crystallographic defects and iii) potential framework vacancies (Al, Ga, Fe etc..). Trivalent elements are thusconsideredas structural defects with respect to mesopore formation. A high density of structural defects will lead in most cases to mesopores formation in the course of dealumination treatments. CONCLUSION In this study, starting from different zeolitic structures (Y, mordenite and Beta) with different Si/A1 ratios, the parameters affecting the genesis of mesopores during dealumination have been investigated Taking into account our results and literature data, we can propose the following scheme for mesopores formation: a single structural factor can be identified which plays the major role in the formation of mesopores during classical dealumination treatments. This parameter is the structural defects density and distribution, and is related to: i) the density of existing vancies in as-synthesized zeolites, ii)the presence of crystallographic defects, and iii) the density of trivalent elements incorporated in the framework (Al, Ga, Fe..). Initial Si/Al ratio and synthesis conditions are thus indirectly two factors controlling the genesis of mesopores in zeolites. This general scheme has the advantage of predicting the behaviour of other solids not studied here. It thus appears for instance that it will be very difficult to improve the porosity of high silica zeolites by conventional dealumination treatments if the as-synthesized zeolites have a low density of structural defects. ACKNOWLEDGMENTS We would like to sincerely acknowledge Mrs BURNICHON, DUPONT, LEVEQUE,RUSSMANN and TOROSSI for the preparation of dealuminated zeolites and adsorption measurments. REFERENCES V. Bosacek, V. Patzelova, D. Tvaruzkova, D. Freude, U. Lohse, W. Schimer, H. Stach and 1. H. Thamm. J. of Catal., 61 (1980) 435-442. A. Zukal, V. Patzelova and U. Lohse, Zeolites, Vo16 (1987) 133-136. 2.

3. 4.

J. Lynch, F. Raatz and P. Dufresne, Zeolites, Vol7 (1987) 333-340. W. Schirmer and H. Tham, Izv Akad Nauk Gruz SSR Ser Khim, 5 (1979) 217.

590

5. 6. 7. 8. 9.

B. Chauvin, P. Massiani, R. Dutame, F. Figueras, F. Fajula and T. Des Courieres, Zeolites, V0110 (1990) 174-182. C. Fernandez, J. Vedrine, J. Grosmangin and G. Szabo, Zeolites, Vo16 (1986) 484-490. B.L. Meyers, T.H. Fleish, G.J. Ray, J.T. Miller and J.B. Hall, J. of Catal., 110 (1988) 82-95.

S. Cartlidge, H.U. Nissen and R. Wessicken, Zeolites, Vol9 (1988) 346-349 J. Lynch, F. Raatz and Ch. Delalande,Studies in Surface Science and Catal, Elsevier, 39 (1988) 547-557. 10. non published results 11. J.M. Newsam, M.M.J. Treacy, W.T. Koetsier and C.B.De Gruyter, proc. R. Soc.London, A, 1988,420 (1859), 375. 12. J.B. Higgins, R.B. Lapierre, J.L. Schlenker, A.C Rohrman, J.D. Wood, G.. Kerr and W.J. Rohrbaugh. Zeolites. Vol8 (1988), 446-452.

F. Rodriguez-Reinoso et al. (Editors), Characterization of Porous Solids II 0 1991 Elsevier Science Publishers B.V., Amsterdam

591

VACUUM THERMAL STABILITY AND TEXTURAL PROPERTIES OF ATI'APULGITE

J.M. CASES(~),Y. GRILLET(~),M. FRANCOIS(~),L. MICHOT(~),F.VILLIERAS(~) and J. YVON(l) (1) Centre de Recherche sur la Valorisation des Minerais et U.A. 235 - B.P. 40 54501Vandoeuvre Cedex (France). (2) Centre de Thermochimie et de Microcalorim6trie - 26, rue du 1412me R.I.A. 13003Marseille (France). SUMMARY Evolution of the external surface area and the two types of microporosity of attapulgite (structural and inter-fiber) were examined as a function of a vacuum thermal treatment upt to 500OC. The methods used include: controlled transformation rate thermal analysis, N2 and Ar low temperature adsorption calorimetry, water vapor adsorption gravimetry and quasi equilibrium gas adsorption procedure of N2 at 77K and C02 at 273 and 293K. Depending on the outgassing conditions,i.e. the residual pressure, the structure folds 150 to 7OOC. For lower temperature, only a part (18%) of the structural microporosity is available to N2, 13% to argon and 100% to C02.With water, the structure can rehydrate after the structure is folded up to an outgassing temperature of 225°C. INTRODUCI'ION Attapulgite or palygorskite is a fibrous aluminum-magnesianclay rare used by man for a long time because of their sorptive properties (refs. 1-2).Studies of the structure have shown that attapulgite is made up of talc-like layers arranged in long ribbons stuck together to form the fibers and in staggered rows separated by channels parallel to the fiber axis. These channels are referred to as structural micropores or intramicropores. The unit cell parameters are: a sin p = 12.7 A; b = 17.9 A; c = 5.2 A (ref. 1). In a half unit cell, four H20 molecules are present in the channels (zeolitic water) and four others are bound to octahedral cations. On heating, these latter water molecules are lost in two stages; when the first two water molecules are lost, the structure collapses by alternate rotation of ribbons folding, (refs. 3-4). The porous structure is complicated by the sticking of fibers with each other which creates an intermicroporosity (ref. 5). As many authors suggested that the availability of the structural channels to different adsorbents as nitrogen molecules is limited (ref. 2), the aim of this study was to use different adsorbents (N2, Ar,C02, H20 vapor) and methods able to reveal information about relative pressures < 0.07 in order to distinguish the filling of the two kinds of microporosity and the adsorption on external surface mainly consisting of (011 ) crystal corrugated faces. These studies were made as a fonction of both surface coverage and thermal treatment, i.e. as the porous structure progressively folds and fibers sinter.

592

SAMPLE AND METHODS The attapulgite studied here was from the Montagne de Reims (France) and was supplied by BRGM (OrlCans, France). The approximate structural formula is si8 (A11.38 Fe0.22~' Fe().312+ 0 0 . 8 9 ) 0 2 0 (OH)2 (H20)4 (H20)4 Kg.13+ Nq.01+ C q 0 2 ~ + The . major impurities are quartz (4%), anorthite (0.8%), calcite (0.6%), anatase (1%) and mica (1.0%). Seen under transmission microscope, the size of fibers is variable ranging from 0.5 to 2.0 p m in length and 250 to 360 A wide. Outgassing for adsorption microcalorimetry and thermal analysis was carried out by controlled transformation rate thermal analysis (CTRTA) (ref. 6). Its interest is both the rather high resolution achieved on the thermal analysis curves (ref. 7) and the possibility of carrying out the experiment directly with the sample bulbs needed for adsorption microcalorimetry. The experimental conditions selected were a sample mass of about 0.260 g, a residual pressure of 2 Pa over the sample and a dehydration rate of 2.77 mglh. Adsorption microcalorimetry of N2 and Ar at 77K was carried out with an equipment described by Rouquerol (ref. 8) and which associates quasi equilibrium adsorption volumetry with isothermal low temperature microcalorimetry (using Tian Calvet heat flow-meters) so that two curves are continuously recorded (heat flow and quasi equilibrium pressure) as a function of the amount of gas introduced into the systems. Continuous plots of the adsorption isotherm and of the derivative enthalpy of adsorption Aads h vs surface coverage may easily be derived (refs. 4,7).

A quasi equilibrium gas adsorption procedure recently presented (ref. 9) was used to examine surface heterogeneity and microporosity of attapulgite in more details. With this method a slow, constant and continuous flow of adsorbate (C02 at 273 and 293K, nitrogen at 77K) was introduced into the adsorption cell. From the recording of the quasi equilibrium pressure (in the range of 0.01 to 5 . lo4 Pa) vs time, the adsorption isotherms were derived. The experimental conditions were a sample mass of about 0.400 g with outgassing under 0.1 Pa up to a final temperature of 25,70, 100, 130 and 15OOC for C 0 2 and 25,70 and 380°C for nitrogen. Adsorption gravimetry of water vapor was carried out with the experimental apparatus described in ref. 10. Prior to each experiment 100 mg samples were outgassed with a residual pressure of 0.1 Pa during 18 h and a temperature of 25,70, 100, 130,225,300,380 and 500OC. RESULTS AND DISCUSSION The dehydration curve can be divided in three steps that successively correspond to the evolution of 1) the zeolitic and adsorbed water on external surface (T < 75"C), 2) coordination water linked at the edge magnesium atoms inside of the channels (in two times, domains 75-150OC and 15O-37O0C,two molecules each and weight losses 10.48% of the final mass), 3) structural(2.61%), one molecule due to two hydroxyls from the octahedral layer of the talc ribbon) and decomposition of calcite. According to ref. 3, the structure folds when approximately half of the coordination water is removed, i.e. here under 2 Pa residual pressure between 100 and 130OC. Regarding now the enthalpy curves (Fig.1 and 2) notice that the curves obtained for outgassing temperatures lower than that corresponding to the folding may be separated into three parts:

593

lbads

'hl A

25 -0-

100°C

-'-130°C

20

150°C +

225°C

+

380°C

-x-

500°C

15

10

5 i 0

I

0,2

0,4

0,6 0.8 surface coverage

1

1.2

Fig. 1. Derivative enthalpy of adsorption versus coverage for attapulgite-nitrogen systems at 77K and various outgassing temperatures - Part a,where the derivative enthalpy of adsorption is constant as it has been observed either

on homogeneous surface or homogeneous porous solid (molecular sieves). It is therefore reasonable to assume this part corresponds to the filling of the structural or intramicroporosity. The value indicated at point A is no longer detectable on samples obtained for outgassing temperature higher than that corresponding to the folding of the crystal, suggesting that the structural microporosity is not available to nitrogen or argon molecules. Point A corresponds to a nitrogen liquid volume adsorbed of about 38.8 mm3 . g-l, and 26.5 mm3 . g-l for argon and final outgassing temperature of 25°C (Table 1). - Part 0,where the derivative enthalpy of adsorption decreases (down to inflexion point C) and which is likely due to the filling of the inter-fiber microporosity or to defect in the arrangement of the structural units (ref. 5). The inter-fiber micropore volume, as measured from the width of region 0, is not influence; by final outgassing temperature for nitrogen (- 22.2 mm3. g-l - Table 1). The values of IAadS hl measured with nitrogen increase up to 380°C (more than 26 KJ . mole-l). This phenomenon is more likely due to the increased energy of the adsorption sites for the quadrupolar nitrogen molecules than to a smaller size of the micropores (only a slight increase is observed with argon). - Part y, where the monolayer capacity is reached on the external surface of the fibers. This part goes up to 6 = 1 (which corresponds to Emmett and Brunauer's point B). The width of y allows determination of an external surface area which is kept constant with outgassing temperature up to 500"C.The arithmetical mean value obtained with nitrogen (64m2/g) is higher than for argon (54 m2/g). The difference could be attributed to the cross sectional area taking into account the

594

calculation of the specific surface area (nitrogen 16.2 A2, argon 13.8 Az).The molecules do not cover the same area on the corrugated attapulgite surface as on a flat surface. In contrast to sepiolite (ref. 4), the constancy of domains 13 or y with outgassing temperature suggests that there is no important change in shape or size for inter-micropores or fibers due to the folding of the crystal and to structural modification at higher temperature. The value of external surface area, thus calculated, corresponds to that obtained from statistical measurements by transmission electron microscopy (58 m2 g-1) (ref. 7).

IAads

19

'hl

Jr(kJ'mo'e'

A

-0-

100°C

-I-

130°C

-

-O-

-

150°C 225°C 380°C

-"- 500°C

5

I

0

0,2

0,4

0.6

0,8

1

1,2

surface coverage

Fig. 2. Derivative enthalpy of adsorption versus coverage for attapulgite-argon system at 77K and various outgassing temperatures The liquid volume VB corresponding to the amount adsorbed at "point B" may also be used to calculate an "equivalent specific surface area" (Table 1, column 3). Here the word equivalent is, of course, used to point out the partial inadequacy of the above calculation for a microporous solid in which the molecule does not cover all the same area as on a flat surface (ref. 11) Table 1 shows that area for attapulgite is maximum at 100°C when the zeolithic water has been lost and then decreases up to about 130 m2. g-l after the structure is tilted when about half of the bound water is driven off, and alternate ribbons rotate positively or negatively to close the channels (intramicroporosity)forming what is known as folded structure. Tables 2 and 3 give the main results obtained from C 0 2 and water vapor adsorption respectively. The folding of the structure under different outgassing condition (0.1 Pa) is associated with a decrease of the micropore volume accessible to C02 observed between 70 and 130OC. The volume of gas, which once adsorbed is able to completely fill the micropores, was calculated using Dubinin's equation (ref. 12) and convertied into liquid volume using 1.08 and 1.05 g/cm3 for liquid C 0 2 at 273K and 293K respectively. The values obtained for temperature lower than that

595

corresponding to the folding of the structure are higher than the values observed for nitrogen and argon.

TABLE 1. Low temperature adsorption calorimetry results for palygorskite

(1) Total specific surface area ; (2)monolayer capacity obtained from the B point per unit mass of adsorbent; (3) micropore volume per unit mass of adsorbent as calculated with density of the liquid adsorptive; (4) external specific surface area. TABLE 2. Micropore volumes Vo (liq) of paligorskite obtained from C@ adsorption

25

70

100

130

273

0.2279

0.2556

0.1438

0.0241

293

0.2274

0.0719

150

0.0373

596

For water, the monolayer capacity calculated by the B.E.T. method was converted in equivalent surface area using a cross sectional area of 14.8 A2 for the water molecule. Results plotted in table 3 (column 4) show that regarding rehydration after heating at different temperatures, the attapulgite can rehydrate after the structure is folded up to a final outgassing temperature of 225OC. This value is the same that observed for sepiolite (ref. 4). Beyond this temperature, the new bonds originating in the anhydrous structure resist rehydration. From the structural parameter and formula it is possible to calculate the theoretical microporosity. The value obtained is 0.2096 0 3 g-1. If the value of intermicroporosity obtained from nitrogen and argon are taken into account (arithmetical mean 0.0241 cm3/g), the sum (0.2337 cm3/g) is in good agreement with the value derived from C02 adsorption. It is possible to conclude, as observed with sepiolite (ref. 9), that C02 fills all the microporosity, nitrogen no more than 18% and argon about 13%. Classical parameters given for the dimension of channels (3.7 x 6.4 A2) (ref. 1) and that derived from the zeolitic water content give a value for intramicroporosity of about 0.085 cm3 g-l. This is, incidently, near of the total volume obtained either for nitrogen and argon at point TABLE 3. Equivalent specific surface area and energetic constant as calculated from the BET theory and obtained from water adsorption

s total

C

m2/g

0.0580 0.0819 0.0805 0.0774

381

0.0819

399

0.0198

98

~~

I I I

22.5 25

I

0.0198

98

0.0270

135

I

50 13

597

B or for water from the monolayer, capacity calculated from the BET therory. But these values contain the inter-fiber microporosity and the external surface area. Thus, the dimension usually given for the channels are too low to account of all the adsorption data. In order to check the influence of vacuum condition on the folding temperature, an another run was conduced with the quasi-equilibrium gas adsorption procedure on a sample outgassed at 7OoC during 4 hours with a residual pressure of 10-5 Pa. The isotherm obtained with N2 at 77K is plotted in Fig. 3 in the form 8 (where 8 = Va/Vm) vs In (P/Po) where Va represents the adsorbed volume, Vm the monolayer capacity, and P/Po the relative equilibrium pressure. This plot can be used to study surface heterogeneity (ref. 13). The BET treatment leads to a liquid V, value of 0.0415 cm3 g-1 that corresponds well to the values given in Table 1 indicating that the structure is already folded. Then it is possible to plot (AWA In P/Po) against In (P/Po). That plane gives access to the different

homogeneous domains of the surface (ref. 13). Using a special procedure and BET treatment (ref. 14) for each homogeneous domain, three different domains are observed : 1) high energetic domain A which represent 27% of the total liquid volume V, 2) moderate energetic domain B (16%), 3) low energetic domain C (56%). In these conditions, the cumulative BET isotherms fit completely the experimental curve. The domain C corresponds to a surface of 65 m2 g-1 in good agreement with the value for the external surface area given in Table 1 and the general interpretation of the adsorption enthalpy curves. This complementary run show that the inter-fiber microporosity could be divided in two domains (A + B) corresponding to a liquid volume of 0.0178 cm3/g, a value slightly lower than those presented in Table 1.

I

IFTA 0.5

0

-20

-13.6

-10

-6.2

-3.5

I.@G ( P / h J

Fig. 3. The heterogeneity of attapulgite outgassed at 7OoCand 10-5Pa observed by quasi equilibrium gas adsorption procedure and calculated after special Ueatment (I) : isotherm, (11) derived isotherm.

0

598

ACKNOWLEDGEMENT This research was supported by the Phygis program of the Ministkre de la Recherche. REFERENCES 1 2 3 4 5 6 7 8 9 10 11

12 13 14

Jones, B.F., Galan, E. in Review in Mineralogy: S.W. Bailey, ed., Hydrous Phyllosilicates (exclusive of micas), 19, Mineral. Soc. of America, Washington, 628-674. 1988. Barer, R.M., Mackenzie, N., and MacLeod, D.M., J. Phys. Chem., 58 (1959) 568-573. Van Scoyoc, G.E., Serna, C., Ahlrichs, J.L., Am. Mineral., 64 (1979) 216-223. Grillet, Y., Cases, J.M., Franqois, M., Rouquerol, J., Poirier, J.E., Clays and Clay Minerals, 36 (1988) 233-242. Rautureau, M. and Tchoubar, C., Clays and Clay Minerals, 24 (1976) 43-49. Rouquerol, J., Thermochimica Acta, 144 (1989) 209-224. Cases, J.M., Grillet, Y., Franqois, M., Michot, L. VilliCras, F., Yvon, J,to be published in Clays and Clay Minerals. Rouquerol, J., J. Thermal Analysis, 2 (1970) 123-140. Michot, L., Franqois, M., Cases, J.M., Langmuir., 6 (1990) 677-681. Poirier, J.E., Franqois, M., Cases, J.M., Rouquerol, F. in Fundamentals of Adsorption, T. Athanasios, T. Laiapis eds., A.I.C.H.E., New York, 472-782, 1987. Sing, K.S.W., Everett, D.H., Haul, R.A.W., Moscou, L., Pierotti, R.A., Rouquerol, J. and Siemieniewska, T., Pure Appl. Chem., 57 (1985) 603-619. Dubinin, M.M., Pure Applied Chem., 10 (1966) 309-321. Cases, J.M, Bull. Minkral., 102 (1979) 684-707. VilliCras, F. Internal communication. (1990)

F.Rodriguez-Reinosoet al. (Editors),Characterization of Porous Solids II

599

1991 Elsevier Science PublishersB.V., Amsterdam

CHARACTERISATION OF POROUS Si02-A1203 SOL-GELS: MODEL HETEROGENEOUS CATALYSTS

* , T.J.

P.A. SERMON

WALTON, M.A. MARTIN LUENGO (YATES) and M. YATES

Department of Chemistry, Brunel University, Uxbridge, Middlesex UB8 3PH, UK

SUMMARY Silica-alumina jql-gels have been prepared with a variety of compositions; the addition of A1 reduces the adsorption capacity, the total surface area and the microporosity os+the gels. This can be explained if the adsorption or reduces the charge on the silica sol-gel particle? and incorporation of A1 + and enhances their adhesion. The gels readily allowed ion-exchange with Cu temperature-programmed reduction and X-ray photoelectron spectroscopy has been used to probe the environment of these cations in model precursors of heterogeneous catalysts. The potential of this approach for the analysis of solutions is considered. INTRODUCTION It has been argued [ l ] that many of the intricacies ofheterogeneous catalysts arise prior to producing the supported catalyst surface itself, i.e. at a precursor state when species are adsorbed from solution at the solid/solution interface during catalyst preparation.

Such species probably template and

define irreversibly the selectivity and reactivity of the catalyst surface produced after reduction, calcination or sulphidation. Multinuclear NMR has been used to probe the prevailing precursor chemistry at the solution/solid interface in the pores of such catalysts [ l ] . attempted to use X-ray photoelectron spectroscopy (XPS).

Here we have

Traditionally XPS of

solutions has only been possible in thin films [2] which are constantly replenished to compensate for rapid evaporation under high vacuum conditions. Porous oxide gels provide an alternative framework for a new mode of analysis of liquid phases contained therein. These are readily prepared via the sol-gel route [3] involving alkoxide hydrolysis M(OR),

+

X H ~ O= M(oH)~(oR)~-~ + XROH

and subsequent condensation -M-OH

+ OH-M-

c

-M-0-M-

+

H 0 2

In such preparations the prevailing acidity-alkalinity and the H20:M(OR)n alkoxide ratio are critical in defining the properties of the gel produced.

The

introduction of a second (or third) metal cation is possible and in the case of silica-alumina gels the Si04 and A104

-

tetrahedral building blocks have ready

600

similarities which allow

incorporatian a f the two producing:

Si-OH 0 1

-0-Si-0-A1-OH 1

0 1

Si-OH Naturally then the Si:A1 ratio will define the surface area, acid site density, etc. of the gel.

The latter property may well modify the ion-exchange

capacity of the gels.

This in turn will affect their ability to incorporate other say transition metal or IB metal cations. Such as ion-exchange

mechanisms have been postulated [4] to produce: S i-OH

0 1

-0-Si-0-Al-0-Cu(0H ) + 2 5 1

+ H+

0 Si-OH when the solvated Cu2+ cation is used and similar process are thought to occur with Pt, etc. [5]. These porous sol-gel derived matrices are therefore model of heterogeneous catalysts.

Since the surface area exhibited by the internal surface of the

pore volume (V ) (if this is composed of non-intersecting uniform cylindrical P pores of radius r) is given by S int where S int=2V /r and s o their high P surface-are a will enable a high fraction of surface-held catalyst precursors to be investigated per unit volume.

In addition their small pore size may reduce

the rate of solution l o s s under vacuum conditions and allow in-situ X-ray pnotoelectron spectroscopy of these species at the solution-solid interface of this precursor to heterogeneous catalysts. This approach is illustrated here in terms of the study of model porous Si02-A1203 sol-gels with and without the addition of Cu2+.

EXPERIMENTAL Tetraethoxysilane (Si(OC2H5)4

TEOS), absolute ethanol, water and 3M HC1 were

used in the molar ratio 1:4:4:0.07

in the sol-gel preparations.

TEOS in

ethanol at 298K was mixed with constant stirring with HC1-water at 298K for 60min before allowing gelation in a polyethylene beaker. aluminium nitrate (A1(N03)3.9H20)

was added.

In some samples

An attempt was made to introduce

Cu2+ to each of the gels by immersing the gel in an aqueous solution of cupric

601 nitrate. Total surface areas were investigated by application of BET theory to the extent of N

2 adsorption at 77K measured in a Carlo-Erba 1800 Sorptomatic instrument after outgassing samples (0.3-0.5g) at 393K for 16h, assuming that the cross-sectional area of N 2 in the monolayer was 0.162nm2 Thermogravim-

.

metric analysis was carried out in a Stanton Redcroft 780 and X-ray photoelectron spectroscopy in a Kratos ES300.

Temperature-programed reduction was

carried out in 4%H / N during heating at 5K/min. 2 2 RESULTS AND DISCUSSION The adsorption isotherms for N2 at 77K on the silica-alumina sol-gel derived samples are shown in Figures 1-2 and the surface area data derived from BET analysis of these isotherms are shown in Table 1.

TABLE 1 Textural Information in SiO -A1 0 Samples Derived from the Sol-Gel Route 2 2 3 %Si02%A1203

'total

100 0 75 25 50 50 25 75

653 410 261 23

C

387 252 191 15

'ext

53 377 234 16

int

600 33 27 7

t'

0.31 0.33 0.24 0.06

'mic

0.24 0.04

0.01 0.0

In Figure 1 and Table 1 it can be seen that Si02 with a surface area of 2 653m /g showed substantial micropososity (r

B

2

4

6

B

t tx,

E

2

4

Fig. 2.-"t" plots for water vapour sorption at 20°C upon Li-M: initial (A), vacuum and air preheated at 300°C (B); upon A1-CLM nitrogen preheated at 300°C during 10 h (C) and 30 h (D). The lower straight line corresponds to only multilayer adsorption.

P/ P o

__ -

0w

0

Fig. 3.- "t" plots for water vapour sorption at 20°C upon Al(La)-CLM nitrogen preheated at 300°C during 10 h (A), 2 0 h (B) and 30 h (C). The lower straight line corresponds to only multilayer adsorption.

2

4

c 6

8

Fig. 4 . - "t" plots for water vapour sorption at 20°C upon A1-CLM nitrogen preheated during 10 h at 300°C (A), 500°C (B) and 700°C (C). The lower straight line corresponds to only multilayer adsorption on the sample preheated at 300°C.

612

Furthermore, the previous XPS data already mentioned demonstrate that they remain in the interlamellar spacing after heating. The nature of the interaction of the interlamellar pillars with the tetrahedral and/or octahedral sheets of the montmorillonite could afford an explanation. New experiments are being carried out in order to interpret these results. It is noticeable that the SBETand d(001) parameters are not appreciably influenced by preheating Al(La)-CLM, :Table I. In spite of this, spacing is generally used to follow the thermal evolution of these materials. Apart from the present results, examples from the literature show the non-existence of relationship between both parameters and the pore (V,) and micropore volumes. In (14) the values: 18.4 A (d(001)), 242 rn2.g-' (SBET) and 0.20 cm3 .g-1 (V,) were obtained for an alumina-montmorillonite; while for another one, prepared under different experimental conditions, the values: 15.5 A (d(001)), 249 m2.9-' (SBET)and 0.23 cm3.g-' were found. TABLE I : INTERLAMELLAR MOLECULAR WATER ( v cm3

Sample

g-'

d(001)

V

(A) Li-M A1-CLM A1-CLM A1-CLM A1-CLM Al(La)-CLM Al(La)-CLM Al(La)-CLM

300 300 300 500 700 300 300 300

10 10 30 10 10 10 20 30

95 225 225 150 50 215 215 215

9.6 18.2 18.2 17.2 v.b. 18.4 18.4 18.4

0 86 77 31 15 91 70 41

Pretreatment by heating at temperatures higher than 300°C determines a decrease of the interlamellar water content for the A1-CLM, which is not accompanied by a parallel change in the basal spacing, Table I. Strong reductions in the catalytic activity of montmorillonite pillared with alumina, which were not accompanied by appreciable changes in the basal spacing have been observed in the literature. The diminution of activity has been related exclusively to poisoning effects or to changes in the Lewis-Bronsted acid sites ratio. For example, Matsuda and Kikuchi (15) have observed the activities: 41.8% (300"C), 19.4% (400"C), 7.0% (550°C) in the reaction of conversion of 1,2,4-trimethylbenzene, at the indicated temperatures.

613

The interlamellar water content calculated on the basis of a 8.6 A interlamellar thickness and the above mentioned apparent density of 0.36 kg.dm-3 is 120 cm3(NPT). The experimental values, Table I, are expected to be decreased by: i) interstratification between collapsed and open lamellar; ii) variable heights of the pillars, sometimes too small to allow the efficient packing of HzO molecules; and iii) different types of ordering of the pillars within the interlamellar space. Some of these effects must influence the time of preheating at 300°C, in Al(La)-CLM and the temperature of preheating of A1-CLM. From these data it is concluded that the basal spacing and BET specific surface area are not sufficient by themselves to represent the potential activity as adsorbents and/or catalysts of the pillared-smectites. ACKNOWLEDGEMENT

We thank CICYT for financial support. REFERENCES

1.-F.Figueras; Cat.Rev. -Sci.Eng. 30(3), (1988) 457-499. 2.-J.ShabtaiIM.Rosel1 and M.Tokarz; Clays and Clay Miner. z ( 2 ) I (1984) 99-107. 3.-M.Tokarz and J.Shabtai; Clays and Clay Miner. 33(2), (1985) 89-98 4.-E.ReyesIF.Huertas and J.Linares, in A.Pietracaprina (Ed.), Proc. 1st Congr.Bentonites, Sassari-Cagliari (Cerdefia), (1978) 149-157. 5.-J.PoyatoIM.M.Tobias and J.M.Trillo; Applied Clay SCi., 4,(1989) 499-508. 6 .-~.M.Trillo,J.Poyato,M.M.Tobias and M.A.Castro;Clay Miner. In press. 7.-G.W.Brindley and S.Yamanaka; Am.Miner. 64, (1979) 830-835. 8.-J.Y.BotteroI J.M.Cases, F.Flessinger and J.E.Poirier; J.Phys.Chem. 84, (1980) 2933-2939. g.-E.C.Ormerod and A.C.D.Newman; Clay Miner. Is, (1983) 289-299. lO.-R.Pusch; Applied Clay S c i . 2, (1987) 343-352. 11.-J.Jr.Hagymassy,S.Brunauer and R.Sh.Mikhai1; J.Colloid Interface Sci. 29, (1969) 485-491. 12.-T.M.El-AkkadI N.S.Flex, N.M.Guindy, S.R.El-Massry and S.Nashed; Surface Techn. J J , (1982) 69-77. 82, (1985) 13.-H.Van Damme and J.J.Fripiat; J. Chem.Phys. 2785-2790. 14.-J.Sterte,J.E.Otterstedt H.Thulin and F.E.Massoth; Applied .~ Catal. (1988) 119-129. 15.-T.MatsudaIM.Asanuma and E.Kikuchi; Applied Catal. 38, (1988) 289-299.

a,

This Page Intentionally Left Blank

F. Rodriguez-hinoso et al. (Editors),Characterization of Porozu Solids ZI

615

0 1991 Elsevier Science Publishers B.V., Amsterdam

EYOLUTION OF WROSIlY DUFUNG CONVERSION OF ~-ATJMlJUTo A NOVEL FOROUS a-ALWEN?. FIBRE

By

M.H.STACEY

ICI manced Materials, P . 0 . W 11, The Heath, Runcorn, England

ABSTRACT AI-I exprimental sol-gel 1.9% silica-doped almina fibre has been studied before and after the n t o a-almina phase change. The initial fibres contained roughly equal munts of randm pores and pores aligned parallel to the fibre axes, but only the f o m r were eliminated during the phase change. The product a-alumina fibre has therefore 90% axially-aligned pores and should have an excellent s p x i f i c modulus. This behaviour is contrasted with that of 5% silica-doped alumina fibres previously studied.

IN'IRODUCTION

Generally alumina fibres made by sol-gel mthcds and calcined below On heating t o higher 1000°C consist of nesoporous 0-almina. temperatures eventually the thermodynamically stable a-almina i s formed (ref 1). This phase transition results i n a significant voluw shrinkage (10-20%) of the alms and so a reorganisation of the pore structure i s t o be expected. It is also generally knm that the

details of this phase transition are strongly affected by s i l i c a doping. In particular the transition temperatures are &creased markedly and the porosity elimination is delayed t o higher terqxratues.

For example, a t

about 4% s i l i c a the initial msoporosity can be almost ccanpletely eliminated, whereas without s i l i c a considerable porosity remains. The fibres studied here were experimental fibres made by a proprietory sol-gel prccess incorporating 1.9% s i l i c a additive.

This additive i s in a lower m u n t than i n previously reported materials (refs 2.3) but i s s t i l l expected t o influence the phase change m r a t u r e significantly. A particular feature of these fibres i s that about 50% of the i n i t i a l porosity was preferentially aligned w i t h the fibre axis: this i s again different frm the fibres previously reported (ref 2) which contained only randcanly orientated cylindrical pores w i t h a narrow pore size distribution. The effects of the r- to a phase change i n these fibres has m been studied using X-ray m

r diffraction (XRD),

616

nitrogen adsorption isotherms, true density determinations, the optical properties, -1-Angle Neutron Scattering (SANS), and TEN t o derive a canplete description of the microstructural changes. The resulting a-almina pssesses an unusual type of porosity due t o the nature of the precursor. WERIMENTFL

Silica-doped sol-gel aligned fibre t a w were ma& by a proprietory process w i t h a man fibre diameter of 3 p . They were finished a t 900°C in order to produce the mesoprous q-alumina phase. They were then further calcined a t 1300°C in a muffle furnace i n order t o convert the fibres t o the a-alumina phase. P o k i e r XRD patterns here determined t o confirm the phases. characterisation of the two typs of fibres was by nitrogen adsorption a t 77K using a Micrcmxitics Inc Digisorb 2500 equi-t. Samples were degassed beforehand to 2 5 0 T and 0.01 mbar for 16 hrs. BJTC surface areas were calculated frm results below a relative pressure of 0.3 and the Gurvitsch pore volurne frm the plateau uptake a t relative pressure approaching saturation using a liquid nitrogen density of 0.8081g/ml. Pore-size distributions w r e calculated frm the adsorption branches using the &sH mthcd assuming cylindrical p r e s . The optical properties were evaluated using a Nikon transmitted light microscope equipped w i t h polarisor and analyzer and using a S m n t canpensator to determine the amount of double refraction.

The difference

between refractive indices in the axial and radial directions for a fibre

was calculated frm the equation

na-nr

=

e*A/l80*d

where e i s the angle of rotation of the Senannont ccanpensator w h i c h causes maximum darkening of the fibre image, h is the wavelength of the light used ( 0 . 5 5 ~ ) and d= fibre d i a m t e r ( p ) . Smdll-Angle Neutron Scattering expriments were performed either a t Institute Laue-Langevin. Grenoble using spectrmter D17, or a t Rutherford-Appleton Laboratory, Harwell, using the LCQ spxtrcneter. The centre of the detector for D17 was offset frm the main neutron beam axis so as t o obtain a greater Q-range frm the results. A t IJL 12.0A neutrons were used, whereas a t RAL the pulsed neutron source has a range of wavelengths (4-1OA). In both cases standard data reduction p r o g r m s enabled the scattering intensity t o be calculated as a function of the

617

scattering vector Q defined by

where 28 is the scattering angle and h ( A ) is the wavelength of the neutrons. The Q-range accessible w a s 0.006-0.3A-1on D17 and 0.0056-0.228-1 on

a. The fibre sarrg?les (ca 0.5g), consisting of tows of aligned fibres with a volume fraction of ca 10% were loaded into l h id fused silica tubes, heated under vacuum (0.01mbar) at 200°C and the tubes then sealed under vacuum. In this way absorbed water was eliminated f r m the fibres. me neutron transmission was ca 70-80% for these m u n t s of fibres. The scattering data from the two-dimensional area detector were found to be anisometric and were therefore converted to one-dimensional data by using sector masks. Scattering in the fibre direction was derived from a 75" wide mask parallel to the fibres and the scattering normal to the fibres was derived from a 15" wide mask perpndicular to the fibre direction. Samples were prepared for TEM by embedding in epoxy resin, and thinning in an Ion Tech A t m M i l l operated at 5kV and 100 nm, mesoporous if d=3-100 nm and microporous if d10Qnm d=3-100nm macro meso

~~

-

ST-DVB Styrene-divinylbenzene (refs.7-12) ST-DVBmodified agent Polystyrenexylylenedichloride Polystyrenemonochlorodimethyl ether (refs.13-15)

PS-XDC Styrosorb PS-MCDE Styrosorbmodified agent

d 1 . 2 nm

.

Because the i s o s t e r i c heat of adsorption of benzene on the zeolite NaX is practically independent on the amount adsorbed "(ref -4)" and the volume V

3

(=0.295 cm / g ) of supercages of this zeolite is known "(refs.5-6)", i t s a a state p , v , T relations on NaX may be evaluated by the equation (1) and by the relation v a =Vo/a(p8) from the adsorption isotherms. Similarly by the use of the adsorption isotherms of benzene, krypton, ethane e t c . on zeolites NaX and mordenites, w e have found that the s t a t e p r o p e r t i e s of this fluids adsorbed in micropores may be described by the Amagate state equation a a p (V -vb) where v

b

=

iRT

,

(2)

is the covolume of adsorbed molecules and i the parameter which cha-

r a c t e r i z e s the interaction between the adsorbed molecules. T h i s 3D analogy

761

of the Schofield-Rideal s t a t e equation h a s been f u r t h e r accepted as a useful a a approach t o a r e a l p , v , T r e l a t i o n s of fluids confined in m i c r o p o r e s .

THE ADSORPTION ISOTHERM OF FLUIDS ON ENERGETICALLY HOMOGENEOUS MICROPOROUS SOLIDS The derivation of the adsorption isotherm equation is based on the thermodynamics of small systems in the field of adsorption f o r c e s . The adsorbed fluid in the uniform microporous solid c o n s i s t s from a l a r g e number of equivalent, distinguishable, independent systems of fluid, each with fixed c e n t e r of m a s s , what eliminates the t r a n s l a t i o n d e g r e e s of freedom of individual systems. The s t a t e equation of the adsorbed fluid d e s c r i b e s the relation a a between the mean values of the p r e s s u r e p and the molar volume v , a t given temperature T , taken o v e r a l l ensemble of individual systems of the fluid, localized in individual m i c r o p o r e s . Since a l l systems of the ensemble a r e a equivalent, p and va a r e a l s o time a v e r a g e s f o r a single system. The quantit i e s r e f e r r i n g t o the adsorbed fluid are denoted by the s u p e r s c r i p t a and that concerning of the bulk g a s by s u p e r s c r i p t g . The derivation s t a r t s from the known Gibbsian condition of the diffusional equilibrium of the fluid in the field of e x t e r n a l f o r c e s pa

+ Nr)

=

pg

,

T=const.

,

(3)

where pa and pg a r e the chemical potentials of adsorbed and equilibrium bulk g a s , respectively and @ is the potential e n e r g y of the adsorbed molecules. From the statistico-thermodynamicalderivation "(ref. 7)" follows, that the equation (1) is quite c o r r e c t only in the c a s e , when the potential @ does not depend on the position r . Generally, condition (1) contains additional t e r m , which accounts the influence of the potential e n e r g y gradient d @ / d r . The chemical potential pg of the bulk g a s c a n be e x p r e s s e d by the known relation

pg

=

p+o

+ R T M p g /P+)g + B(P!

-

P

g

1 ,

(4)

where po is the chemical potential of the bulk fluid in the standard s t a t e ,

+ p+ the standard p r e s s u r e of this fluid and B the second v i r i a l coefficient of the

B e r l i n e r form of the v i r i a l g a s s t a t e equation. F o r convenience, we chose f u r t h e r the bulk fluid s t a t e as s t a n d a r d , w h e n i t s

762

pressure pg i s equal to the adsorbed fluid p r e s s u r e at half filling of the ada The fraction of saturation of sorbent with sorbate 8 sorption space p 8-0.5’ a i s here defined a s the ratio of the amount adsorbed a(-V /v 1 to the hypotheti0

c a l limiting amount adsorbed a (=V /v 1 i . e . o o b 8 = a / a o = vb/v

a

.

According to the above definition, a s follows from eqns. (2) and

’+

‘:=0.5

= iRT/vb

(5)

.

The evaluation of the chemical potential pa i s based on the thermodynamics of small systems. The change of the chemical potential connected with the transport of the fluid from the standard to the adsorbed state may be divided into two p a r t s . The f i r s t , further denoted a s perturbation change of the chemical potential Ap* is the change of p

t

, which

corresponds to the separa-

+

tion of the bulk fluid a t the standard p r e s s u r e pg into small systems localized in micropores. The second part is the change of chemical potential connected

+

with the compression of the adsorbed fluid from the standard pressure pg to a the pressure p Hence

.

where p

0

+

i s the chemical potential of the bulk fluid in the standard state.

w

According to the definition of free energy, Ap

+

X

Ap+ = RTlnv

=

AH:

-

may be written a s

,

TAS:

where v i s the perturbation activity, AH

+

(8) X

+

the molar perturbation enthalpy

and A S x the molar perturbation entropy, which correspond to the separation of the fluid into small systems and its localization i n the micropores. The effect of this separation may be illustrated by the hypothetical adsorption of the fluid on idealized hard wall noninteracting microporous solid of the same geometric structure a s the r e a l sorbent. For this idealized c a s e , when @SO, it can be shown on the basis of equa’tions

V=P,fPf where po

(3),(4),(7) and ( 8 ) that (9)

3

is the hypothetical equilibrious gas pressure above the idealized

microporous solid with @=O

,

when pa = P +

763

The perturbation change of enthalpy of the bulk gas a t adsorption, when w e assume that behaves a s the van d e r Waals fluid, may be evaluated by the relation

A =2iay/v BH=ibRy/v and where y depends on the degree of sepab ’ b H ration. When the molecules a r e completely s e p a r a t e d , y = l . a and b a r e the

where

constants of v . d . W equation. The perturbation change of the entropy A S

x

+ e. g.

f o r a known microporous s t r u c t u r e of the zeolites, may be evaluated theoretiY

cally on the b a s i s of s t a t i s t i c a l thermodynamics. It is always negative ( A S < O )

t

a s r e s u l t of the loss of the translation d e g r e e s of freedom of small systems of fluids confined in micropores. When the p r e s s u r e pg may be neglected in the l a s t term of eqn.(4) in compar i s o n with pg

+’

then equations (2)

-

(10) yield the following equation of ad-

sorption isotherm of fluids on energetically homogeneous solids

determines the temperature dependence of adsorption isotherms and a l s o the form of adsorption i s o s t e r e at the filling

Qd.5.

The connection between the parameters of equation (11) and the i s o s t e r i c heat and entropy of adsorption i s obvious. It c a n be obtained from the widely used (but not quite c o r r e c t ) e x p r e s s i o n f o r the i s o s t e r i c heat of adsorption Q (blnpg/bTla

=

Q/(RT2,

.

(13)

When we assume, that the perturbation entropy does not depend on the temperat u r e , then from equations (12) and (13) follows the relation between the potential energy

8+

AH

=

8 and the

RT

heat of adsorption Q

- QQs0.

@PO. 5

a t half filling

(14)

The integration of the equation (13) and of Clausius-Clapeyron equation yields

764

the known r e l a t i o n s lnpg

=

+c

-Q/(RT)

,

a=const.

and

where C and C

0

a r e the integration c o n s t a n t s , A i s the heat of condensation

and pg the normal vapour saturation p r e s s u r e . The physical meaning of integr0

ation constants follows from a l s o widely used relation f o r the change of the f r e e e n e r g y AG=RTln(pg/pg) = AH 0

+ RT(C-Co),

where AH= - ( Q - A ) is the change

of the enthalpy and A S = -R(C -C ) is the change of the entropy of the t r a n s f e r 0

of the bulk fluid from the s t a t e of normal liquid t o the adsorbed s t a t e .

By means of the above r e l a t i o n s , the equation of adsorption isotherm (11) may be r e w r i t t e n in the following alternative form

lnpg

=

5 c0 - "Q=O. R ~

-

'Q=O.

5

RT

where the i s o s t e r i c heat Q

Q=O.5

AsQ=O. 5

t

iPn(i-$

0

0

t 1-8 -

11

1

and the change of the entropy a t adsorption

c o r r e s p o n d t o the half filling of adsorption space i . e . 8=0.5.

The

relation between the entropy changes used i n equations of isotherm (11) and

(17)

is

where

AS. is the change of entropy A S id €Lo.5 f o r the idealized c a s e , when is z e r o . F r o m equations (11),(14) and (17) the perturbation entropy AS:

then follows the e x p r e s s i o n f o r A S . id ASid

=

-R[ln(ieRT/vb)

-

Co]

+

BH

+

,

iBR/v,,

(19)

where e is the b a s i s of the n a t u r a l logarithm.

All p a r a m e t e r s of the equation (11) of the adsorption isotherm have a c l e a r physical meaning. On energetically homogeneous solids the d e c r e a s e of the parameter i indicates the i n c r e a s i n g r o l e of the interactions between the ads o r b e d molecules. The influence of this parameter on the c h a r a c t e r i s t i c isotherms r e p r e s e n t i n g the dependence of 8 on ln(pg/pg

)

8=0.5

from the equation (11), is illustrated on the F i g u r e 1.

as evaluated

765

Fiq. 1. The c h a r a c t e r i s t i c adsorption isotherms of fluids on energetically homogeneous solids, evaluated bv means of the eauation (11). The parameter i is the measure of the a t t r a c t i v e interactions between the adsorbed molecules,

THE ADSORPTION E O T H E R M S ON ENERGETICALLY HETEROGENEOUS

SOLIDS Energetically homogeneous microporous solid is more o r less the idealization only.

P r a c t i c a l l y in e v e r y microporous solid t h e r e e x i s t s any distribution

of the potential energy

0 i n the

adsorption s p a c e . Evidently the experimentally

measured isotherms must be related t o the f r a c t i o n of saturation Q averaged t over a l l possible adsorption potential energy values by the integral

'min where X ( @ > is the differential distribution of the adsorption space volumes according to the potential energy

0

of adsorbed molecules. This function con-

tains a l s o the additive term a r i s i n g from the influence of potential energy gradients, when the condition ( 3 ) is used in the more c o r r e c t form. A s evident from eqns. (11) and ( 2 0 ) and the F i g . 1, the heterogeneity "draw out" the isotherms in coordinates 8 v s . lnpg and effectively i n c r e a s e s the parameter i . The attractive f o r c e s between molecules and energetic heterogeneity effect

thus i n a somewhat opposite manner, when manifest himself on the shape of the adsorption isotherm "(ref. 8)". By analysing the experimental adsorption

766

isotherms of benzene on zeolite NaX, using

X(0)

function evaluated from the

benzene molecule potential e n e r g y profiles "(ref.9)" and eqn. (ZO), found that the r e a l value of the parameter i f o r this system is 0.70 r i s o n t o the effective value i=1.0

.

The effective values of

0

we have in compa-

+

and A S w

are n e a r to the mean values o v e r a l l ensembles of small systems of the adsorbed fluid. GENERAL PROPERTIES OF THE ADSORPTION ISOTHERMS A s h a s been shown e a r l y "(ref.

lY', the adsorption isotherms on energetical-

l y homoqeneous solids, when expressed a s the function of amount adsorbed on lnpg may be separated in two p a r t s , one of which depends on the potential enerqy

8

and the perturbation entropy AS

x

+

and the other f(aJ, which depends

on the siate p r o p e r t i e s of adsorbed fluids only. A s shown, the general equation can be written

where z=exp[(@+Ap*)/RT] = exp{((@+ AH)/RT]

- [(AS:

+ B H l / R]

-

iB/vb)

.

For adsorbed s u p e r c r i t i c a l fluids with state relations given by the equation(2J

0

+

0

-

- 11 and pg =iRT/vb (cf. eqn.(6)). Similar f(a) functif(a) =i[ln(-) 1-Q 1-0 o n s , corresponding to the v i r i a l , v.d. W . e t c . state equations, are a l s o independent on the temperature T . Thus the functions a = q[ln(p g / p g z)] , which -Ia r e inversional to f(a) , d e s c r i b e the "new c h a r a c t e r i s t i c curve" universal

+

for a l l temperatures. It is interesting that although the condition ( b q / b T ) -0 a a s h a s been

h a s been derived f o r energetically homogeneous adsorbents

proved experimentally, well c h a r a c t e r i z e s the adsorption equilib,rium on the r e a l a d s o r b e n t s . The above condition is not in contradiction with the known Polanyi postulate, but in many c a s e s may be used even f o r the systems, where the Polanyi postulate is failed ( e . g . benzene on the zeolite NaX).

EXPERIMENTAL PART The described theory h a s been verified on the adsorption isotherms of benzene measured mainly qravimetrically on t h r e e typical samples of microporous solids. The zeolite NaX and the microporous active carbon (a. c . ) (industrially steam activated beech wood carbonaceous products) r e p r e s e n t s the samples No 36 and 29 of o u r found of p r o b e s , respectively. The isotherms

.

on a . c 29 have been overtaken from "(ref. 10)'' and a l s o analysed e a r l y

767

"(ref. 11)". A s an example of supermicroporous solid the new type of active c a r b o n , prepared by L . Kavan by the chemical reaction of perfluorobenzene with the lithium amalgame, f u r t h e r denoted as a . c . from C6F6, h a s been used. The parameters of the equation (11) have been determined as follows. The ex0 0 perimental isotherms have been plotted in the coordinates h(-) 1 1-63 1-Q v s . Inpg, of the linearized form of equation (11), where the parameter a is

+

-

0

optimalized. The r e c i p r o c a l value of the sloDe determines i and the intercept

of the linearized isotherm with the lnpg a x i s the value of lnpg F r o m the 8-0.5' and A S on 1 / T , the parameters Q Q=O. 5 8-0.5 have Q=0.5 been determined according the equations (16) and (17). The parameters 8 and x AS have been determined by means of the following q(T) function obtained dependence of lnpg

t

from equations (2)

- (12).

+

q=-(@+Ap*)=-@ -(Rlnv)T=qo*SY+B +

{

H )T=RT ln[(iRT/vb)/pg8-0.5

1 -iB/vb) ,

(22)

where q =-(@+A ) and Rlnv = ( A / T ) - ( A S x S B ). When the coefficients A H 0 H H + H and B a r e small and the dependence of q on T l i n e a r , the tangens (=-Rlnv)

H

is equal t o A S

w

+

x

and the intercept with q a x i s is q =-(@+AH). When AS+ 0

depends on T , ASX(T)-(q-q )IT and the value -(@+AH) is equal to ?(T+O).

+

0

The covolumes v have been determined exactly on the zeolites only, where b the volumes V are known "(refs.5-6)". On active c a r b o n s i t h a s been assumed that the adsorption space volumes V a r e equal t o the volume VMI of micro0

p o r e s , determined e . g . by the t / F method "(ref. 12)". On microporous solids, the derived equation (11) c h a r a c t e r i z e s well all the

experimental adsorption isotherms of benzene and i t s dependence on the temperature, a s shown on the F i g . 2 . The small e x c e s s of the experimental amounts in comparison with the amounts evaluated a t high fillings, is probably caused by the changes of packing of the highly compressed fluid at high p

a

p r e s s u r e s o r eventually partially by the c a p i l l a r y condensation in contacts between the p a r t i c l e s of the zeolite N a X or in the mesopores of the active carbon. The another situation h a s been observed on typically supermicroporous active carbon p r e p a r e d from perfluorobenzene. Here in spite of co-operative condensation of benzene, the isotherms may be c h a r a c t e r i z e d by the equation (11) in n a r r o w e r region of 8 (0.4s active carbon (29) a t the temperatures 30,39.5,49.5,60,84,111.5,143.5, 181.4,226.8and 288.5OC,denoted a s c u r v e s 1-10,respectively. The c o r r e s ponding parameters of eqn. (11) a r e given in the Table 1.

400

200

F i g . 3. a ) the adsorption isotherms and b) the c h a r a c t e r i s t i c adsorption isotherms of benzene on supermicroporous active carbon p r e p a r e d by the chemical reaction of perfluorobenzene with lithium amalgame, a t 2OoC (o), 4OoC (A) and 6OoC (0). The full points desorption.

-

769

C

g

lnPQ=O. 5

1) lnff

S

(pg, torr)

2) lnpz

3) a . c . from C F 6 6

10

4) a . c . 29 5) NaX

5 0

-5 1

Fig.

2

3

4

4.

The illustration of the evaluation of the i s o s t e r i c differential h e a t s of adsorption from the dependence and the entropy changes A S 8-0 5 Q=o'50f lnpg on 1I T , for micropokous solids studied. The value C (pg 0 .o' P a L 2 2 . 9 3 hkk%%n used in the evaluations of the entropy changes according --R(C-C ). The value CO(fg Pa) is 21.89, where fg is the relation A S 0 0 0' the fugacity of &%&-saturated vapours. The condensation heat of benzgne h 133.45 kJ/mole. QQ=0.5=-@+(RT-AH) a s follows from the equation (Id).

Q

TABLE I Pa.rameters of the equation (11) of benzene on the zeolite NaX, microporous active carbon (29) and supermicroporous active carbon p r e p a r e d by the chemical reaction of C F with L i amalgame. 6 6 O+AH

As:

"Q=O.

5

i

Probe

V n

kJ/mole NaX(36) -76.7K -54.5 a.c.(29) a . c . from -48.5

J/(mole K ) J/(mole K)

-67.0* -63.0 -67.5

b

3

a

vO n

3

cm /mole cm / g -

-32.0*

1.00

92.3*

-29.2

1.93

-11.6

0.42

61.5+ 88.8

0.295 0.400

0.876

0 ______

mmole/g 3.20K

6.50t 9.87

'gF6

_ - _ _ _ _ _ _

K

0

sliqhtly depends on T , given data c o r r e s p o n d s to T between 120-200 C + t h e effective values in spite of the energetical heterogeneity (cf. i > l ) .

D I S C U S SION It h a s been shown that benzene confined in the cavities of the zeolite NaX behaves a s a s u p e r c r i t i c a l fluid, the s t a t e p r o p e r t i e s of which may be evaluated by the Amagate s t a t e equation, with the r e a l i s t i c value of the parameter i = l . The e x c e s s of this parameter o v e r one observed on the microporous

active carbon N o 29 may be explained by the i n c r e a s e of the energetical heterogeneity of this adsorbent. In agreement with the theory of Evans and h i s

770

co-workers, the co-operative condensation of benzene confined in the supermicropores of a . c . prepared from C6F6, seems to be presented. This follows from the low value i=O.42 of the Amagate equation. But this equation i s not the most appropriate for the description of properties of fluids condensable in supermicropores

. In the future the energetical heterogeneity of

supermicro-

porous active carbons should be accounted in the attempts to found the r e a l state properties of fluids confined in supermicropores. CON C LU S IONS On the b a s i s of the thermodynamics of small systems in the field of adsorpti-

on forces the adsorption isotherm equation has been derived, which i s able to characterize well the isotherms of fluids on zeolites a s well a s on microporous active carbons. This has been demonstrated on the isotherms of benzene, Quite analogous results have been obtained by above mentioned hydrocarbons on the zeolite NaX. The parameters of the equation,such a s (3, agree well with the values evaluated independently theoretically. E . g . the value of @ + A H -76.7 kJ/mole found f o r benzene on the zeolite NaX(cf.Tab. 1) agrees well with the mean value of (3-81.6

kJ/mole, evaluated f o r the same system by

A . V . Kiselev and his co-workers "(ref. 9)" on the basis of the theory of

intermolecular forces (the value of A

i s not probably higher than 10 kJ/mole). H Similar agreement has been a l s o found for methane on the zeolite NaX, where

both experimental and theoretical mean values of the potential energy n e a r to

0

are

- 17 kJ/mole.

REFERENCES O.Kadlec, Pure and Appl.Chem. , 6 1 (1989) 1867. P . C .Ball and R . Evans, Langmuir, 5 (1989) 714. D . W.Breck, W. J.Eversole,R.M.Milton,T .D.Read and T . L. Thomas 3. J . A . C . S . , 78(1956) 5963. 0. M.Dzigit, A . V . Kiselev, T . A.Rakhmakova, Zeolites, 4 (1984) 389. 4. 5. R . M . B a r r e r and W.M.Meier, T r a n s . Faraday S O C . , 54 (1958) 1074. 6. M. M. Dubinin, E . G . Zhukovskaya and K . 0. Murdmaa, Izv. Akad. Nauk USSR, Otd. Khim. Nauk, (1962) 760. J. S Rowlinson and B. Widom, Molecular Theory of Capillarity, 7. Clarendon P r e s s , Oxford, 1982. 8. W.Rudzinski and J. Jagiello, Ads. Sci.and Technology, 6 (1989) 35. A . G . Bezus, M . KoCiFik, A . V . Kiselev, A . A . Lopatkin and E . A.Vasilyeva. 9. Zeolites, 6(1986) 101. 10. A.Zukal, Disertation , Inst. Phys.Chem.Acad. of S c i . Prague, 1967. 11. O.Kadlec, Chemical P a p e r s (J.of Slovak Acad.of Sci.),29 (1975) 653. 12. 0. Kadlec, Collection of Czechoslovak Chem.Commun., 36 (1970) 2415. 1.

2.

.

771

AUTHOR INDEX Adkins, B.D.; 543 Ajot, H.; 161, 583 Al-Kaisi, A.R.S.; 293 Alba, M.D.; 607 Albiniak, A. 357 Almela-AlarcQ, M.; 367 Alvero, R.; 607 Andersen, S.I.; 151 Avery, R.G.; 235 Bach, P.; 141 Bahceli, S.; 293 Bariou, B.; 209 Bell, J.; 75 Belyakova, L.D.; 701 Benito, F.; 625 Bhowmik, S.B.; 273 Birdi, K.S.; 151 Bittner, H.R., 141 Blancher, S.; 659 Bonnetain, L.; 189 Boon, A.Q.M.; 717 Bracconi, P.; 677 Brotas de Carvdho, M.M.; 341, 635 Briickner, P.; 491 Buckley, P.; 199 Carrott, P.J.M.; 341, 635, 685 Cases, J.M.; 591 Castro, M.A.; 607 Cather, M.E.; 727 Caullet, P.; 583 Christensen, S.V.; 151, 199 Comer, W.C.; 31, 199 Coulom, J.P.; 535 Davis, B.H.; 543 Davis, P.J.; 301, 709 Day, M.; 75 Daza, L.; 747 Del Arco, M.; 645 Demlehner, U.; 97 Denoyel, R.; 399 Dore, J. C. ; 245 Drobny, G.P.; 709 Duffie, J.; 75 Dufresne, P.; 565

Earl, W.L.; 709 Efremov, D.K.; 115 Elm’Cjapiro. A.; 565 Eltekov, Yu. A.; 575 Eltekova, N.A.; 575 Ewing, B.; 709 Fatemi-Sadr, M.; 677 Fenelonov, V.B.; 115 Fernindez-Colinas, J. 399 Fletcher, R.; 75 FranCois, M.; 357, 591 Freeman, J.J.; 319 Frykman, P.; 737 Fuertes, A.B.; 347 Fujiwara, Y.; 389 Genoni, F.; 553 Gem, J.W.; 717 Gimblett, F.R.G.; 319 Ginoux, J.L.; 189 Glittenberg, B.; 141 Gonplves da Silva, A.M. 341 Gonzaez, F.; 625 Grillet, Y.; 311, 357, 535, 591 Gubbins, K.E.; 21 Guet, J.M.; 379 Hampson, J.A.; 509 Hansen, J.A.; 199 Hayes, R.A.; 319 Hernindez. E.; 645 Hurd, A.J.; 179, 267 111in-G6mez, M.J.; 367 Isirikjan, A.A.; 525 Jaroniec, M.; 469 Jasra, R.V.ii 509 Jessop, C.A.; 123 Johnston, G.P.; 179 Joly, J.F.; 161, 565, 583 Kaczmarczyk, J.; 357 Kadlec, 0.,759 Kakei, K.; 429 Kaneko, K.; 389, 429

112

Kanellopoulos, N.; 61 Karnaukhov, A.P.; 105 Kartel, N.T., 439 Kenny, M.B.; 685 Kessels, P.Y.; 659 Klich, I.; 727 Koch, Chr.E.; 737 Krebs, K.F.; 133 Krim, J.; 217 Krynicki, K.; 293 Lentz, H.; 499 Leofanti, G.; 553 Lecloux, A.J.; 659 Lin, Q.; 379 Linares-Solano, A.; 367, 379, 419 Lorenzana, J.J., 459 Lynch, J.; 583 Mahamud, M.; 347 Majors, P.D.; 709 Marchot, P.; 659 Marsh, H.; 459 Martin, C.; 645 Martin-Martinez, J.M.; 311, 419, 449, 469 Martinez-Sknchez, M.A.; 449 Martin-Luengo, M.A.; 599 Mason, G.; 41 Mate-os, J.; 645 Mather, R.R.; 409 Mayagoitia, V.; 51 Mays, T.J.; 477 McEnaney, B.; 477 McInally, A.; 409 McMurray, R.; 273 Mellor, D.W.; 41 Mendioroz, S.; 625, 747 MenCndez, R.; 459 Merlo, J.L.; 659 Mersmann, A.B.; 225, 519 Michot, L.; 591 Milburn, D.R.; 543 Mohd. Amin, Z.; 319 Molina-Sabio, M.; 329 Mdler, P.J.; 737 Morrow, N.R.; 727 Miiller, U.; 535 Muiiecas-Vidal, M.A.; 329 Muiioz-Guillena, M. J. ; 367 Nafis, M.; 565

Nameri, N.; 209 Neimark, A.V.; 67 Nicholson, D.; 11 Nishikawa, K.; 389 North, A.N., 245 Noville, F.; 659 OrgilCs-Barcel6, A.C.; 449 Ozeki, S.; 429 Padovan, M.; 553 Pajares, J.A.; 347, 747 Pan, D.; 519 Panella, V.; 217 Parker, I.B.; 75 Parra, J.B.; 347 Parthun, G.; 199 Payatakes, A.C.; 169, 267 Pkrez, A.J.; 347, 459 Pesquera, C.; 625 Petrini, G.; 553 Petropoulos, J.H.; 61 Petrou, J.K.; 61 Pfeifer, P.; 179 Pirard, J.P.; 659 Pis, J.J.; 347, 459 Poyato, J.; 607 Puzy, A.M.; 439 Quinson, J.F.; 209 Quirke, N.; 123 Raatz, F.; 161, 565, 583 Radeke, K.H.; 491 Ragai, J.; 693 Rakhmatkariev, G.U.525 Ramsay, J.D.F.; 235, 257 Rees, L.V.C.; 509 Reichert, H.; 535 Ribeiro Carrott, M.M.L.; 341, 635 Riddiford, S.M., 123 Rives, V.; 645 Robens, E.; 133 Roberts, R.A.; 685 Rodriguez-Reinoso, F.; 311, 329, 419, 449, 469 Romero, E.; 459 Rouquerol, I.; 311, 535, 399 Rouquerol, F.; 311, 535 Russell, P.J.; 257 Russmann, C.; 161

773

Salinas-Martinez de Lecea, C.; 367, 379 Sato, T.; 283 Scholl, S.E.; 225 Seaton, N.A.; 123 SellCs-PCrez, M.J.; 449 Sermon, P.A.; 599 Sernetz, M.; 141 Siemieniewska, T.; 357 Sitnonot-Grange, M.H.; 565 Sing, K.S.W.; 1, 319, 409, 635, 653, 669, 685, 693 Smith, D.M.; 179, 267, 301, 709 Stacey, M.H.; 615 Stentoft, N.; 737 Strange, J.H.; 293 Strelko, V.V., 439 Suzuki, T.; 389, 429 Swanton, S.W., 257 Tan, Z.; 21 Tennison, S.R.; 273 Theocharis, C.R.; 653, 685 Thomas, M.; 75 Tobias, M.M.; 607 Tomkow, K.; 357 Topsere, H.; 151, 199

Torregrosa, R.; 419 Trezza, G. 553 Trillo, J.M.; 607 Tsakiroglou, C.D.; 169 Unger, K.K.; 535 Van Veldhuizen, A.J.W.; 717 Van der Grift, C.J.G.; 717 Villieras, F.; 591 Vu, D.T.; 151 Waldram, S.P., 273 Walton, J.P.R.B.; 123 Walton, T.J.; 599 Webb, S.W.; 31, 199 Weber, G.; 565 Winter, A.; 85, 151 Yates, M.; 599, 669, 693 Yeates, D.; 653 Yvon, J.; 591 Zecchina, A.; 553 Zhou, Y.; 499

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115

KEYWORD INDEX Activated carbon, 319, 329, 367, 379, 419, 429, 449, 469, 477, 491 Activated charcoal, 399 Activation, 367 Activation by CO,, 347 Active carbon, 347, 499 Adsorbents, 235 Adsorption, 11, 21, 31, 51, 115, 123, 179, 189, 225, 329, 357, 369, 379, 509, 525, 565, 591, 685, 73 continuous, 161 enthalpies of, 3 11 from solution, 341, 399, 439 heats of, 535 hysteresis, 115 isotherm, 217, 341, 399, 477, 519, 701 of acid gases, 701 of Argon, 429 of Benzene, 491 of Methanol, 341 of Neopentane, 635 of Nitrogen, 635 of Water, 179, 319, 341, 389 Adsorption apparatus, 189 Adsorption processes, 235 Affinity coefficient, 469 Air gasification, 419 Al-CLM stability, 607 Al-pillared montmorillonite, 607 Alumina, 161, 615 Alumina-supported vanadia, 645 Aluminophosphates, 535 Argon, 591 Attapulgite, 591 BET method, 133, 737 Binary mixtures, 509 Bituminous coal, 459

Cadmium halides, 311 Calcium hydroxide, 653 Capillary, 41, 51, 97 Capillary condensation, 115 Capillary hysteresis, 67 Capillary network, 61 Carbon, 273, 439, 575 gasification CO,, 419

sorption, 319, 591 Carbones dioxide, 357 Carbonate rock, 737 Catalysis/catalysts (heterogeneous), 7 17 Catalytic activation, 367 Catastrophic desorption, 161 Cations, 525 Cement, macrodefect free, 669 Cement microstructure, 669 Ceramics, 659 Charcoal cloth, 409, 341 Charcoals, 357 Chromatography, 141 Chromium oxide, 449 Classification, 701 Coal oxidation, 347, 459 Coke porosity, 459 Computer simulation, 21 Condensation, 5 1 Contact angle, 97 Continuous adsorption, 161 Contrast variation technique, 235 Controlled porosity gels, 257 Cotton, 409 Dealumination, 565, 583 Densification, 319 Density functional theory, 21 Desorption , 161 Diffusion, 273, 293 Diffusion limitation, 717 Diffusion, relation to pore structure, by SGC, 199 Disordered media, 85 Drainage-imbibition, 41 Dubinin-Radushkevich equation, 469 Dusty gas model, 225 Dye, 409 Enthalpies of adsorption, 311 Epifluorescent microscopy, 727 Evaporation of liquid, 151 Faujasite, 565, 583 Fibres, 319, 615 Filling, 357 Film surface area, 179 Fractal, 217

116

porosity, 141 Fumed silica, 267 Gas adsorption, 369, 379 Gaseous, 273 Gasification by air, 419 by C 0 2 , 419 Gel precipitation, 257 Gels, 257 Glass, porous, 499 Gold, 217 Graphite, 11 Gypsum, 693 Heats, 525 of adsorption, 535 of inmersion, 151 Henry’s constants, 535 Heterogeneity, 61 Heterogeneous catalysts, 599 Heteroporosity, 61 High pressure hysteresis, 419, 535 HRADS, 31 Hydraulic conductivity, 283 Hydrocarbons, 509 Hydroxy-Al, 625 Hysteresis, 51, 67, 115 high pressure, 419, 535 low pressure, 419, 535 of water-retention, 283 Image, 709 Imbibition, 97 Immersion calorimetry, 491 Immersion, heat of, 151 Interferometry, 141 Isotherm crossing, 31 1 Kelvin Equation, 21 Kevlar, 319 Kinetics, 225 Lanthanum, 607 Leather waste, 449 Limited selfsimilarity, 141 Low pressure hysteresis, 419, 535 Macrodefect free cement, 669 Macromolecular porosimetry, 575 Macroporosity, 747 Magnesium hydroxide, 635

Magnesium oxide, 635 Magnetic susceptibility, 293 Mean-field theory, 123 Membrane, 209 Meniscus, 41 Mercury, 75 Mercury penetration, 379, 439, 543, 693 Mercury porosimetry, 459, 499 Mercury porosimetry, simulation of, 169 Mesopores, 161, 583 Mesoporosity, 67 Metallic oxides, 645 Microcalorimetry, 399 Micrographitic structure, 389 Micropore filling, 429 Micropore size distribution, 469 Micropore sizes, 477 Micropores, 11, 179, 525 Microporosity, 319, 357, 399, 449, 599, 607, 635, 653, 685 Microporous carbon, 389 Microporous solids, 685 Microscopy, 727 Model, 75 Model porous adsorbents, 235 Modelling, 105 Molecular probes, 469 Monolayer filling, 429 Montmonillonite, Al-pillared, 607 Mordenite, 583 Mortars, 693 Nay, 509 Needl-like materials, 105, 519 Nwpentane adsorption, 319 Network, 75 model, 283 Neutron diffraction, 535 Neutron scattering (small-angle), 235 Nitrogen, 123, 591 Nitrogen adsorption, 257, 319, 409, 429, 543 NMR, 293, 301, 709 Non-inert adsorbent, 519 Non-isobaric, 225 Optical microscopy, 379 Ores, 677 Oxidation treatments, 329 Oxide gels, 257 Oxygen surface groups, 329

Partially saturated soil, 283 Particles, 133 Percolation, 41 Percolation theory, 67 Permeability, 61, 209, 273, 669 Petrography, 727 Phase-change, 615 Pillaring, 625 Polanyi-Dubinin, 565 Polymer adsorption, 575 Polymeric sorbents, 701 Pore, 75, 615 dimension, 293 networks, 169 quality, 727 size, 189, 709 size distribution, 31, 123, 169, 245, 575 Pore structure, 199, 225, 439, 669, 685 volume, 543 size measurement, 283 Porosimetry, 75, 575, 677 Porosimetry, relation to diffusion, 199 Porosity, 141, 329, 669, 693, 709, 747 determination, 189 development, 367 measurement, 727 of organic tissue, 141 Porous, 51, 273 glass, 709 materials, characterization of, 169 media, analysis of, 169 medium, 97 networks, 115 silica, 293 solids, 85, 105, 115, 151 structure, 701, 717 materials (Synthetic and natural), 245 Power compaction, 267 Preadsorption, 449 Pycnometry, 677 Pyrolysis, 347 Reference material, 133 SAXS (small angle X-ray scattering), 379 Selectivity, 21 Silica, 311, 543, 575 Silicalite-1, 509 Silicates, 747 Silver, 217 Simulation, 11

Sintering, 659 Small angle X-ray scattering, 245, 389 Small-angle neutron scattering, 257, 267 Small-angle scattering (SANS and SAXS), 245 Smectite, 625 Soil, 283 Sol-gel, 615 SiO,-AI,O,, 599 Solvent, 209 Sorption of carbon dioxide, 319 Specific surface area, 625 Sphere packing, 41 Standardisation, 133 Statistical mechanics, 123 Steam and carbon dioxide activation, 367 Sulfides, 677 Sulphyrization, 747 Supported metallic oxides, 645 Surface area, 151, 179, 189, 543, 625 excess, 341 groups, 329 homogeneity, 31 1 roughness, 179 texture, 245 Swelling, 209, 677 Synthetic carbons, 439 Textile, 409 Textural properties, 347 Texture (porous), 659 Thermal stability, 553, 625 Thermoporometry, 209 Thiele theory, 717 Thin film, 85 Thin section, 727 Titania-supported vanadia, 645 Titanium-silicalite, 553 Tortuosity and pore structure, 199 Ultra-low small angle X-ray scattering (USAXS), 245 Vanadia, 645 Vanadia, Al,O,-supported, 645 Vapour adsorption, 439 Washburn equation, 97 Water, 565 Water adsorption, 179, 319, 341, 389 isotherm, 607 vapour, 685

778

vapour sorption, 653 Wet materials, 301 Wetting, 85 transition, 85 X-ray diffaction, 389 Xylene adsorption, 553

Yttrium oxide, 659 Zeolite and aluminophosphates, 535 Zeolite channels, 553 Zeolites, 31, 161, 525 Zirconium dioxide, 659

779

STUDIES IN SURFACE SCIENCE AND CATALYSIS Advisory Editors: B. Delmon, Universith Catholique de Louvain, Louvain-la-Neuve, Belgium J.T. Yates, University of Pittsburgh, Pittsburgh, PA, U S A .

Volume 1 Preparation of Catalysts I.Scientific Bases for the Preparation of Heterogeneous Catalysts. Proceedings of the First International Symposium, Brussels, October 1417,1975 edited by B. Delmon, P.A. Jacobs and G. Poncelet Volume 2 The Control of the Reactivity of Solids. A Critical Survey of the Factors that Influence the Reactivity of Solids, with Special Emphasison the Control of the Chemical Processes in Relation to Practical Applications by V.V. Boldyrev, M. Bulens and B. Delmon Volume 3 Preparation of Catalysts II. Scientific Bases for the Preparation of Heterogeneous Catalysts. Proceedings of the Second International Symposium, Louvain-la-Neuve, September 4-7, 1978 edited by B. Delmon, P. Grange, P. Jacobs and G. Poncelet Volume 4 Growth and Properties of Metal Clusters. Applications to Catalysis and the Photographic Process. Proceedings of the 32nd International Meeting of the Socibte de Chimie Physique, Villeurbanne, September 24-28, 1979 edited by J. Bourdon Volume 5 Catalysis by Zeolites. Proceedings of an InternationalSymposium, Ecully (Lyon), September 9- 1 1, 1980 edited by B. Imelik, C. Naccache, Y. Ben Taarit, J.C. Vedrine, G. Coudurier and H. Praliaud Volume 6 Catalyst Deactivation. Proceedings of an International Symposium, Antwerp, October 13- 15,1980 edited by B. Delmon and G.F. Froment Volume 7 New Horizons in Catalysis. Proceedings of the 7th InternationalCongress on Catalysis, Tokyo, June 30-July 4, 1980. Parts A and B edited by T. Seiyama and K. Tanabe Volume 8 Catalysis by Supported Complexes by Yu.1. Yermakov, B.N. Kuznetsovand V.A. Zakharov Volume 9 Physics of Solid Surfaces. Proceedings of a Symposium, Bechyiie, September 29October 3, 1980 edited by M. Liznieka Volume 10 Adsorption at the Gas-Solid and Liquid-Solid Interface. Proceedings of an InternationalSymposium, Aix-en-Provence, September 2 1-23, 198 1 edited by J. Rouqueroland K.S.W. Sing Volume 1 1 Metal-Support and Metal-Additive Effects in Catalysis. Proceedings of an InternationalSymposium, Ecully (Lyon), September 14-16. 1982 edited by B. Imelik, C. Naccache, G. Coudurier, H. Praliaud, P. Meriaudeau, P. Gallezot, G.A. Martin and J.C. Vedrine Volume 12 Metal Microstructures in Zeolites. Preparation - Properties - Applications. Proceedings of a Workshop, Bremen, September 22-24, 1982 edited by P.A. Jacobs, N.I. Jaeger, P. JirQand G. Schulz-Ekloff Volume 13 Adsorption on Metal Surfaces. An Integrated Approach edited by J. BBnard Volume 14 Vibrations at Surfaces. Proceedings of the Third International Conference, Asilomar, CA, September 1-4, 1982 edited by C.R. Brundle and H. Morawitz

780 Volume 15 HeterogeneousCatalytic Reactions Involving Molecular Oxygen by G. I.Golodets Volume 16 Preparation of Catalysts 111. Scientific Bases for the Preparation of Heterogeneous Catalysts. Proceedings of the Third International Symposium, Louvain-la-Neuve, September 6-9,1982 edited by G. Poncelet, P. Grange and P.A. Jacobs Volume 17 Spillover of Adsorbed Species. Proceedings of an International Symposium, LyonVilleurbanne, September 12-1 6, 1983 edited by G.M. Pajonk, S.J. Teichner and J.E. Germain Volume 18 Structure and Reactivity of Modified Zeolites. Proceedings of an International Conference, Prague, July 9-13, 1984 edited by P.A. Jacobs, N.I. Jaeger, P. Jire, V.B. Kazansky and G. Schulz-Ekloff Volume 19 Catalysis on the Energy Scene. Proceedings of the 9th Canadian Symposium on Catalysis, Quebec, P.Q., September 30-October 3, 1984 edited by S. Kaliaguine and A. Mahay Volume 20 Catalysis by Acids and Bases. Proceedings of an InternationalSymposium, Villeurbanne (Lyon), September 25-27, 1984 edited by B. Imelik. C. Naccache, G. Coudurier, Y. Ben Taarit and J.C. Vedrine Volume 2 1 Adsorption and Catalysis on Oxide Surfaces. Proceedings of a Symposium, Uxbridge, June 28-29, 1984 edited by M. Che and G.C. Bond Volume 22 Unsteady Processes in Catalytic Reactors by Yu.Sh. Matros Volume 23 Physics of Solid Surfaces 1984 edited by J. Koukal Volume 24 Zeolites: Synthesis, Structure, Technology and Application. Proceedings of an InternationalSymposium, Portoroi-Portorose, September 3-8, 1984 edited by B. Deaj, S. HoEevar and S. Pejovnik Volume 25 Catalytic Polymerization of Olefins. Proceedings of the InternationalSymposium on Future Aspects of Olefin Polymerization, Tokyo, July 4-6, 1985 edited by T. Keii and K. Soga Volume 26 Vibrations at Surfaces 1985. Proceedings of the Fourth InternationalConference, Bowness-on-Windermere, September 15-1 9, 1985 edited by D.A. King, N.V. Richardsonand S. Holloway Volume 27 Catalytic Hydrogenation edited by L. Cervenq Volume 28 New Developments in Zeolite Science and Technology. Proceedings of the 7th InternationalZeolite Conference, Tokyo, August 17-22, 1986 edited by Y. Murakami, A. lijima and J.W. Ward Volume 29 Metal Clusters in Catalysis edited by B.C. Gates, L. Guczi and H. Knozinger Volume 3 0 Catalysis and Automotive Pollution Control. Proceedings of the First International Symposium, Brussels, September 8-1 1, 1986 edited by A. Crucq and A. Frennet Volume 3 1 Preparation of Catalysts IV. Scientific Bases for the Preparation of Heterogeneous Catalysts. Proceedings of the Fourth InternationalSymposium, Louvain-la-Neuve, September 1-4, 1986 edited by 6. Delmon, P. Grange, P.A. Jacobs and G. Poncelet Volume 32 Thin Metal Films and Gas Chemisorption edited by P. Wissmann Volume 33 Synthesis of High-silica Aluminosilicate Zeolites by P.A. Jacobs and J.A. Martens Volume 3 4 Catalyst Deactivation 1987. Proceedings of the 4th InternationalSymposium, Antwerp, September 29-October 1, 1987 edited by B. Delmon and G.F. Froment

781 Volume 35 Keynotes in Energy-RelatedCatalysis edited by S. Kaliaguine Volume 36 Methane Conversion. Proceedings of a Symposium on the Production of Fuels and Chemicals from Natural Gas, Auckland, April 27-30, 1987 edited by D.M. Bibby, C.D. Chaney, R.F. Howe and S. Yurchak Volume 37 Innovation in Zeolite Materials Science. Proceedings of an International Symposium, Nieuwpoort, September 13-17, 1987 edited by P.J. Grobet, W.J. Mortier, E.F. Vansant and G. Schulz-Ekloff Volume 38 Catalysis 1987. Proceedings of the 10th North American Meeting of the Catalysis Society, San Diego, CA, May 17-22, 1987 edited by J.W. Ward Volume 39 Characterization of Porous Solids. Proceedings of the IUPAC Symposium (COPS I), Bad Soden a. Ts., April 26-29, 1987 edited by K.K. Unger, J. Rouquerol, K.S.W. Sing and H. Kral Volume 40 Physics of Solid Surfaces 1987. Proceedings of the Fourth Symposium on Surface Physics, Bechyne Castle, September 7-1 1, 1987 edited by J. Koukal Volume 4 1 HeterogeneousCatalysis and Fine Chemicals. Proceedings of an International Symposium, Poitiers, March 15-17, 1988 edited by M. Guisnet, J. Barrault, C. Bouchoule, D. Duprez, C. Montassier and G. Pdrot Volume 42 Laboratory Studies of Heterogeneous Catalytic Processes by E.G. Christoffel, revised and edited by Z.Pa61 Volume 43 Catalytic Processes under Unsteady-State Conditions by Yu. Sh. Matros Volume 44 Successful Design of Catalysts. Future Requirementsand Development. Proceedings of the Worldwide Catalysis Seminars, July, 1988, on the Occasion of the 30th Anniversary of the Catalysis Society of Japan edited by T. lnui Volume 45 Transition Metal Oxides: Surface Chemistry and Catalysts by H.H. Kung Volume 46 Zeolites as Catalysts. Sorbents and Detergent Builders. Applications and Innovations. Proceedings of an InternationalSymposium, Wirrzburg, F.R.G., September 4-8, 1988 edited by H.G. Karge and J. Weitkamp Volume 47 Photochemistry on Solid Surfaces edited by M. Anpo and T. Matsuura Volume 48 Structure and Reactivity of Surfaces. Proceedings of a European Conference, Trieste, Italy, September 13-16, 1988 edited by C. Morterra, A. Zecchina and G. Coste Volume 49 Zeolites: Facts, Figures, Future. Proceedings of the 8th InternationalZeolite Conference, Amsterdam, The Netherlands, July 10-1 4, 1989 edited by P.A. Jacobs and R.A. van Santen Volume 5 0 Hydrotreating Catalysts. Preparation, Characterizationand Performance. Proceedings of the Annual International AlChE Meeting, Washington, DC, November 27-December 2, 1988 edited by M.L. Occelli and R.G. Anthony Volume 5 1 New Solid Acids and Bases. Their Catalytic Properties by K. Tanabe, M. Misono, Y. Ono and H. Hattori Volume 52 Recent Advances in Zeolite Science. Proceedings of the 1989 Meeting of the British Zeolite Association, Cambridge, April 17-1 9, 1989 edited by J. Klinowski and P.J. Barrie Volume 53 Catalyst in Petroleum Refining 1989. Proceedings of the First International Conference on Catalysts in Petroleum Refining, Kuwait, March 5-8, 1989 edited by D.L. Trimm, S. Akashah, M. Absi-Halabi and A. Bishara

782 Volume 54 Future Opportunities in Catalytic and Separation Technology edited by M. Misono, Y.Moro-oka and S. Kimura Volume 55 New Developments in Selective Oxidation. Proceedings of an International Symposium, Rimini, Italy, September 18-22, 1989 edited by G. Centi and F. Trifiro Volume 56 Olefin Polymerization Catalysts. Proceedings of the International Symposium on Recent Developments in Olefin PolymerizationCatalysts, Tokyo, October 23-25, 1989 edited by T. Kelli and K. Soga Volume 57A Spectroscopic Analysis of Heterogeneous Catalysts. Part A: Methods of Surface Analysis edited by J.L.G. Fierro Volume 578 Spectroscopic Analysis of Heterogeneous Catalysts. Part 6: Chemisorption of Probe Molecules edited by J.L.G. Fierro Volume 58 Introduction t o Zeolite Science and Practice edited by H. van Bekkum, E.M. Flanigen and J.C. Jansen Volume 59 Heterogeneous Catalysis and Fine Chemicals II. Proceedings of the 2nd International Symposium, Poitiers, October 2-5, 1990 edited by M. Guisnet, J. Barrault, C. Bouchoule, D. Duprez, G. Perot, R. Maurel and C. Montassier Volume 6 0 Chemistry of Microporous Crystals. Proceedings of the InternationalSymposium on Chemistry of Microporous Crystals, Tokyo, June 26-29, 1990 edited by '6. Inui, S. Namba and T. Tatsumi Volume 6 1 Natural Gas Conversion. Proceedings of the Natural Gas Conversion Symposium, Oslo, August 12- 17, 1990 edited by A. Holmen, K.-J. Jens and S. Kolboe Volume 62 Characterization of Porous Solids II. Proceedings of the IUPAC Symposium (COPS 11). Alicante, May 6-9, 1990 edited by F. Rodriguez-Reinoso,J. Rouquerol, K.S.W. Sing and K.K. Unger Volume 63 Preparation of Catalysts V. Proceedings of the Fifth InternationalSymposium on the Scientific Bases for the Preparation of Heterogeneous Catalysts, Louvain-laNeuve, September 3-6, 1990 edited by G. Poncelet, P.A. Jacobs, P. Grange, and 6. Delmon