Characterisation of Porous Solids V (Studies in Surface Science and Catalysis)

Studies in Surface Science and Catalysis 128 CHARACTERISATION OF POROUS SOLIDS V

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Studies in Surface Science and Catalysis Advisory Editors: B. D e l m o n and J.T. Yates

Vol. 128

C H ARACTE R IS ATI O N OF POROUS SOLIDS V Proceedings ofthe 5th International Symposium on the Characterisation of Porous Solids (COPS-V), Heidelberg, Germany, May 30-June 2, 1999

Edited by

K.K. Unger Johannes Gutenberg-Universit#t, Institut fSrAnorganische Chemie undAnalytische Chemie, D-55099Mainz, Germany G. Kreysa and J.P. Baselt Deutsche Gesellschaft for ChemischesApparatewesen, Chemische Technikund Biotechnologie e. V.,Forschungsf6rderung, D-60486Frankfurt am Main, Germany

2000 ELSEVIER

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First edition 2000 Library of Congress Catalo~ng-in-Publication Data International Symposium on the Characterisation of Porous Solids (5th : 1999 Heidelberg, Germany) Characterisation of porous solids V : proceedings of the 5th International Symposium on the Characterisation of Porou.s Solids (COPS-V), Heidelberg, Germany, May 30-June 2, 1999 / edited by K.K. Unger, G. Kreysa, J.P. Baselt.-- I st ed. p. cm. -- (Studies in surface science and catalysis ; 128) Includes bibliographical references and index. ISBN 0-444-50259-9 ( a l l paper) 1. Porous materials--Congresses. I. Unger, K. K. (Klaus K.), 1936- H. Kreysa, Gerhard. UI. Baselt, J. P. IV. Title. V. Series. TA418.9.P6 I59 2000 620.1'16--dc21

ISBN: 0-444-50259-9

00-021306

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

Contents Foreword Scientific Committee Financial Support

XIII XV XV

Theory, Modelling and Simulation Adsorption of argon and xenon in silica controlled porous glass: A grand canonical Monte-Carlo study R.J.-M. Pellenq, A. Delville, H. van Damme, P. Levitz

10

The role of isosteric enthalpy of adsorption in micropore characterisation: A simulation study D. Nicholson, N. Quirke

11

Capillary condensation and hysteresis in disordered porous materials L. Sarkisov, P.A. Monson

21

Molecular simulation study on freezing in nano-pores M. Miyahara, H. Kanda, K. Higashitani, K.E. Gubbins

31

Characterisation of porous materials using density functional theory and molecular simulation C.M. Lastoskie, K.E. Gubbins

41

Density functional theory of adsorption hysteresis and nanopore characterisation A.V. Neimark, P.I. Ravikovitch

51

Characterisation of controlled pore glasses: Molecular simulations of adsorption L.D. Gelb, K.E. Gubbins

61

A new method for the accurate pore size analysis of MCM-41 and other silicia based mesoporous materials M. Jaroniec, M. Kruk, J.P. Olivier, S. Koch

71

Comparison of the experimental isosteric heat of adsorption of argon on mesoporous silica with density functional theory calculations 3.P. Olivier

81

A computational exploration of cation locations in high-silica Ca-Chabazite T. Grey, J. Gale, D. Nicholson, E. Artacho, J. Soler

89

11

Density functional theory: Diatomic nitrogen molecules in graphite pores N.N. Neugebauer, M. v. Szombathely

12

Modelling studies of the influence of macroscopic structural heterogeneities on nitrogen sorption hysteresis S.P. Rigby

111

Condensation-evaporation processes in simulated heterogeneous three-dimensional porous networks S. Cordero, I. Kornhauser, C. Felipe, J.M. Esparza, A. Dorninguez, J.L. Riccardo, F. Rojas

121

14

Characterisation of porous solids for gas transport O. Solcov/L, H. Snajdaufov/l, V. Hejtm/mek, P. Schneider

131

15

Experimental and simulation studies of melting and freezing in porous glasses M. Sliwinska-Bartkowiak, J. Gras, R. Sikorski, G. Dudziak, R. Radhakrishnan, K.E. Gubbins

141

A fast two-point method for gas adsorption measurements J.A. Poulis, C.H. Massen, E. Robens, K.K. Unger

151

13

16

99

Highly OrderedPorous Inorganic Systems Rational design, tailored synthesis and characterisation of ordered mesoporous silicas in the micron and submicron size range M. Grun, G. B0chel, D. Kumar, K. Schurnacher, B. Bidlingmaier, K.K. Unger

155

Relationship between intrinsic pore-wall corrugation and adsorption hysteresis of N2, 02, and Ar on regular mesopores S. Inoue, H. Tanaka, Y. Hanzawa, S. Inagaki, Y. Fukushirna, G. B0chel, K.K. Unger, A. Matsumoto, K. Kaneko

167

19

Study of the morphology of porous silica materials C. Ali6, R. Pirard, J.-P. Pirard

177

20

Adsorption hysteresis and criticality in regular mesoporous materials S.K. Bhatia, C.G. Sonwane

187

21

Comprehensive structural characterisation of MCM-41" From mesopores

17

18

22

to particles C.G. Sonwane, A.D. McLennan, S.K. Bhatia

197

Characterisation of mesoporous MCM-41 adsorbents by various techniques J. Goworek, W. Stefaniak, A. Borowka

207

vii 23

24

25

26

27

28

29

30

31

32

Characterisation of mesoporous molecular sieves containing copper and zinc: An adsorption and TPR study M. Hartmann

215

On the applicability of the Horwath-Kawazoe method for pore size analysis of MCM-41 and related mesoporous materials M. Jaroniec, J. Choma, M. Kruk

225

Dynamic and structural properties of confined phases (hydrogen, methane and water) in MCM-41 samples (19,~, 25,~ and 40,~) J.P. Coulomb, N. Floquet, Y Grillet, P.L. Llewellyn, R. Kahn, G. Andre

235

Estimating pore size distribution from the differential curves of comparison plots H.Y. Zhu, G.Q. Lu

243

Rotational state change of acetonitrile vapor on MCM-41 upon capillary condensation with the aid of time-correlation function analysis of IR spectroscopy H. Tanaka, A. Matsumoto, K.K. Unger, K. Kaneko

251

Systematic sorption studies on surface and pore size characteristics of different MCM-48 silica materials M. Thommes, R. Kohn, M. Froba

259

Synthesis and characterisation of ordered mesoporous MCM-41 materials J.L. Blin, G. Herrier, C. Otjacques, B.-L. Su

269

Textural and spectroscopic characterisation of vanadium MCM-41 materials - Application to gas-phase catalysis P. Trens, A.M. Feliu, A. Dejoz, R.D.M. Gougeon, M.J. Hudson, R.K. Harris

279

On the ordering of simple gas phases adsorbed within model microporous adsorbents N. Dufau, N. Floquet, J.P. Coulomb, G. Andre, R. Kahn, P.L. Llewellyn, Y. Grillet

289

Textural and framework-confined porosity in S+I- mesoporous silica P. Agren, M. Linden, P. Trens, S. Karlsson

297

Carbons

33

Use of immersion calorimetry to evaluate the separation ability of carbon molecular sieves C.G. de Salazar, A. Sepulveda-Escribano, F. Rodriguez-Reinoso

303

viii 34

35

36

37

38

39

40

41

42

43

44

Molecular simulations and measurement of adsorption in porous carbon nanotubes E. Alain, Y.F. Yin, T.J. Mays, B. McEnaney

313

Application of the as method for analysing benzene, dichloromethane and methanol isotherms determined on molecular sieve and superactivated carbons P.J.M. Carrott, M.M.L. Ribeiro Carrott, I.P.P. Cansado

323

Characterisation of porous carbonaceous sorbents using high pressurehigh temperature adsorption data G. De Weireld, M. Frere, R. Jadot

333

Influence of the porous structure of activated carbon on adsorption from binary liquid mixtures A. Derylo-Marczewska, J. Goworek, A. Swiatkowski

347

Adsorption mechanism of water on carbon micropore with in situ small angle x-ray scattering T. Iiyama, M. Ruike, T. Suzuki, K. Kaneko

355

Ultra-thin microporous carbon films R. Petricevic, H. Pr0bstle, J. Fricke

361

Electrochemical investigation of carbon aerogels and their activated derivatives H. Pr0bstle, R. Saliger, J. Fricke

371

Evolution of microporosity upon C02-activation of carbon aerogels R. Saliger, G. Reichenauer, J. Fricke

381

On the determination of the micropore size distribution of activated carbons from adsorption isotherms D.L. Valladares, G. Zgrablich, F. Rodriguez-Reinoso

391

Role of pore size distribution in the binary adsorption kinetics of gases in activated carbon S. Qiao, X. Hu

401

Confined state of alcohol in carbon micropores as revealed by in situ x-ray diffraction T. Ohkubo, T. Iiyama, T. Suzuki, K. Kaneko

411

Interpretation of Data, Membranes 45

46

47

48

49

50

51

Critical appraisal of the use of nitrogen adsorption for the characterisation of porous carbons P.L. Llewellyn, F. Rouquerol, J. Rouquerol, K.S.W. Sing

421

Structural characterisation and applications of ceramic membranes for gas separations E.S. Kikkinides, T.A. Steriotis, A.K. Stubos, K.L. Stefanopoulos, A.C. Mitropoulos, N.K. Kanellopoulos

429

SANS charcterisation of mesoporous silicas having model structures J.D.F. Ramsay, S. Kallus, E. Hoinkis

439

Pore-scale complexity of a calcareous material by time-controlled mercury porosimetry A. Cerepi, L. Humbert, R. Burlot

449

SANS analysis of anisotropic pore structures in alumina membranes L. Auvray, S. Kallus, G. Golemme, G. Nabias, J.D.F. Ramsay

459

Zeolite membranes - charcterisation and applications in gas separations S. Kallus, P. Langlois, G.E. Romanos, T.A. Steriotis, E.S. Kikkinides, N.K, Kanellopoulos, J.D.F. Ramsay

467

A modified Horvath-Kawazoe method for micropore size analysis

C.M. Lastoskie

475

Miscellaneous techniques 52

53

54

55

Further evidences of the usefullness of CO2 adsorption to characterise

microporous solids J. Garcia-Martinez, D. Cazorla-Amoros, A. Linares-Solano

485

Interaction between menisci in adjacent pores G. Mason, N.R. Morrow, T.J. Walsh

495

Studies on the formation and properties of some highly ordered mesoporous solids M.J. Hudson, P. Trens

505

Pore structure of zeolites of type Y and pentasii as the function conditions of preparation and methods of modification A.V. Abramova, E.V. Slivinsky, A.A. Kubasov, L.E. Kitaev, B.K. Nefedov, O.L. Shahnovskya

515

Characterisation of activated carbon fibers by positron annihilation lifetime spectroscopy (PALS) D. Lozano-Castello, D. Cazorla-Amoros, A. Linares-Solano, P.J. Hall, J.J. Fernandez

523

Investigation of the textural characteristics and their impact on in vitro dissolution of spray dried drug product size fractions H. Elmaleh, M. Sautel, F. Leveiller

533

The response function method as a novel technique to determine the dielectric permittivity of highly porous materials S. Geis, B. MOiler, J. Fricke

545

59

Mesopore characterisation by positron annihilation T. Goworek, B. Jasinska, J. Wawryszczuk, K. Ciesielski, J. Goworek

557

60

Characterisation of vanadia-doped silica aerogeis U. Klett, J. Fricke

565

61

Shear strength of mineral filter cakes O. Ozcan, M. Ruhland, W. Stahl

573

62

A frequency-response study of diffusion and adsorption of C x-C5 alkanes and acetylene in zeolites Gy. Onyestyak, J. Valyon, L.V.C. Rees

587

Novel Mn-based mesoporous mixed oxidic solids V.N. Stathopoulos, D.E. Petrakis, M. Hudson, P. Falares, S.G. Neofytides, P.J. Pomonis

593

64

Mercury porosimetry applied to precipitated silica R. Pirard, J.-P. Pirard

603

65

Synthesis and textural properties of amorphous silica-aluminas C. Rizzo, A. Carati, M. Tagliabue, C. Perego

613

66

Porous texture modifications of a series of silica and silica-alumina hydrogels and xerogels: A thermoporometry study

56

57

58

63

J.P. Reymond, J.F. Quinson 67

Comparison of specific surface areas of a micronised drug substance as

determined by different techniques M. Sautel, H. Elmaleh, F. Leveiller 68

623

633

Investigations on the surface properties of pure and alkali or alkaline

earth metal doped ceria I. Pashalidis, C.R. Theocharis

643

69

70

Comparison of the porosity evaluation results based on immersion calorimetry and gravimetric sorption measurements for activated chars from a high volatile bituminous coal A. Albiniak, E. Broniek, M. Jasienko-Halat, A. Jankowska, J. Kaczmarczyk, T. Siemieniewska, R. Manso, J.A. Pajares

653

Measuring permeability and modulus of aerogels using dynamic pressurisation in an autoclave J. Gross

663

Author Index

671

Other volumes in the series

675

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xiii

Foreword

The Fiith International Symposium on the Characterisation of Porous Solids (COPS-V) was held at Heidelberg, Germany, from May 30 to June 2, 1999. Heidelberg showed its best side with beautiful summer weather, friendly atmosphere and superb hospitality. About 220 participants from 25 countries enjoyed a very successful meeting with 32 lectures and 155 poster presentations. The Symposium started with a highly stimulating lecture by Sir John Meurig Thomas, Cambridge, highlighting the recent developments in engineering of new catalysts. The following two full sessions were devoted to theory, modelling and simulation which provide the basis for the interpretation of pore structural data of adsorbents and finely dispersed solids. Session 2 and 3 focused on the advances in the synthesis and characterisation of highly ordered inorganic adsorbents and carbons. Session 4 and 5 addressed important questions with respect to the characterisation of porous solids by sorption measurement and other related techniques. The intensive three-day programme provided a stimulating forum for the exchange of novel research findings, concepts, techniques and materials. I would like to express my thanks to the members of the Scientific Committee (J. Rouquerol, R. Rodriguez-Reinoso, K.S.W. Sing) and of the Organisation Committee (U. Mtiller, F. Sch~ith, L. Nick) for their tireless efforts in composing a scientific programme of outstanding quality. I want to thank the DECHEMA (L. Nick, I. Langguth, C. Hess) for their excellent work in preparing and organising the Symposium. The generous support of sponsors (BASF Aktiengesellschat~, Engelhard Technologies GmbH&Co OHG [Hannover], Henkel KGaA, Merck KGaA, Quantachrome GmbH, Porotec GmbH and Elsevier Science Publishers) is acknowledged: this enabled the Symposium organiser to provide 21 grants to students to participate. It has been decided that COPS-VI will be held on May 8 - 11, 2002 in Alicante, Spain.

K.K. Unger

Mamz, Germany

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XV

Scientific Committee

J. Rouquerol, CTM du CNRS, Marseille, France R. Rodriguez-Reinoso, Universidad de Alicante, Spain K.S.W. Sing, Universities of Exeter und Bristol, United Kingdom K.K. Unger, Universitat Mainz, Germany

Organising Committee

F. Schuth, MPI fur Kohlenforschung, Mulheim an der Ruhr, Germany U. Muller, BASF Aktiengesellschafi, Ludwigshafen, Germany L. Nick, DECHEMA e.V., Frankfurt am Main,Germany

Financial Support The organisers gratefully acknowledge the financial support of the following sponsors: BASF Aktiengesellschatt, Ludwigshafen, Germany Engelhard Technologies GmbH & CO.OHG, Hannover, Germany Henkel KGaA, Dtisseldorf, Germany Merck KGaA, Darmstadt, Germany Quantachrome Gmbh, Odelzhausen, Germany Porotec GmbH, Frank~rt am Main, Germany

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Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) 92000 Elsevier Science B.V. All rights reserved.

A d s o r p t i o n o f A r g o n a n d X e n o n in Silica C o n t r o l l e d P o r o u s Glass: A Grand Canonical Monte-Carlo Study R.J.-M. Pellenq*, A. Delville, H. van Damme and P. Levitz Centre de Recherche sur la Mati6re Divisde, CNRS et Universit6 d'Orl6ans l b rue de la Fdrollerie, 45071 Orl6ans, cedex 02, France.

We have studied adsorption of argon (at 77 K) and xenon (at 195 K) in a mesoporous silica Controlled Porous Glass (CPG) by means of Grand Canonical Monte-Carlo (GCMC) simulation. Several numerical samples of the CPG adsorbent have been obtained by using an offlattice reconstruction method recently introduced to reproduce topological and morphological properties of correlated disordered porous materials. The off-lattice functional of Vycor is applied to a simulation box containing silicon and oxygen atoms of cubic cristoballite with an homothetic reduction of factor 2.5 so to obtain 30A-CPG sample. It allows to cut out portion of the initial volume in order to create the porosity. A realistic surface chemistry is then obtained by saturating all oxygen dangling bonds with hydrogen. All numerical samples have similar textural and structural properties in terms of intrinsic porosity, density, specific surface and volume. The adsorbate (Ar,Xe)/adsorbent potential functions as used in GCMC simulations are derived from the PN model. Ar and Xe adsorption isotherms are calculated for each sample: they exhibit a capillary condensation transition but with a finite slope by contrast to that obtained in simple geometries such as slits and cylinders. The analysis of the adsorbed density reveals that the adsorption mechanism for argon (at 77 K) differs from that for xenon (at 195 K): Ar forms a thin layer which covers all the surface prior to condensation while Xe condensates in the higher surface curvature regions without forming a continuous film. This is interpreted on the basis of the Zisman law for wetting: it is based on a contrast of polarizability between the adsorbate and the atoms of the adsorbent. The difference of behavior upon adsorption has important implications for the characterization of porous material by means of physical adsorption especially as far as the specific surface measurement is concerned.

1. I N T R O D U C T I O N Disordered porous solids play an important role in industrial processes such as separation, heterogeneous catalysis... The confinement and the geometrical disorder strongly influence the thermodynamics of fluid adsorbed inside the porous network. This raises the challenge of describing the morphology and the topology of these porous solids [1]. A structural analysis can be achieved by using optical and electron microscopy, molecular adsorption... Vycor is a porous silica glass which is widely used as a model structure for the study of the properties of confined fluids in mesoporous materials. The pores in vycor have an average radius of about 30-35 A (assuming a cylindrical geometry) and are spaced about 200 A apart [23]. A literature survey indicates that there are two kinds of (Coming) vycor glasses: one type has a specific surface around 100 m2/g while the other is characterized by a specific surface around 200 m2/g (both values are obtained from N 2 adsorption isotherms at 77 K). The aim of this work is to provide an insight in the adsorption mechanism of different rare gases (argon and xenon) in a disordered connected mesoporous medium such as vycor at a microscopic level.

2. SIMULATION PROCEDURES 2.1 Generating vycor-like numerical samples We have used on an off-lattice reconstruction algorithm in order to numerically generate a porous structure which has the main morphological and topological properties of real vycor in terms of pore shape: close inspection of molecular self-diffusion shows that the off-lattice reconstruction procedure gives a connectivity similar to experiment. One challenge was to define a realistic mesoporous environment within the smallest simulation box. In a previous study, it was shown that chord distribution analysis on large non-periodic reconstructed 3D structures of disordered materials allows to calculate small angle scattering spectra. In the particular case of vycor, the agreement with experiment is good: on a box of several thousands ,A in size, the calculated curve exhibits the experimentally observed correlation peak at 0.026 /~,-1 [4]. The first criterium that our minimal reconstruction has to meet is to reproduce this correlation peak in the diffuse scattered intensity spectrum which corresponds to a minimal (pseudo) unit-cell size around 270 A. In fact, such a simulation box size still remains too large to be correctly handled in an atomistic Monte-Carlo simulation of adsorption. This is the reason why we have applied an homothetic reduction with a factor of 2.54 so that the final numerical sample is contained in a box of about 107 A in size (see below). This transformation

preserves the pore morphology but reduces the average pore size from 70 A to roughly 30 A. Note that a reconstructed minimal numerical sample is still well within the mesoporous domain. The atomistic pseudo-vycor porous medium has been obtained by applying the offlattice functional to a box containing the silicon and oxygen atoms of 153 unit cells of cubic cristoballite (a siliceous non-porous solid). This allows to cut out portions of the initial volume in order to create the vycor porosity. The off-lattice functional represents the gaussian field associated to the volume autocorrelation function of the studied porous structure [5]. This approach encompasses a statistical description: it allows to generate a set of morphologically and topologically equivalent numerical samples of pseudo-vycor. Periodic boundary conditions are applied in order to simplify the Grand Canonical Monte-Carlo (GCMC) adsorption procedure. In order to model the surface in a realistic way and to ensure electroneutrality, all oxygen dangling bonds are saturated with hydrogen atoms (all silicon atoms in an incomplete tetrahedral environment are also removed). The gradient of the local gaussian field allows to place each hydrogen atom in the pore void perpendicular to the interface at 1 ,~ from the closest unsaturated oxygen.

2.2. The Grand Ensemble Monte-Carlo simulation technique as applied to adsorption In this work, we have used a PN-type potential function as reported for adsorption of rare gas in silicalite (a purely siliceous zeolite): it is based on the usual partition of the adsorption intermolecular energy which can written as the sum of a dispersion interaction term with the repulsive short range contribution and an induction term (no electrostatic term in the rare gas/surface potential function) [6]. The dispersion and induction parts in the Xe/H potential are obtained assuming that hydrogen atoms have a partial charge of 0.5e ( q o - - l e and qsi=-2e respectively) and a polarizability of 0.58 ~3. the adsorbate/H repulsive contribution (BornMayer term) is adjusted on the experimental low coverage isosteric heat of adsorption (13.5 and 17 kJ/mol for argon [7,8] and xenon [9,10] respectively). The adsorbate-adsorbate potential energy was calculated on the basis of a Lennard-Jones function (~= 120 K and ~=3.405 A for argon and ~=211 K and 6=3.869 A for xenon). In the Grand Canonical Ensemble, the independent variables are the chemical potential, the temperature and the volume [11 ]. At equilibrium, the chemical potential of the adsorbed phase equals that of the bulk phase which constitutes an infinite reservoir of particles at constant temperature. The chemical potential of the bulk phase can be related to the temperature and the bulk pressure. Consequently, the independent variables in a GCMC simulation of adsorption in vycor are the temperature, the pressure of the bulk gas and the volume of the simulation cell containing the porous sample as defined above. The adsorption isotherm can be readily obtained from such a simulation technique by evaluating the ensemble average of the number of adsorbate molecules. Note that the

bulk gas is assumed to obey the ideal gas law. Control charts in the form of plots of a number of adsorbed molecules and internal energy versus the number of Monte-Carlo steps were used to monitor the approach to equilibrium. Acceptance rates for creation or destruction were also followed and should be equal at equilibrium. After equilibrium has been reached, all averages were reset and calculated over several millions of configurations. In order to accelerate GCMC simulation runs, we have used a grid-interpolation procedure in which the simulation box volume is split into a collection of voxells [12]. The adsorbate/pseudo-vycor adsorption potential energy is calculated at each corner of each elementary cubes.

3. RESULTS AND DISCUSSION 3.1. Properties of pseudo-vycor numerical samples We have generated a series of ten numerical samples. The porosity ranges from 0.291 to 0.378 % while the density ranges from 1.369 to 1.562 g/cm 3. The average density and porosity values are 1.467 g/cm 3 and 0.334 respectively (the values for real vycor are 1.50 g/cm 3 and 0.30). Density and porosity exhibit fluctuations that are due to a small-size effect: the numerical reconstruction procedure uses the volume autocorrelation function of (real) vycor as obtained from the analysis of MET images on a macroscopic vycor sample [5]. In a previous study [13], we have shown that the small angle diffusion spectra (SAS) of the numerical reconstructed samples of pseudo-vycor are characterized (i) by a correlation peak at 0.067 A-1 and (ii) an algebraic law decay of the simulated diffused intensity with exponent -3.5 in good agreement with experiment [14] (note that the shift of the correlation peak from 0.026 ~-1 (real vycor) to 0.067 A-1 is again a consequence of the homothetic transformation" the ratio 0.067/0.026=2.54 ie the homothetic factor). The SAS spectrum calculated on samples with a smooth interface (using the off-lattice functional with no atomic description) obey the Porod law (exponent-4) [15]. We have therefore demonstrated that the deviation to the Porod law in the case of atomistic reconstructed samples was due to surface roughness without invoking the fractal theory. Specific surface can be measured by calculating the first momentum of the in-pore chord length distribution [5]. We have evaluated this distribution for all numerical samples by making use of the potential energy grids for both adsorbates: at each current probe position of a given chord, the energy is calculated and the interface is found when the energy changes of sign. This allows the direct determination of the intrinsic specific surface for each porous structure taking into account surface roughness. Interestingly, we found that for a given pseudo-vycor sample, both the argon and xenon in-pore chord length distributions were almost identical for chords larger than 4/~ in length leading to very close values of the specific

surface. We found no direct linear correlation between porosity (or density) and the specific surface: Ssp=258, 241, 208, 225 and 206 m2/g for samples 3 to 7 respectively (the corresponding porosities are 0.344, 0.378, 0.301,0.298 and 0.291). Globally, large values of specific surface are obtained for high value of porosity although the intrinsic specific surface exhibits a maximum value for a porosity around 0.344. Note that the values of the intrinsic specific surface are more than twice that of the real (low specific surface) vycor sample used to build up the volume autocorrelation function (from MET 2D-images) which underlies the off-lattice reconstruction method [5]. This is one further effect of the homothetic reduction. This is in line with that observed experimentally: the smaller the pore size, the larger the specific surface [16]. It will be very valuable to compare those intrinsic specific surface values with that obtained from adsorption isotherms applying the usual BET method [17]. The intrinsic specific surface values shoull are upper bound limits of adsorption-derived ones since the interface in the chord length analysis is found at the frontier between negative and positive values of the adsorbate/matrix energy; the primary adsorption sites being further away from this somewhat arbitrary interface. Assuming the formation of a molecular film, the specific surface as seen from adsorption of a spherical molecule of radius 2 A in a cylindrical pore of radius 15 A is 93 % of the intrinsic value.

3.2. Grand Canonical Monte-Carlo simulation of adsorption Figures 1 and 2 present the simulated argon and xenon adsorption isotherms on pseudovycor sample n~

In both cases, capillary condensation is observed: at maximum loading, the

fluid density and structure is close to that of the bulk 3D-liquid at the same temperature (0.0194 Ar/A 3 and 0.0129 Xe/A3). The specific volume as measured from the xenon adsorption isotherms at maximum loading is found at 0.239, 0.276, 0.196, 0.193 and 0.186, cm3/g for sample 3 to and 7 respectively. Interestingly enough, the specific volume as measured from the argon experiment equals that obtained with xenon. This validates the Gurvitch rule [17] in the case of argon and xenon adsorption at 77 and 195 K respectively. By contrast to that obtained for a single infinite cylinder, the slope at the transition has a finite value. This is in qualitative agreement with experimental studies [7,9] and recent Monte-Carlo simulations of nitrogen adsorbed in disordered porous glasses [18]. Therefore such a behavior can be considered as the signature of disordered mesoporous structure. The pseudo-vycor adsorption curves are shifted to the lower pressure region compared to the experimental curve since the pore size distribution of reconstructed samples is shifted toward a smaller size domain due to the homothetic reduction. They also exhibit the hysteresis loop upon desorption characteristic of sub-critical adsorption/condenstion phenomenon [19].

Pressure (Pa) Figure 1 : Argon adsorption isotherm at 77 K

-

GCMC data (sample 5) Experiment

-

I

Oe+O

I

1.e+5

I

2.e+5

Pressure (Pa) Figure 2: Xenon adsorption isotherm at 195 K

Most important is the adsorption mechanism as seen from equilibrium configuration snapshots (Figures 3 and 4). At 195 K, xenon does not wet the vycor surface: adsorption and condensation take place in the places of highest surface curvature (this corresponds to regions where the confinement effect is maximum). This leads to an unexpected situation where regions of the pores are filled with condensate while other parts of the interface remain uncovered. By contrast, argon at 77K does cover the entire surface before condensation occurs by forming a contiunous film. The specific surface values as measured from the adsorption isotherms (using the BET equation with cross-section values of CYAr=13.8 ~2 and CYXe=17.0 ~2 [17]) are 137 m2/g and 80 m2/g in the case of argon and xenon. This difference cannot be

only attributed to the difference in size of the adsorbate probe (which can also leads to

Figure 3: snapshot equilibrium configuration of argon in numerical sample 7 at different pressures (one sees "through" the matrix: small dots are hydrogen atoms which delimitate the interface, grey spheres are argon atoms. micropore sieving effects for the largest) but is clearly due to the adsorption mechanism which is different the two adsorbates considered in this work. The values of specific surface as obtained from simulated adsorption isotherms (by measuring the so-called BET monolayer capacity) are well below that calculated from chord-length distribution. It is thus clear that monolayer-based method (such as the BET approach) cannot be used for determining the specific surface in non-wetting situations for temperatures below the wetting temperature of the confined fluid (xenon is not a good probe of curved silica surfaces). Note that wetting should be here understood as a phenomenon leading to the formation of a thin adsorbate film (few adsorbate layers in thickness ie the so-called statistical monolayer capacity in the BET theory) on the available surface and not as the first order pre-wetting transition encountered on homogeneous surfaces. In the case of argon, the pre-wetting transition in disordered porous glasses

is probably not first order as shown by a recent simulation study of pre-wetting on rough (flat) surface

[20].

It

is

interesting

to

mention

that

GCMC

simulations

of

nitrogen

adsorption/condensation in similar siliceous glass have shown that nitrogen does form a continuous film on the inner surface [ 18]. Therefore, one can infer that there are different adsorption mechanism depending on the adsorbate (and on the temperature). Note that a similar wetting behavior to that presented in this work for xenon was found in a GCMC study of adsorption of a Lennard-Jones fluid in a disordered porous medium characteristic of silica xerogel [21] (an assembly of nanometric silica spheres): it is shown that adsorption and condensation take place in the highest sphere density regions where the confinement effect is maximum.

Figure 4: same as Figure 3 but for xenon. The difference in specific surface as obtained from Ar and Xe adsorption isotherms deserves more attention. Many year ago, Zisman rationalized the wetting phenomenon (on flat surfaces) on the basis of a difference of polarizability between the adsorbate and the atomic species of the substrate [22] (assuming that the attractive part of the adsorbate/surface potential energy is mainly of dispersive nature). If the adsorbate has a polarizability equal or lower than that of the substrate species then there is wetting. In the opposite case, the adsorbate has a weak affinity with the surface compared to that for other adsorbate molecules; in those conditions, the adsorbate does not wet the surface. Of course, wetting has the status of a thermodynamic transition and depends on temperature. In fact, Zisman criterium for wetting is only valid at low temperature where enthalpic effect dominates. In the particular case of silica porous glasses, oxygen is the most polarizable species (its polarizability o~O_ equals 1.19 ~3) [23]. Our results conform to the predictions of Zisman's rule since O~Ar=l.64 ~3 and OtXe=4.06 /~3. argon polarizability is much closer to that of silica oxygen as compared to

xenon. It is interesting to note that a similar evolution of the specific surface values is found experimentally: for the Ar/vycor system, Ssp--150 m2/g [7] while for the Xe/vycor system, Ssp=106 m2/g [10]. Note that in each case, the corresponding nitrogen adsorption experiments lead to a vycor specific surface around 200 m2/g [7,10]. Restricting ourselves to rare gas adsorption, we can conclude that an adsorption experiment will give a good measure of the specific surface if one carefully chooses the adsorbate so that its polarisability is lower or close to that of the solid matrix species.

4. C O N C L U S I O N We have performed atomistic Grand Canonical Monte-Carlo (GCMC) simulations of adsorption of argon and xenon in a vycor-like matrix at 77 and 195 K respectively. This disordered mesoporous network is obtained by using a numerical 3D off-lattice reconstruction method: the off-lattice functional when applied to a simulation box originally containing silicon and oxygen atoms of a non-porous silica solid, allows to create the mesoporosity which has the morphological and the topological properties of the real vycor glass. In order to reduce the computational cost, we have applied a homothetic decrease of the box dimensions which preserves the morphology and the topology of the pore network. The surface chemistry is also obtained in a realistic fashion since all dangling bonds are saturated with hydrogen atoms. The argon and xenon simulated isotherm calculated on such disordered connected porous networks, show a gradual capillary condensation phenomenon: the shape of the adsorption curves differ strongly from that obtained for simple pore geometries. By contrast to argon, xenon adsorbed density distribution indicates partial wetting depending on the local surface curvature and roughness. This leads to an interesting situation in which, parts of the porous network are already filled with liquid while other regions of the interface remain uncovered with an adsorbate film. The difference of adsorption mechanism between argon and xenon is interpreted of the basis on Zisman's type law for wetting. We further give some guide lines for the measurement of specific surface in porous materials.

ACKNOWLEGEMENTS Drs. G. Tarjus and M.-L. Rosinberg (University of Paris, France), S. Rodts (CRMD, orleans, France) are gratefully acknowledged for very stimulating discussions. We also thank

10 the Institut du D6veloppement et des Ressources en Informatique Scientifique, (CNRS, Orsay, France) for the computing grant 98/99281.

REFERENCES 1. P. Levitz, V. Pasquier, I. Cousin, Caracterization of Porous Solids IV, B. Mc Enanay, T. J. May, B., J. Rouquerol, K. S. W. Sing, K. K. Unger (eds.), The Royal Soc. of Chem., London, (1997), p 213. 2. M. Agamalian, J. M. Drake, S; K. Sinha, J. D. Axe, Phys. Rev. E, 55 (1997), p 3021-3027. 3. J. H. Page, J. Liu, A. Abeles, E. Herbolzheimer, H. W. Deckman, D. A. Weitz, Phys. Rev. E., 52 (1995), p 2763-2777. 4. P. Levitz, D. Tchoubar, J. Phys.I, 2 (1992), p 771-790. 5. P. Levitz, Adv. Coll. Int. Sci., 76-77 (1998), p 71-106. 6. R. J.-M. Pellenq, D; Nicholson, J. Phys. Chem., 98 (1994), p 13339-13349. 7. M. J. Torralvo, Y. Grillet, P. L. Llewellyn, F. Rouquerol, J. Coll. Int. Sci., 206 (1998), p 527-531. 8. G. L. Kington, P. S. Smith, J. Faraday Trans. 60 (1964), p 705-720. 9. C. G. V. Burgess, D. H. Everett, S. Nuttal, Langmuir, 6 (1990), p 1734-1738. 10. S. Nuttal, PhD thesis, University of Bristol, UK, (1974). 11. D. Nicholson and N. G. Parsonage in "Computer simulation and the statistical mechanics of adsorption", Academic Press, 1982. 12. R. J.-M. Pellenq, D; Nicholson, Langmuir, 11 (1995), p 1626-1635. 13. R. J. M. Pellenq, S. Rodts, V. Pasquier, A. Delville, P. Levitz, Adsorption, 1999, in press. 14. F. Katsaros, P. Makri, A. Mitropoulos, N. Kanellopoulos, U. Keiderling, A. Wiedenmann, Physica B, 234 (1997), p 402-404. 15. P. Levitz, G. Ehret, S. K. Sinha, J. M. Drake, J. Chem. Phys., 95 ( 1991 ), p 6151-616 i. 16. R. H. Torii, K. J. Maris, G. M. Seidel, Phys. Rev. B, 4 i (10), p 7167-7181. 17. F. Rouquerol, J. Rouquerol and K. Sing, in "Adsorption by powders and porous solids', Academic Press, 1998. 18. L. Gelb, K. Gubbins, Langmuir, 14 (1998), p 2097-2111. 19. P. C. Ball, R. Evans, Langmuir, 5 (1989), p 714-723. 20. S. C urtarolo, G. Stan, M. W. Cole, M. J. Bojan, W. A. Steele, Phys. Rev. E., 59 (1999), p 4402-4407. 21. K. S. Page, P. A. Monson, Phys. Rev. E, 54 (1996), p 6557-6564. 22. P. G. de Gennes, Rev. Mod. Phys., 57 (1985), p 289-305. 23. R. J.-M. Pellenq, D. Nicholson, J. Chem. Soc. Faraday Trans., 89 (1993), p 2499-2505.

Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 9 2000 Elsevier Science B.V. All rights reserved.

11

The role o f isosteric enthalpy o f adsorption in micropore characterisation: A simulation study. D. Nicholson and N. Quirke Department of Chemistry, Imperial College, London SW7 2AY, London, UK. A database of isotherms and isosteric enthalpies for methane adsorption in graphitic slit pores at 273K has been constructed from simulation. The data have been used to explore the role of the pore size distribution in determining composite adsorption enthalpies and isotherms. An important advantage of simulation is that intermolecular and adsorbent contn'butions to the isosteric enthalpy can be distinguished, giving insight into underlying molecular processes. Pore size distribution analysis of adsorption by composite adsorbents, assuming a lognormal distribution, gives good agreement with the input composite structure, and suggests that pore size distribution derived from enthalpy data, may improve the characterisation of smaller pores. 1. I N T R O D U C T I O N

The isosteric enthalpy of adsorption q~t, is usually shown as a function of adsorbate density, p. Plots of q~t against p can exhibit several distinctive features that reflect the properties of the adsorbent. For exan'tple, a steep decrease o fq~, at low density is customarily associated with the occupation of the most strongly adsorbing sites in the early stages of adsorption; an increase in q~, with density is attributed to increasing mutual attraction between adsorbate species as their concentration increases. As a consequence of these features, isosterie enthalpy curves can show more structure than the associated isotherms which, in the ease ofmicroporous adsorbents, may show a simple monotonic (type I) increase of density with adsorbate pressure. Additionally, isosterie enthalpy curves may have eusped maxima and/or minima when the corresponding isotherms have transition steps. In a recent simt~tion study[1 ], the effects of thermal disordering of surfaces on qst -density curves for methane in model oxide pores was examined. It was found that even a high degree of disorder had only minor effects, and did not account for the magnitude of the initial steep decrease observed in similar experimental systems. On the other hand, when structural heterogeneity was modelled by a distribution of slit pore widths, enthalpy curves representative of such experiments could be obtained. The explanation lies in the existence of a sufficiently high population of pore spaces having widths close to the adsorbate molecule diameter (structural heterogeneity). Very high adsorbent fields exist in these spaces. Such cavities are unlikely to be created by thermal disruption of the adsorbent, since they constitute improbable vacancy defects of several atoms and, should they occur, might equally be described as pores. Another source of heterogeneity that may also give rise to structuring in the enthalpy curves can occur when strong, localised, electrostatic interactions arise between adsorbate and adsorbent. The commonest examples are found in zeolites when extra-framework cations are present. Direct electrostatic interactions do not have any relevance for rare gas species, although weak induced

12 interactions may contribute. Electrostatic interactions are likely to be of minor importance for adsorptive species of high symmetry with high order leading multipoles such as methane. It follows that, in the context of a suitable choice of adsorbate and temperature, the enthalpy of adsorption may be of value in characterising pore structure, especially in the regime of small micropores. Simulation or density functional calculations can play an important part in evaluating this possibility, and when used to comtruct databases relating to simple pore models. In addition, because in theoretical studies it is possible to separate the adsorbate-adsorbent ("wall") contribution to the enthalpy from the adsorbate-adsorbate ("molecule") contribution, insight can be gained into the underlying molecular processes during adsorption. Although nitrogen adsorption at 77 K remains the most widespread choice for assessing surface area and pore size distribution, other techniques have been explored; particularly in recent years. In low temperature nitrogen adsorption, micropores fill at extremely low pressures, and although the presence of micropores may be detected, it has increasingly come to be appreciated that low temperature nitrogen adsorption is imufficiemly sensitive to analyse the distribution of very small micropores, unless very high resolution methods are employed [2 ]. Carbon dioxide as an adsorbate at around ambient temperatures has several attractions as an altemative [3, 4], but both these adsorptives have quite large quadrupoles, and therefore tend to see strong electrostatic sites as heterogeneities as well as small pore spaces. Methane suffers less from this problem since its leading multipole is a relatively weak octopole, on the other hand its interaction with adsorbents is sufficiently strong that there is substantial uptake in micropores at ambient temperatures. Argon as an adsorbate at low temperature also offers an attractive alternative [5], but like nitrogen, high resolution adsorption is necessary if micropores are to be probed. In the present work we have used simulation as a basis for exploring the adsorption of methane in graphitic slit pores in the micropore size range and in composite structures built using a database established from simulation~ Methane adsorption on activate carbon has been studied experimentally in conjunction with both DFT theory [6] and simulation[7]. Experimentally, there are some difficulties in using methane or carbon dioxide as a probe at ambient temperatures. One is the need to adsorb at high pressures (in reference 6 pressures of up to 40 atmospheres were used). A second problem is that the correction needed to convert from surface excess to absolute adsorption, implying an assmnption about the accessible pore volume, cannot be ignored, and may become dominant at high pressure. 2. RESULTS

2.1. Adsorption in single slits Grand canonical simulations of methane adsorption in graphitic slit pores were carried out at 273K. The pores were modelled as slits with parallel continuum surfaces interacting with the adsorbate through a standard 10-4-3 potential [4,6,7]. The methane was modelled as LennardJones spheres with e/k=-148K and 0=0.3812nm. Typical run lengths were 107 configurations for 100-300 molecules. Physical pore widths, H, were chosen to cover the range, H =- 0.7nm to 3.0ran, where H is the distance normal to the pore surface between carbon nuclei on opposite pore walls. In the smallest pore, there is a single potential minimum of depth about twice that of the potential minimum at a plane graphitic surface. S n e e r pore widths have higher potential minima and below H=O.64nm, methane molecules are excluded completely. The adsorption isotherms from GCMC simulation are shown in figure 1 as plots of absolute adsorbate density versus fugacity. They are all of type I in the Brunauer classification, showing a

13

10

1 .Onto- -~_ 1.~ nm- -~. ~ 8 1.2~nnn~~ _,,,-,. _~_ . . . . . . .

L2

,-

. . . . . . . ~ :~ . . . . . . . : ...........................

.

.

~/

I[:

0.7nm 0"7 0.8nm

"~4 I I

09nm

I

0.5 t }

.

~'

f/bar

10 8

.

J ~ ,'"

~'r

"~'4

./-

II//Jfl

oo

50

.

//

/

o.oV.

0

.

-,---4 ~ ! ~

o2

I

o4

100

I

2 o

150

0

50

f/bar

100

150

Figure 1. Adsorption isotherms for methane in smooth graphitic slit pores at 273K. Isotherms were calculated for slit widths of 0.7,0.8,0.9,1.0,1.1,1.2,1.4,1.6,1.8,2.0,2.2,2.4,2.6,2.8 and 3.0nm. The isotherms from the top to bottom in the fight hand panel cover the range 1.4nm to 3.0nm. The inset in the left hand panel shows the same isotherms in the range of subatmospheric pressures. continuous monotonic increase in density up to high pressure. It must be emphasised that these are absolute isotherms; isotherms of the excess adsorption density show maxima at pressures as low as 1 bar for the smallest pore size. The corresponding isomeric enthalpy curves are shown in figure 2, together with the component wall and molecule parts. The shape of the total differential enthalpy curves shows a steady alteration as the pore width increases. The underlying molecular reasons can be deduced from the component curves. At the smallest pore size, the wall part of qst (q~) remains constant over the whole density range since adsorbate molecules sitting in the single potential minimum vibrate normal to the pore walls and translate along the pore axis. The high

"7

30 -~

25

25

20 . .......................................

"~=15 -~,--''~ .--"" ,.,-,--a" ~ _ _ L ' " ~ - " ~ " _ , - - - -----" ~

"--

~

~

,

-----

-'-"--

'

5~

5 0

~ ~ ~.10

2

4 p/nm 3

6

8

0

0

........ 2

4

6

8

p/nm-3

Figure 2 Isosteric enthalpies of adsorption (q,,) in smooth graphitic slit pores at 273K (lett hand panel); separate contributions from wall (q~) and intermolecular parts (qm) (right hand panel). The highest q,t curve is for 0.7nrn, the lower curves cover the range 0.8nm to 3.0nm over the same range ofpore widths as in figure 1. In the right hand panel the top set ofcurves is for qw, ranging from the smallest pore width at the top to the largest pore width at the bottom. The lines through the origin are %; the lowest four of these are for the four smallest slit widths. The remaining qm lines are not resolved on this scale.

14

value of qw reflects the deep potential minimmrL In these very narrow pores, the adsorbateadsorbate part of q~ (q=) initially increases with density, then passes through a maximum at higher density. The decrease in qm occurs when intermolecular repulsion begins to dominate the interaction. In the wider slits, q~ has the same slope for all pore widths, and shows no maxima. The lower initial slope in the narrow slits reflects the fact that full intermolecular interaction with neighbouring adsorbate cannot be developed in these highly confined environments. It is interesting to note that maxima in q~ have been found previously in the same model for slit widths >0.9nm at similar densities but at the higher temperature of 298K. Clearly removing some kinetic energy from the system by lowering the temperature reduces the repulsive contribution to the total energy. It has been reported in previous work [5,7] that isobars of adsorbate density against pore width show maxima and minima, which are attributed to packing transitions at s n ~ pore widths. Similar effects are also observed for the enthalpies of adsorption and are shown in figure 3 and in figure 4, where the molecule-wall and molecule-molecule components are shown separately. In the system investigated here, the enthalpy curves can be divided roughly into two groups around a fugacity of about 3-4bar. Below this pressure, there is little discernible periodicity in qst, but at higher pressures, a distinct minimum appears at a width of 0.9nm, followed by a maximum at 1.1nm. From figure 4, it can be seen that these features are attributable mainly, but not entirely, to adsorbate molecule-molecule interactions. Indeed at very high pressures clear maxima and minima continue over the whole range of pore widths. However, in the total enthalpy curves they are suppressed because qw is declining quite strongly as newly adsorbed molecules are no longer able to find favourable sites close to the adsorption minimmrL At the higher pressures, it is interesting to see that there is a small, but distinct inflection in qw between 0.9nm and 1.1 nm. This

30

,

....

30

25 ~ \

25

10 I

.

1.0 r

.

1.5

10-

2.0 Hlnm

2.5

3.0

~,~ ~ - ~ _ _ ~

1.0

1.5

2.0

2.5

3.0

Hlnm

Figure 3. Isosteric enthalpies as a function of slit width for a series of fugacities. On the leit hand graph the fugacities (in bar) are 0.037(filled circles), 0.1885 (open circles), 0.302 (filled triangles), 0.754 ( filled squares), 1.885 (open squares). In the fight hand graph, the fugacities are 7.54 (filled circles), 15.08 (open circles), -22.62 filled triangles), 30.15 (open triangles), 37.7 (filled squares), 75.38 (open squares), 113 (filled diamonds), 188 (open diamonds).

15

-

10--

2O

10 9

E .-, 9

o

o

o

"~

3

4 ~

-P

".

D

-r--

,

,.~ - - ~ l v . . . .

)

0

=•20

0 4.

10

0

.....

, . . . . . . . . .

1.0

, . . . . . . . . .

1.5


--~..

'i

.~"~

rE - 6

4 2 0

Igi 0

,\ :.,t 50

100 f/bar

150

10 ,- 1 0

0

5

2

~

4

6

8

p/nm -a

Figure 6. Composite isotherms and isosteric enthalpy curves for the symmetrical distributions shown in the left hand graph. The upper inset shows isotherms over the fugacity range 0-2bar. adsorption occurs into larger pores which do not have such deep energy wells. The trends in qm with skewing of the distribution are of secondary consequence, mainly that the gradient of qm versus density increases as the distributions become more positively skewed, this is due to the increasing number of long range intermolecular attractions in the larger pores, and accounts for the appearance of a minimum in qst. In figure 6, a set of symmetrical distributions is used to examine the effects of altering the width of the distributions (A, B, C) and of removing the smallest pore widths from the distribution (D). As a further aid to comparison, distribution A is identical to distribution 3 in figure 5. Although the isotherm shape changes over this set of distributions, there is no deviation from the type I form. The excess isotherms pass through maxima which shift to higher pressures as the distribution maximum moves to higher pore widths. This trend is expected since more pore space capacity is available for the wider pore distributions, therefore the internal pore density continues to increase more than the external density to higher pressures. For the three distributions (A, B, C) which include the smallest pore size, the enthalpy curves are lower as wider pores are included. At high densities a minimum appears as the distribution broadens (this would correspond to fairly high pressures in the range 40 to 50bar). All these distributions give rise to a sharp initial decrease in qst', the characteristic signature of heterogeneous adsorbents. In contrast the enthalpy curve for distribution D is quite different; since q~ does not have a steep initial decrease, there is a maximum in q,, followed by a minimum at high density. Differential molar enthalpy curves showing a minimum followed by a maximum, similar to that for distribution C, have been observed experimentally for methane adsorption at 30~ and associated with a broad bimodal- distribution [6] in the range 0.7 to 3.0nm, similar curves were also observed[8] for methane on graphoil at 92K.

18 2.3. Analysis of pore size distribution In this section we consider the inversion of composite isotherms and isosteric enthalpy curves to obtain the original input pore size distn'butions(PSD). A particular objective is to ascertain whether the standard inversion procedures, used for example in conjunction with molecular methods of calculating pore size distn'butions[6], can return the original input distributions, and whether the pore size distribution obtained from the inversion of the isotherm is the same as that obtained from the enthalpy curve. We choose, as an example, the symmetrical distribution A of figure 6. Figure 7 shows the composite isotherm and isosteric enthalpy curves as a function of fugacity for the input PSD A represented by a histogram of eleven values of pore sizes. In inverting equations (1) and (2) of section 2.2 we have assumed that the PSD may be expressed as a lognormal function [ 1 9,10]. The PSD was optimised by minimising the difference (r) in the root mean square deviation between the predicted composite isotherm and/or enthalpy curve from the trial PSD, and that calculated from the input PSD curve A (the 'experimental data') normalised by the maximum value of the function. Using the isotherm data alone produces an excellent fit to the input data and a PSD very similar to the curve A, (see figure 7) despite the difference in functional form between the discontinuous triangular function A and the continuous lognormal curve. Using this PSD to predict the enthalpy curve gives a good fit at higher fugacities but a systematic underestimation at lower values, made evident by the log scale in figure 7. Using the enthalpy curve significantly improves the fit, and also produces an acceptable fit to the isotherm data. The PSD. is now closer to the input function A at the smaller pore sizes. Fitting simultaneously to both isotherm and enthalpy curve by minimising the sum of the normalised rmsd's reduces the error from 0.043 (isotherm), 0.024 (enthalpy) to 0.019 (Joint) without making a significant change in the PSD. Further improvement might be obtained by using a weighted stun. From these calculations we conclude that the standard PSD inversion procedures with respect to the isotherm and enthalpy curve data can produce an acceptable PSD even where the underlying structure has a discontinuous distribution of pores and that the enthalpy curve appears to be more sensitive to the presence of the smallest pores.

10-

0.15

8 I

j~,,,,~S

-

6

0.10 !

j;

~

7

i 0.05 i I i

'E 4

i,

,-

.//

9 /'/

,,

//

~ ~" ~

i el /

0.00 t . /

1.0

1.5 H/nm

2.0

O-

0

1

9

9

'~ 16 -

2.5

15

j 2/ /

,,/

.~

~

e "~--e/e'"

0.1

1

f/bar

10

100

Figure 7 (leit hand panel)" The input pore size distribution A (points), and the recalculated distribution from the fit to the isotherm (full line), the isosteric emhalpy curve (dash) and combined isotherm and enthalpy (dotted line). The right hand graphs show the composite isotherms (upper panel) and enthalpies (lower panel). The isotherm fits are indistinguishable on this scale.

19 3. CONCLUSIONS Simulations of methane adsorption in model graphitic slit pores at 273K have been carried out in order to evaluate the poss~ilities for using enthalpy measurements in pore characterisation. The database has been used to construct isotherms for model triangular distributions. The effects of skewing the distribution and of the presence or absence of ultramicropores have been explored. It is found that, whilst the absolute isotherms all show simple monotonic (type I) behaviour, the enthalpy curves can exhibit structural signatures, dependent on the underlying pore size distribution. Amongst these may be noted: - A maximum at low density from distributions with strongly negative skewing. - A steep initial decrease in qn only when pores of approximately molecular width are present. - Low density and high density minima can be associated with certain features of the micropore structure. The ability to separate adsorbate-adsorbate l~om adsorbate-adsorbent conm'butions in simulations enables a clear identification of the underlying molecular causes of these features to be made. Inversion of composite isotherms and enthalpy curves have been made using the constructed database, and assuming a lognormal form for the pore size distribution. The symmetrical distribution underlying the composite data is reproduced well. Significantly however, the isotherm data underestimate the proportion of ultramicropores in the composite; on the other hand, the enthalpy data do not entirely account for the fraction of wider pores present. This initial study suggests that prospects exist for a more precise characterisation of micropore distributions using a combination of enthalpy and isotherm experimental data.

REFERENCES

1.D. Nicholson, Langmuir, 15(1999) 2508. 2. W. C. Conner, Physical adsorption in microporous solids. NATO Adv.Study Inst. C:33 (1997) 491. 3. F. Rodriguez-Reinoso and M. Molina-Sabio, Adv. in Colloid & Interface Sciences 76-77 (1998) 271. 4.S. Samios, A. K. Stubos, N. Kanellopoulos, R. F. CrackneU, G. IC Papadopoulos, and D. Nicholson, Proceedings of the 4th IUPAC Symposium on Characterisation of Porous Solids, Royal Society of Chemistry Special Publication No. 213, eds. B. McEnany, T.J. Mays, J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K.Unger, (1997) 141. 5. J. P Olivier, Carbon 36 (1998) 1469. 6.P.N. Aukett, N. Quirke, S. Riddiford, and S. R. Tennison, Carbon 30 (1992) 913. 7. G. M. Davies and N. A. Seaton, Carbon 36 (1998) 1473. 8. J. Piper and J. A. Morrison, Phys Rev. B, 30 (1984) 3486.

20 9 C. Lastoskie, K. E. Gubbins and N. Quirke, J. Phys. Chem., 97 (1993) 4786. 10 S. R. Tennison, N. Quirke, Carbon 34 (1996) 1281.

Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 9 2000 Elsevier Science B.V. All rights reserved.

Capillary Materials

Condensation

and

21

Hysteresis

in

Disordered

Porous

L. Sarkisov and P. A. Monson Department of Chemical Engineering, University of Massachusetts, Amherst, MA 01003, U. S. A. In this article we consider capillary condensation and hysteresis in molecular models of fluids confined in a disordered porous materials. Capillary phase diagrams for these systems show that the phase behavior is substantially modified by confinement in the porous material. Isotherms from grand canonical Monte Carlo simulations of these systems exhibit hysteresis loops which resemble those seen in experiments on adsorption in sihca xerogels. The hysteresis in the Monte Carlo simulations is associated with metastability of low density states on the adsorption branch and high density states on the desorption branch of the isotherm. It is suggested that further investigation of the stability of these states in Monte Carlo simulations and their relationship with those seen in experiments is worthwhile. In this regard an algorithm for simulation of adsorption via diffusive mass transfer based on the grand canonical molecular dynamics with control volume method is described. An illustrative application to the hysteresis in the bulk vapor-liquid equilibrium for the Lennard-Jones 12-6 fluid is presented. 1. I N T R O D U C T I O N

One of the difficulties in using adsorption measurements for characterization of adsorbent has been the relatively poor understanding of how porous material microstructure influences adsorption isotherms, especially for materials that are structurally and energetically heterogeneous. Molecular modeling research is starting to have an impact on this situation since its reveals important details of the microscopic behavior of fluids in porous materials. Initially understanding had been sought in terms of the behavior of fluids in single pores or networks of single pores and some substantial insights have emerged from such efforts (Evans, 1990; Balbuena and Gubbins, 1993). In recent years new molecular models of adsorbent microstructure developed in our group and by others make it possible to model the full three dimensional complexity of the system in a tractable way (MacElroy and Raghavan, 1990; Kaminsky and Monson, 1991; Segarra and Glandt, 1994; Gordon and Glandt, 1996). These models can be studied using statistical mechanical theories (Madden and Glandt, 1988; Given and Stell, 1992; Vega et al., 1993; Rosinberg et al., 1994; Kierlik et al., 1997) as well as computer simulation. Our recent Monte Carlo simulations of such models (Page and Monson, 1996a,b, Sarkisov et al., 1999) show that the fluid phase diagram is substantially modified

22 by confinement in the porous material. The adsorption isotherms in these studies exhibit hysteresis and this hysteresis is associated with metastability of the low and high density phases present in the system. The hysteresis loops resemble closely those seen in experiments on disordered materials and it is interesting to investigate whether there is a deeper relationship between the phenomena in the two cases. The present paper describes preliminary efforts in addressing this issue. 2.0 C A P I L L A R Y C O N D E N S A T I O N AND H Y S T E R E S I S : B A C K G R O U N D AND R E C E N T R E S U L T S For adsorbents with sufficiently large porosities (often referred to as mesoporous systems) isotherms can exhibit hysteresis between the adsorption and desorption branches as illustrated schematically in figure 1. A classification of the kinds of hysteresis loops has also been made. It is generally accepted t h a t such behavior is related to the occurrence of capillary condensation - a phenomenon whereby the low density adsorbate condenses to a liquid like phase at a chemical potential (or bulk pressure) lower than that corresponding to bulk saturation. However, the exact relationship between the hysteresis loops and the capillary phase transition is not fully understood - especially for materials where adsorption cannot be described in terms of single pore behavior. A t t e m p t s at understanding adsorption hysteresis have a long history (Everett, 1967; Steele, 1973; Gregg and Sing, 1982). An important early contribution was made by Cohan (1938) who applied the Kelvin equation to adsorption in pores. Cohan suggested t h a t the occurrence of hysteresis in a single pore is related to differences in the geometry of the liquid-vapor meniscus in condensation and evaporation. This issue has been revisited more recently using density functional theory (Bettolo Marini Marconi and van Swol, 1989). Another popular concept has been the idea t h a t the hysteresis is caused at the single pore level by the existence of m e t a s t a b l e states analogous to the f supercooled liquid and superheated vapor states which can be encountered in bulk P/Po systems when nucleation of condensation or evaporation is delayed. Hysteresis loops of this Figure 1. An adsorption/desorption isotherm of density type will emerge from any theory vs. relative pressure showing a hysteresis loop of type of the van der Waals or m e a n H2 in the IUPAC classification (Sing et al., 1985). field type. This idea dates back to

23 the work of Cassel (1944) and Hill (1947). More recently it has been considered in the context of density hmctional theory (see, for example, Ball and Evans, 1989). Analysis of behavior in single pores is certainly an excellent place to start an understanding of adsorption hysteresis. On the other hand, real porous materials are in most cases not simply described in terms of single pore behavior. At the very least a distribution of pores of different sizes should be contemplated. The first analysis of hysteresis loops using a theory of adsorption in single pores together with a pore size distribution was the "independent domain" theory of Everett and coworkers (Everett, 1967). The most sophisticated application of this kind of approach was made by Ball and Evans (1989) who used density functional theory for adsorption in a distribution of cylindrical pores and compared the hysteresis loops obtained with those for xenon adsorbed in Vycor glass. What is missing from the above treatments is the inclusion of collective phenomena spanning regions of the porous material beyond the length scale of a single pore. A significant contribution to our understanding of such effects has come from the application of percolation concepts. From this point of view a porous material is a network of interconnected pores of different sizes. The adsorption/desorption phenomena depend on the accessibility of the pores for m a s s transfer to the external surfaces of the porous material, and this will be determined by the topology of the network. Hysteresis in desorption is associated with the inability of liquid in larger pores to evaporate due to blockage by smaller pores in which the evaporation does not occur until lower values of the chemical potential are reached. The so called 'ink bottle' mechanism (Everett, 1967; Gregg and Sing, 1982) can be viewed as a early example of such approaches. Important recent contributions in this context have been made by Mason (1988) and by Seaton (1991). Ball and Evans (1989) have combined the network percolation concepts with density functional theory for adsorption in cylindrical pores and have shown that for adsorption in Vycor glasses such an approach delivers results which are more in accord with experiment than those based on the "independent domain" approach. Even with the incorporation of network or pore blocking effects, in the above treatments the adsorption thermodynamics is still modeled at the single pore level and only simple pore geometries are considered. In order to go beyond this we m u s t consider models which attempt to describe the microstructure of the porous material at a length scale beyond that of a single pore. One approach is to treat a disordered adsorbent as a collection of solid particles in some predetermined microstructure. Such models, which have been developed in this research group (Kaminsky and Monson, 1991) and by others (MacElroy and Raghavan, 1990; Segarra and Glandt, 1994; Gordon and Glandt, 1996), are playing an increasingly important role in the modeling of adsorption phenomena for disordered materials such as silica gels and activated carbons. Even more sophisticated models of controlled porous glasses have recently been developed which mimic the development of the pore structure in the materials preparation (Gelb and Gubbins, 1998). In all these cases the fluid thermodynamics is determined by phenomena spanning the pore network.

24 In recent work (Page and Monson, 1996a,b; Sarkisov et al., 1999) we h a v e made Monte Carlo computer simulations of a model representative of adsorption of a simple fluid in a silica xerogel, focusing on conditions where the adsorbed fluid can undergo phase transitions including capillary condensation. The model t r e a t s the adsorbent as a collection of particles with a disordered microstructure (Kaminsky and Monson, 1991). The capillary phase diagrams and adsorbate m i c r o s t r u c t u r e s determined in these calculations reveal i m p o r t a n t behavior t h a t cannot be described by treating the system as a collection of independent pores. Effects associated with confinement, wetting and adsorbent disorder are all significant and these effects are coupled. Figure 2 shows some visualizations of coexisting fluid phases in the system. The effect of the disorder is revealed through the comparison with visualizations for an ordered (fcc) a r r a y of the solid particles which are also shown in this figure. Hysteresis between adsorption and desorption isotherms is observed in the simulation results. This hysteresis is associated with t h e r m o d y n a m i c metastability of the low and high density phases of the adsorbed fluid. However, these phases span the system and are not associated with individual pores. The phenomena in the different p a r t s of the void space are fully coupled via the fluid-fluid and fluid-matrix correlations. Figure 3 shows sub-critical adsorption isotherms for two different strengths of the a t t r a c t i v e fluid-solid interaction at one t e m p e r a t u r e (the p a r a m e t e r a is the ratio of the fluidsolid 12-6 well depth to the fluid-fluid 12-6 well depth). By changing the strength of the attractive fluid-solid interaction (Sarkisov et al., 1999) we see a transition between classes IV and V in the IUPAC classification of adsorption isotherms (Sing et al., 1985). The isotherms in figure 3 bear a strong resemblance to those seen Figure 2. Computer graphics visualizations of in experiments on silica configurations from GCMC simulations for confined fluids (Machin and in near saturated states. The top visualizations are for the xerogels Golding, 1990). The disordered material and the bottom ones are for an ordered material with the same porosity. The visualizations on the hysteresis loops seen here left hand side are for saturated vapor states and those on the are closest to those of the category H2 in the IUPAC right hand side are for saturated liquid states. classification (similar

25 hysteresis has been seen in recent Monte Carlo simulation studies of adsorption in porous glasses (Gelb and Gubbins, 1998)). In s u m m a r y , by considering a more realistic molecular model of the adsorbent microstructure for a heterogeneous adsorbent we obtain adsorption isotherms which are quite similar to those obtained from experiment. A striking feature of this a g r e e m e n t is t h a t the hysteresis loops are so similar to those seen experimentally. A major question to be resolved, however, is w h e t h e r the hysteresis we are seeing in these Monte Carlo simulations has anything at all to do with t h a t seen experimentally. By investigating this question we m a y find a new way of understanding capillary condensation phenomena in mesoporous materials. We expand on this issue in the next two sections of the paper. 0.6

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26 be a connection between the hysteresis observed in GCMC simulations and t h a t seen experimentally. This a r g u m e n t has significant merit. However, it is possible t h a t the difficulty in sampling the fluctuations in the GCMC method is in some sense analogous to the kinetic barriers to the occurrence of true vapor-liquid equilibrium in the adsorption experiments. Why should we expect any relationship between hysteresis seen in experiments and t h a t observed in GCMC simulations ? The commonly held belief is that the C~MC creation and destruction moves should m a k e the adsorption/desorption processes in the two cases very different. A possible answer to this question lies in the fact t h a t creation and destruction moves in the grand ensemble have a very low acceptance rate except in regions of low density. During adsorption the density increases in the simulations primarily through addition of molecules at the boundary of clusters of molecules or in other regions of low density. On desorption the density decreases primarily through removal of molecules from the same regions. We should note t h a t in discussing the efficiency of the C~MC method, the focus is oi~en placed on the difficulty of inserting molecules into dense phase configurations. However, because of the strong binding energy of such configurations arising from intermolecular attractions, it is also difficult to remove molecules from dense clusters except a t the boundary. This suggests t h a t if network or pore blocking effects are unimportant, the m e c h a n i s m of hysteresis should be similar in experiment and C~MC simulations, provided t h a t the model of the adsorbent microstructure used in the simulations is sufficiently realistic. In the next section we describe a computer simulation algorithm which can be used to investigate this issue further. 4. AN ALGORITHM FOR MOLEC~ SIMULATION OF A D S O R P T I O N VIA D I F F U S I V E Figure 4. Schematic representation of a two cell M A S S T R A N S F E R system for a grand ensemble simulation with a control volume. Molecules can enter or leave the In order to probe the issues discussed right hand cell by diffusion or by above more carefully we have creation/destruction moves (signified by the arrows developed a computer simulation at the bottom of that cell). Molecules can enter or leave the left hand cell by diffusion only. algorithms which a t t e m p t to mimic the physical process of adsorption or desorption in a porous material. The essential idea is illustrated in figure 4 and was inspired by the grand canonical molecular dynamics algorithm for studying adsorption (Papadopoulou et al., 1992) and t r a n s p o r t diffusion through porous materials (MacElroy, 1994; Heffelfinger and van Swol, 1994; Cracknell et al., 1995). Instead of a single simulation cell in periodic boundaries we use two adjacent cells in periodic boundaries. The configuration of the solid particles in the two cells is identical and molecules can diffuse between the cells via random walk in a Monte Carlo simulation or by molecular dynamics. In this work we use molecular dynamics. Only in the right hand cell can molecules be created and destroyed via the grand ensemble procedure. The process of adsorption or desorption of fluid into or out of the left hand cell can only occur through diffusive m a s s transfer. This

27 more closely models the behavior in experiments, although the relatively small system size t h a t m u s t be used in the simulations greatly reduces the distance t h a t a molecule has to diffuse over between the external surface and the interior of the porous material. Likewise the adsorption or desorption for the right hand cell should be similar to t h a t in a single cell GCMC calculation. Since the m e c h a n i s m s of adsorption and desorption are different in the two cells we can investigate whether this leads to a difference in the hysteresis loops 0.8 observed for the two cells. We do this as follows. We s t a r t with an e m p t y s y s t e m 0.0 at a low activity. The system is allowed p* to reach equilibrium at t h a t activity- this 0.4 of course takes longer for the left hand cell. Once equilibrium has been reached for both cells the average density is 0.2 calculated for each cell over a large n u m b e r of configurations. This procedure 0.01 0.02 0.03 0.04 0 05 is repeated over a sequence of increasing activities to generate the adsorption branch of the isotherm using, for each new state, the configuration from the Isotherms of density versus activity previous state as the initial configuration. for the bulk Lennard-Jones 12-6 fluid. The Starting from the state at the highest lines are from GCMC simulations and the activity studied on the adsorption b r a n c h points are from GCMD simulations for increasing activity (circles) and decreasing the system is then simulated over a sequence of decreasing activities to activity (triangles). generate the desorption branch. If the m e c h a n i s m of hysteresis for each cell is similar then the observed h y s t e r e s i s should be the same for both cells. Since the molecules entering or leaving the left h a n d cell m u s t come from (or go to) the control volume, we should expect t h a t the left cell will exhibit at minimum the same hysteresis as in the control volume. However, the method will detect any additional hysteresis associated with t r a n s p o r t (pore blocking) effects in the left hand cell. As an illustration of the method we consider the case of the bulk Lennard-Jones 12-6 fluid. Although this is not an adsorption problem our knowledge of the v a p o r liquid equilibrium is rather precise and it is an important test case for studying the stability of m e t a s t a b l e states. We have considered a system where the two cells are cubes of side 6.250, which for dense liquid states m e a n s t h a t there will be about 400 molecules in each cell. In the molecular dynamics the t e m p e r a t u r e w a s controlled using the damped force method of Brown and Clarke (1984). The simulations were r u n over as m a n y as 320,000 time steps with up to 160,000 time steps for equilibration. In the control volume 200 creation and deletion a t t e m p t s were made at intervals of 4 time steps. The long runs are required due to the time t a k e n for the density in the left cell to equilibrate via m a s s transfer. The LennardJones potential was truncated and shifted at 2.5 so t h a t the truncation of the potential did not impact the comparison between molecular dynamics and Monte

28 Carlo simulations on the same system. Figure 5 shows the fluid density versus chemical potential isotherm obtained from the GCMD calculation together with results obtained from a GCMC calculation with a single cell of side length 6.25(~. The results from the GCMD calculation are for the lei~ hand cell where the density can increase or decrease only by diffusive mass transfer from the other cell. Notice that the results show hysteresis between the isotherms for increasing activity (adsorption) and decreasing activity (desorption). The agreement between the two sets of calculations is excellent. Thus for this system size the stability of the metastable states in the hysteresis loop is independent of the mechanism by which the density of the system changes. Calculations are currently underway in which this methodology is being apphed to the molecular models of adsorption in disordered porous materials discussed above. 5. C O N C L U S I O N S In conclusion, we have seen that molecular models of fluids in disordered porous materials are now available which make it possible to investigate the phenomena of capillary condensation and hysteresis without simphfying assumptions about pore geometry and connectivity. Adsorption isotherms for molecular models of simple fluids adsorbed in a silica xerogel exhibit hysteresis which is similar to t h a t seen in experiments. On the basis of this observation the need for a more detailed study of the origin of hysteresis in the molecular simulations was indicated. For this purpose we have developed a simulation algorithm which allows the study of adsorption and desorption via diffusive mass transfer. A test of this method for hysteresis associated with the vapor-liquid transition in the bulk Lennard-Jones 12-6 system was made. The results suggest that the stability of the metastable states in the computer simulation is insensitive to whether the density changes by creation/destruction moves, as in the grand canonical ensemble, or via diffusive mass transfer. Extension of these calculations to models of fluids in disordered porous materials is underway and will be reported in due course. We hope that this will lead to a better understanding of the relative importance of metastability and transport effects in determining adsorption hysteresis. 6. A C K N O W L E D G M E N T S This work was supported by a grant from the National Science Foundation (CTS970O999). REFERENCES Balbuena, P. B., and Gubbins, K. E., 1993, Langmuir, 9, 1801-1814. Ball, P. C., and Evans, R., 1989, Langmuir, 5, 714-722. Bettolo Marini Marconi, U., and van Swol, F., 1989, Europhys. Lett., 8, 531-536 Brown, D. and Clarke, J. H. R., 1984, Molec. Phys., 51, 1243-1252. Cohan, L. H., 1938, J. Amer. Chem. Soc., 60, 433-435. Cassel, H. M., 1944, J. Phys. Chem., 48, 195-202.

29 Cracknell, R. F., Nicholson, D., and Quirke, N., 1995, Phys. Rev. Lett., 7..~4,24632466. Evans, R., 1990, J. Phys.: Condens. Matter, 2, 8989-9007. Everett, D. H., 1967, in The Solid-Gas Interface, E. A. Flood, editor, vol. 2, Dekker. pp. 1055-1113. Gelb, L., and Gubbins, K. E., 1998, Langmuir, 1.44,2097-2111. Given, J. A., and Stell, G., 1992, J. Chem. Phys., 97, 4573-4574. Gordon, P. A., and Glandt, E. D., 1996, J. Chem. Phys., 105, 4257-4264. Gregg, S. J., and Sing, K. S. W., 1982, Adsorption Surface Area and Porosity, Academic Press. Chapter 3. Heffelfinger, G. S., and van Swol, F., 1994, J. Chem. Phys., 100, 7548-7552. Hill, T. L., 1947, J. Chem. Phys., 1..55,767-777. Kaminsky, R. D., and Monson, P. A., 1991, J. Chem. Phys., 9__55,2936-2948. Kierlik, E., Rosinberg, M. L., Tarjus, G., and Monson, P. A., 1997, J. Chem. Phys., 106, 264-279. Lee, T. D., and Yang, C. N., 1952, Phys. Rev., 8__77,410-419. MacElroy, J. M. D., and Raghavan, K., 1990, J. Chem. Phys., 9_33,2068-2079. MacElroy, J. M. D., 1994, J. Chem. Phys., 101, 5274-5280. Machin, W. D., and Golding, P. D., 1990, J. Chem. Soc. Faraday Trans., 8..66,175179. Madden, W. G., and Glandt, E. D., 1988, J. Stat. Phys., 5._!1,537-558. Mason, G., 1988, Proc. R. Soc. Lond. A, 415, 453-486. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A.N., and Teller, E., 1953, J. Chem. Phys., 2_!, 1087-1092. Page, K. S., and Monson, P. A., 1996a, Phys. Rev. E, 54, R29-R32. Page, K. S., and Monson, P. A., 1996b, Phys. Rev. E., 54, 6557-6564. Papadopoulou, A., Becker, E. D., Lupkowski, M. and van Swol, F., 1993, J. Chem. Phys., 9_88,4897-4908. Peterson, B., and Gubbins, K. E., 1987, Molec. Phys., 6..22,215-226. Rosinberg, M. L., Tarjus, G., and Stell, G., 1994, J. Chem. Phys., 100, 5172-5177. Sarkisov, L., Page, K. S., and Monson, P. A., 1999, in Fundamentals of Adsorption, F. Meunier, editor, Kluwer. Schoen, M., Rhykerd, C. L., Cushman, J. H., and Diestler, D. J., 1989, Molec. Phys., 6__66,1171-1182. Seaton, N. A., 1991, Chem. Eng. Sci., 46, 1895-1909. Segarra, E. I., and Glandt, E. D., 1994, Chem. Eng. Sci., 4_99,2953-2965. Sing, K. S. W., Everett, D. H., Haul, R. A. W., Moscou, L., Pierotti, R. A., Rouqerol, J., and Siemieniewska, T., 1985, Pure and Appl. Chem., 5..~7,603-619. Steele, W. A., 1973, The interaction ofgases with solid surfaces, Pergamon, pp. 247269. Swendsen, R. H., and Wang, J.-S., Phys. Rev. Lett., 5__.88,86-88. Vega, C., Kaminsky, R. D., and Monson, P. A., 1993, J. Chem. Phys., 99, 30033013. Walton, J. P. R. B., and Quirke, N., 1989, Molec. Sim., 2, 361-391. Wolff, U., 1989, Phys. Rev. Lett., 6_22,361-364.

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Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScienceB.V.All rightsreserved.

31

M o l e c u l a r Simulation Study on Freezing in N a n o - p o r e s M. Miyahara a, H. Kanda a, K. Higashitani a and K. E. Gubbins b aDepartment of Chemical Engineering, Kyoto University, Kyoto 606-8501, Japan bDepartment of Chemical Engineering, North Carolina State University, Raleigh, NC 276957905, USA

Freezing phenomena in confined space were explored, looking at three of possible major factors: i) strength of pore wall potential (compressing effect), ii) geometrical shape of pore (geometrical hindrance), and iii) equilibrium vapor-phase pressure (tensile effect). Each effect was clarified quantitatively by molecular simulation technique suitable for each purpose. A perspective of the whole phase diagram for LI fluid in nanopores are discussed from the viewpoint of "the pressure felt by the confined fluid," which proves its usefulness in understanding and estimating freezing behavior in nanopores.

1. INTRODUCTION While the vapor-liquid transition in pores (capillary condensation) has been much studied theoretically and experimentally, and is relatively well understood, the liquid-solid transition in nanopores remains largely unexplored. An understanding of freezing phenomena in narrow pores is of importance, e.g., in the fabrication of nanomaterials, nanotribology and in the determination of pore sizes. Many experimental studies of freezing in porous materials have reported that freezing points are usually lowered [1 ]. The porous bodies often used includes Vycol glass, controlled-pore glass, silica gels, and so on. Such glasses do not have variety in the base material, and the shape of the pores are thought to be roughly cylindrical. In contrast to the above results, a study with SFA (Surface Force Apparatus) reported an increase in the freezing temperature for liquids confined between mica surfaces [2]. The general trends of freezing in confined space have not been made clear, nor have been the mechanisms. Freezing phenomena in confined space must be affected, we suppose, by at least the following three factors: i) strength of pore wall potential energy (compressing effect), ii) geometrical shape of pore (geometrical hindrance), and iii) equilibrium vapor-phase pressure (tensile effect). Molecular simulation techniques are appropriate for clarifying each contribution, while experimental measurements may suffer from complication by simultaneous affection of the above factors or others. In this paper we report, first, grand canonical Monte Carlo (GCMC) simulations of LJ fluid modeled on methane in slit-shaped nanopores that are kept equilibrium with saturated vapor, or pure liquid, in bulk phase. Depending on the strength of the attractive potential energy from pore walls, fluid in a pore shows freezing point elevation as well as depression,

32 and the critical strength to divide these two cases is found to be of the potential energy exerted by the fluid's solid state [partly reported in ref.3]. The "excess" attraction relative to the critical one is considered to bring the confined liquid to a higher-density state that resembles a compressed state, which would result in the elevated freezing point. Second, similar simulations in cylindrical pores are reported, in which non-planar wall would hinder the liquid's freezing even with favorable "excess" potential energy. Nonmonotonous variation of freezing point against the pore size, which was observed for LJmethane in carbon pores, can be interpreted as the result of competition between the geometrical difficulty and the compression by the excess potential energy. Finally, the effect of equilibrium vapor-phase pressure p is examined, our motive being as follows. Contrary to the case with the saturated vapor Ps for the bulk condition, the capillary-condensed liquid with p/ps< 1 is subjected to far lower pressure than that in the bulk. Negative pressure, or tensile condition can easily be the case for liquids in nanopores, which then should bring depressing effect in freezing point. Because of a difficulty related with hysteresis, GCMC simulation was not suitable for this purpose. We employed a molecular dynamics (MD) technique in a unit cell with imaginary gas phase developed by the authors [4]. The MD simulations show liquid-solid phase transitions, at a constant temperature, with the variation in the equilibrium vapor-phase pressure below saturated one, and prove the importance of the tensile effect on freezing in nanopores. Through the above investigations a perspective of the whole phase diagram for LJ fluid in nanopores will be discussed. We understand that, in nanopores, the pressure would exhibit anisotropic nature and a "pressure" cannot be treated as done in bulk phase. Nevertheless the viewpoint of the pressure felt by the confined liquid will prove its usefulness in understanding and estimating freezing behavior in nanopores, which would be much effective for application in engineering aspects

2. FREEZING IN SLIT PORE EQUILIBRATED WITH SATURATED VAPOR One of the authors once examined apparent molar volume of physisorbed phase in nanopores and found that the molar volume would become smaller against the increase in the chemical potential in the equilibrium bulk phase up to a saturated concentration, which was able to be modeled as a compression caused by attractive potential from pore walls [5]. If such kind of jamming would be the case, the strength of pore wall potential energy must considerably affect the freezing behavior within a pore subjected to saturated vapor: This condition also corresponds to a pore system immersed in pure liquid. This effect was studied in pores of the simplest geometry.

2.1. GCMC simulation The grand canonical Monte Carlo (GCMC) method was employed because it allows us to find the thermodynamic state of the bulk phase in equilibrium with the pore. The potential model for fluid-fluid interaction was Lennard-Jones 12-6 potential modeled on methane (e~/k - 148.1 K, a g = 0.381 nm [6]). The cut-off distance was 5ate, which was thought to be large enough to represent fluid with the full LJ potential. Thus no long-range correction was attempted.

33 The solid modeled on graphite was expressed with Steele's 10-4-3 potential with e , , k 28.0 K, o,, = 0.340 nm, p, = 114 nm -3 and A = 0.335 nm [6]. The Lorentz-Berthelot mixing rules were used to evaluate solid-fluid interaction parameters. A structured graphite surface in terms of additional function based on Fourier expansion to express lateral periodicity [6] was also employed, but the results were almost the same presumably because the size of the

fluid particle was larger than the length of the periodicity, and because the depth of the corrugation was negligibly small within the temperature range investigated. For a given with H of slit pore the potential was calculated as the sum of the two contributions from both walls. To trace the bulk gas-liquid (and gas-solid if depression was the case) coexistence line, the coexistence p-T relation for LJ fluid in the literature [7,8] was used to evaluate corresponding chemical potentials. Thus obtained combinations of T-/I were used as inputs to the simulations. A few to several hundred millions of elemental GCMC steps (movement, insertion or deletion) were conducted for each condition.

2.2. Freezing in graphite pores of various widths Figure 1 illustrates the observed variation of apparent overall densities of fluids in pores with various widths against temperature. For higher temperature range, the decrease in temperature, or cooling, brings gradual increase in the density whose slope corresponds to the thermal expansion factor for bulk LJ liquids. Within a narrow temperature range steep rises in the density occur, and examinations of other various properties such as pair correlation, structure factor, and snapshots show that these changes correspond to a freezing transition. Two layers in the vicinity of the pore wall, or contacting layer and the second layer, however, shows ordered structure well above the apparent freezing temperature, and they do not cooperate in the steep change in the apparent density. Further decrease in temperature makes essentially no change either in density or other properties. These freezing temperatures for confined fluid are all above the bulk freezing point for LJ fluid (T* = 0.68-0.69 [8.9]), which corresponds to ca. 101 K for the LJ-methane employed here. The freezing point elevation is the case in these slit graphite pores, and the extent of this elevation increases as the pore width decreases. This is in contrast to most experimental findings, in which a decrease in freezing point is the case [ 1]. An exception is the experimental finding for cyclohexane and OMCTS in slit mica pores [2], which showed increase in freezing temperature, in agreement with our 1.0 findings here. H*=10

| . . . . .

2.3. Freezing in pores of various potential

'

~'~ 0.9

'-

-

--~--'--

tt*--

9.5

H*--

7.5

strengths The above dependence of elevation against ~ pore size would be consistent with our ~ 08 perspective of the importance of the pore potential because stronger attraction occurs in a smaller pore. The idea is tested more directly, 9 07 Freezing point employing additional two kinds of walls with for bulk weaker attraction. In such pores the extent of r the elevation is thought to decrease, and a 0"690 100 110 120 130 140 150 depression in freezing temperature may arise. Temperature [K] One is a smooth pore wall made up of LJ- Fig.1 Variation of overall density in pores with methane molecules expressed again by 10-4-3 various sizes against temperature I

|

I

I

34 1.0 potential with Ps --- 0.963a~,2 and A = 0.928at~, Graphite wall -----w---- - - " . . . . . . . which was determined from density of the LJ Methanewall ~ - , i Hard wall ----o---- ',1 ~ solid at its triple point [8]. Approximately the "7 0.9 well depth of this wall's potential is about 40% of the graphite wall. We refer to this wall as 0.8 "methane wall." The other is the hard wall ~5 with no attraction as an extreme case. --o 0.7 The results are shown in Fig. 2 for all three types of pores with the same width H* =7.5. >. Contrary to the case with graphite walls, the O 0.6fluid in hard wall show appreciable decrease in freezing point. For the methane wall, there is 0.5 L almost no change in freezing temperature from 60 80 O0 120 40 Temperature [ K ] the bulk value. This is quite a reasonable result since the fluid-fluid and fluid-solid Fig.2 Freezing behavior for pores with different potential strengths intermolecular attraction is the same: The fluid confine in methane walls would behave like a part of bulk methane phase and freeze at almost the same temperature as the bulk freezing point. Thus the fluid-wall interaction strength for the methane wall is thought to be a critical one, at which the behavior of the fluid in pore changes its nature. -

2.4. Mechanism and simple model The above results reinforces strong connection between fluid-wall interaction potential and the freezing point. Through a simple thermodynamic treatment the following equation was obtained to express the extent of freezing point elevation 6/'. a'r = A -~

T~

(1)

Ah m

where Tf is bulk freezing point, Ahm - (SrSL,)Tf is the latent heat absorbed on melting (>0). The "excess" potential A# is defined as the difference between the pore potential @or~and that for methane pore ~"rmpore ethane each averaged over the portion of the pore where the structure actually changes on apparent freezing; excluding the contacting layer and the second nearest layer as mentioned earlier. The underlying assumption includes: The perturbation in the structure of solid phase is negligible in the slit pore; thus the temperature dependence of the chemical potential of solids in slit pore can be expressed with the entropy of the bulk solid s,. Further details on the model is available in [3]. For a strongly attractive wall A~0 is negative, thus results in elevated freezing point. For larger pores IA01 becomes small and the freezing point approaches to the bulk value. The methane wall do not change the freezing point because A~ stays to be zero regardless of the pore width. The model was tested quantitatively, and showed good agreement with the simulation results of graphite pores. More intuitively the elevating effect of the attractive pore potential can be understood as follows. In a pore with strongly attractive potential, a liquid-like state can hold even with lower vapor pressure than the saturated one. When this system is equilibrated with pure liquid or saturated vapor, the excess potential must be balanced with the increase in density

35 that resembles a compressed state under higher pressure. Solidification at elevated temperature is possible because of this compressing effect. Since no additional "compression" is needed for liquid-like methane within the methane wall, the freezing point should stay almost the same as in bulk.

3. FREEZING IN CYLINDRICAL PORE EQUILIBRATED WITH SATURATED VAPOR Other than the slit shape, a cylindrical pore would be one of the simplest geometry that would be worth exploring. This geometry is of importance in connection with recentlydeveloped new porous materials of great interest such as MCM-41, FSM-16 and carbon nanotubes. In this "simple" geometry, however, freezing phenomena is thought to be much complicated because constraints for frozen molecular structure would prevail contrary to the case in slits. Under saturated vapor the fluid in pore must have higher density that would force them to form preferably their natural solid structure, but the presence of the curved wall may hinder its formation. A compromise is found in the following.

3.1. GCMC simulation The GCMC simulation method of the same manner as the previous section was employed. The pore-wall potential employed was that for a structureless LJ solid derived by Peterson et al. [10] with cylindrical coordinate integration. A carbon-like wall was set using the same energy and size parameter as stated in section 2.1, and again a methane wall was also employed here. 3.2. Freezing in carbon pores of various diameters Figure 3 shows the obtained overall density of U-methane in carbon cylindrical pore with various diameters. What is similar to the slit case is the manner of density variation that shows steep change within narrow temperature range, which is thought to be a freezing transition. Again these freezing temperatures are higher than in bulk. However, what should be noted here is the dependency of the elevation: The freezing temperatures here have no clear tendency against the pores size, contrary to the monotonous dependence found for slit pores. The arrangement of the U-particles in frozen state was examined, and they are found to form a hexagonal array within each layer at a constant radial position, as similarly shown by Maddox and Gubbins [11]. Since the observed quasi-hexagonal array is circumferentially curved, it must be accompanied with less stability compared with the flat array formed in slit pores. This kind of geometrical constraint then must lower the freezing point, and the degree of the hindrance is thought to be greater for smaller pores with greater curvature. At the same time, however, smaller pores provide stronger attractive potential, which act as the enhancing factor for freezing. The observed non- Fig.3 Density variation for carbon monotonous variation of the elevation against the pore cylindricalpores

36 size is thought to come from the competition of the above two factors. 3.3.

Freezing

in cylindrical

pores

made

of

methane wall

For quantitative understanding of the freezing phenomena in cylindrical pore, the geometrical hindrance effect should somehow be evaluated. The most suitable system to elucidate this effect, we think, is a cylindrical pore made of solid state of LJmethane itself, or methane wall. The results are shown in Fig. 4. All the pores exhibit depressed freezing temperatures, and the extent of the lowering is greater for smaller pores. Fig.4 Density variation for cylindrical pores made of methane wall. This series of the pores with various sizes apparently provide various potential strengths, but their "excess" potential energy relative to the fluid's solid state is commonly zero for these methane walls. Thus the results would not suffer from the complication by the enhancing effect, and the geometrical effect only would prevail here, showing reasonable tendency of greater hindrance for smaller pores. The observed depressions will be utilized to model the hindrance effect, together with information on microstructure of the frozen state in cylindrical pores, which is hoped to be published soon.

4. FREEZING IN SLIT PORE UNDER TENSILE CONDITION The results stated so far has been with saturated vapor or liquid as the equilibrium bulk phase. Liquid-like state in pore, however, can hold with reduced vapor pressure in bulk: the well-known capillary condensed state. One of the most important feature of the capillary condensation is the liquid's pressure: Young-Laplace effect of the curved surface of the capillary-condensed liquid will pull up the liquid and reduce its pressure, which can easily reach down to a negative value. In the section 2 we modeled the elevated freezing point as a result of increased pressure caused by the compression by the excess potential. An extension of this concept will lead to an expectation that the capillary-condensed liquid, or liquid under tensile condition, must be accompanied with depressed freezing temperature compared with that under saturated vapor. Then, even at a constant temperature, a reduction in equilibrium vapor pressure would cause phase transition. In the following another simulation study will show this behavior.

4.1. MD simulation with imaginary gas phase A possible method of simulation may be the GCMC, but it was not suitable for the investigation here because of the large artificial hysteresis in condensation/evaporation encountered in GCMC [12]. Suppose a reduction in equilibrium relative pressure would cause a melting in a pore. We do not, however, immediately find if the liquid state in the pore would be thermodynamically stable. It might be on a metastable branch of the condensed liquid, and the stability can be confirmed only after complicated procedure for finding grand potential employing thermodynamic integral that needs a great number of

37 simulation runs including various temperature. Instead, we employed an MD simulation scheme with an imaginary gas phase [4]. The feature of the simulation is briefly explained below. Figure 5 illustrates the simulation cell. In the middle of the cell between -ly and +ly is the pore space in question with a given potential energy. At each end of the cell distant lB from the edge of the full potential field, we set a border plane with an imaginary gas phase with which molecules in pore can have interaction. Since the absolute value of external potential energy in gas phase must be zero, there should exist a connecting space with slope of potential energy between the Fig.5 Unit cell with imaginary gas phase gas phase and the pore space. This space is called potential buffeting field (PBF). The benefit of this simulation cell is easy determination of equilibrium vapor pressure. Molecules trying to desorb from the pore space must climb up the potential slope in PBF, and only those with sufficient kinetic energy can reach the border plane. If we set a perfect reflection condition at the border, the frequency of the particles' coming up should be a direct measure of the vapor pressure that is in equilibrium with given adsorbed/condensed phase. Thus by 'counting' molecules reaching the border, the equilibrium pressure can easily be determined. Further, we confirmed that the liquid in pore shows almost no hysteresis, and this feature is quite desirable for the purpose here. Before exploring into tensile conditions, this simulation method was confirmed to give almost the same results as those obtained in the section 1, under saturated vapor as the equilibrium bulk-phase condition. Starting from a solid-like state obtained in the above test under the condition of p-p,, state of the phase in pore under the condition of p/p~ 0.8 o

%) =

t

0.7

.--, ->' "7,.~ 0.2 ~,.. _'~ -~ 0.1

I

!

I

_O~~(b)

--

I

I

Diffusivity

i i i i i i 1

0

pores. ~ 0.2 0.4 0.6 0.8 Suppose we have a solid-liquid coexistence point (T, Relative pressure P/Ps [ - ] p) for pore fluid on the bulk phase diagram. Though the bulk pressure is at p, the fluid in pore is supposed to Fig.6 Variation of density and diffusivity under tensile condition have different pressure ppore because of the pore-wall potential and the capillary effect. Not for the bulk pressure but for this pressure felt by fluid in pore, ppore, the Clausius-Clapeyron equation for the bulk is assumed to hold.

dPP~

(~vv /

dT

pore

(~VV~b ulk

const.

(2)

To find the freezing point shift relative to the freezing condition at p/p,-1 [point A in Fig. 7: (Ta, p.,(Ta))], the difference in ppore is considered below, in which physical properties of pore fluid are often substituted by those for bulk. The chemical potential difference A/z of the state (T, p), relative to point A can be determined following the three steps of change in/1 for bulk fluid: i) from T, to T for liquid at constant pressure( = p,), ii) from p, to p.~ for liquid at T, and iii) from p, to p for gas (assumed to be ideal) at T. All=-

fieI s l d T

+ ~ p s (T ) vldp + kT ln

Pa

Ps(T)

(3)

=_- s I (T - T a ) + kT In Ps(T) The vldp term is neglected compared with the first and the third term. The pore liquid must have the same A~ when following the solid-liquid coexistence curve.

39

A~t= --~ sP~

,,

IpPpoP~176

~ (4)

= -sI(T -Ta ) + vl(Pp~

'

I

H/aft =7.5

- Pa-P~ )

2

'

I

O MD simulation proposed model

Equating the above two, we find ~

Ap pore _-- P pore

pore

-Pa

= ~kTl n vl

p Ps(T)

The above equation is intuitively understandable because it is the basis for the Kelvin equation: If the

I

!

I

lO0 1 lO 12o Temperature T [K] pressure difference is equated with the Young-Laplace Fig.7 Solid-liquid transition points under equation it yields the Kelvin one. It should be noted tensile condition, superimposed on here that Eq.(5) does not suffer from the incorrectness bulk phase diagram of the Kelvin equation for nanopores because it does not include any pore-size related factor. Thus knowing the pressure difference for pore fluid, integration of Eq.(2) and rearrangement will yield the following equation to describe the relation between freezing point and the vapor-phase pressure on the bulk phase diagram.

p = p,(T)exp - ~ v h.,~ k-T(T" - T )

(6)

We examined the performance of this simple model by comparison with the simulation data. For LJ fluid, bulk properties such as vt and As/Av are known well. T,,, the freezing point under saturated vapor, has already been modeled in section 1. Thus the above equation includes no adjustable parameters. The dashed line in Fig.7 is the calculated results of the Eq.(6). Surprisingly, such a simple model gives quite a good performance in expressing freezing point shift under tensile condition in a pore of width as small as ca. 3 nm. This agreement would be a proof for usefulness of the concept of pressure felt by the pore fluid, in understanding the freezing in nanopores. Of course, we tested only in a limited number of systems, and further examination must be made before concluding the validity of the above mechanism and the model, which is now under way.

5. C O N C L U S I O N Freezing phenomena in nanoscale pores were investigated with the aid of various molecular simulation techniques. The benefit of employing molecular simulation would be that we were able to observe individual contribution of important factors that may affect the phenomena, while experimental measurements may suffer from complication by simultaneous affection of some factors. In the following summarized conclusions are shown referring to Fig. 8. 1) Simulations of LJ fluid in slit-shaped nanopores that are kept equilibrium with saturated vapor in bulk clarified the importance the excess potential relative to the one exerted by the fluid's solid state. The "excess" attraction relative to the critical one is considered to bring

40 the confined liquid to a higher-density state that resembles __ (1) a compressed state, which would result in the elevated freezing point. Quantitative model successfully described the simulation results. 2) For cylindrical pores under the same condition as above, non-monotonous variation of freezing point against the koO'~ / :"o,~ ." ,~ ,,~ .~, pore size was observed for U-methane in carbon pores, ," 9 - .~O and was interpreted as the result of competition between oOr "i" the geometrical hindrance and the compression by the i Temperature T excess potential, through comparison with results for methane wall that would have no elevating effect. Fig. 8 Conceptual phase diagram for 3) The effect of equilibrium vapor-phase pressure is fluid in nanopores, superimposed on bulk phase diagram. examined employing a molecular dynamics (MD) technique in a unit cell with imaginary gas phase. The MD simulations showed liquid-solid phase transitions, at a constant temperature, with the variation in the equilibrium vapor-phase pressure below saturated one, and prove the importance of the tensile effect on freezing in nanopores. The capillary effect on shift in freezing point was successfully described by a model based on the concept of pressure felt by the pore fluid. Through the above investigations a perspective of the whole phase diagram for IA fluid in nanopores would be as in Fig. 8. We understand that, in nanopores, the pressure would exhibit anisotropic nature and a "pressure" cannot be treated as done in bulk phase. Nevertheless the viewpoint of "the pressure felt by the confined fluid" proved its usefulness in understanding and estimating freezing behavior in nanopores, which would be effective for application especially in engineering aspects.

~

~=

(2) ~ . . ~ o.~

/

.

9

REFERENCES

1. Over more than half a century many studies were reported: e.g., W.A. Patric and W.A. Kemper, J. Chem. Phys., 42, 369 (1938); J.A. Duffy, N.J. Wilkinson, H.M. Fretwell, M.A. Alam and R. Evans, J. Phys. Cond. Matter, 7, L713 (1995). 2. J. Klein and E. Kumacheva, Science, 269, 816 (1995) 3. M. Miyahara and K.E. Gubbins, J. Chem. Phys., 106, 2865 (1997). 4. M. Miyahara, T. Yoshioka and M. Okazaki, J. Chem. Phys., 106, 8124 (1997) 5. M. Miyahara, S. Iwasaki and M. Okazaki, Fundamentals of Adsorption, M.D. LeVan ed., p. 635, Kluwer Academic Publishers, Boston (1996). 6. W. Steele, The interaction of gasses with Solid Surfaces, Pergamon, Oxford (1974). 7. D.A. Kofke, J. Chem. Phys., 98, 4149 (1993) 8. R. Agrawal and D.A. Kofke, Mol. Phys., 85, 43 (1995) 9. J.P. Hansen and L. Verlet, Phys. Rev., 184, 151 (1969) 10. B.K. Peterson, J.P.R.B Walton and K.E. Gubbins, J. Chem. Soc. Faraday Tram. 2, 82, 1789 (1986) 11. M.W. Maddox and K.E. Gubbins, J. Phys. Chem, 107, 9659 (1997) 12. e.g., S. Jiang, C.L. Rhykerd and K.E. Gubbins, Mol. Phys., 79, 373 (1993)

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 2000 ElsevierScienceB.V. All rightsreserved.

41

CHARACTERIZATION OF POROUS MATERIALS USING DENSITY FUNCTIONAL THEORY AND MOLECULAR SIMULATION C h r i s t i a n M. L a s t o s k i e ~ and K e i t h E. G u b b i n s b

Department of Chemical Engineering, Michigan State University, East Lansing, MI 48824-1226, U.S.A. b Department of Chemical Engineering, North Carolina State University, Raleigh, NC 27695-7905, U.S.A. a

1. INTRODUCTION Characterization methods for porous materials that are based on adsorption measurements involve two distinct types of approximation: 1. A model for the pore structure 2. A theory estimating the adsorption for pores of a particular size The most commonly used model for pore topology is to represent the material as composed of independent, non-interconnected pores of some simple geometry; usually these are of slit shape for activated carbons, and of cylindrical geometry for glasses, oxides, silicas, etc. Usually, the heterogeneity is approximated by a distribution of pore sizes, it being implicitly assumed that all pores are of the same geometry and surface chemistry. In this case the excess adsorption, F(P), at a pressure P can be represented by Hmax

r(P)- [.r(e,z-z)y(ma.

(1)

Hmin

where F(P,H) is the excess adsorption for a material in which all the pores are of width H (the local isotherm), and~H) is the pore size distribution, so that flH)dH is the fraction of pores with width between H and H+dH. The integration in eq. (1) is over all possible pore widths from H,,,, to /-/max. Eq. (1) assumes that geometric and chemical heterogeneity are either absent, or can be treated as effectively equivalent to pore size heterogeneity, with regard to adsorption. An alternative approach [ 1] is to approximate the heterogeneity as due entirely to chemical heterogeneity, so that there is a distribution of adsorbate-adsorbent interaction energies, f(e), in which case eq. (1) is replaced by 6"max

F(P)=

IF(P,t)f(e)de

(2)

cmin where F(P, ~) is the local isotherm for pores with interaction energy ~. At this level of approximation, the problem is to invert the Fredholm integral of eq. (1) or (2). This is an ill-posed problem in general. The usual method of solution is to assign a functional form to the distribution function fill) or fir), such as a multimodal gamma distribution, and then fit the parameters in this function to a least squares match to the experimental isotherm. In addition to limiting the treatment to only one kind of heterogeneity, eqs. (1) and (2) omit any effects of networking or pore connectivity. Approximation (2) is more straightforward to deal with. We need a theory that accurately describes the local isotherm in either eq. (1) or (2). The classical approach has

42 been to assume that the Kelvin equation, or a modified form of it, correctly predicts the pore filling pressure P (capillary condensation pressure) as a function of pore width. The modified Kelvin equation is

In(P/Po) - - 2rt /RTpl ( H - 2t) (3) where it is assumed that the liquid wets the walls. In eq. (3), Po is the bulk vapor pressure, yt is the surface tension, P7 is the liquid density, R is the gas constant, T is temperature, and t is the equilibrium film thickness on the pore wall. The film thickness is often obtained from an experimental isotherm carried out on a nonporous substrate of the same material as the porous solid. However, t will depend strongly on the pore width, as well as temperature and pressure, for smaller pores. It has been known for about 20 years, from experiments [2] and from comparisons with exact molecular simulation results for a variety of pore geometries [3-8], that the Kelvin and modified Kelvin equations give pore sizes that are too low, and that the error becomes very large for small mesopores and for micropores. These tests indicate that the Kelvin and modified Kelvin equations give significant errors for pore sizes below about 7.5 nm [2,5]. One such test is shown in Fig. 1, where the pore filling pressure is plotted against pore width for nitrogen in slit carbon pores. In micropores, interactions between adsorbate molecules and the pore surfaces become greatly enhanced. Given that the Kelvin adsorption models largely neglect these gas-solid interactions, it is not surprising that the Kelvin equation yields inaccurate micropore filling pressures. Density functional theory (DFT) or molecular simulation offer a much more accurate theory for the local isotherm. For simple adsorbates (near-spherical nonpolar molecules) and simple pore geometries (slits, cylinders), DFT is easy to apply, and the results for capillary condensation pressures, and for the remainder of the isotherm, are in A

I

llgOl

~ lE412 r ~ IEJB

~'3.5
__0(no negative pore area). To do this we create the matrix q' by augmenting ~,D to the bottom of the q matrix. We also create the vector Q ' by extending the Q vector with zeros:

Q ~

q,=

.

Q,=

(6)

With these definitions:

IQ'- q~l 2 = IQ - qf[2 + A 2lDf[2

(7)

The constant )~ has been introduced to give an adjustment to the relative weight, or importance, of the two terms. The better the model and more error free the data, the smaller ~, should be. The larger ~, is the smoother the result will be. It is useful to define )~ = ~,')~0 where )~02 = Tr(q'q)/Tr(D'D). With this definition, ~,' is a unitless scaling factor for the relative weight of the smoothness constraint. When ~,'=- 1, there is about equal weight given to the smoothing and the data. Finding the vector f that minimizes ]QY~ - q't] 2 subject to the constraint that f~ > 0 is a standard problem in pure linear algebra and can be solved exactly.

2.2. Creating the model matrix In order to calculate the model isotherms, we first define a set of pore widths to be modeled and a set of pressure points at which to calculate quantity adsorbed. The set of pore widths can be chosen somewhat arbitrarily, but the pressure vector should be specifically constructed to properly weight all pore widths. The algorithm for calculating an isotherm point in the matrix of model isotherms, q(p,Hi), proceeds similarly for all the models considered here and is described in the following sections.

2.2.1. Choosing model pore widths In this work we model pore widths from about 0.4 to 50 nm, coveting the micropore and mesopore range. It is convenient to choose widths in a geometric progression with 30 to 60 size classes per decade. In addition, a "flee surface" model is included by specifying an extremely large pore width, such that capillary condensation would not be experimentally

75 observed. The smallest pore classes in the micropore range are spaced at intervals of 0.05 molecular diameters.

2.2.2. Establishing the pressure vector. Experimental adsorption isotherms obtained with well-characterized materials have been used to correlate the critical pore condensation pressure, Pc, with effective pore width. This is shown in Figure 1. The pressure vector should be such that no pair of adjacent pore size classes exhibits the values of Pc that falls between consecutive pressure points. To do this, a smooth least squares interpolating spline routine was used to estimate the value of Pc for each size class and also at the geometric mean of adjacent classes. In this way, a pressure vector with the desired properties and of twice the length of the pore size vector is generated. Once the pressure vector is established, the model matrix can be calculated.

0.8

I

~~o~o

0.6

~

9 9 9 9

0.4

0.2

/

0.0

2

3

I

I

I

1

1

I

4

5

6

7

8

9

10

Pore Size (nm)

Figure 1. Critical relative pressure for condensation in pores as a function of the pore width. Solid points are as predicted from density functional theory. Open points represent experimental correlation based on the data reported in [4, 12-15].

2.2.3. Calculation of the density functional models The model isotherm for each pore size class was calculated by methods described previously [9], modified to account for cylindrical pore geometry. These calculations model the fluid behavior in the presence of a uniform wall potential. Since the silica surface of real materials is energetically heterogeneous, one must choose an effective wall potential for each pore size that will duplicate the critical pore condensation pressure, Pc, observed for that size. This relationship is shown in Figure 2. The Lennard-Jones fluid-fluid interaction parameters ~f and ~f/k B were equal to 0.35746 nm and 93.7465 K, respectively.

76

42 "-=

40

~o

38

=9

36

o ~

34

=

32

.~

30




c --> (~c

(4t

where the subscript c indicates the critical value of the parameter occurring at the percolation threshold, as defined in equation (2). For nitrogen sorption experimental results interpreted using a cylindrical pore model, the bond occupation probability of the pore network model is given by: 0(3

f(v) - [.

OC

(do) o + [. (do)ddo

do*

(S)

0

where d * is the diameter of pores in which nitrogen condenses at pressure P and n is given by:

v (do) ~o/

(6)

where vc is the volume of pores of diameter d . The length of pores l cancels in the numerator and denominator of equation (5). Thus it is possible to determine at which particular corresponding pore diameter (d)c, the percolation threshold occurs for the real material. For the macroscopic model it is also possible to determine the fraction of pixels, fa, that need to be occupied for the image lattice to become percolating. Since each pixel has an average pore size associated with it, it is possible to determine to which actual pore size, ( d ) c , the percolation threshold in the image-derived grid would correspond. These two pore diameters are then placed in correspondance:

(do)c Cz>(da)c.

(7)

It is then assumed that the pore size probability density function in each of the pixels of the pellet image has the same shape and spread, and is thus only shifted in mean pore size between pixels. It is also assumed that the topology and geometry of the pore network underlying each pixel is the same for each pixel. If these assumptions are correct then the underlying topology of the pore network will not affect the value of the fraction of pixels in the image-derived grid that needs to occupied for the grid to become percolating. The order in which the pixels become occupied with decreasing relative pressure in the desorption simulation would not be affected by the underlying network structural topology, and thereby the properties of the macroscopic pellet structure which influence percolation may be deconvolved from the mesoscopic properties. As with experimental sorption data, it is possible to obtain the ratio F f as a function of pressure (and thus pore size via the Kelvin equation) for simulations of the nitrogen sorption experiment on the model grids derived from NMR images. In order to determine the effect, if any, of the macroscopic heterogeneities (non-randomness) in the spatial distribution of voidage and pore size on the nitrogen desorption isotherm it is

115

possible to compare the simulated isotherm for the grid, as obtained from an actual set of experimental images, with that from another model grid constructed by taking the same set of experimental pixel values but allocating them spatially to the grid in a completely random manner. In a real, macroscopically homogeneous, finitely sized sample the structure will become percolating, as pressure is decreased, in random domains across the sample. The correction factor C(P) for F/f is obtained from the simulated isotherm data, similar to that shown in figure 1, thus: C(P)

_

AB

(8)

AC'

where the line segments are those formed by the intersection of the isotherms with the line AD. Thus the corrected value of the ratio (FJ~' is given by

~. 8 0 0

,i,,,o rll

A oo

800

ell o

600

o 600

B

O O

o

o

•

"~. 4 0 0

-~ 4 0 0

o 200

200

O

O

o ~ O

>o

E = o >

0

0.93

0.94 Relative pressure

0.95

Figure 1. Simulated isotherms for models of G3. i"1 adsorption; x desorption (uniform porosity); o desorption (randomised pore size, uniform porosity); + desorption (spin density image porosity). Macroscopic model pore size allocated from T 1 image except where stated.

0 ' 0.6

,.~

!

!

0.7 0.8 0.9 Relative pressure

1.0

Figure 2. Experimental isotherms for whole (x adsorption; o desorption) and powdered (+ adsorption; r'! desorption) samples of G1.

The correction factor for a given pore diameter in the experimental results is obtained from the correction factor for the simulated results using the correspondance between the critical pore diameters at the percolation threshold. It is the general shift in pore size between individual pixels that determines when they actually become percolating relative to each other. The correction factors for the model are thus related to the experimental results via the differences between a given model, or experimental, pore diameter and its respective critical pore diameter. Thus the correction factor at a particular experimental diameter d o is:

116

(lo)

C(do) = C'((do)c + [do - (do)c]).

Once the correction to the experimental (F J) ratio data has been made using the above procedure the general method described by Seaton [1] for determining pore network connectivity may be continued as Seaton suggests. The method is described in great detail elsewhere [1 ] and will not be reported here.

3.2. An alternative method of estimating pore connectivity The pore space of a unimodal real material is represented by a three-dimensional cubic lattice, with unoccupied lattice sites considered "nodes", cubic site faces considered "bonds" and occupied sites considered solid matrix. The connectivity of a particular site is defined as the number of unoccupied site neighbours it has. For example, in the case of a completely unoccupied lattice all the sites (nodes) would have a connectivity of 6. For a cubic lattice, Elias-Kohav et al. [11] have described a method for the determination of tortuosity. The tortuosity is approximated by the number of sideways diversions that a molecule needs to proceed in the void (unoccupied cubic sites). If M is the locally averaged number of blocked lattice sites adjacent to an empty site, then the probability of a one site diversion is M/6. M is obviously analogous to six minus the so-called connectivity of the lattice. After such a move there is a similar probability of a further diversion and when M does not vary with every diversion the local tortuosity after n steps is: 2

"c- 1 +

+

'

+

+

---> 1 - (M/6)

(11)

where the limit holds for large n. A connectivity for the lattice may thus be deduced from a suitable experimental determination of tortuosity (~P~sE), since in this model M is equal to six minus the connectivity. A suitable experimental method for macroscopically heterogeneous materials is Pulsed-field Gradient Spin-Echo (PGSE) NMR [6] because this method measures the self-diffusivity of liquid molecules in a pore space over small lengthscales (-10 Bm) and is equally weighted over a whole sample. Experimental methods involving diffusion under an imposed concentration gradient may sample the pore space differently to PGSE NMR and be influenced by structural effects at the macroscopic scale [5], which this work has saught to deconvolve. From the relation obtained from the limit of equation (11) an alternative estimate of pore connectivity is given by 6/'CPGsE. This model is thus an abstract adjunct to the basic model of interpretation [6] for the log-attentuation plots of the raw PGSE NMR data. 4. RESULTS

4.1. Pore network connectivity from nitrogen sorption A typical example of the hysteresis loop from simulated isotherms is shown in figure 1. In the case of sample G3 two different models were constructed, one using the NMR spin density map to allocate pixel pore volume and a second assuming a constant voidage across the sample. It can be seen from figure 1 that the isotherms for both models are coincident. This result suggests that there appears to be no spatial correlation between voidage and pore size for this sample. Similar results were obtained for all other samples. Also shown in figure 1 is the simulated desorption isotherm for a model consisting of a

117 completely random spatial allocation of the individual pixel intensity values from T 1 maps. It can be seen that the desorption isotherm for this model is clearly different from that for the actual images themselves. The model isotherm hysteresis loops are much narrower than those typically observed experimentally. This is because the value of T1 in each pixel is a quantity averaged over the whole pixel volume which is several orders of magnitude larger than a "single pore". Table 1 Comparison of pore connectivity values obtained by different methods Sample Seaton [ 1] Connectivity (pre-treatment connectivity (as received temperature) parameters (Z/L) sample) Whole pellets

Corrected Corrected Powdered (Image #1) (Image #2) sample

E1 300 ~ 350 ~

3.0/3.5 3.0/3.6

3.0/3.5 3.0/3.6

3.0/3.5 3.0/3.6

E2 300 ~ 350 ~

3.5/5.0 3.1/5.0

3.55/11.0

4.1/9.0

E3 300 ~ 350 ~

2.6/7.0 2.8/7.3

-

G1 300 ~ 350 ~ 400 ~

3.5/9.0 2.95/9.5 2.4/17.0

-

G3 350 ~

3.0/3.1

2.0/9

Diffusion method (6/~PGSE) a

3.11 +/-0.35 3.0/3.0 4.0/4.0 4.0/4.0

3.33 +/-0.37 3.26 +/-0.21

3.0/4.5 2.94 +/-0.09 3.1/11.0 2.24 +/-0.27

3.87 S1 +/-0.18 300 ~ 3.4/10.0 3.7/10.0 3.8/6.5 350 ~ 3.2/10.0 3.4/20.0 Notes: "values of tortuosi.ty from PGSE NMR obtained previouslybv Rigby and Gladden [13] The Seaton [ 1] theory has been applied to the nitrogen sorption isotherms for samples of whole pellets and powdered pellets for a set of six different types of catalyst support pellet. A typical comparison of the nitrogen sorption isotherms for a set of whole pellet and powdered pellet samples is shown in figure 2. It can be seen that the powdering of the sample leads to a significant narrowing of the hysteresis loop. This would suggest that the macroscopic structure of the porous pellets is significantly influencing the form of the desorption isotherm, and thus the percolation transition. The surface area, obtained using the B.E.T. equation, and pore volume, obtained from B.J.H. analysis of the adsorption isotherm, were measured for the various whole and powdered samples, pre-treated to different temperatures. It was found that, for a given temperature, there

118 was no significant difference in the specific surface areas, or pore volumes over the mesopore size range, between the whole and powdered samples of each type of pellet. This suggests that the milling procedure employed to produce the powder does not alter the pellet micro/mesoscopic structure and create any significant extra surface area, beyond the relatively small increase in external geometric surface area due to the reduction in the average particle size. Particle size analyses by laser diffraction indicate that the median powder particle sizes were -~10-50 btm (i.e. of the same order in size as the MRI in-plane pixel resolution). The particles are therefore of sufficiently large size that there is expected to be no capillary condensation occurring in the inter-particle spaces. Only pellet G1, a sol-gel sphere, was found to have significant variation in the parameters obtained from B.E.T. and the connectivity analysis depending on sample thermal pre-treatment because of surface reconstruction. The parameters obtained from the percolation connectivity analysis are shown in table 1. From the results of the Seaton analysis it can be seen that the values of Z and L obtained are different between the whole and powdered samples for some types of pellets. In general the value of L is smaller for the powdered sample than for the whole pellet sample, as might be expected. However it is also clear that the value of Z may also be affected by the macroscopic structure.

8

-

3.0

ha6

/

c5 ~4

#

c5 < 2

N

//

/~alJ o

~

O O o~

! ./t ./

0 -10

-5 0 5 10 (Zf-3/2)LA(1/0.88)

(D L~

15

Figure 3. Evaluation of percolation parameters for sample E2.- generalised scaling function; x original data; 9 corrected data (T~ image #1); Q corrected data (T~ image #2).

2.5 2.0

1.5

I

1.0 0.5 1.58

I

L,

I

,

1.66 1.60 1.62 1.64 Image ffactal dimension

Figure 4. Variation of the ratio of lattice sidelengths (L) with T~ image fractal dimension. 9 L(whole pellet)/L(powder); 9 L(model corrected whole pellet)/L(whole pellet)

In order to confirm the theory that it is the macroscopic structural heterogeneities in porosity and pore size that are responsible for a significant fraction of the observed hysteresis, simulations (as described above) of the nitrogen sorption experiment were carried out in model structural representations derived from NMR images. Also shown in table 1 are the results for the values of Z and L for the Seaton analysis of the nitrogen sorption data for some of the pellet types but also applying the corrections arising from

119 the simulations of the influence of the macroscopic structure on the hysteresis. An example of the experimental data fit and MRI-corrected experimental data fits for pellet type E2 to the generalised scaling function is shown in figure 3. It can be seen that the corrected connectivity values for whole pellets are closer to the values obtained for powdered pellets than the original whole pellet results are. It should also be noted that the corrected values of the lattice size are significantly larger than the original values for whole pellets and for powdered pellets. These results show that macroscopic structural heterogeneities do significantly influence nitrogen sorption hysteresis.

4.2. Correlation of percolation connectivity analysis parameters with structural heterogeneity The observed effect of macroscopic heterogeneities is larger for some pellets than for others. For example the connectivity results of the percolation analysis of the sorption data for whole E1 pellets are identical to the results for corrected whole pellet E1 data and the powdered E 1 samples. However for sample E2 the values of connectivity for the corrected whole pellet and powdered pellet results are quite different to the value for whole pellets alone. This observation would suggest that different pellets have differing degrees of macroscopic heterogeneity. As mentioned above, non-random macroscopic heterogeneities in pore size may have an effect on the desorption isotherm such that if the material is modelled as a completely random pore network lattice as in the Seaton theory the size of the lattice would appear smaller (or larger) than it might otherwise do, hence the so-called lattice size parameter, L, may give an indication as to the degree of heterogeneity. The deviation from unity of the ratio of the lattice size for the corrected whole pellet and whole pellets results, LcI.L., should therefore give an indication of the degree of non-random heterogeneity in the macroscopic spatial distribution of pore size. In previous NMR imaging work [5] on porous catalyst support pellets NMR images were analysed using an image analysis algorithm employing fractal concepts. A completely random arrangement of pixel intensities was found to have a fractal dimension equal to 1.75. Values of fractal dimensions lower than this were said to be associated with increasing degrees of structural heterogeneity. Figure 4 shows a correlation of the ratio L / L w with the image fractal dimension for three different pellets. It can be seen that, in general, the higher the fractal dimension the closer the ratio L J/, is to a value of 1.0. As the lattice size becomes increasingly large it tends to the percolation behaviour expected for an infinite lattice [12]. It is therefore supposed that the ratio of the parameter L for whole pellet and powdered pellet samples, L Lp may also give some indication of the degree of macroscopic heterogeneity in a sample. This is because even though the powdered pellet sample particle size is of the order of 10-50 lam, and therefore -~100 times smaller than the whole pellet (-3 mm), it is still -1000 times larger than the typical "pore size" (10-50 rim) and thereby represents a fairly large lattice-size itself. If the pore structure is homogeneous over lengthscales greater than the powder particle size then the ratio L,/Lp would obviously be expected to be explicitly related to the sizes of the powder particles and the whole pellets. However the percolation behaviour of large macroscopically homogeneous lattices becomes closer and closer to that of the infinite lattice as L gets bigger [12]. This means that the percolation analysis fit to scattered experimental data becomes increasingly insensitive to the actual value of L in the fit when L is large [12], and the value of the ratio L Lp from the fits might be

120 expected to tend t o - 1 . The presence of macroscopic heterogeneities would be expected to imply that the fit to the generalised scaling function in the percolation analysis would still be highly sensitive to the value of L used in that fit. An increasing deviation of the ratio L/Lp from -1 at large particle sizes (or the ratio of particle characteristic dimensions at small particle sizes) would imply that there were increasing degrees of macroscopic heterogeneity present. Figure 4 also shows a correlation of the ratio L.,Lp against image fractal dimension. It can be seen that there is a general trend down in the ratio L/~Lp with increased fractal dimension. The agreement between the direction of the trends in the two data sets in figure 4 suggests that neither is the result merely of random experimental error and is consistent with what might be anticipated due to the presence of macroscopic structural heterogeneity. It is therefore suggested that a comparison of the results of the percolation analysis of nitrogen sorption experimental data for whole and powdered pellets will yield similar statistical information as it is possible to obtain from MRI experiments. A possible explanantion for the results in figure 4 based on a diffusional effect might also be discounted because repeats of the initial nitrogen sorption experiments with equilibration times ten times longer (50 s) than the first set (5 s) made no difference to the values of the connectivity parameters obtained. Table 1 also shows a comparison with the values of connectivity obtained from the analysis of PGSE NMR data. It can be seen that these values are in good agreement with the corrected nitrogen sorption values, thereby validating the two theoretical approaches. 5. CONCLUSIONS Experimental nitrogen sorption results for whole and powdered pellet samples indicate that macroscopic heterogeneities in the spatial distribution of average pore size will influence the percolation transition in nitrogen desorption. The combined experimental/simulated nitrogen sorption approach presented here can be used to probe the pellet macroscopic structure. A comparison of the values of connectivity obtained for various materials from the new sorption methodology and PGSE NMR techniques has shown that the corrected sorption approach gives rise to better estimates of pore network connectivity. REFERENCES

1. N.A. Seaton, Chem. Engng Sci., 46 (1991) 1895. R.L. Portsmouth and L.F. Gladden, Chem. Engng Sci., 46 (1991) 3023. 3. M. Yanuka, F.A.L. Dullien and D.E. Elrick, J. Colloid Interface Sci., 112 (1986) 24. 4. M.P. Hollewand and L.F. Gladden, J. Catal., 144 (1993) 254. 5. S.P. Rigby and L.F. Gladden, Chem. Engng Sci., 51 (1996) 2263. 6. M.P. Hollewand and L.F. Gladden, Chem. Engng Sci., 50 (1995) 327. 7. K.R. Brownstein and C.E.Tarr, J. Magn. Reson., 26 (1977) 17. 8. S.P. Rigby and L.F. Gladden, Chem. Engng Sci., 54 (1999) 3503. 9. W.D. Harkins and G. Jura, J. Am. Chem. Soc., 66 (1944) 1366. 10. D. Stauffer, Introduction to Percolation Theory, Taylor and Francis, London, 1985. 11. T. Elias-Kohav, M. Sheintuch and D. Avnir, Chem. Engng Sci., 46 (1991) 2787. 12. H. Liu, L. Zhang and N.A. Seaton, Chem. Engng Sci., 47 (1992) 4393. 13. S.P. Rigby and L.F. Gladden, J. Catal., 173 (1998) 484. .

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScienceB.V. All rightsreserved.

Condensation-evaporation processes dimensional porous networks

121

in

simulated

heterogeneous

three-

S. Cordero a, I. Kornhauser a, C. Felipe a, J. M. Esparza a, A. Dominguez a, J. L. Riccardo b and F. Rojas ~'" aDepartamento de Quimica, Universidad Aut6noma Metropolitana-Iztapalapa, P.O.Box 55-534, M6xico 09340, D.F., Mexico bDepartamento de Fisica, Universidad Nacional de San Luis, Chacabuco 917, 5700 San Luis, Argentina Heterogeneous three-dimensional porous networks consisting of void entities endowed with variations in both size and coordination number and allowing for geometrical restrictions are constructed. The condensation-evaporation behaviour of a fluid is simulated inside these topologically heterogeneous porous substrata. Morphologies of the liquid and gas phases, at a certain stage of the sorption process, are visualized through domain complexion diagrams. 1. INTRODUCTION The topological features of the porous space are of such importance in many processes occurring wherein that they must be consistently incorporated in any theoretical description [1, 2]. In general, the complexity of real porous media may be rationalized in terms of four main characteristics common to real porous networks, namely: (i) heterogeneity in size (i.e., that the basic entities of the porous space, say pore bodies and throats, are size-distributed); (ii) correlation (there exists a statistical correlation between the sizes of neighbouring entities); (iii) non-uniform connectivity (the number of throats emerging from a pore is not constant throughout the network); (iv) geometrical restrictions (pore throats cannot interpenetrate each other before meeting into the pore bodies). These characteristics are of course not independent of each other. A proper model of a porous network should selfconsistently embody size heterogeneity (H), correlation (Co), non-uniform connectivity (C) and geometrical restrictions (Gr). Moreover, it should be easily representable through computer simulation of three-dimensional networks in order to be used for numerical studies of processes that are difficult to be treated exactly (e.g. capillary condensation-evaporation, percolation, imbibition, drainage, penetration, etc.). This work includes three main contributions to the modeling and computer simulation of porous materials. First, the Dual Description (DD) of Mayagoitia [3] is extended as to selfconsistently embody not only size heterogeneity and spatial correlation but also non-uniform connectivity and geometrical restrictions in the network. More precisely, the input of the model will be the size distributions of sites (pore cavities) and bonds (throats); then Co, C and Corresponding author, electronic address: [email protected].

122

Gr will arise merely as consequences of a Construction Principle (CP) and of the maximum randomness size-assignation procedure applied to simulate the network from these distributions. Second, a general Monte Carlo methodology will be implemented to represent three-dimensional (3D) networks where H, Co, C and Gr coexist. Third, a simulation of the condensation-evaporation characteristics of a fluid within the simulated 3D networks will be performed. 2. THE DUAL DESCRIPTION (DD) The dual site-bond description (DD) of disordered structures [3] allows a proper modeling of the porous structure. In the context of this treatment, two kinds of alternately interconnected void entities are thought to conform the porous network, i.e.: the sites (cavities) and the bonds (capillaries, necks). C bonds meet into a site and each bond is the link between two sites. Thus a twofold distribution of sites and bonds is required to construct a porous network. For simplicity, the size of each entity can be measured in terms of a quantity, R, defined as follows: for sites, considered as hollow spheres, R is the radius of the sphere; while for bonds, idealized as hollow cylinders open at both ends, R is the radius of the cylinder. Under the DD scheme, Fs(R ) andFB(R) are the size distribution density functions, for sites and bonds respectively, on a number of elements basis and normalized; so that the probabilities to find a site or a bond having a size R or smaller are: R

R

S(R)= I F s ( R ) d R

;

B ( R ) = J'FB(R)dR.

0

(1)

0

An important parameter is the degree of overlapping f2, defined as the common area shared by FS (R) and FB (R) which is a natural measure of site-bond correlation. If C bonds are going to meet into a site, there arise physical restraints among these entities that depend on the geometries of the network and of the pores. If two cylindrical bonds of radii RB! and RB2 meet orthogonally into a site, then the radius of the site, Rs, should be such 2 1/2 that Rs > (RBI + RB22) . For a given twofold distribution, all sets of C bonds that can fit together into a given site (without any mutual interference) constitute the incumbent hypervolume (since this is a multivariate event) of the site, which is measured through a quantity Bc. In the case of C orthogonal cylindrical bonds meeting at a spherical site, Bc is given by [4]:

Bc(Rs) =

Rs

]l

/C

I .-.

I

0

0

FB(Rm).-.FB(RBc) dRBI-..dRBc

(2)

If a heterogeneous porous network is to be constructed from a twofold distribution a

Construction Principle (CP) can be established as follows: the size of each site should be larger than the sizes of any of its C delimiting bonds and of a value high enough as to avoid geometrical interferences between all pairs of its adjacent bonds. Two self-consistency laws guarantee the fulfilment of the CP. Thefirst law states that the fraction of sites, S(Rs), of sizes smaller than or equal to any certain size Rs, must be lesser than the fraction of bonds Bc(Rs)

123 that can be possibly attached to those sites (i.e. a sufficient provision of smaller bonds than sites should be assured): Bc(Rs) > S(Rs)

V Rs

(3)

This is a necessary but not a sufficient condition and a second law is required since, when the site and bond-size-distributions overlap or are close to each other, there exist topological size correlations between neighbouring elements. In consequence, the probability of finding a size R s for a site and sizes RB1... RBc for its C bonds, is not an independent event. The probability density for this joint event is: p(Rs c~ RBI~... RBC ) = Fs(Rs)'FB(RBI)'... FB(RBc) ~(Rs, RBI...RBc)

(4)

where ~ is a correlation function between the size of a site and the sizes of its neighbouring bonds, whose form will be explicited afterwards. This second law has a local character and prevents the union of sites and bonds that would violate the CP. The second law can be expressed in the following way: ~(Rs,Rs,..RBc) : 0

outside the incumbent hypervolume of the site

(5)

If when constructing a porous network, the randomness on the topological assignation of sizes to elements is maximized, under the restriction imposed by the CP, the most verisimilar (i.e. likely) form of ~ for the correct case, (RBI ~ RB2~... RBC) < R S, is obtained [4]" S(R s) exp~(Rs,RB1...RBc ) =

B(Rs)

dS d S(.. c ) Bc - S

B c ( R s ) - S(R S )

exp=

dBc Bc (Rc) BC - S

Bc(Rc)-S(Rc)

(6)

where RE is the size of the smallest site able to accommodate the C bonds of sizes RBI...RBc. Based upon the relative positions of the size distributions of sites and bonds, a classification of porous structures has been proposed [5] and five types have been recognized. During the course of a capillary process each pattern of the confined phases is astonishingly characteristic within each type of structure. The fingerprint of porous morphology is embodied in r and is present in all kinds of capillary processes [ 1]. 3. VARIABLE CONNECTIVITY IN POROUS NETWORKS Assume a porous material in which pores have a maximum connectivity Cm. In general, some pores will be lesser connected than others, then the number of bonds linking a given site to its nearest neighbouring ones, C, can vary from C = 0 (i.e., an isolated pore within the solid matrix) to C = Cm (i.e. a fully connected site). In this situation the porous space can be readily represented by an a priori regular network of sites and bonds with connectivity Cm , but

124 where a certain number of bonds have R = 0. Indeed, a "bond" of size equal to zero represents a virtual neck not connecting the two sites at its extremes, because of the presence of the solid natrix. Hereafter we refer to such neck as a closed or blind bond. So, for every site of the network it holds that: C i = C m - Ci, 0

'v' i

(7)

where Ci, 0 and C i are the number of closed bonds and open bonds attached to the site i, respectively. Taking averages over the sites on both sides of equation (7), one gets

(8) where N O and N B are the number of closed bonds and total number of bonds in the network, respectively, and f0 denotes the fraction of closed bonds. The less restrictive way to include non-uniform connectivity into a network representation of the porous space is to set the fraction f0 of closed bonds (i.e. the mean connectivity). Consequently non-uniform connectivity can be very easily introduced in the framework of the DD by redefining the bond size density function FB(R B) as: for R B = 0 FB (RB)

[ FB(RB)

for R B > 0

(9)

where it has been simply assumed that the size-density of bonds is a delta function at R B = 0. In this way all previous definitions and equations (1) to (6) are still valid. Additionally because of the normalization condition, F~(RB) must fulfil: oo

J'F~ (RB) dR B = l - f o o

(10)

4. M O N T E C A R L O S I M U L A T I O N OF H E T E R O G E N E O U S POROUS N E T W O R K S Assume a three dimensional network of M = L x L x L sites connected by bonds. In principle, all sites will have a connectivity Cm. An arbitrary initial network configuration x is generated assigning sizes to every site and its Cm bonds from their own pre-established distributions Fs(Rs) and FB(RB). It is obvious this configuration x will not reproduce the joint distribution P(Rs ~ R B1 ~ ...R BE) but something else i~(Rs ~ R BI ~ ...R BE ). The key step is to perform changes of configuration x ~ x' (for instance, by switching the sizes of two sites or bonds in the network) with a properly chosen transition probability W(x ~ x') such that a sequence

x ~ x' ~ x" ~ . . .

makes the distibution

i~(Rs ~ RB1 ~...RBC)

125 converge to the desired stationary* distribution. For this to occur, the transition probability W(x ~ x') can be defined as [6]: P(x') } W(x -~ x ' ) = min 1,-p(x)

(11)

where P(x)is the probability of having the network in the configuration x. This is the well known Metropolis scheme which allows the Detailed Balance Principle to be fulfilled: P(x) W(x --~ x ' ) = P(x') W(x' -~ x)

(12)

Finally, applying the properties of the function ~ a very simple result is obtained:

{

W(x ~ x')= min 1, P(x)

=

{1o

if x' fulfils the construction principle otherwise

(13)

Equation (13) can be proved to be valid for any arbitrary change of configuration x ~ x' (e.g., transitions involving the swapping between the sizes of two bonds selected at random in the network).

The procedure for simulating a heterogeneous 3D network consists of the following steps: Define a regular lattice of sites linked by bonds (i.e., simple cubic, face-centered cubic, etc.), this already involves a maximum connectivity Cm per site. ii) Assign sizes to sites from Fs (Rs), sizes equal to zero to a fraction f0 of the total bonds, iii) iv)

and sizes to the remaining bonds from F~(RB) (equation (9)). Choose two sites k, l at random; swap their sizes if the CP is observed for both sites in the final configuration. Repeat this operation for two bonds k, l chosen at random. Repeat iii) M x C m times.

Steps iii) and iv) define one Monte Carlo step (1 MCS). A number M 0 >> 1 of MCS must be performed before the joint density frequency function in the simulated network equals (within a given accuracy) the desired function p(Rs n RBln... RBC ). In practice this function can be monitored for different network configurations until no significant variations are observed. It is worth noticing that the lattice size plays an important role since a multivariate distribution function is to be reproduced. Finally, it should be mentioned that the procedure outlined above applies regardless of the particular forms of F s ( R s ) a n d F a ( R B ) . Furthermore, it does not require a priori the knowledge of ~(Rs,RB1...RBc) (equation (6)) whose calculation would demand a significant numerical effort in most of cases.

t Here the term stationary means that once the joint distribution in the network is p(Rs, Ra~... Rac) a sequence of further transitions according to W(x--}x') would leave this form unchanged.

126 5

R E S U L T S ON T H E S I M U L A T I O N OF 3D P O R O U S N E T W O R K S

Cubic porous networks (Cm = 6) of 32 x 32 x 32 sites and its corresponding 32 x 32 x 32 x Cm / 2 bonds were computer simulated. Sites were considered as hollow spheres and bonds as hollow cylinders open at both ends. Gaussian twofold distributions were used as precursors of networks with either constant or variable connectivity. Parameters were as follows: 1) Mean radius of sites, Rms = 144 A, mean radius of bonds, Rmb = 72 A, standard deviations for sites and bonds as = cB = 12 A (f2 = 0 regardless of C). Network la: C = 6. Network lb: C = 4.5, network 1c: C = 3. 2) Rms = 132 A, Rmb = 72 A, as = aB = 12 A (f2 = 0.010 for C = 6). Network 2a: C - 6. Network 2b" C = 4.5, network 2c" C = 3. 3) Rms = 120 A, Rmb = 72 A, as = aB = 12 A (f2 = 0.043 for C = 6). Network 3a: C - 6. Network 3b" C = 4.5, network 3c" C = 3. 4) Rms = 108 A, Rmb = 72 A, as = aB = 12 A (f2 = 0.1315 for C = 6). Network 4a: C = 6. Network 4b" C = 4.5, network 4c" C = 3. m

The number of sites in these networks was Ns = 32768 and the maximum number of bonds (because of variable C) was NB = 101376. Note that NB and ~ vary with f0. An initial network configuration was set up by randomly choosing sizes for all sites and bonds, while observing the imposed twofold size distribution. Sites were placed at the nodes of the cubic lattice and bonds in between the nodes. Node to node distance was constant (i.e. equal to the diameter of the largest site); the length of each bond was adjusted to a value enough to connect its two neighbouring sites. This particular selection of bond-site distance defined the porosity of the network. The initial configuration was then left to evolve into more likely arrangements through a random swapping process among its pore elements. A bond or a site could be exchanged with other homologous elements, only if the CP was fulfilled. All times Gr was taken into account within the framework of the CP, by not allowing exchanges between entities that would redound in further bond interference. Constant or variable connectivity was considered by letting f0 the fraction of closed bonds to assume the values of 0, 0.25 and 0.5. In the case of C < 6, blind bonds could be exchanged without restriction throughout the network; the number of non-closed bonds that surrounded a site defined its real connectivity. The number M0 of MCS needed to obtain a self-consistent porous network (i.e. that fulfilling equation 4) was m

about 1000 for f2 = 0 and 50,000 for f2 = 0.13. M0 also depended on f0, being lesser as f0 was larger. The topology of the porous structure was visualized in the following way. The site- and bond-size distributions were equally divided in three size zones (i.e. with the same number) of small, intermediate and large entities. Topological diagrams, consisting in a view of the spatial arrangement of the porous entities (classified according to these three size ranges) on a plane of the simulated cubic network, are shown in figures l a-c, together with the site- and bond-size distributions used for the simulation. Larger entities are white-filled, medium ones grey-filled and smaller ones black-filled. Geometrical restrictions induced the structuralization of the porous network into pore domains that incorporate elements of similar sizes. Segregation zones, specially those consisting of big and small elements, emerge more and more clearly as the overlap f2 increases. Elements of intermediate size are located between the large and small elements as a surrounding layer. These features can be seen in figures l a-c. In figure l a the bond and site

127

Figure 1. Twofold size distributions (at let~) and topological diagrams of planes (at fight). Sites are circles and bonds are cylinders. Small pores are represented in black, intermediate ones in gray and larger ones remain blank, a) Network 1a, b) Network 1c and c) Network 3a.

128 distributions lie apart; the three types of element sizes are distributed in a somewhat homogeneous manner, although some signs of segregation are already evident. In figure 1c the distributions are the closest possible, since f2 has been made to assume its largest possible value in order to fulfil the CP. This greater correlation between sites and bonds causes the appearance of a large zone (black) of small elements that predominates on most of the plane chosen for visualization. Due to the fact that larger sites exist in the same proportion as smaller ones throughout the network, one could also find planes in which large elements would predominate over the smaller ones. As it can also be seen in the figures, medium-size elements delimit the zones between large and small pores. There also arises a connectivity segregation effect. Smaller elements have a smaller mean connectivity than larger entities, this can be seen in Figure lb by noticing that the number of bonds around a small site is lower than for the largest ones.

6

SORPTION OF NITROGEN ON H E T E R O G E N E O U S POROUS N E T W O R K S

Nitrogen sorption isotherms at 77 K were calculated by means of the simulated 3D networks. Besides the Kelvin equation, necessary for determining the critical radius of curvature Rc, at which condensation and evaporation would occur, it is also necessary to consider specific menisci interactions and network effects that can influence the sorption phenomena [5, 7]. The existence of an adsorbed layer is indeed of great importance on the outcome of a sorption process, but for simplicity it will not be considered in this treatment. Condensation in a site occurs if the two following conditions are concurrently fulfilled: i) the critical radius of curvature of the liquid-vapour interface is lower than that predicted by the Kelvin equation (a spherical meniscus being assumed), and (ii) C or at least C-1 bonds are already filled with condensate [5]. Condensation in a bond occurs either: (i) by an independent mechanism, i.e. assuming a cylindrical meniscus, condensation presents when the radius of curvature of the interface is lower than or equal to the critical radius predicted by Kelvin, or (ii) by an assisted mechanism if the neighbouring site is being filled by condensate so that a spontaneous filling of the bond will follow. The above conditions apply whether the adsorption process occurs along a boundary adsorption or any ascending scanning process within the hysteresis loop. Evaporation from a porous element initially filled with liquid occurs if: (i) the interface has a radius of curvature higher than the critical radius predicted by Kelvin and, (ii) there exists a continuous vapour trajectory from the element in question to the bulk vapour phase. These criteria are valid for a boundary desorption or any descending scanning curve. Adsorption isotherms, including boundary ascending (BA), boundary descending (BD), primary ascending (PA) and primary descending (PD) curves, are shown in figure 2 for networks 2a, 2b and 2c. In this figure it is plotted the volume degree of filling of the pores (sites and bonds) against the relative vapour pressure p/p0. The following relationship between the critical Kelvin radius and p/p0 has been used for Nz at 77 K: ln(p/p ~ = - 9.54/(Rc / A). The percolation threshold for vapour invasion is a function of the connectivity: this threshold moves towards smaller relative pressures as C diminishes. On the other hand condensation in sites (that occurs at a p/p0 higher than that predicted by the Kelvin equation due to meniscii interactions) develops earlier in lesser-connected sites; this effect is however less dependent on C than is percolation by vapour. The series of isotherms shown in figure 2 corresponds to the same twofold distribution but with different values of f0 (i.e. 0, 0.25 and 0.5). It can be seen that the hysteresis loop widens with lower C. At high C the PA curves show sharp m

I

129

Figure 3. Domain-complexion diagrams (at left) and phase distribution (at fight, condensate in black, vapour in blank) within the pores (sites: circles, bonds: cylinders) on planes of 3D porous networks for actual states of diverse sorption processes, a) Boundary ascending (BA) curve on network l a, b) boundary descending (BD) curve on network 2a, c) primary ascending (PA) curve on network 3a and d) primary descending (PD) curve on network 4a. Rc is the critical radius of curvature at the present state of the sorption process and Rc* is the critical radius of curvature at the point of reversal for scanning curves. Shaded areas (pores filled with condensate) delimited by full lines in the complexion diagrams represent current states of the sorption systems, broken lines delimit states at the points of reversal.

130 intersections with the BA curve while the PD approach asymptotically to the BD curve. At lower C, PA curves cross smoothly the hysteresis loop and run asymptotically to the BA. This would mean that the more size correlated the porous entities are, the faster is the approach of primary scanning curves to the boundary ones. PD scanning curves show a locus at which they meet on the BD curve, this locus is displaced towards smaller relative pressures as C decreases. Domain complexion diagrams corresponding to BA, BD, PA and PD sorption processes are represented in figures 3a-d, together with topological diagrams of a plane of the porous network that illustrates the arrangements of the fluid phases at the final states of such processes. Although each of these figures represent a different sorption process, the highest degree of structuralization of the fluids is observed for network 4a, the one that has the highest degree of size correlation between its pore elements. This is an example of how the fingerprint (topology) of the porous network manifests in all kinds of capillary processes that develop wherein.

CONCLUSIONS Heterogeneous porous networks can be simulated taking into account characteristics proper of real media such as variations in pore size and connectivity. Real substrata display also physical or geometrical restraints that should be taken into account for an adequate modeling. Sorption characteristics can be studied in these simulated 3D networks. Comparison with actual isotherms of real porous media in order to infer or predict textural parameters should be the next step of this research. Thanks are due to CONACyT (Project: Medios Porosos, Superficies, Procesos Capilares y de Adsorcirn 28416E) and FOMES (98-35-21) for financial aid.

REFERENCES 1. V. Mayagoitia, F. Rojas, I. Kornhauser, G. Zgrablich and J. L. Riccardo, in Characterization of Porous Solids III, Studies in Surface Science and Catalysis, Vol. 87, F. Rodriguez-Reynoso, J. Rouquerol, K. S. W. Sing, and K. K. Unger (eds.), Elsevier. Amsterdam, 1994, pp. 141-150. 2. G. N. Constantinides and A. C. Payatakes, Chem. Eng. Comm. 46 (1991) 55. 3. V. Mayagoitia, F. Rojas, I. Kornhauser and H. Prrez - Aguilar, Langmuir 13 (1997) 1327. 4. V. Mayagoitia, F. Rojas, I. Kornhauser, G. Zgrablich, R. J. Faccio, B. Gilot and C. Guiglion, Langmuir 12 (1996) 211. 5. V. Mayagoitia, F. Rojas and I. Kornhauser, J. Chem. Soc. Faraday Trans. 1 84 (1988) 785. 6. J. L. Riccardo, W. A. Steele, A. J. Ramirez-Cuesta and G. Zgrablich, Langmuir 13 (1996) 1064. 7. V. Mayagoitia, B. Gilot, F. Rojas and I. Kornhauser, J. Chem. Soc. Faraday Trans. 1 84 (1988) 801.

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScienceB.V.All rightsreserved.

131

Characterisation o f Porous Solids for Gas Transport O. ~;olcov5., H. Snajdaufov& V. Hejtmfinek, P. Schneider Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Rozvojovfi 135, 165 02 Praha 6, Czech Republic The aim of this study is to compare pore structure characteristics of two industrial catalysts determined by standard methods of textural analysis (physical adsorption of nitrogen and mercury porosimetry) and selected methods for obtaining parameters relevant to transport processes (multicomponent diffusion and permeation of gases). The Mean Transport Pore Model (MTPM) described diffusion and permeation; the model (represented as a boundary value problem for a set of ordinary differential equations) are based on Maxwell-Stefan diffusion equation and Weber permeation law. Parameters of MTPM are material constants of the porous solid and, thus, do not dependent on conditions under which the transport processes take place. Both catalysts were mono- or bidispersed with mean pore radii about 70 and 2000 nm; diffusion and permeation measurements were performed with four inert gases (H2, He, N2 and Ar). 1. INTRODUCTION The industrial application of porous solids is quite widespread. Porous heterogeneous catalysts, adsorbents and membranes are used in chemical industry and in biotechnology, porous materials are common in building engineering, porous catalysts form the basis of car mufflers, etc. The rates of processes, which take place in pore structure of these materials, are affected or determined by the transport resistance of the pore structure. Inclusion of transport processes into the description of the whole process is essential when reliable simulations or predictions have to be made. Trends in modem chemical/biochemical reaction engineering point to utilization of more sophisticated, and therefore more reliable, models of processes. The basic idea is that the better the description of individual steps of the whole process the better its description and, perhaps, even extrapolation. Because of the unique nature of pore structure of different materials the pore structure characteristics relevant to transport in pores have to be determined experimentally. Two approaches are used in this respect: 1.1. textural analysis of the porous solid 1.2. evaluation of simple transport processes taking place in the porous solid in question The advantage of the first approach derives from the complexity of available experimental methods and evaluation procedures (physical adsorption of gases, high-pressure mercury porosimetry, liquid expulsion permoporometry, permporometry with pores blocked by capillary condensation, etc.). The relevance of the second approach stems from the possibility to use the same porestructure model as used in description of the process in question (counter-current (isobaric) diffusion of simple gases, permeation of simple gases under steady-state or dynamic conditions, combined diffusion and permeation of gases under dynamic conditions, etc.).

132

1.1. Textural analysis of porous solids At present two methods are applied routinely for the analysis of texture of porous solids, viz. physical adsorption of inert gases (e.g. nitrogen, argon, krypton) and high-pressure porosimetry (see e.g. [ 1]). Precise automatic commercial instruments are available for determination of physisorption isotherms. The latest models can determine adsorption at relative pressures down to 10.6 - 107", data at such low pressures are required for analyses of microporous solids (e.g. molecular sieves). Less favorable is the situation with analyses of obtained data, viz. the most common cases of solids containing both micro- and meso-pores. Here the Brunauer-Emmet-Teller (BET) isotherm is nearly always incorrectly applied. The t-plot method [1] is only of limited applicability because it requires knowledge of adsorption isotherms on non-porous solids of the same chemical nature as the measured sample (master isotherm). Only recently it was shown in this Laboratory [2] that an extension of BET isotherm together with non-linear parameter fitting could solve this problem. Pore-size distributions (PSD) are routinely obtained by an algorithm dating back to Barret, Joyner and Halenda [3-4]. Either cylindrical or slit-shaped pores are assumed in these calculations. The BJH method virtually represents numerical solution of an integral equation, which describes adsorption and capillary condensation of adsorbate in pores and utilizes the Kelvin equation. Because the validity of Kelvin equation in micropores can be questioned a new approach based on statistical physics is developing, viz. the density functional theory [57]. This approach can supply adsorption isotherms for cylindrical or slit-shaped pores of different sizes in carbonaceous or oxide matrix. The problem then is to sum up these isotherms so that the experimental isotherm is reproduced. Expensive commercial programs are available for this purpose. Mercury porosimetry is performed nearly exclusively on automatic commercial instruments that differ mainly in the highest operative pressure, which determines the size of smallest attainable pores. The highest pressure is limited by the uncertainty about the validity of the Washburn equation, which forms the basis of data evaluation. In pores with sizes similar to the mercury atom the assumption that physical properties of liquid mercury (surface tension, contact angle) are equal to bulk properties is, probably, not fully substantiated. For this reason the up-to-date instruments work with pressures up to 2000 - 4000 atm, only. With the advance of porous membranes, the permporometry methods gained fresh impetus. The basic idea is to block pores of some sizes by a wettable liquid and measure either permeation of counter-current diffusion fluxes through the open pores. In liquid-expulsion permporometry [8], the porous solid is saturated with a liquid and by application of a pressure difference across the sample the liquid is forced out of the largest pores. The rate of gas permeating through these pores is then measured. Then, the pressure difference is increased which frees another pores, etc. As a result, pore-size distribution is obtained. Another possibility is to fill some pores by capillary condensation and to determine the counter-current diffusion flux of an inert gas pair through the unblocked pores [9-11]. By changing the partial pressure or temperature of the condensable vapor different groups of pores can be blocked and the pore-size distribution determined.

133 1.2. Determination of transport parameters of porous solids Transport parameters, i.e. model parameters that are material constants of the porous solids (independent of temperature, pressure and kind and concentration of gases) are evaluated through application of a suitable model of porous solids to results of measurements of simple transport processes in the porous structure. A great number of studies have been published to deal with relation of transport properties to structural characteristics. Pore network models [12,13,14] are engaged in determination of pore network connectivity that is known to have a crucial influence on the transport properties of a porous material. McGreavy and co-workers [15] developed model based on the equivalent pore network conceptualisation to account for diffusion and reaction processes in catalytic pore structures. Percolation models [16,17] are based on the use of percolation theory to analyse sorption hysteresis also the application of the effective medium approximation (EMA) [ 18,19,20] is widely used. Today two models are available for description of combined (diffusion and permeation) transport of multicomponent gas mixtures: the Mean Transport-Pore Model (MTPM)[21,22] and the Dusty Gas Model (DGM)[23,24]. Both models enable in future to connect multicomponent process simultaneously with process as catalytic reaction, gas-solid reaction or adsorption to porous medium. These models are based on the modified StefanMaxwell description of multicomponent diffusion in pores and on Darcy (DGM) or Weber (MTPM) equation for permeation. For mass transport due to composition differences (i.e. pure diffusion) both models are represented by an identical set of differential equation with two parameters (transport parameters) which characterise the pore structure. Because both models drastically simplify the real pore structure the transport parameters have to be determined experimentally. MTPM assumes that the decisive part of the gas transport takes place in transportpores that are visualised as cylindrical capillaries with radii distributed around the mean value (first model parameter). The second model parameter can be looked upon as ratio of tortuosity, qt, and porosity of transport-pores, ~t, 9 -- ~t/qt 9The third transport parameter, [25], characterises the width of the transport pore size distribution and is required for description of viscous flow in pores. DGM visualises the porous medium as a collection of giant spherical molecules (dust particles) kept in space by external force. The movement of gas molecules in the space between dust particles is described by the kinetic theory of gases. Formally, the MTPM transport parameters and ~g can be used also in DGM. The third DGM transport parameter characterises the viscous (Poiseuille) gas flow in pores. The best way for obtaining transport parameters of porous structures is to follow experimentally a simple transport processes in the pores under uncomplicated process conditions (temperature, pressure, etc.) and to evaluate the model parameters by fitting the obtained experimental results to the theory. The experimentally performed transport processes used for evaluation of transport parameters include: counter current binary or multicomponent gas diffusion under steadystate or chromatographic conditions, steady permeation of simple gases, dynamics of combined transport of binary or multicomponent gas mixtures, etc. Of significance, however, is that no automatic commercial instrument is available for these processes. Thus, the necessary apparatuses must be homemade. To obtain the transport parameters with acceptable confidence large numbers of experiments is required. It would be, therefore, of significant importance if at least part of the transport parameters could be obtained from standard textural analysis.

134 The aim of this study is to compare pore structure characteristics of two porous catalysts determined by standard methods of textural analysis (physical adsorption of nitrogen and mercury porosimetry) and selected methods for obtaining parameters relevant to transport processes (multicomponent gas diffusion and permeation of simple gases). MTPM was used for description of these processes. 2. E X P E R I M E N T A L Two porous catalysts in the form of cylindrical pellets were used: industrial hydrogenation catalyst Cherox 42-00 with monodisperse pore structure (Chemopetrol Litvinov, Czech Rep.; height x diameter- 4.9 x 5.0 mm) and laboratory prepared a-alumina, A5 (based on boehmite from Pural SB, Condea Chemie, Germany) with bidisperse pore structure (height x diameter = 3.45 x 3.45 mm). Four nonadsorbable gases (argon, helium, hydrogen, nitrogen; 99.9% purity.) were selected for transport measurements. Thus, the surface transport of adsorbed gases was absent. Catalysts were characterised by two standard textural-analysis methods: mercury porosimetry (AutoPore 9200, Micromeritics, USA) and physical adsorption of nitrogen (ASAP2010M, Micromeritics, USA). Two non-standard transport processes (counter-current isobaric ternary diffusion and permeation of simple gases were chosen for obtaining pore-structure transport characteristics. MTPM was used for evaluation of transport parameters. The modified W i c k e - Kallenbach cell developed in our laboratory [26,27], was used for measurement of isobaric counter-current ternary diffusion. Figure 1 shows schematically the diffusion set-up including the modified Wicke-Kallenbach cell.. G1-4 are gas sources; FMC are flow-meter controllers; D is the diffusion cell; O1-2 are gas outlets; V 1-3 are valves; B is a calibrated glass burette with soap film. The diffusion cell contains a metallic disc with cylindrical holes into which the porous pellets are mounted. Volumes of cell compartments are approximately 150 cm 3. Measurement procedure: A mixture of gases "1" and "2" flows through the bottom cell and another gas flows through the upper cell compartment (flow-rates of gases in both cells are 150 cm3/min). Valves V1 and V3 are closed and valve V2 opened at the same time. Movement of the soap film in the burette follows the net diffusion flux. The net volumetric diffusion flux, V, gradually decreased with the increase of the gas "3" concentration in the bottom cell compartment. Net volumetric diffusion flux is determined from the slope at zero time of the V(t) dependence.

Figure 1 Scheme of diffusion cell set-up

135

Figure 2. Scheme of the permeation cell. 1 flow-through cell compartment, 2 closed cell compartment, 3 pressure transducer, 4 metallic disc with pellets mounted into cylindrical holes, 5 gas inlet valve, 6 capillary, 7, 8 connection to vacuum pump. Data evaluation: The evaluation of model parameters by non-linear fitting of experimental net diffusion flux densities to theory requires solution of a set of coupled ordinary differential equations which describe diffusion in porous solids according to MTPM (integration of differential equations with splitted boundary conditions). Permeation (gas transport caused by pressure gradient) of simple gases is the second non-standard process used for obtaining pore-structure transport characteristics. Permeation cell is shown in Figure 2. It is divided by metallic disc with cylindrical pellets into two parts. The upper compartment of the cell is filled by one of the inert gas through a capillary (with known length and diameter) to prevent undesirable pressure shocks. Pressure is measured in lower cell compartment by an absolute pressure transducer (range 0 - 101 kPa, Omega Engineering, Inc., USA). Computer controls the whole measurement. Measurement procedure: Both cell chambers are evacuated to the same pressure. Then the upper cell compartment is filled with the gas to the required pressure (approximately 101 kPa). This pressure step starts the permeation process in the porous material; the progress is followed by monitoring the pressure increase in the lower cell compartment. The time of gas filling is negligible in comparison with the length of the pressure response. Data evaluation." Model parameters were obtained by fitting of experimental time dependencies of pressure in the lower cell compartment to theory. Obtaining of theoretical time - pressure courses represents integration of mass balance (partial differential equation, or, assuming pseudo-steady-state, ordinary differential equation).

3. RESULTS AND DISCUSSION The isobaric counter-current diffusion measurements in the modified WickeKallenbach cell employ the validity of the Graham law which states that under isobaric

136

conditions the ratio of diffusion molar flux densities of components 1 and 2 equals the square root of the inverse ratio of molecular weights of the g a s e s - Equation 1. (1)

N I / N 2 = - ( M 2 / M 1 ) 1/2

It follows, then, that both diffusion flux densities, N l and N2, can be determined from the easily measurable net diffusion flux density N = N I + N2. For a system with three gas components, arranged so that gases 1 and 2 are in the bottom compartment of the diffusion cell and gas 3 is in the upper compartment, the system of ordinary differential equations is solved for porous pellets with length L. The situation is described by the following system of equations

dy

1

. . . . -~-/-+ dx c T D, j=l

m' D,j

dN, =0 dx

Y3 = I - y ' y J j_~

i=1,2

(2)

9

N3= -

• j=l

i=1,2

Nj .M

3

N=y'N~ 3

(3)

(4)

j=l

with initial conditions atx=0 at x = L

y,=y~';y2 =y2" Y3 =0 y~ = 0; Y2 = 0; Y3 =

(5)

L

Y3

Here x is the geometric co-ordinate in the porous pellet, Ni are the molar flux densities of gas mixture components, N is the net diffusion flux density, Mi are molecular weights of mixture components and y~ are component mole fractions. Superscripts o and L denote the bottom and upper part of the cell, resp. In the applied experimental arrangement the stream of pure heavier gas, or gas mixture containing the heavier gas, passed through the upper compartment. The net volumetric diffusion fluxes for catalyst A5 with He in the upper cell compartment and mixtures of Ar and H2, or Ar and N2, in the lower compartment, are shown in Figure 3. The dependent variable is the mole fraction of Ar in the (Ar+H2) or (Ar+N2) binary gas mixture. As can be seen mixture composition in the bottom compartment influences significantly the net diffusion fluxes. In agreement with Graham law, this is the more marked the more differ the molecular weights of gases. This figure also illustrates the change of the net diffusion flux direction (which appears as sign change of the net diffusion flux density). For the transport parameter optimisation the set of 66 data points for both catalysts were used. These sets included data for binary cases (pure gases in both compartments) and ternary cases (pure gas in one compartment and a binary mixture in the other compartment). In Figure 4 the experimental net volumetric diffusion fluxes are compared with calculated values based on the optimum sets of transport parameters. It can be seen that experimental and

137

Figure 3 Net volumetric diffusion fluxes; catalyst A5

Figure 4 Comparison of experimental and calculated net diffusion flux densities; catalyst A5

calculated diffusion fluxes are in a good agreement and experimental error does not exceed 3%. The optimum transport parameters for both catalysts are summarized in the Table 1. Permeation. The permeation flux density, N, is described by the Darcy constitutive Equation 6, 0c N = -B~ 0x

(6)

where B is the effective permeation coefficient. Weber Equation 7 describes the pressure dependence of effective permeability coefficient B, B

=

Dk 0) + K n

~ + l+Kn

c

BoRT-kt

(7)

where D k is the effective Knudsen diffusion coefficient defined as 2/3 tr (8RT/nM) 1/2, B0 is the Poiseuille parameter (B0 = ~/8) and Kn is the Knudsen number at unit gas concentration (ratio of mean free-path length of the gas molecules and the pore diameter) and co characterises the slip at the pore wall For each catalyst and gas six experimental pressure dependencies (each with more then 100 data points) were obtained with different initial pressure. Figure 5 compares experimental (points) with calculations (lines) for permeation of N2 through Cherox 42-00. The optimum transport parameters are summarised in Table 1 together with transport parameters obtained from diffusion measurements. Radii of transport pores were obtained as Z~/~ (for permeation) or as ~/~ (for diffusion). It is evident from Table 1 that for A5 pellets the transport parameters ~ from permeation and diffusion measurements are nearly the same (deviation about 10%); the agreement for Cherox 42-00 is slightly worse (deviation about 20%). Nearly the same results were obtained for calculated radii of mean transport pores, . For A5 pellets = 1818nm (from diffusion) and 1770nm (from permeation), i.e. an excellent agreement. For the Cherox 42-00 catalyst the agreement is less satisfactory.

138 Table 1. Transport parameters from permeation and diffusion measurement Porous solid

Permeation V [rim] • [nm2]

[nm]

V [nm]

Diffusion V [nm]

Into]

A5

236

417732

1770

211

0.116

1818

Cherox 42-00

5.6

497

88

4.6

0.134

34

Textural properties of both tested porous solids were determined by physical adsorption of nitrogen and mercury porosimetry, also. Pore-size distributions of catalysts obtained from physical adsorption of nitrogen (BJH algorithm) and from mercury porosimetry are compared with mean transport pore radii (-diffusion, <rp>-permeation) in Figure 6. It is seen that the A5 pellets have bidisperse pore structure with maxima at 290 nm and 2070 nm. The mean transport pore radii are slightly smaller then the macropore peak of the pore-size distribution. Hence, the transport of gases passes mainly through the wider pores. For catalyst Cherox 4200 the maximum of pore radii determined by the BJH algorithm is about 30 nm lower than from mercury porosimetry. The mean transport pore radii from diffusion and permeation measurements are in a good agreement with the position of macropores as determined by mercury porosimetry. From physical adsorption of nitrogen (BJH algorithm) and from mercury porosimetry are compared with mean transport pore radii (-diffusion, <rp>permeation) in Figure 6. It is seen that the A5 pellets have bidisperse pore structure with maxima at 290 nm and 2070 nm. The mean transport pore radii are slightly smaller then the macropore peak of the pore-size distribution. Hence, the transport of gases passes mainly through the wider pores. For catalyst Cherox 42-00 the maximum of pore radii determined by the BJH algorithm is about 30 nm lower than from mercury porosimetry. The mean transport pore radii from diffusion and permeation measurements are in a good agreement with the position of macropores as determined by mercury porosimetry.

Figure 5. Comparisonof pressure difference for N2 permeation in Cherox 42-00; points - experimental, line - calculated

139 0 . 5

IHI

!

,I,|.|

I

,

,||I|H

=27nm [ ~~[

0.3

0.2 > "~

, IIl|ll[

I

,

||wll|l

I

Hi|

!

i

,,llu|

|

Cherox 42-00

0.4 ~'~l)

,

i ill;ll

I

|

v I|lll|

I

!

, ,ltlll

l

A-5

8,nm

=1819 nm I

..l

<rp>=1770nm

i/

o.,

~'1l,_/ /r,J ~ l

0.0

I ~........I ,L

. ~~~

~?~'--J. I . . . . . . . . . . . . . . . .

l 0~ 101 102

r (nm)

103

,

/

104 10~ l 01

10z

103

104

r (nm)

Figure 6. Pore-size distributions mercury porozimetry - solid line, nitrogen physical adsorption -dashed line 4. CONCLUSIONS Textural properties of two porous solids with different pore size distributions were determined by two standard methods; physical adsorption of nitrogen and mercury porosimetry. The same porous solids were characterised by measurements of isobaric countercurrent diffusion and permeation of gases. MTPM was used for evaluation of transport parameters, which characterise textural properties in relation to gas transport. Transport parameters obtained from both nonstandard processes are in a good agreement. Mean transport pore radii from non-standard processes and maxima of pore-size distributions from standard methods are similar for monodisperse pore structures; for solids with bidisperse pore-size distributions this difference is significant. It was confirmed that gas transport occurs mainly through wider pores. With respect to the complicated structure of porous catalysts it is hardly possible to use information on textural properties obtained from the two applied standard methods for prediction of gas transport in pores. It might be possible, however, to select another standard method, the physical principle of, which is more similar to gas, transport in pores. One can consider (e.g.) liquid-expansion permporometry. This method is based, among other, on the Washburn permeation equation for individual groups of pores. Acknowledgement

The authors greatly appreciated financial support by the Grant Agency of the Academy Science of the Czech Republic (A4072804, A4072915) REFERENCES

1. 2. 3. 4.

S. J Gregg., K. S. W.Sing, Adsorption, Surface Area and Porosity, 2 no Edition, Academic Press, London, 1982. P. Schneider, Appl. Catal., A 129 (1995) 157. E.P.Barret, L.G.Joyner, P.P.Halenda, J. Am. Chem. Soc., 73 (1951) 373. B.F.Roberts, J. Colloid Interf. Sci., 23 (1967) 266.

140

.

6. 7. 8. 9. 10. 11. 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

N. A. Seaton, J.P.R.B. Walton, N. Quirke, Carbon, 27 (1989) 853. N. A. Seaton, J.P.R.B. Walton, Gubbins K. E.: J. Chem. Soc., 82 (1986) 1789. J.P. Olivier, Porous Materials, 2 (1995) 9. P. Schneider, P. Uchytil, J. Membr. Sci., 95 (1994) 29. F.P. Cuperus, D. Bargeman, C.A. Smolder, J. Membr. Sci., 71 (1992) 57. G.Z. Cao, J. Meijerinmk, H.W. Brinkman, A.J. Burggraaf, J. Membr. Sci., 83 (1993) 221. P. Huang, N. Xu, J. Shi, Y.S. Lion, J. Membr. Sci., 116 (1996) 301. M. Sahimi, G.R. Gavalas, T.T. Tsotsis, Chem. Eng. Sci., 45 (1990) 1443. L. Zhang, N.A. Seaton, Chem. Eng. Sci., 49 (1994) 41. S.L. Bryant, P.R. King, D.W. Mellor, Transport in Porous Media, 11 (1993) 53 C. McGreavy, J.S. Andrade Jr., K. Rajagopal, Chem. Eng. Sci. 47 (1992) 2751 S. Kirkpatrick, Rewiews of Modern Physics 45 (1973) 574 N.A. Seaton, Chem.Eng.Sci. 46 (1990) 1895 T. Nagatani, J. Phys. C. 14 (1981) 4839 J. Sax, J.M. Ottino, Polym. Eng. Sci. 23 (1983) 165 D. Nicholson, J.K. Petrou, J.H. Petropoulos, Chem. Eng. Sci. 43 (1988) 1385 E.A. Mason, A.P. Malinauskas, Gas Transport in Porous Media, The Dusty Gas Model., Elsevier, 1983 R. Jackson, Transport in Porous Catalysts., Elsevier, Amsterdam, 1977. P. Schneider, D. Gelbin, Chem. Eng. Sci., 40 (1985) 1093. P. Fott., G. Petrini, P. Schneider, Coll. Czech. Chem. Commun., 48 (1983) 215. P. Schneider, Chem. Eng. Sci., 46 (1991) 2376. J. Value, P. Schneider, Appl. Catal., 1 (1981) 355. J. Value, P. Schneider, Appl. Catal., 16 (1985) 329.

Studies in Surface Scienceand Catalysis 128 K.K. Unger et al. (Editors)

2000 ElsevierScienceB.V. All rightsreserved.

141

Experimental and simulation studies of melting and freezing in porous glasses M. Sliwinska-Bartkowiak a, J. Gras ~, R. Sikorski ~, G. Dudziak ~ R. Radhakrishnan b and K. E. Gubbins b a Instytut Fizyki, Uniwersytet im Adama Mickiewicza. Umultowska 85, 61-614 Poznan, Poland. b Department of Chemical Engineering. North Carolina State University, 113 Riddick Labs, Raleigh, NC 27695. USA We report both experimental measurements and molecular simulations of the melting and freezing behavior of simple fluids in porous media. The experimental studies are for nitrobenzene in controlled pore glass (CPG) and Vycor. Dielectric relaxation spectroscopy was used to determine melting points of bulk and confined nitrobenzene. Structural information about the different confined phases was obtained by measuring the rotational dielectric relaxation times. Monte Carlo simulations were used to determine the shift in the melting point, for a simple fluid in slit pores having both repulsive and attractive walls. A method for calculating the free energy of solids in pores based on order parameter formulation is presented. Qualitative comparison between experiment and simulation are made with respect to the shift in the freezing temperatures, structure of confined phases and hysteresis behavior.

1

Introduction

Freezing in porous media has been widely employed in the characterization of porous materials. In the method termed thermoporometry, the shift in freezing temperature of water is determined, and the pore size distribution is inferred from a thermodynamic analysis which is analogous to the use of Kelvin's equation for capillary condensation: such an analysis breaks down in the case of micropores as the limit of small and inhomogeneous systems demand a more rigorous statistical mechanical treatment, hnportant questions regarding melting and freezing in pores are the nature of the phase transition (first order vs. continuous, due to varied dimensionality), the direction of shift in the melting temperature, nature and origin of hysteresis, structural changes of the condensed phases in the restricted pore geometries, the effect on latent heats, etc. Answers to these questions warrant a rigorous study of the free energy surfaces as a function of the relevant thermodynamic variables. A classical thermodynamic argument based on simple capillary theory determines the freezing temperature as the point at which the chemical potential of the solid core inside

142 the pore equals that of the surrounding fluid. This leads to the Gibbs-Thomson equation,

Tyb

rib

HA:b

where T:b is the bulk freezing temperature, ?,~,~ and q~,t are the corresponding wall-solid and wall-fluid surface tensions, p is the molar volume of the liquid, AZb is the latent heat of melting in the bulk and H is the pore width. Experiments on freezing that have used porous silica glass as the confinement medium have always resulted in a decrease in the freezing temperature, Tf, as compared to the bulk [1,2]. In a subsequent molecular simulation study of the effect of confinement on freezing of simple fluids in slit pores by .~Iiyahara and Gubbins [3], it was shown that Tf was strongly affected by the strength of the attractive forces between the fluid molecules and the pore walls. For repulsive or weakly attractive potentials, the shift in the freezing temperature AT/ was negative. For strongly attracting walls such as carbons, an increase in T: was observed. Thus. Miyahara and Gubbins explained the disparate experimental trends on the direction of the shift in the freezing temperature and provided the connection to the Gibbs-Thomson equation. The predictions of Miyahara and Gubbins were confirmed by free energy studies, that calculated the thermodynamic freezing temperature in confined systems and established the order of the phase transition [4,5]. Radhakrishnan and co-workers [6] also studied the freezing of CC14 in activated carbon fibers (ACF) of uniform nano-scale structures, using Monte Carlo simulation and differential scanning calorimetry (DSC). Micro-porous activated carbon fibers serve as highly attractive adsorbents for simple non-polar molecules. The DSC experiments verified the predictions about the increase in Tf. and the molecular results were consistent with equation (1) for pore widths in the mesoporous range; they also explained the deviation from the linear behavior in the case of micropores. In this paper we examine the effect of the fluid-wall potential on the free energy surface and the structure of the confined fluid. We make qualitative comparisons between simulated and experimental results, regarding the fluid structure and hysteresis behavior.

2

Methods

Dielectric r e l a x a t i o n spectroscopy" The relative permittivity of a medium. ~* = ~c'- in", is in general a complex quantity whose real part n' (also known as the dielectric constant) is associated with the increase in capacitance due to the introduction of the dielectric. The imaginary component e;" is associated with mechanisms that contribute to energy dissipation in the system, due to viscous damping of the rotational motion of the dipolar molecules in alternating fields. The latter effect is frequency dependent. The experimental setup consisted of a parallel plate capacitor of empty capacitance Co = 4.2 pF. The capacitance, C. and the tangent loss. tan(6), of the capacitor filled with nitrobenzene between the plates were measured using a Solartron 1260 gain impedance analyzer, in the frequency range 1 Hz - 10 XIHz. for various temperatures. For the case of nitrobenzene in porous silica, the sample was introduced between the capacitor plates

143 as a suspension of 200 #m mesh porous silica particles in pure nitrobenzene. ~,=

C . ~,, _ tan(5)

(2)

In equation (2), C is the capacitance, Co is the capacitance without the dielectric and is the angle by which current leads the voltage. Nitrobenzene was confined in porous silica (CPG and VYCOR), of pore widths H = 50 nm to 4 nm at 1 atm. pressure. The freezing temperature in the bulk is 5.6 ~ (the liquid freezes to a monoclinic crystal). ec* = s ' - i e c " , the complex dielectric permittivity is measured as a function of temperature and frequency. For an isolated dipole rotating under an oscillating electric field in a viscous medium, the Debye dispersion relation is derived using classical mechanics,

I

t

ec* = s " + ~" - ~ 1 + icon-

(3)

The dielectric constant is a natural choice of order parameter to study freezing of dipolar liquids, because of the large change in the orientational polarizability between the liquid and solid phases. The dielectric relaxation time was calculated by fitting the dispersion spectrum of the complex permittivity near resonance to the Debye model of orientational relaxation. In the Debye dispersion relation (equation (3)), w is the frequency of the applied potential and T is the orientational (rotational) relaxation time of a dipolar molecule. The subscript s refers to static permittivity (low frequency limit, when the dipoles have sufficient time to be in phase with the applied field). The subscript oc refers to the optical permittivity (high frequency limit) and is a measure of the induced component of the permittivity.

Simulation: We performed GCMC simulations of Lennard-Jones methane adsorbed in regular slit shaped pores of pore width H = 7.5c~ff and varying fluid-wall strengths. Here H is the distance separating the planes through the centers of the surface-layer carbon atoms on opposing pore walls. The interaction between the adsorbed fluid molecules is modeled using the Lennard-Jones (12,6) potential with size and energy parameters chosen to describe methane (crff = 0.381 nm, e i : / k B = 148.1 K). The fluid-wall interaction is modeled using a "10-4-3" Steele potential [8],

~)fw(Z) =

2 [~ (O'f__.___~w) 10 -- (O'f.___~w) 4 -- ( Cr}w )] 2~p~c:~of~.A z z 3A(z + 0.61A) 3

(4)

Here, the cr's and e's are the size and energy parameters in the LJ potential, the subscripts f and w denote fluid and wall respectively, z is the coordinate perpendicular to the pore walls and kB is the Boltzmann's constant. The fluid-wall interaction energy parameters corresponding to a graphite pore were taken from Ref. [8]. For a given pore width H, the total potential energy from both walls is given by, =

+

-

(5)

The strength of the fluid wall interaction is determined by the parameter a = 27rpw~fwa~wA.

144

1 2 3

Model

Type

c~

Purely repulsive Weakly attractive Strongly attractive

Hard wall Silica wall Graphite wall

0 0.76 2.0

The simulation runs were performed in the grand canonical ensemble, fixing the chemical potential #, the volume V of the pore and the temperature T. The system typically consisted of 600-700 adsorbed molecules. For the case of attractive pore-wall interaction. the adsorbed molecules formed seven layers parallel to the plane of the pore walls. A rectilinear simulation cell of lOo.:ff by lOof.f in the plane parallel to the pore walls was used, consistent with a cutoff of 5oi. 1, for the fluid-fluid interaction. The simulation was set up such that insertion, deletion and displacement moves were attempted with equal probability, and the displacement step was adjusted to have a 50% probability of acceptance. Thermodynamic properties were averaged over 100-500 million individual Monte Carlo steps. The length of the simulation was adjusted such that a minimum of fifty times the average number of particles in the system would be inserted and deleted during a single simulation run. F r e e e n e r g y m e t h o d : The method relies on the calculation of the Landau free energy as a function of an effective bond orientational order parameter ~, using GCMC simulations [5]. The Landau free energy is defined by,

A[~] = -kBr ln(P[~]) + constant

(6)

where P[~] is the probability of observing the system having an order parameter value between ~ and (I)+ 5(I). The probability distribution function P[~] is calculated in a GCMC simulation as a histogram, with the help of umbrella sampling. The grand free energy t2 is then related to the Landau free energy by exp(-/~)

f d~ e x p ( - ~ a [ ~ ] )

(7)

The grand free energy at a particular temperature can be calculated by numerically integrating equation (7) over the order parameter space. We use a two-dimensional order parameter to characterize the order in each of the molecular layers. 1

Nb

~bb E exp(/60k) = [(exp(i6Ok))j] (8) k=l 9j measures the hexagonal bond order within each layer j. Each nearest neighbor bond has a particular orientation in the plane of the given layer, and is described by the polar coordinate 0. The index k runs over the total number of nearest neighbor bonds Nb in layer j. The overall order parameter 9 is an average of the hexagonal order in all the layers. We expect ~j = 0 when layer j has the structure of a two-dimensional liquid, 9j = 1 in the crystal phase and 0 < ~j < 1 in a orientationally ordered layer. ~J =

145

3

Results

D i e l e c t r i c s p e c t r o s c o p y : The capacitance C and tangent loss tan(d) were measured as a function of frequency and temperature for bulk nitrobenzene and for nitrobenzene adsorbed in CPG and Vycor glass of different pore sizes ranging from 50 nm to 4.0 nm. The typical behavior of ~' vs. T is shown in Figure l(a). For pure, bulk nitrobenzene, there was a sharp increase in ~' at T = 5.6 ~ corresponding to the melting point of the pure substance. For nitrobenzene confined in CPG, the sample is introduced as a suspension of nitrobenzene filled CPG particles in pure nitrobenzene, between the capacitor plates. Thus capacitance measurement yielded an effective value of the relative permittivity of the suspension of CPG in pure nitrobenzene. Thus ec' showed two sudden changes. The increase that depended on pore size was attributed to melting in the pores, while the increase at 5.6 ~ corresponded to the bulk melting [7]. The shifts in the melting temperature are plotted against the reciprocal pore width in Figure l(b) for nitrobenzene in CPG obtained using both DSC and dielectric spectroscopy (DS) measurements. The deviations from linearity, and hence from the Gibbs-Thomson equation are appreciable at pore widths as small as 4.0 nm. 35.0

25 n m p o r e 30.0

- ~ 25.0

'

i

O

,

i

20.0

15.0 -10.0

9

'

a

il .

9Dielectric Method 9DSC

; " " *-" ~-" % ' ~ - - - ' ,

co =1 M H z

1

q

,

-100

E -200

i -5.0

0.0

5.0 -3o O 00

(~)

9

T/~

(b)

010

H-'

nm

9,20

0 3o

F i g u r e 1. (a) Relative permittivity, s', as a function of temperature, showing melting and freezing along with the hysteresis. (b) Shift in the melting temperature AT,~ as a function of 1/H for nitrobenzene in CPG. The linear behavior is consistent with the Gibbs-Thomson equation. The spectrum of the complex permittivity (ec', s" vs. a~) is fit to the dispersion relation (equation (3)), to determine the dielectric relaxation time 7-, which gives valuable information about the structure of the condensed phase. The frequency range in this study is expected to encompass the resonant frequencies corresponding to the dielectric relaxation in the solid phases. To probe the liquid relaxation behavior would require a frequency range that is 4 to 5 orders of magnitude higher. The spectrum plots for nitrobenze in a 7.5 nm CPG at temperatures below the freezing temperature in the pore show a Debye type relaxation with a single time scale that is estimated to be ~- = 1.44 ms. At temperatures above the pore melting temperature, (e.g., see Figure 2 at T = - 4 ~ the behavior

146 is significantly different. From the double peak structure of the ~"(~o) and the double inflection in the ~'(co) curve, two different dielectric relaxation times are calculated. There is a shorter relaxation time 71 = 43.6 #s, in addition to the longer component T2 = 1.7 ms. The longer component relaxation, r2 = 1.7 ms, is attributed to the bulk crystalline phase of nitrobenzene. The shorter relaxation component, rl = 43.6 #s, is attributed to the molecular dynamics of the contact layer. 300

9

K"

K'

A

." 0o4 o

~~

9

,m

i . . . . . . . . .

-20

.

A

-

r

Phase

rl ~ 1.0 ms r2 ~ 10.0 #s

Crystal phase Contact layer (liquid) Not measured here

Tliquid

,'~

10-9S

=...- ="= i

O0

Ioglo (co / kHz)

" --- n=- _ m 20

9

9

9

40

F i g u r e 2. Spectrum plot for nitrobenzene in a 7.5 nm pore at T = - 4 ~ this plot yields two distinct dielectric absorption regions. The solid and the dashed curves are fits to the Debye dispersion relation. Simulation: The Landau free energy calculations showed that for the case of the hard walled and the silica walled pores, the freezing temperature in the pore was depressed compared to the bulk, while for the case of the graphite wall freezing temperature in the pore was greater than in the bulk [9]. This behavior is consistent with the trends observed in the literature and the Gibbs-Thomson equation. For the case of a hard wall pore, the confined system exists as either a liquid or a solid. For a weakly attractive pore that mimicks the silica interaction, the free energy surface in Figure 3(a) shows the presence of three phases. Phase A is the liquid phase and Phase C is the crystal phase. An intermediate phase B also exists, whose structure is plotted in Figure 3(b). The plots represent two-dimensional, in-plane pair correlation functions in each of the molecular layers. The pair correlation function of the contact layer (the layer adjacent to the pore walls) is isotropic, representing a liquid-like layer while the pair correlation functions for the inner layers show a broken translational symmetry corresponding to a 2-d crystalline phase; for this system the contact layers freeze at a temperature below that of the inner layers. For a strongly attractive pore such as graphite, the free energy surface in Figure 4(a) also shows the presence of three phases. Phase A is the liquid phase and Phase C is the crystal phase. In this case the intermediate phase B has a different structure that is plotted in Figure 4(b); for this system the contact layers are crystalline while the inner layers are liquid-like. The contact layers freeze at a temperature higher than that of the inner layers.

147

The Landau free energy surfaces provide clear evidence of the existence of a contact layer with different structural properties compared to the pore interior, thereby supporting the experimental observation. The nature of the contact layer phase depends on the strength of the fluid-wall potential. For purely repulsive or mildly attractive pore-walls, the contact layer phase exists only as a metastable phase. As the strength of the fluidwall attraction is increased, the contact layer phase becomes thermodynamically stable. Like the direction of shift in the freezing temperature, the structure of the contact layer phase also depends on the strength of the fluid wall interaction (i.e., whether the contact layer freezes before or after the rest of the inner layers).

C

15

-~ 10

5

A

0.0

B

0.2

0.4

2O

0.6

0%

0.8

(a)

1o r/nm

(b)

2o

I

F i g u r e 3. (a) The Landau free energy for methane confined in a model silica pore. The three minima correspond to three different phases. (b) The structure of phase B, showing that the contact layer is a fluid while the inner layers are frozen. 80

T=118K 60

Contact Layer

[-. ~40

'~ 20.0

< 100

o%0

02

I

2O

A

04

(~

06

08

0

00 ~

_.

0

.

05

r/nr~

15

(b) F i g u r e 4. (a) The Landau free energy for methane confined in a model graphite pore. (b) The structure of phase B showing that the contact layer is frozen, while the inner layers remain fluid-like.

148

H y s t e r e s i s : Figure l(a) shows n' vs. T during melting and freezing and the hysteresis behavior in a 25 nm pore. The melting branch shows a step at T = 0 ~ that is consistent with the melting of the contact layer. The second step at T = 1 ~ corresponds to the melting of the inner layers in the pore, (a third increase at T = 5.6 ~ corresponding to the bulk melting, is outside the range of the plot [7]). This behavior is consistent with the presence of the intermediate phase B with liquid-like contact layer: however, such a step is absent in the freezing branch. The asymmerty in the hysteresis behavior is explained by the Landau free energy curves. During melting, the system starts from the local minimum corresponding to the crystal phase in Figure 5(a), rolls over the barrier and gets trapped in the global minimum corresponding to the molten contact layer phase (this process is schematically represented by the arrow). The system jumps to the liquid phase at a lower temperature when the liquid phase becomes the thermodynamically stable phase. When the liquid freezes, however, the system starts at the local minimum corresponding to the liquid phase in Figure 5(b); as the system jumps over the barrier, it rides over the metastable minimum of the intermediate phase and gets trapped directly in the crystal phase. The behavior of the simple slit pore model is consistent with the real experimental system, which also suggests that the hysteresis behavior is due to metastable phases rather than kinetic factors.

15

25

[-,

20

"i

g" 5

0.0

0.2

0.4

(a)

.... 0.6

~

.

0.8

0.0

L

0.2

,

1

0.4

0.6

(b)

F i g u r e 5. Landau free energy for methane in silica pore; (a) at 86 K, a temperature close to that where the crystal becomes unstable on heating; (b) at 80 K, a temperature close to that where the liquid phase becomes unstable on cooling.

4

Conclusions

The melting point of nitrobenzene in the pore is always depressed. The linear relationship between the shift in the pore melting temperature and the inverse pore diameter is consistent with the Gibbs-Thomson equation for larger pore sizes . The deviations from linearity, and hence from the Gibbs-Thomson equation are appreciable at pore widths as small as 4.0 nm. The quantitative estimates of the rotational relaxation times in the fluid and crystal phases of confined nitrobenzene support the existence of a contact layer with dynamic and structural properties different than the inner layers. The Landau free

149 energy calculation for the simple model that mimicked the weak silica wall interaction confirmed the existence of such a contact layer with different structural properties. The Gibbs-Thomson equation is valid when the effect of the contact layers are negligible on the inner layers. When the number of inner layers are comparable with the number of contact layers, a deviation from linear behavior (G-T regime) is observed. The freezing temperature in the "non-linear" regime is influenced by the freezing of the contact layers [6]. A systematic study of the influence of the strength of the fluid-wall interaction parameter c~ revealed that, for c~ < 0.5, the intermediate phase B remains metastable for all temperatures. For the range 0.5 < c~ < 1.2, phase B becomes thermodynamically stable with the contact layer freezing at a temperature below that of the inner layers and for c~ > 1.6, phase B becomes thermodynamically stable with the contact layer freezing at a temperature above that of the the inner layers [9]. The comparison of the hysteresis behavior in simulation and experiment, shows that the hysteresis is mainly due to the existence of metastable states rather than due to kinetic effects. The asymmetry in the freezing and melting branches of the adsorption curve is explained based on the Landau free energy surfaces. The Landau free energy approach is a powerful tool in determining the freezing temperature, nature of the phase transition, structure of the confined phases, existence of metastable states and origin of the hysteresis behavior. Efforts are underway to use more realistic fluid potentials and pore models in the simulation. Recently Gelb and Gubbins [10] proposed a novel mechanism to realistically model porous silica glasses using spinodal decomposition of a binary fluid mixture in the two-phase liquid-liquid region. This model is known to closely represent the actual pore size distribution of real porous silica, and incorporates complex pore networking. We plan to study freezing of simple fluids using the free energy method in such a pore model, and to quantitatively compare with the experimental results for CC14 in CPG. It is a pleasure to thank Katsumi Kaneko for helpful discussions. R.R thanks Adama Mickiewicz University, Poznan, Poland for their hospitality during a visit in the summer of 1998, when this work was carried out. This work was supported by grants from the National Science Foundation (Grant No. CTS-9896195) and KBN (Grant No. 2 PO3B 175 08), and by a grant from the U.S.-Poland Maria Sklodowska-Curie Joint fund (grant no. MEN/DOE-97-314). Supercomputer time was provided under a NSF/NRAC grant (MCA93S011).

5

References 1. Warnock J., Awschalom D.D., M.W. Shafer, Phys. Rev. Lett., 1986, 57(14), 1753. 2. Unruh K.M., Huber T.E., Huber C.A., Phys. Rev. B, 1993, 48(12), 9021. 3. Miyahara M., Gubbins K.E., J. Chem. Phys., 1997, 106(7), 2865. 4. Dominguez H., Allen M.P., Evans R., Mol. Phys., 1999, 96, 209. 5. Radhakrishnan R., Gubbins K.E., Mol. Phys., 1999, 96, 1249.

150 6. Radhakrishnan R, Gubbins KE, Watanabe A, Kaneko K, 1999, submitted to J. Chem. Phys. 7. Sliwinska-Bartkowiak M., Gras J.. Sikorski R., Radhakrishnan R., Gelb L.D. and Gubbins K.E., Langmuir, 1999 (in press). 8. W.A. Steele, 1973, Surf. Sci. 36, 317. 9. Radhakrishnan R, Gubbins KE, M. Sliwinska-Bartkowiak, 1999, to be submitted to J. Chem. Phys. 10. Gelb L.D., Gubbins K.E., Langmuir, 1998, 14, 2097.

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScienceB.V. All rightsreserved.

151

A f a s t t w o - p o i n t m e t h o d for g a s a d s o r p t i o n m e a s u r e m e n t s J o h a n n e s A. Poulis a, Carel H. Massen", Erich R o b e n s b, Klaus K. U n g e r b "Faculty of Technical Physics, Technical University E i n d h o v e n , P o s t b u s 513, N L - 5 6 0 0 MB E i n d h o v e n , The N e t h e r l a n d s N n s t i t u t ffir A n o r g a n i s c h e u n d Analytische C h e m i e d e r J o h a n n e s Gutenberg-Universitgtt, D - 5 5 0 9 9 Mainz, G e r m a n y

In m a n y c a s e s the m e a s u r e m e n t time of g a s a d s o r p t i o n after a p r e s s u r e c h a n g e of the sorptive c a n be r e d u c e d s u b s t a n t i a l l y by m e a s u r i n g only two p o i n t s in the initial p a r t of the kinetic curve a n d e x t r a p o l a t i o n of the e q u i l i b r i u m value. The m e t h o d is useful in the case of very slow a d s o r p t i o n p r o c e s s e s a n d for the stepwise m e a s u r e m e n t of i s o t h e r m s .

I.

INTRODUCTION

The d e t e r m i n a t i o n of the a d s o r p t i o n of g a s e s on solids c a n be a time c o n s u m i n g m a t t e r . Already in 1969 Jgmtti I s u g g e s t e d to m e a s u r e t h r e e p o i n t s of the initial c o u r s e of the kinetic a d s o r p t i o n curve a n d to e x t r a p o l a t e the e q u i l i b r i u m value (3PM). W h e n the specific m o l e c u l a r model of the a d s o r p t i o n of a g a s on a solid s u r f a c e is k n o w n a n d w h e n it c a n be expected t h a t only one kind of a d s o r p t i o n is at stake, this m e t h o d delivers good r e s u l t s a n d allows a very fast stepwise m e a s u r e m e n t of a d s o r p t i o n i s o t h e r m s 2. As a variation we d i s c u s s in the p r e s e n t p a p e r a n even s i m p l e r p r o c e d u r e w h e r e we m a k e u s e of only two m e a s u r e d p o i n t s (2PM). In o u r p a p e r we c o m p a r e both m e t h o d s a n d we a s s e s s the a c c o m p a n i e d i n c r e a s e of m e a s u r e m e n t i n a c c u r a c y . T h o u g h the following a p p r o a c h is b a s e d on gravimetric m e a s u r e m e n t s it is valid likewise for a n y o t h e r m e a s u r i n g m e t h o d e.g. the v o l u m e t r i c one.

2.

THE TWO-POINT METHOD

We s t a r t from a n e q u a t i o n w h i c h c h a r a c t e r i s e s the e x p o n e n t i a l p r o g r e s s i o n of a d s o r p t i o n :

m(t)= m.o(1-e -~!~)

(1)

We i n t e n d to e x t r a p o l a t e in o r d e r to o b t a i n the e q u i l i b r i u m value m, after a c h a n g e of the sorptive p r e s s u r e from two m e a s u r e m e n t s at t i m e s t~, t2 a n d we r e a d m~ a n d m2, respectively. The r e s u l t s of the two m e a s u r e m e n t s :

152

(/1, "71) and (t 2, m2) we u s e into eq. (1). We t h a n deal with two e q u a t i o n s a n d two u n k n o w n s . B e c a u s e of the n o n - l i n e a r c h a r a c t e r of t h e s e e q u a t i o n s , the solving d e m a n d s a careful a p p r o a c h . R e n a m i n g m = y and r - x yields for the first m e a s u r i n g point: m~=y l-e;x For t~

4oo 300 20O

loo 0

0,00

9

'

0,20

9

I

0,40

--.o---

adsorption

~

desorption

,

I

0,60

relative pressure

a,,,

I

0,80

,

1 O0

P/P0

Figure 3. Nitrogen sorption isotherms of a calcined silica sample (open circles 9 adsorption, open squares 9desorption), particle size 91.8 l~un, template 9 n-hexadecylamine. A linear increase of absorbate at low relative pressures is followed by a steep increase in nitrogen u p t a k e at a relative pressure p/p0 = 0.25-0.35, which is due to capillary condensation in the mesopore system. The fully reversible isotherm can be classified as a type IV isotherm according to the IUPAC n o m e n c l a t u r e which is typical for mesoporous materials. Scanning electron micrographs given in figure 4 demonstrate the wide size range in which these particles can be prepared.

particle size : 500 nm.

Figure 4b. Scanning electron microscope images of silica spheres, average particle size : 1.0 pm.

Figure 4c. Scmn w c ~ r n nmicroscope images of silica spheres, average particle size : 2.3 +I. One of of the the disadvantages disadvantages of of the the synthesis synthesis was was that that the the silicas silicas had had pores pores in in the the One 2 and 4 nm. In adsorption and chromatographic low mesopore size range between low mesopore size range between 2 and 4 nm. In adsorption and chromatographic processes however however larger larger mesopores mesopores are are needed needed to to avoid avoid size size exclusion exclusion effects. effects. processes

161 The enlargement of pores is achieved by a hydrothermal aftertreatment which is performed in the presence of water at elevated temperatures where the pH can be adjusted from 1 to 10 (15-17). The aim of the hydrothermal aftertreatment is to shift the pore size distribution symmetrically to larger pores. It is mandatory that the particle morphology is maintained. Another more economic route is to use appropriate templates which allow adjusting the pore diameter during the synthesis without carrying out a posttreatment (18). 4.

D E N O V O D E S I G N OF O R D E R E D M E S O P O R O U S S I L I C A S

In the following part the most decisive synthesis parameters and their influence the particle and pore structural properties of the silica beads are described. 4.1. I n f l u e n c e o f t h e s i l i c a p r e c u r s o r

Different n-alkoxysilanes with increasing hydrophobicity were employed as silica precursors. The porosity parameters as determined by nitrogen sorption measurements are summarised in table 2. Table 2 Influence of the silica precursor on the porosity of the silica particles silica precursor

spec. surface area [m2/g]

spec. pore volume [cm3/g]

avg. pore diameter [nm]

tetramethoxysilane

664

0.59

2.5

tetraethoxysilane

787

0.63

2.4

tetra-n-propoxysilane

710

0.65

2.6

It is obvious that the influence of the silica precursor on the porosity is not very pronounced. All porosity parameters remain at approximately the same values for the different silica precursors. Table 3 Influence of the silica precursor on the morphology of the silica particles silica precursor

morphology

dp (min) [nml

dp (max) [nm]

dp (avg.)

tetramethoxysilane

spherical

300

400

350

tetraethoxysilane

spherical

1300

1600

1500

tetra-n-propoxysilane

spherical

1600

2200

2000

[nm]

A more pronounced effect on the morphology of the resulting silica particles can be observed when different silica precursors are used. With longer chain lengths of the alkoxygroups in the silica precursor the average particles increases significantly. Simultaneously the polydispersity of the particle size distribution

162

increases. This may originate from the formation of an emulsion in the first stage of the reaction as the solubility of the silica precursors decreases rapidly.

4.2. I n f l u e n c e of t h e w a t e r / 2 - p r o p a n o l r a t i o The influence of the water/2-propanol on the pore structure of the resulting silica beads is summarised in table 4. The specific surface area and specific pore volume reach a m a x i m u m at a water/2-propanol of 4.38 while the average pore diameter increases further. Table 4 Influence of the water/2-propanol ratio on the porosity r(water/2-PrOH) [mol/mol]

spec. surface area [m2/g]

spec. pore volume [cm3/g]

2.22

19

0.03

E c

avg. pore diameter [nm]

3.15

163

0.18

2.67

4.38

741

0.79

2.88

6.10

551

0.49

2.86

8.69

517

0.47

3.46

6000

I I

5000

E

4000

:-~

3000

o

2000

Q.

1000

~

o

spherical

irregular

,

.

1

2

3

4

.

.

.

5

6

ratio 2-propanol/water [mol/mol]

Figure 5. Influence of the water/2-propanol ratio on the morphology. Below a water/2-propanol ratio of 4.0 spherical particles are obtained. The particle diameter increases for higher water contents of the reaction mixture. For higher w a t e r contents only irregularly shaped particles could be obtained while the average particle diameter still increases.

4.3. I n f l u e n c e o f t h e r e a c t i o n t e m p e r a t u r e The easiest way to adjust the particle size without changing the composition of the reaction mixture is the precise control of the reaction conditions during the

163

formation of the particles. Increasing reaction temperature leads to the formation of smaller particles. However, for a given reaction mixture composition there is a limiting temperature below which only irregularly shaped particles are formed. '-~" 2000

.c. 1500

E looo

.___

"- 500 o3 c~ >

0

lo

" 1's

" to

" 2'5

" i o

" 3'5

,

" 4o

9

,

9

,

50

45

9

55

reaction temperature [~

Figure 6. Influence of the reaction temperature on the morphology.

4.4. H y d r o t h e r m a l a f t e r t r e a t m e n t Hydrothermal treatment of the reaction mixture allows enlargement of the pore system. Typical nitrogen isotherms are shown in figure 7. 700

e,)

o

600

---

after treatment I

500 09

400

:3

300

"~

200

"~

100

o

"0

9

0,00

!

.

0,20

i

0,40

!

I

0,60

!

I

0,80

.

1,00

relative pressure P/Po Figure 7. Nitrogen sorption isotherms of silicas beads before (squares) and after (triangles) hydrothermal treatment, duration" 24 h, temperature" 110 ~ particle size" 1.8 pm. The isotherms clearly indicate that the pore system distribution is shifted towards higher pore diameter without losing the relatively narrow pore size distribution. Scanning electron micrographs prove that the particle morphology remains unchanged during the treatment. After hydrothermal aftertreatment the surface can be modified with eg. noctadecyldimethylchlorosilane to make the surface hydrophobic. These so-called reversed-phase materials are widely employed in HPLC and CEC.

164

Table 5 Pore strucural properties before and after hydrothermal t r e a t m e n t spec. surface area [m2/g]

spec. pore volume [cm3/g]

avg. pore diameter [nm]

untreated

posttreatment

untreated

posttreatmen.t

untreated

posttreatment

717

411

0.59

0.94

2.4

6.7

4.5. Controlled agglomeration by spray drying A representative scanning electron micrograph is shown in Figure 8.

Figure 8. Scanning electron micrograph of agglomerates obtained by spraydrying, size of the primary particles : 200-300 nm. The agglomeration of the primary particles creates a secondary pore system which adds to the pore system of the primary particles. These agglomerated particles could be applied in preparative chromatography. The size of the agglomerates can be adjusted between 2 and 20 nm by changing various p a r a m e t e r s such as flow rate of the silica suspension and the diameter of the jet nozzle. 5.

C O N C L U S I O N AND P E R S P E C T I V E S

The hydrolysis and condensation of tetra-n-alkoxysilanes in the presence of nalkylamines as templates is a versatile method for the preparation of spherical silica beads in the submicrometer and micrometer size range. The morphological and pore structural properties of the products can be independently controlled by adjusting various synthesis parameters. This allows precise tailoring of all properties for special application environments. F u r t h e r advantages of this synthesis route are a high ruggedness combined with excellent upscaling possibilities. These materials are promising adsorbents in various chromatographic and separation processes as well in catalytic applications.

16~

6.

REFERENCES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Ferch, H in ,,The Colloid Chemistry of Silica", Advances in Chemistry, series 234, ed. H.E. Bergna, ACS, Washington, DC, 1994. K.K. Unger ,,Packings and Stationary Phases in chromatographic separation techniques", M. Dekker, New York 1989. K.K. Unger, K.D. Lork and H.J. Wirth in ,,HPLC of Proteins, Peptides and Polynucleotides", VCH Weinheim, 1991, p. 59. A.I. Liapis and K.K. Unger in ,,Highly Selective Separations in Biotechnology", ed. G. Street, Blackie Academic & Professional, London, 1994. R. Ditz, Merck KGaA, SLP Products, Darmstadt, oral communication. M. Grfin, D. Kumar, K.K. Unger, in preparation. J.S. Beck, J.C. Vartuli, W.J. Roth, M.E. Leonowicz, C.T. Kresge, K.D. Schmitt, C.T-W. Chu, D.H. Olson, E.W. Sheppard, S.B. McCullen, J.B. Higgins, J.L. Schlenker, J. Am. Chem. Soc., 114 (1992) 10834. D. Zhao, J. Feng, Q. Huo, N. Melosh, G.H. Frederickson, B.F. Chmelka, G.D. Stucky, Science, 279 (1998) 548. Q. Huo, J. Feng, F. Schfith, G.D. Stucky, Chem. Mater., 9 (1997) 14. P.T. Tanev, M. Chibwe, T.J. Pinnavaia, Nature, 368 (1994) 321. P.T. Tanev, T.J. Pinnavaia, Science, 267 (1995), 865. P.T. Tanev, T.J. Pinnavaia, Chem. Mater., 8 (1996) 2068. P.T. Tanev, T.J. Pinnavaia, Science, 271 (1996), 1267. W. StSber, A. Fink, E. Bohn, J. Colloid Interface Sci., 26 (1968) 62. M. Kruk, M. Jaroniec, A. Sayari, J. Phys. Chem. B, 103 (1999) 4590. M. Kruk, M. Jaroniec, A. Sayari, J. Phys. Chem. B, 101 (1997) 583. A. Sayari, P. Liu, M. Kruk, M. Jaroniec, Chem. Mat., 9 (1997) 2499. K. Schumacher, S. Renker, K.K. Unger, to be published.

This Page Intentionally Left Blank

Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 9 2000 Elsevier Science B.V. All rights reserved.

Relationship between intrinsic pore-wall corrugation h y s t e r e s i s of N2, 02, a n d A r o n r e g u l a r m e s o p o r e s

167

and adsorption

S. Inoue, t H. Tanaka, * Y. Hanzawa, t S. Inagaki, ~Y. Fukushima, * G.Btichel, ~ K. K. Unger, ~, A.Matsumoto ~, and K. Kaneko t *Physical Chemistry, Material Science, Graduate School of Natural Science and Technology, Chiba University, l-33 Yayoi, Inage, Chiba 263, J a p a n *Toyota Central R&D Labs. Inc., Yokomichi, Nagakute, Aichi, 480-11, J a p a n ~Institute for Inorg. Chem. Anal. Chem. Johannes Giitenberg Univ.D-6500,Mainz, Germany The effects of the pore width on the hysteresis of the adsorption isotherm of N2, O~., and Ar on mesoporous silica at 77 K were examined. A new analysis for the adsorption hysteresis was developed using the Saam-Cole theory. The critical thickness difference Ale (= lc - le) for adsorbed film, which was derived from this analysis, was associated with the intrinsic mesopore width distribution due to the surface corrugation, giving the theoretical dependence of the adsorption hysteresis on the pore width and adsorbate; the critical pore width for N2 is about 4 nm and those for 02 and Ar are about 3 nm, agreeing with the experimental results. 1. Introduction Porous solids having a regular pore structure have gathered much attention in the fields of chemistry and physics[l-7]. Those solids are expected to elucidate the interaction of gas with pores from the microscopic level. IUPAC classified pores into micropores, mesopores, and macropores using pore width w ( micropores : w < 2nm, mesopores : 2 nm < w< 50 nm, and macropores: w> 50 nm)[8]. Physical adsorption occurs by the mechanism inherent to the pore width. Vapor is adsorbed on the mesopore wall by multilayer adsorption in the low pressure range and then vapor is condensed in the mesopore space below the saturated vapor pressure To. This is so called capillary condensation. Capillary condensation has been explained by the Kelvin equation given by eq. (1).

ln(P/Po) =

- (2 y V m c o s 0 ) / (r m RT).

(1)

Here, the mean radius r m of curvature of the meniscus of the condensate in a pore is associated with the vapor pressure P of the condensate. ~/ and Vm are the surface tension and molar volume of the condensate; 0 is the contact angle (0 has

168 " been believed to be nearly zero). As P is smaller t h a n P0, vapors condense in mesopores even below Po- The Kelvin equation determines the condensation (Pc) and evaporation (P~) pressures which are governed by r m. When Pc and P~ are different from each other due to the different r m values for the meniscus on condensation and evaporation, adsorption and desorption branches do not overlap each other to give an adsorption hysteresis. This classical capillary condensation theory predicts that an adsorption isotherm of N,) on cylindrical mesopores being open at both ends has a clear adsorption hysteresis of IUPAC H119,10]. Recently silica having regular cylindrical mesopores was synthesized by two groups using different methods[2,3]. This mesoporous silica has a honeycomb structure of cylindrical straight mesopores whose long range order leads to an explicit X-ray diffraction in a low diffraction angle region. High resolution electron microscopic observation gives an evidence for the regular pore structure. Many physical adsorption studies on the regular mesoporous silica have been actively done[ll-18]. Branton et al stressed at first the absence of the adsorption hysteresis in N., adsorption isotherm on mesoporous silica at 77 K[ll]. Later It was shown that the presence of the adsorption hysteresis loop depends on the pore width and the adsorbate. Llewellyn et al[12] reported that the adsorption isotherm at 77 K for mesopores of w > 4 nm has an adsorption hysteresis. The dependence of the adsorption hysteresis on the pore width was also studied by the density functional theory[14]. The pore width dependence of the adsorption hysteresis on the adsorbate was reviewed by Sonwane et al[18]; the critical pore widths near 77 K are 4.0~4.5 nm for N,., and 2 . 5 - 3 n m for Ar. The effect of the pore width on the adsorption hysteresis is one of essential subjects in adsorption science. Then, we need to u n d e r s t a n d more sufficiently the adsorption hysteresis p h e n o m e n a in mesopores. In this work, we measured the dependence of the adsorption hysteresis on the pore width of mesoporous silica for N,2, O,,, and Ar at 77 K. The Saam-Cole analysis was extended to the examination of the hysteresis problem and the cause for the difference of the pore-width dependence of the hysteresis was associated with the corrugation of the pore-walls. 2. ANALYTICAL APPROACH The Kelvin equation takes into account molecule/solid and intermolecular interactions using contact angle and surface tension, respectively. However, the Kelvin approach is not appropriate for description of adsorption on small mesopores. Saam and Cole developed the thermodynamic theory with the average molecular potential for liquid helium in a cylindrical pore in order to u n d e r s t a n d u n u s u a l properties of liquid helium[19,20]. Findenegg et al have applied the Saam-Cole theory to elucidate fluid p h e n o m e n a near the critical temperature[21]. The Saam-Cole theory includes the molecule/solid interaction in a form of the sum of the dispersion pair interactions. The Saam-Cole theory is fit for description of adsorption phenomena in regular mesopores[22]. The extended Saam-Cole analysis is as follows. The chemical potential change of a

169 multi-layer adsorbed film thickness l on a flat surface is given by eq.2 [23].

13 .

(2)

where U(/) is the net attractive interaction energy between the adsorbed molecule and surface; a which is experimentally determined by Frenkel-Halsey-Hill Multilayer adsorption (FHH) analysis of the adsorption isotherm, is an interaction parameter depending on the molecule and solid. Figure 1 shows the model of the adsorption state in a cylindrical mesopore whose pore width is R. The symmetrical state in Figure 1 (a) expresses multilayer adsorption, whereas Figure l(b) shows the asymmetrical state due to a partial Capillary condensation capillary condensation. The chemical potential change A~t of the adsorbed Figure 1. Adsorbed model molecules in the cylindrical pore is generally described by the summation of the gas/solid surface (A/~g~) and the interfacial (Afli) chemical potential terms.

I

R

A/u = A/~gs + A/uj

(3)

Here Apg~ is expressed by eq.2. Ap, depends on the shape of the meniscus in the pore. For the transformation of multilayer adsorption to capillary condensation, Ag, is given by -yV,/a, where y and V,,, denote the surface tension and molar volume of the condensate; a = R - ]. Hence, the chemical potential change of the multilayer adsorbed state, Ags, is expressed by eq.4. c~

yV,,,

(4) .

07

< 0 the adsorbed film grows. '

In the case of

d

becomes unfavorable, giving rise to the capillary condensation.

> 0, the film growth Hence, (A~I~") = 0 \

-

-

/

determines the critical thickness lc from the multilayer to condensation transformation. On the other hand, the chemical potential of the condensation state (Apa) for the condensation to multilayer transformation is given by

170

A/z. : -

a (R_a)~

This is because condensate is

(5)

2rL, a

the r a d i u s of the m e a n c u r v a t u r e of the m e n i s c u s of the different from that of the multilayer-to-condensation

t r a n s f o r m a t i o n . Evaporation needs the conditions of ( A d ~ , ) ( A>0. S/~, ) = 0 leads to 07c7 the critical thickness l~ for evaporation. The condensation state transforms into the multilayer one at l = l~. If le = lc, the adsorption isotherm has no adsorption hysteresis. If lc > le, an adsorption hysteresis can be observed. In order to determine the critical thickness difference Ale (= lc- le) , ZI/./s and A/l~ must be calculated as a function of l using the FHH plot of the adsorption isotherm, the pore width, and literature values of 7 and Vm. Both lc and le values can be determined from the top of the A/(~ vs. l and A/4~ vs. l curves. Then, we can examine the relationship between the Al~ value and the adsorption hysteresis with the above analysis, which was reported in the preceding letter[24]. 3. E X P E R I M E N T A L We used both of mesoporous silica so called FSM and MCM-41, and mesoporous silica of a spherical morphology (GB). FSM samples were prepared by Toyota's group, while MCM41 and GB were prepared by the group of Johannes Gfitenberg University. In this article, FSM and GB samples of the different porosity are denoted by the number like FSM1. Their porosities are shown in Table 1. The pore width of used samples is in the range of 2.5 to 4.6 nm. The detailed preparation conditions and pore structures were published on previous journals[25,26]. Table 1. Porosity of m e o s p o r o u s silica s a m p l e s

Pore volume, mlg -~ Surface area, rn"g l Pore width, nm

FSM1 0.56 870 2.5

GB1 0.31 404 3.0

MCM-41 0.74 940 3.2

FSM2 0.92 941 3.4

GB2 0.42 382 4.4

FSM3 0.77 804 4.6

The detailed adsorption isotherms of N2, 02, and Ar on mesoporous samples at 77 K were gravimetrically determined with a computer-aided apparatus. Only the adsorption isotherms of MCM41 were measured volumetrically using a commercial equipment (Quantachrome, Autosorb-1). The desorption branch was measured after the measurement of the adsorption branch and it took 20 min-1 h to reach the desorption equilibrium. The samples were preevacuated at 383 K and 1 mPa for 2 hr prior to the adsorption experiment (the preheating temperature for the volumetric measurement was 423 K). The IR spectra of MCM-41 were m e a s u r e d in vacuo and at the presence of acetonitrile vapor at 303 K with an FT-IR s p e c t r o m e t e r (JASCO FT/IR-550) after p r e - e v a c u a t i o n at conditions similar to t h a t for a d s o r p t i o n m e a s u r e m e n t [ 2 7 ] .

171

4. RESULTS AND DISCUSSION

4.1. Surface oxygen states 0.5 Figure 2 shows the FT-IR spectra of MCM-41 and MCM-41 with the 1.5 monolayer of acetonitrile adsorbed on the mesopore walls at 303 K. ~= Here, the spectrum of the ~O 1 o,1 acetonitrile adsorbed sample is -0.5 expressed by the difference of *-1 absorption intensities at presence 0.5 and absence of the monolayer of acetonitrile. The sharp peak at 3743 cm ], which is assigned to free 0 3800 3600 3400 3200 3000 hydroxyls, and a very broad peak in the range of 3000 to 3600 cm:, W a v e n u m b e r / c m "l which is assigned to the hydrogenFigure 2. FT-IR spectra of MCM-41. (a) MCM-41 bonded hydroxyls, are observed on in vacuo. (b) MCM-41 with adsorbed acetonitrile the spectrum of MCM-41. When the monolayer of acetonitrile is formed on the mesopore walls, the difference peak of the free surface hydroxyls at 3744 cm" becomes negative, losing free hydroxyls upon the monolayer formation. On the contrary, the broad band increases upon the monolayer formation, suggesting the change of the free state to the perturbed one upon adsorption. As acetonitrile is a polar molecule, the interaction of an acetonitirle molecule with the surface hydroxyls can be sensitively detected. The FSM samples gave similar results. The previous studies also showed the presence of surface hydroxyls on the regular mesoporous silica[28]. Hence the surface oxygen of our mesoporous silica is presumed to be hydroxylated, which should be taken into account on the hysteresis mechanism of the adsorption isotherm. .

.

,,

,

,

,

i

,

,,,

9

,

i

-

-

_

9

'

-

l

4.2. Adsorption isotherms of N2, 02, and Ar Figure 3 shows adsorption isotherms of N,_, on mesoporous silica at 77 K. The amount of adsorption in Fig.3 is reduced using the pore volume W0. The adsorption isotherms of mesoporous silica have a jump in the P/P0 range of 0.2 to 0.5; the P/P0 for the jump shifts to a higher value with the increase of w. These jumps stem from capillary condensation in mesopores. The gradual plateau above the jump comes from multilayer adsorption on the external surface. Adsorption isotherms of MCM-1 and FSM2 have no hysteresis, whereas those of GB and FSM-3 have a clear hysteresis. The adsorption isotherm of FSM1 has a considerably steep increase until P/Po = 0.2 and is reversible. Although the precise critical width for appearance of the adsorption hysteresis cannot be shown in this work, it should be between 3.4 and 4.4 nm, which agrees with the results by Llewellyn et al that the critical pore width is between 4.0 and 4.5 nm[12]. Then, the critical pore width should be around 4 nm.

172

Figure 4 shows the adsorption isotherms of O., on mesoporous silica at 77 K. The amount of adsorption is also reduced using the pore volume W 0 determined by the O,; adsorption. The adsorption isotherms of mesoporous silica have a gradual jump in the P/Po range of 0.2 to 0.5" the P/Po for the jump shifts to a higher value with the increase of w, as well as the N._, adsorption isotherm. The 0.2 adsorption isotherm of FSM1 has a slight hysteresis which should come from the measuring conditions at 77 K. Hence, we presume that FSM1 has no hysteresis. The O,2 adsorption isotherms of GB1 and MCM-41 have a clear hysteresis, whereas

0.5

Figure3. N,_,adsorption isotherms at 77 K. a: MCM-41 b: FSM2 c: GB2 d: FSM3 Solid and open symbols denote adsorption and desorption.

o

0.5

0

0.5

0

0.5

P/P

1

0

/'--

1.0

0.5

f

b

f

d

Figure4. O., adsorption isotherms at 77 K. a: FSM 1 b: GB1 c: MCM-41 d: FSM2 Solid and open symbols denote adsorption and desorption.

0.5

9

o

,

,

i

o.5

,

i

0.5

o

P/P

0

1.0

173 those for N 2 have no hysteresis. Then, the critical width for 0,; adsorption at 77 K is smaller than that for N~.. The critical pore width should be in the range of 2.5 and 3.0 nm. The adsorption isotherms of Ar on mesoporous silica at 77 K were close to those of 02, although the adsorption jump is more gradual than that of 0,2. The critical width of Ar adsorption was similar to that of O,_,. The critical pore width should be in the range of 2.5 and 3.0 nm for Ar, which coincides with the previous results. The above data clearly showed that the adsorption hysteresis depends on both of the pore width and adsorbate. 4.3. Theoretical determination of condensation and evaporation pressures The critical thickness values ]c for condensation and ]e for evaporation can be determined experimentally from the maximum of the chemical potential vs. ] relation using eqs. 4 and 5. The FHH plots were linear below the condensation jump for all isotherms and the determined FHH constant (~ values were used for calculation of the chemical potential energy. The surface tension (8.85 mNm 1) for condensed N2 at 77K was obtained from the value at different temperatures using the K a t a y a m a and Guggenheim equation[29]. The surface tension values of O2 (17.1 mNm ~) and Ar (15.6 mNm 1) at 77 K were used for the calculation for O~ and Ar at 77 K, assuming that the condensation in mesopores is similar to that in the bulk liquid phase. The molar volumes at boiling temperature were used for calculation. Figure 5 shows the chemical potential changes for multilayer adsorption and capillary l -1000 condensation with the progress of the adsorption for 02 "~176176176176 adsorption on FSM2 (w= 3.4 nm). -20OO B o Here, the progress of adsorption 7.~ ** l ~ e is expressed by the thickness of -3000 the adsorbed film under the -o.. assumption that all adsorbed -4000 molecules are participated to the multilayer formation even in the I case of capillary condensation. -5000 The solid line denotes the possible path, whereas the -6000 broken one denotes an 0.6 0.8 1 1.2 1.4 1.6 1.8 0.4 impossible path. Adsorption l/nm proceeds along the allowed multilayer adsorption path from left to right and reaches an Figure 5. Chemicalpotential changes of multienergy maximum at ]c, layer adsorption and condensation models with thickness of physisorbed layer (02/FSM2). tr ans fe rring anot he r condensation path whose energy r

_

_

l

I

t

I

I

_

I

174 is lower t h a n t h a t of the multi-layer adsorption. This expresses the transition from the m u l t i l a y e r adsorption to capillary condensation in the direction of adsorption. On the other hand, the desorption course should p u r s u e a trail different from the adsorption. The energy m a x i m u m point ]e of the condensation curve is not the same as the transition point ]c from the m u l t i l a y e r adsorption curve to the condensed one. Hence, the s u b s t a n t i a l difference b e t w e e n ]~ and ]e should give rise to a clear adsorption hysteresis, because the different values of ]c and ]e indicates t h a t Pc and P~ are different from each other. Here the difference of ]~ and ]~ is expressed by the critical thickness difference A]c. The critical thickness difference h]~ was d e t e r m i n e d using the chemical potential vs. ] plot for all adsorption isotherms, as shown in Table 2. 4.4. Adsorption hysteresis d i s a p p e a r a n c e due to the pore-wall corrugation Table 2 clearly shows an critical value for presence and absence of the adsorption hysteresis. The critical b o u n d a r y value is different from one adsorbate to another. The critical b o u n d a r y value for N,_, is about 0.1 nm, w h e r e a s those for O.o and Ar are 0.08 ~ 0.09 nm. In principle, if the pore-wall is perfectly flat, the adsorption hysteresis should be absent in the case of A]c(= l~- le)- 0. This is because P~ and Pe are identical each other for h ] ~ - 0. However, table 2 shows t h a t the h]c value depends on the pore width. The critical thickness difference Ale m u s t shift to a positive value in real surfaces h a v i n g the corrugation structures. Figure 6 shows the relationships between calculated A]c and w for N,;, 02, and Ar adsorption on mesoporous silica. Three plots are s i t u a t e d at different positions. The relation for N,2 occupies at the lowest position, while both plots for 02 and Ar are very close to each other. We need the reason why the h]c value plays an essential role in the adsorption hysteresis. Figure 7 illustrates the surface model of the regular cylindrical pore of the mesoporous silica[30]. The superficial pore walls are composed of oxygen; the effective pore wall is not flat Table 2.

Dependence of hysteresis on pore width and A]c

Sample FSM 1 GB 1 FSM2 GB2 FSM3 Pore width, nm 2.5 3.0 3.4 4.4 4.6 N,2 adsorption A]c, nm 0.06 0.09 0.09 0.12 0.14 Hysteresis • • • O O 02 adsorption A]c, nm 0.07 0.10 0.12 Hysteresis x r-,. ~, Ar adsorption Ale, nm 0.07 0.10 0.12 Hysteresis X ~'~ ( x and C) denote reversible and irreversible,respectively).

175 and is a p p r o x i m a t e d by the e n v e l o p e d curve. Hence even the r e g u l a r cylindrical pore has an intrinsic p o r e - w a l l r o u g h n e s s i n h e r e n t to the atomic s t r u c t u r e . The effective pore size d i s t r i b u t i o n due to the p o r e - w a l l r o u g h n e s s for N2 on silica is e s t i m a t e d to be 0.09 nm, w h e n we use the radius of the c o v a l e n t oxygen of 0.063 nm and r a d i u s of a s p h e r i c a l N2 molecule of 0.18 nm. The r a d i u s of oxygen in solid oxygen c h a n g e s with the ionicity by about 0.05 nm[31]. Also the IR e x a m i n a t i o n showed t h a t surface oxygen atoms are c o n v e r t e d into surface h y d r o x y l s which have an effective r a d i u s from 0.13 to 0.18 nm[30]. In this case the m a x i m u m pore r a d i u s d i s t r i b u t i o n is e s t i m a t e d to be 0.12 (0.18-0.06) nm for the on-top c o n f i g u r a t i o n of a d s o r b e d N2 molecule. Thus, the i n t r i n s i c pore radius d i s t r i b u t i o n is p r e s u m e d to be about 0.12 nm which a g r e e s briefly with the o b s e r v e d A]c value. The intrinsic pore r a d i u s d i s t r i b u t i o n gives rise to an a m b i g u i t y for Pc and Pe values. Accordingly, if Ale is less t h a n this intrinsic d i s t r i b u t i o n , no a d s o r p t i o n h y s t e r e s i s is observed. Thus, the absolute value of A]~ has an e s s e n t i a l m e a n i n g . The above discussion and e x p e r i m e n t a l results indicate t h a t A]c- 0.12 nm is a p p r o p r i a t e for the critical value for N., adsorption. Fig.7 gives the pore w i d t h c o r r e s p o n d i n g to A]c- 0.12 nm; the critical pore width for N2 on silica is about 0.4 nm, a g r e e i n g with the e x p e r i m e n t a l results. The intrinsic pore w i d t h d i s t r i b u t i o n s for O ~ a n d Ar are e s t i m a t e d to be 0.11 and 0.10 nm, i n d i c a t i n g t h a t the critical b o u n d a r y pore widths for both o f O , ~ a n d Ar are 3 nm, being close to the e x p e r i m e n t a l values (2.5 to 3.0 nm). Thus, this a n a l y s i s can explain briefly the d e p e n d e n c e of the a d s o r p t i o n h y s t e r e s i s on the pore w i d t h and a d s o r b a t e , a l t h o u g h we need more e x a m i n a t i o n s . This work was funded by the G r a n t in-Aid for Scientific R e s e a r c h from Japanese Government

Figure 6. The pore-wall structure for a n N 2 molecule.

Figure 7. Alevs. R relations. a: 02, b: Ar, c: N 2

176 REFERENCES

1. S. Iijima, Nature, 354 (1991) 56. 2. J. S.Beck, J.C.Vartuli, W.J.Roth, M. E.Leonowicz, C.T.Kresge, K.D.Schmitt, C. T.-W Chue, D.H.Olson. E.W.Sheppard, S..B.MacCullen, J.B.Higgins and J.L. Schelender, J. Am. Chem. Soc., 14 (1992)10824. 3. S. Inagaki, Y. Fukushima and K. Kuroda, J. Chem. Soc. Chem.Commun. (1993) 680. 4. Q.Huo, D.I.Margolese, U.Ciesla, P.Feng, T.E.Gier, P.Sieger, R.Leon, P.M. Petroff, F. Schiith and G. D. Stucky, Nature, 368 (1994) 317. 5. T. J.Pinnavaia and M. F. Thorpe (eds.), Access in Nanoporous Materials, Plenum Press, New York, 1995. 6. S. H. Tolbert, P.Sieger, G. D. Stucky, S.M.J.Aubin, C-C. Wu and D. N. Hendrickson, J. Am. Chem. Soc., 119 (1997) 8652. 7. K. Kaneko, J. Membrane Sci., 96, 1994, 59. 8. K.S.W.Sing, D.H.Everett, R.A.W. Haoul, L. Moscou, R.A.Pierotti, J.Rouquerol and T. Siemieniewska, Pure Appl. Chem., 57 (1985) 603 9. D.H.Everett, The Solid-Gas Interface, (Flood E.A. ed.), Marcel Dekker, New York, 1967, chap.3. 10. S. J.Gregg and K.S.W.Sing, Adsorption, Surface Area and Porosity, Academic Press, London, 1982. 11. P.J. Branton, P.G. Hall and K. S. V~\ Sing. J. Chem. Soc. Chem.Commun., (1993)1257. 12. P.L.Llewellyn, Y. Grillet, F. Schiithe, H. Reichert and K.K. Unger, Microporous Mater., 3 (1994) 345. 13. R. Schmidt, M.StScker, E. Hansen, D. Akporiaye and O.H. Ellestad, Microporous Mater., 3 (1995) 443. 14. P.I.Ravikovitch, S.C.O.Domhnaill, A.V. Neimark, F. Schtith and K.K. Unger, Langmuir, 11 (1995)4765. 15. P.J.Branton, K. Kaneko and K.S.W. Sing, J.Chem.Soc.Chem. Commun.,(1999) 575. 16. K.Morishige, H. Fujii, M. Uga and D. Kinukawa, Langmuir, 13 (1997) 3494. 17. M. Kruk, M. Jaroniec and A. Sayari, J. Phys. Chem., 101 (1997) 583. 18. C.G. Sonwane, S.K. Bhtia and N. Calos, Ind. Eng. Chem. Res., 37(1998) 2271. 19. M.W. Cole and W.F. Saam, Phys. Rev. Lett., 32 (1974) 985. 20. P.C Ball and R. Evans. Langmuir, 5 (1989) 714. 21. T. Michalski, A. Benini and G.H. Findenegg, Langmuir, 7(1991),185. 22. Y. Hanzawa, K. Kaneko, N. Yoshizawa, R.W.Pekala and M.S.Dresselhaus,Adsorption, 4 (1998)187. 23. T.L. Hill, Adv. Catal.,4 (1952) 211. 24. S. Inoue, Y. Hanzawa and K. Kaneko, Langmuir, 14 (1998) 3041. 25. S. Inagaki, Y. Fukushima and K. Kuroda, J. Colloid Interface Sci.,180(1996) 623. 26. G.Btichel, M. Grtin, K.K. Unger, A. M a s t s u m o t o and K. Tsutsumi, S u p r a m o l e c u l a r Sci., 5 (1998) 253. 27. H. Tanaka, T. Iiyama, N. Uekawa, T. Suzuki, A. M a s t s u m o t o , M. Grtin, K.K. U n g e r and K. Kaneko, Chem. Phys. Lett., 292 (1998) 541. 28. X.S. Zhao, G.Q. Lu, A.K. Whittaker, G.J. Millar and H.Y. Zhu, J. Phys. Chem., 101 (1997) 6525. 29. A. Harashima, Theory of Liquids (Japanese), Iwanami, Tokyo, 1954, pp.153. 30. A.F. Wells, Structural Inorganic Chemistry, Oxford Univ. Press, Oxford, 1967, pp.546. 31. L.Abrams and D.R. Corbin, Inclusion Chemistry, with Zeolites 9Nanoscale Materials by Design: (Herron, N. and Corbin,D.R. eds.) Kluwer Academic Pub.,Boston, 1995, Chap. 1.

Studies in Surface Scienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScience B.V. All rightsreserved.

177

Study o f the m o r p h o l o g y o f p o r o u s silica materials Christelle Alie, Rene Pirard and Jean-Paul Pirard Laboratoire de Genie Chimique, Universite de Liege, Institut de Chimie B6a, B-4000 Liege, Belgium

Siliceous mineral materials can be either crushed or invaded by mercury during mercury porosimetry experiments. Compacted slabs prepared from powders of monodisperse non aggregated silica spheres in the diameter range 8-200 nm show only intrusion during mercury porosimetry experiments. When submitted to mercury pressure, aerogels and highly porous xerogels, with sizes of the elementary particle varying from 7 to 25 nm, only collapse in case of very small aggregates whereas they are crushed an then intruded in case of larger silica aggregates. As the size of the silica particles and thus the size of the aggregates increases, the strength towards crushing increases and the change of mechanism from crushing to intrusion takes place at a lower pressure. The resistance towards compression is not directly related to the size of the elementary particles but is linked to the size of the aggregates of silica particles.

1. INTRODUCTION It has been shown [ 1] that during compaction, the isostatic mercury pressure P completely crushes pores of size larger than a limit size L and leaves the pores of smaller size unchanged. The model for the mechanical shrinking mechanism is the buckling of the brittle filaments of mineral oxide under an axial compressive strength. The relation between L and P is given by Euler's law for the buckling of a cubic structure: L = k / P 0.2s

(1)

where k - (n r~~ E / ) 1/4 with I = rt d 4 / 64. k is therefore a function of the elastic modulus of the mineral oxide filaments E, n which is the number of lateral edges in the polyhedron (cube : n - 4) and d the diameter of the filaments. The aim of this work is to relate the resistance towards compression of silica materials to the morphological characteristic which suits : elementary particle or the aggregate. By elementary particle, we mean the smallest homogeneous entity visible by transmission electron microscopy and by aggregate, we mean the filaments constituted of elementary particles which build up the three-dimensional network of the material. The behaviour of three silica materials with elementary particles similar in size was compared when submitted to mercury isostatie pressure. In the three methods for obtaining those materials, the size of the silica particles can be tailored. They differ by the presence or absence of aggregation or by

178 the type of aggregation. Gels were prepared from tetraethylorthosilicate (TEOS) in a singlestep base catalysed hydrolysis with addition of 3-(2-aminoethylamino)propyltrimethoxysilane (EDAS) [2]. This addition of a small quantity of EDAS to the TEOS alcoholic solution avoids the complete shrinkage of the material during the drying at ambient conditions. EDAS acts as a nucleation agent leading to silica particles with a hydrolysed EDAS core and a shell principally made of hydrolysed TEOS. This enables to tailor the size of the silica particles. The first type of material, hyperporous xerogels, is obtained by drying those gels under vacuum whereas the second type of material, aerogels, is obtained by drying them in supercritical conditions. Silica sphere powders [3] were made by the controlled hydrolysis of TEOS in a basic medium (NH4OH). Those powders were then compacted into slabs. The silica spheres are monodisperse and microporous. The compaction modifies very slightly the distribution of micropores. On the other hand, the distribution of the voids between the spherical particles is shifted towards the smaller sizes.

2. EXPERIMENTAL

The xerogels X and aerogels A were synthesised according to the sol-gel process by hydrolysis and condensation of tetraethylorthosilicate (TEOS) and a small proportion of 3-(2-aminoethylamino)propyltrimethoxysilane (EDAS) in an alcoholic solution [2]. The compositions are given in table 1. TEOS and EDAS were hydrolysed by an aqueous 0.18 M NH4OH solution in ethanol at room temperature and under magnetic stirring. The dilution parameter that is molar ratio R - ethanol/(TEOS+EDAS) was taken equal to 10 for the xerogels and 20 for the aerogels except A5 for which R -10. The solution was kept at 60~ in a tight flask for gelation and aging. After 7 days, the gels are either dried under vacuum leading to xerogels (samples X) or dried supercritically leading to aerogels (samples A). The xerogels X were obtained according to the following procedure : the flasks were opened and put into a drying oven heated to 60~ and the pressure was slowly decreased (to prevent gel bursting and spreading in the whole oven) to the minimum value of 1200 Pa after 90 h. The drying oven was then heated at 150~ for 72 h. The aerogels A were obtained by drying in an autoclave after immersing in excess alcohol. The temperature is increased from ambient temperature to 600 K at a rate of 2~ The initial pressure of 0.5 MPa is established by introducing nitrogen in the autoclave. The pressure is increased up to 8 MPa. This pressure is maintained until the temperature reaches its maximum (600 K) and then the pressure is slowly decreased down to 0.1 MPa. The autoclave is purged with nitrogen (0.2-0.5 MPa) and then put under vacuum and let cool down slowly. Finally, the organic residues of both xerogels and aerogels are removed by burning in air at 450~ in an oven for 72 hours. The monodisperse silica spheres were obtained by the controlled hydrolysis of TEOS in ethanol in presence of liquid ammonia [4]. The final size of the spheres depends on the concentration in liquid ammonia, the hydrolysis ratio and the temperature. Slabs (diameter 25 mm and thickness 2 mm) were obtained by pressing the monodisperse silica sphere powders at 300 MPa and 300~ with Mowioll as binding agent. The thermal treatment destroys the organic radicals present on the surface of the spheres. Samples with the following particle diameters were prepared: S 1 = 8 nm, $2 - 16 nm, $3 = 25 nm, $4 = 40 nm, $5 = 64 nm, $6 102 nm, $7 = 206 nm.

179 Table 1 Synthesis operating variables of xerogels an d aerogels Sample TEOS EDAS Ethanol mol/l mol/l mol/1 XI X2 X3 X4 X5 X6 X7 A1 A2 A3 A4 A5

111 110 1 08 1.06 1.04

0.99 0.95 0.67 0.65 0.63 0.57 1.05

0.028 0.044 0.065 0.084 0 104 0 149 0 190 0016 0 033 0064 0.115 0.106

114 114 114 11.4 11.4 11.4 11.4 137 137 137 137 113

H20 mol/l 4.53 4.51 4.50 4.48 4.46 4.42 4.38 2.72 2.71 2.72 2.63 4.52

EDAS/TEOS

R

0.025 0.04 0.06 0.08 0.1 0.15 0.2 0.025 0.05 0.1 0.2 0.1

10 10 10 10 10 10 10 20 20 20 20 10

The bulk densities were calculated from weight and volume measurements. Skeletal densities were measured by He pycnometry. N2 adsorption-desorption isotherms were determined at 77 K on a Carlo Erba Sorptomatic 1900 and their analysis was done using a set of well-known techniques [5]. Mercury porosimetry up to a pressure of 200 MPa is performed on a Carlo Erba Porosimeter 2000. Samples were examined using a transmission electron microscope to obtain particle and aggregate sizes [2].

3. R E S U L T S

Xerogels X1-X6 and aerogels A1-A3 and A5 exhibit two successive behaviours (Fig. 1) when submitted to mercury porosimetry [6] : at low pressure, the sample collapses under mercury pressure and above a pressure of transition Pt (table 2), which is characteristic of the material composition and microstructure, mercury can enter into the network of small pores not destroyed during the compression at low pressure. The pore size distribution was determined by Pirard's collapse model [1, 6] below Pt and by Washburn's intrusion theory [5, 7] above Pt. The k constant present in Pirard's collapse theory can be different for each sample. The determination of k is easy for samples showing collapse and then intrusion because at Pt both equations, the buckling law L=k / P 0.25 and Washburn's law L = -4o cos0/P (where o is the surface tension of mercury and 0 is the angle of contact between the solid and mercury) _= 1500/P (if P is expressed in MPa and L in nm) are simultaneously valid and k is given by the relationship k = 1500/Pt~ Xerogel X7 and aerogel A4 which contain the most EDAS only collapse under mercury pressure as traditionally observed on aerogels [1, 8] and show no trace of trapped mercury after a mercury porosimetry experiment. The whole pore size distribution is determined by Pirard's collapse model.

180 T .......................................

E

~ 9 0 A ~ ~~

>

lJ ~t3-Et-t~

. !

&

II i

00.01

0.1

1

10 Ht

100

t000

pressure ( r y e ) Figure 1. Mercury porosimetry of sample X1 (~), X4 (A), X6 (O)and X7 (~). For both xerogels and aerogels, [~g decreases when the content in EDAS increases (table 2). The pressure of transition Pt increases and thus the constant k of the buckling equation decreases when the ratio EDAS/TEOS increases (figure 2).

200

-

~5o

~I00 E =

=

I

i

5o ~

o~ 0

0.05

0.1

EDASlTEOS

0.15

0.2

Figure 2. Buckling model constant k versus EDAS/TEOS for xerogels (11) and aerogels (~).

181

The monodisperse non aggregated silica sphere slabs undergo only intrusion during mercury porosimetry experiments. Due to the very compact arrangement of the spheres, the pore volume V,g is very small (table 2). l;'Hg increases when the size of the spheres increases from 8 to 206 nm.

Table 2 Sample textural properties v.g Sample /9bulk Vp g/cm 3 cm3/g cm3/g _+0.1 _+0.05

tm

r,,

pt

SBET

cm3/g

cmVg

g/cm 3

+0.01

+0.1

+0.01

+5

+1

P,

m Z / g MPa

do

So

nm

mVg

error

+0.02

_+7%

X1

0.28

0.8

3.05

0.12

3.2

0.27

285

20

23.0_+1.7

117

X2

0.30

0.7

2.75

0.13

2.9

0.30

325

28

18.3_+0.8

147

X3

0.30

1.2

2.60

0.16

2.8

0.31

385

45

15.9_+0.9

170

X4 X5 X6

0.32 0.34 0.40

1.2 1.1 1.8

2.40 2.35 1.95

0.17 0.18 0.22

2.7 2.6 2.3

0.32 0.33 0.36

400 425 560

55 70 150 b

X7

0.52

1.6

0.95

0.26

1.4

0.54

570

-r

error

+0.005

+0.1

+0.1

+0.01

+0.1

+0.01

+5

+1

A1

0.030

0.5

16.1

0.06

16.2

0.06

160

30

12.5+1.1

220

A2

0.040

0.8

15.9

0.13

16.1

0.06

260

60

8.7_+0.5

320

A3

0.055

1.1

15.1

0.17

15.4

0.06

420

175 b

7.7+1.0

360

A4 A5

0.060 0.080

2.0 0.8

14.0 10.1

0.19 0.14

14.3 10.3

0.07 0.09

460 345

-r 85

_a 11.3+1.4

_a 245

error

+0.05

+0.01

+0.01

+0.01

+0.05

+0.01

+5

S1

1.15

0.37

0.11

0.22

0.45

1.05

550

-c

8

366

$2

1.30

0.39

0.08

0.17

0.40

1.11

445

-~

16

183

$3

1.30

0.28

0.08

0.11

0.30

1.25

265

_c

25

117

$4

1.25

0.28

0.19

0.08

0.35

1.18

185

_c

40

73

$5

_a

0.26

0.17

0.03

0.25

1.33

75

-c

64

45

$6

1.35

0.26

0.25

0.02

0.30

1.25

50

-~

106

29

$7

1.30

0.28

0.25

0.01

0.25

1.33

20

-~

206

14

_a _a 13.8+1.4 193 12.0_+0.7 226 9.7_+0.6

278 +10%

+3%

_a not measured; b e r r o r + 5; _c not applicable pbutk " bulk density measured by mercury pycnometry; lip " specific liquid volume adsorbed at saturation pressure of N2; VHg specific pore volume measured by mercury porosimetry; t"m" microporous volume; /~v total pore volume obtained by addition of l,h g , the cumulative volume .of pores of diameter between 2 and 7.5 n m Voam 25 nm) show a mixed behaviour and that samples with particles of nearly 10 nm but small aggregates (- 15 nm) undergo only crushing reinforces the assumption that the size of the aggregates is

186 the major morphological property controlling the behaviour during mercury porosimetry experiments.

ACKNOWLEDGEMENTS C. Alie is grateful to the Belgian Fonds pour la Formation ~i la Recherche dans l'Industrie et dans l'Agriculture, F.R.I.A., for a Ph. D. grant. The authors also thank the Belgian Fonds National de la Recherche Scientifique and the Fonds de Bay for their financial support.

REFERENCES

1. R. Pirard, S. Blacher, F. Brouers and J. P. Pirard, J. Mater. Res. 10 (1995) 2114. 2. C. Alie, R. Pirard, A. J. Lecloux and J. P. Pirard, J. Non-Cryst. Solids 246 (1999) 216. 3. J. Bronckart, A. J. Lecloux, F. Noville, C. Dodet, P. Marchot, J. P. Pirard, Colloids Surf. 19 (1986) 359. 4. W. StOber, A. Fink and E. Bohn, J. Colloid Interface Sci., 26 (1968) 62 5. A. J. Lecloux, in: . J.R. Anderson, M. Boudart (Eds.), Catalysis : Science and Technology, vol. 2, p 171, Springer, Berlin, 1981. 6. R. Pirard, B. Heinrichs and J. P. Pirard, in : B. McEnaney, T. J. Mays, J. Rouquerol, F. Rodriguez-Reinoso, K. S. W. Sing and K. K. Unger (Eds.), Characterisation of porous solids IV, The Royal Society of Chemistry, Cambridge, 1997, p 460. 7. E. W. Washburn, Proc. Nat. Acad. Sci. 7, 115 (1921 ) 8. L. Duffours, T. Woignier and J. Phalippou, J. Non-Cryst. Solids 194 (1996) 283. 9. J. C. P. Broekhoff and J. H. de Boer, J. Catal. 9 (1967) 8 and 15. 10. J. C. P. Broekhoffand J. H. de Boer, J. Catal. 10 (1967) 153, 368, 377 and 391. 11. M. M. Dubinin : Chem. Rev. 60 (1960) 235. 12. M. M. Dubinin : J. Colloid Interface Sci. 23 (1967) 487 13. B. Heinrichs, P. Delhez, J. P. Schoebrechts and J. P. Pirard, J. Catal. 172 (1997) 322.

Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 9 2000 Elsevier Science B.V. All rights reserved.

187

Adsorption Hysteresis and Criticality in Regular Mesoporous Materials S. K. Bhatia* and C. G. Sonwane Department of Chemical Engineering The University of Queensland St. Lucia, Brisbane, QLD 4072, Australia In the present work, various theories predicting the critical diameter for the absence of capillary condensation and hysteresis are applied to experimental adsorption isotherms of vapors on regular mesoporous materials. Among the various theories studied, the tensile strength approximation proposed by the authors was found to be the most successful. Reversibility of nitrogen adsorption at 77.4 K was studied on pure MCM-41 of various pore sizes, as well as mixtures of pure MCM-41 samples in a 1:1 ratio. The results of PSD and hysteresis on MCM-41 mixtures are close to that expected from studies of the pure materials. The estimates of hysteresis critical temperature and diameter of MCM-41, HMS, FSM and KIT materials are also provided. 1. I N T R O D U C T I O N Adsorption isotherms of vapors on mesoporous materials are generally type IV (according to the BDDH classification[l]), consisting of multflayer adsorption followed by a capillary condensation step associated with the hysteresis loop. Many previous attempts to explain hysteresis involved memscus theory, networked pore structure or inkbottle pore structure models, however these models could not be conclusively verified. Recently invented mesoporous molecular sieves MCM-41 [2] are considered as the most suitable model adsorbents currently available due to their array of uniform size pore channels (hexagonal/cylindrical pores) with negligible pore-networking or pore blocking effects. These materials have attracted a lot of attention because of prominent features which include tunability of their pore diameter (in the range of 1.5-10 nm), a high surface area of 600-1300 m2/g, high thermal, hydrothermal and mechanical stability, ease of modification of the surface properties by incorporating heteroatoms such as A1, B, Ti, V and Mo as well as anchoring organic ligands, and their use as host materials for the construction of nanostructured materials [3]. Due to their model porous structure, MCM-41 materials have attracted considerable attention for developing and refining theories related to adsorption, hysteresis and criticality in mesoporous materials. In this connection, the adsorption of various gases such as N2, 02, Ar, C2H4, C6H6, CH3OH, C2HsOH, C3H7OH, C4H9OH, SO2, CO2, H20, CH4, H2, CO, CC14, CD4, D2, C2H3N, C5Hlo, C6H14, (with few of these adsorbates at different temperature) has been

188

investigated (see reference 4 for details). The adsorption hysteresis data of these adsorbates can be broadly classified mto two major categories: adsorption Table 1 Experimental adsorption hysteresis data along with estimates of DcH. Adsorbate Ar Ar Ar Ar C2H3N C2HsOH C3H7OH C4HgOH C6H14 C6H6

C6H6 C6H6 C6H6 CD4 CH3OH CHsOH CHaOH CO CO2 C02 D2 H20 H20 H20 H20 N2 N~ N2 N2 N2 N2 N2 N2 N2 N~ N~ N~ N~ N~ N2 N2 N2 02 02 S02

Pore Diameter R a n g e (.~) 23-44 23-44 25-45 40 30 40 40 40 30 30 20 40 34 25 35 30 40 25 23-44 40 25 20 40 34 30 23-44 40 22-29 32-45 22-26 21-29 32-36 38-50 38-44 20-65 43-45 25-45 34 40 20-38 34 25-37 23-44 40 40

Temp. (K) 77.4 87.6 77.4 77.4 293 292 298 314 293 293 293 293 298 77.4 77.4 293 290 77.4 77.4 195 16.4 303 303 298 293 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 77.4 273

DCH (.~) 30-34 38-44 < 25 ~ _< 40 ~ _< 30 ~ < 40 ~ < 40 ~ < 40 ~ > 30 ~ > 30 ~ > 20 ~ < 40 ~ _> 34" _< 25 ~ < 35 ~ _> 30 ~ < 40 ~ > 25 ~ 23-27 _< 4(>~ b >__20~ < 40 ~. >__34 ~ < 30 a 38-44 >__40~ > 29 b b b > 36 ~ 38-43 40-44 38-55 < 43 .~ 40-45 >__34 ~ >_ 40 ~ >_ 38 ~ > 34 ~ > 37 ~ 30- 34 _< 40 :~ _< 4(}~

Material MCM-41 ~ M CM-41 ~ MCM-41 MCM-41 MCM-41 MCM-41 MCM-41 MCM-41 MCM-41 MCM-41 Ph-MCM-41 Ph-MCM-41 F S M - 16 MCM-41 MCM-41': MCM-41 MCM-41 HMS MCM-41 c MCM-41 MCM-41 Ph-MCM-41 MCM-41 F S M - 16 MCM-41 MCM-41 ~ CN MCM-41 c H M S (S~ ~ M C M - 4 1 (S§ -) M C M - 4 I(S§ SvI-MCM-41 Pol-MCM-41 PoI-MCM-41 MCM-41 MCM-41 MCM-41 F S M - 16 MCM-41 MCM-41 KIT FSM M C M-41 ~: MCM-41 MCM-41

Hyst. Obs.? d Yes Yes Yes Yes Yes Yes Yes Yes No No No Yes Yes Yes Yes No Yes No Yes Yes b Yes Yes No Yes Yes No No Yes Yes Yes No Yes Yes Yes Yes Yes No No Yes No No Yes Yes

Yes

189 s t u d i e s i n v o l v i n g t h e v a r i a t i o n of m e s o p o r e d i a m e t e r at a given t e m p e r a t u r e (Table 1), a n d v a r i a t i o n of t e m p e r a t u r e for a given pore d i a m e t e r (Table 2). The a n a l y s i s of t h e e x p e r i m e n t a l d a t a in Tables 1 a n d 2 clearly i n d i c a t e s t h a t for each a d s o r b a t e t h e i r exists two critical p a r a m e t e r s : critical h y s t e r e s i s t e m p e r a t u r e (Tc~), defined as t h e t e m p e r a t u r e below w h i c h no h y s t e r e s i s is o b s e r v e d a n d critical h y s t e r e s i s d i a m e t e r (DcH) defined as t h e pore d i a m e t e r below w h i c h no h y s t e r e s i s is observed. T h e s e findings are s u p p o r t e d by t h e r e c e n t a n a l y s i s of M o r i s h i g e a n d S h i k i m i [5], w h i c h e m p i r i c a l l y d i s t m g u i s h e d b e t w e e n two critical pore d i a m e t e r s , one of w h i c h r e p r e s e n t s t h a t below w h i c h c a p i l l a r y c o n d e n s a t i o n is a b s e n t (Dcp) a n d t h e o t h e r DCH. A l t h o u g h t h e o r i e s for p r e d i c t i n g a n d d i s t i n g u i s h m g b e t w e e n t h e s e critical d i a m e t e r s are still u n d e r d e v e l o p m e n t , s t u d i e s w i t h MCM-41 h a v e m d i c a t e d t h a t DCH > DcP, a n d DCH > 2 n m (the I U P A C lower l i m i t for m e s o p o r e w i d t h [1]). The e x i s t i n g t h e o r i e s for e x p l a i n m g criticalities of c a p i l l a r y c o n d e n s a t i o n a n d h y s t e r e s i s can be classified as: m e n i s c u s t h e o r y b a s e d on a single i d e a l i z e d pore c o n s i d e r i n g t h e difference in m e n i s c u s s h a p e [1]; n e t w o r k i n g , pore blocking

Table 2 E x p e n m e n t a l a d s o r p t i o n h y s t e r e s i s _data along w i t h e s t i m a t e s of TcH Adsorbate Range Temp. Pore Dia. TcH (K) Adsorbent (K) (.~) Ar

100 0

,

0.0

~

0.2

i

,

i

0.4

,

0.6

i

~

0.8

,

1.0

P/Po

Fig. 2. Nitrogen adsorption/desorption isotherms of silica SiC12T calcined at 500~ (1) and 300~ (2); (filled points- adsorption, open points-desorption).

2 10

12. I-00

J

800

o

1

9

{:D

E o "5 ..o L,-o (D "o (l)

E

600

9

~mDm~ o m

m e

~

9 c~

400

mm~jmm ~m c) m

2oo

am

~m

D 9D

~.~,

|

o > 0.0

0.2

0.4

0.6

0.8

1.0

P/P-n Fig. 3. Nitrogen adsorption/desorption isotherms of silica SiC18T calcined at 500~ (1) and 300~ (2); (filled points- adsorption, open points-desorption). Table 1 Elementary analysis of the samples investigated Sample

Calcined at 500~

Calcined at 300~ %C

%H

%N

%C

%H

%N

SiC18T

8.43

0.75

0.54

4.16

0.67

0.47

SiC12T

3.64

0.82

0.46

1.74

0.73

0.38

Specific surface areas (SBEr) for investigated samples, were calculated from the linear form of the BET equation over the range of relative pressure between 0.05 and 0.4, taking the cross-sectional area of the nitrogen molecule to be 16.2/~. The pore size distributions were derived from the desorption isotherm using the BJH method [14]. The total pore volumes, Vp, were calculated from adsorption isotherms at P/Po ~" 0.98 by assuming that complete pore filling by the condensate had occurred. The adsorption/desorption isotherms of nitrogen on investigated silica showed the typical shape for MCM-41 with sharp increase of adsorption within narrow range of relative pressure p / p o = 0.1-0.2 (SiC12T sample) or p / p o = 0.3-0.5 (SiC18T sample). A similar step is observed on desorption curves measured in thermogravimetric experiments for both liquid adsorbates. For the SiC12T sample the nitrogen adsorption isotherm is reversible, with absence of the hysteresis loop, indicating that the fluid is super critical in such pores according to the theory of capillary

211 condensation [15-17]. In such case the applicability of the Kelvin equation is restricted. Consequently, BJH procedure for calculation of mean pore radius is not quite valid. Thus, Rp values for SiC12T sample may be calculated taking into account that for cylindrical pores, the pore radius, Rp, is related to the pore volume and the surface area by Rp = 2VJSBEr. The results derived from nitrogen adsorption/desorption data for both investigated silicas are summarized in Table 2 (columns II, III and VI). The pore structure parameters for SiC12T sample from nitrogen method (BJH procedure) and TG method using water as the adsorbate are given for illustrative purposes only and may be considered as a reference data for those obtained by Grfin et al. for the same silicas using the same automated apparatus Micromeritics ASAP 2010. 1600 03

E

oo

0 oo ~o

1200

I1 I I

800

12 I I

400

O

20

i

~

~

i

~

,

40

60

80

1O0

120

140

160

180

Temperature, ~

Fig. 4. Thermal desorption curves of benzene (1) and water (2) from silica SiC12T calcined at 500~

03 03

"i 12

1200

I 11

E

or} 0

800

I I

I

I

m

I L

~o

400

L

20

40

60

80

1O0

120

140

160

180

Temperature, ~

Fig. 5. Thermal desorption curves of benzene (1) and water (2) from silica SiC18T calcined at 500~

212

Figures 4 and 5 show TG curves for water and benzene as a wetting liquids. Similarly as in the case of nitrogen adsorption isotherms the sharp step (weight loss) over narrow range of temperature is observed on these curves. Parts of TG curves above horizontal lines represent evaporation of the bulk liquid out of pores. Intensive evaporation at this stage of the process takes place at the boiling point of the liquid (perpendicular segment). When the first stage is completed, the temperature increases and starts the desorption from pores. Lower parts (solid lines) of TG curves correspond to desorption of adsorbate condensed within the pores or adsorbed on the walls of the pores and are, therefore, a measure of the total pore volume. In the case of SiC12T sample and benzene as a wetting liquid the desorption curve is smooth without characteristic step. It may be explained by not satisfactory wetting of this silica by benzene and restricted penetration of narrow pores. Observed effect is confirmed by small pore volume for the same sample, derived from benzene desorption data. The localization of desorption steps on temperature axis corresponds to emptying of pores with dominant share in total pore volume. Converting the temperature into pore radius, by using the Kelvin equation, the dimensions of pores and pore size distributions PSD, AVJAR~ vs. R, may be calculated in the manner described earher [9]. The pore dimensions and specific pore volumes Vp calculated from TG data are collected in Table 2 (columns IV, VII and VIII). The Vp volumes correspond to amount of liquid desorbed between its boihng point and the end of desorption process. Appropriate corrections for changes of liquid density with temperature were taken into account. Figures 6 and 7 show PSDs calculated from nitrogen adsorption method andthermo-desorption method. 0.10 2

0.08 . . . . . .

rr "o

0.06

"o

0.04 0.02

0.00

1

/ / -

. . . . . . . . . . . . . . . . . . . . . . . . . 6 8 10 12 14 Radius,

A

Fig. 6. Pore size distribution curves for silica SiC12T calcined at 500~ obtained by using various methods; (1)- nitrogen method; (2) - TG method (water).

213 0.14 0.12

3

1

0.10 I::E "o

0.08

"o

0.06 0.04 O.O2

2

0.00

'

'

5

' 10

15

20

25

Radius. A

Fig. 7. Pore size distribution curves for silica SiC18T calcined at 500~ obtained by using various methods; (1) - nitrogen method; (2) - TG method (water); (3)- TG method (benzene). As is seen PSDs calculated from the d a t a obtained by using different t e c h n i q u e s are close together. It should be noted t h a t in the case of the nitrogen desorption data corrections with respect to the surface film thickness were introduced. Table 2 P a r a m e t e r s characterizing the pore s t r u c t u r e of the samples investigated TG m e t h o d (benzene)

Nitrogen m e t h o d

TG m e t h o d (water)

SBET

VpN2

ap N2

VpTG

RpTG

VpTG

m2g -1

cm3g -1

/~

cm3g -1

/~

cm3g -1

SiC18T

974

0.94

14.6 a

0.83

13.9 c

0.94

14.5 ~

SiC12T

1373

0.70

10.0 a 10.2 b

0.32

--

0.75

10.9 b

Sample

RpTG

a - BJH method (nitrogen adsorption data); b - 2Vp/SBET (TG data); c - Kelvin equation (TG data).

4. C O N C L U S I O N S Comparing the results p r e s e n t e d in Table 2 one can conclude, t h a t for both silicas average pore d i a m e t e r s and specific pore volumes e s t i m a t e d by using various techniques are close together. The results indicate t h a t fast t h e r m o g r a v i m e t r i c technique is a useful tool for characterization of porous solids c o n t a i n i n g mesopores.

Acknowledgements The authors thank Prof S. Pikus for help with the XRD analysis.

214

REFERENCES

1. C.T. Kresge, M.E. Leonowicz, W.J. Roth, J.C. Vartuli and J.S. Beck, Nature, 359 (1992) 710. 2. D.T. Tanev and T.J. Pinnavaia, Science, 267 (1995) 865. 3. J.S. Beck, J.C. Vartuli, W.J. Roth, M.E. Leonowicz, C.T. Kresge, K.D. Schmitt, C.T.W. Chu, D.H. Olson, E.W. Sheppard, S.B. McCullen, J.B. Higgins and J.L. Schlenker, J. Am. Chem. Soc., 114 (1992) 10834. 4. S. Ozeki, M. Yamamoto and K. Nobuhara, in: "Characterization of Porous Solids IV", The Royal Society of Chemistry, B. McEnaney, T.J. Mays, J.Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger, (eds.), 1997, p.648. 5. K.J. Edler and J.W. White, J. Chem. Soc, Chem. Commun., (1995) 155. 6. A. Corma, M.T. Navarro and J.P. Pariente, J. Chem. Soc, Chem. Commun., (1994) 147. 7. P.T. Tanev, M. Chibue and T.J. Pinnavaia, Nature, 368 (1994) 321. 8. J. Goworek and W. Stefaniak, Mat. Chem. Phys., 32 (1992) 244. 9. J. Goworek and W. Stefaniak, Colloids Surfaces, 69 (1992) 23. 10. J. Goworek and W. Stefaniak, Colloids Surfaces, 80 (1993) 251. 11. J. Goworek, W. Stefaniak, A. D~browski, Thermochimica Acta, 259 (1995) 87. 12. M. Grfin, K.K. Unger, A. Matsumoto and K. Tsutsumi, in: "Characterization of Porous Solids IV", The Royal Society of Chemistry, B. McEnaney, T.J. Mays, J.Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger, (eds.), 1997, p.81. 13. F. Paulik and J. Paulik, J. Thermal Anal., 5 (1973) 253. 14. E.P. Barrett, L.G. Joyner and P.H. Halenda, J. Amer. Chem. Soc., 73 (1951) 373. 15. P.C. Ball and R. Evans, Langmuir, 5 (1989) 714. 16. K. Morishige and M. Shikimi, J. Chem. Phys., 108 (1998) 7821. 17. K. Morishige, M. Fujii, M. Uga and D. Kinukawa, Langmuir, 13 (1997) 3494.

Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 92000 Elsevier Science B.V. All rights reserved.

215

Characterization of mesoporous molecular sieves containing copper and zinc: An adsorption and TPR study Martin Hartmann* Institute of Chemical Technology I, University of Stuttgart, D-70550 Stuttgart, Germany

Copper and zinc containing mesoporous molecular sieves AIMCM-41 have been studied by 27AI MAS NMR, electron spin resonance, nitrogen and carbon monoxide adsorption and temperature programmed reduction. A1MCM-41 materials with nsi/n.u = 15, 30 and ~c have been synthesized in the presence of copper and zinc. Carbon monoxide adsorption shows the presence of Cu- ions after mild activation, but Zn 2- ions have not been detected indicating that only a ZnO phase is formed. Temperature programmed reduction reveals the presence of CuO clusters of various size depending on the on the ns]n.~ ratio and the zinc concentration. The results of this study allow the preparation of mesoporous molecular sieves with remarkable redox properties, which are potential model catalyst for methanol synthesis. 1. I N T R O D U C T I O N Since the discovery of ordered mesoporous molecular sieves with pore sizes between 2 and 10 rim, much research work has been devoted to this new class of mesoporous materials, denoted M41S. These SiO2-based materials contain large, uniform channels in the mesopore size regime [1,2]. Despite the regularity of the channel system, the wall structure of M41S materials is essentially amorphous. The first structures to be reported were the hexagonal (MCM-41), cubic (MCM-48) and lamellar phases (MCM-50), but other structures have since been synthesized. The properties of MCM-41 and MCM-48 materials can be modified by a variety of different techniques. The silanol groups present at the surface of the walls are suitable for chemical bonding of organic ligands or anchoring inorganic species. Moreover, heteroatoms such as aluminum, boron, titanium and gallium can be introduced into the structure. Transition metals such as iron, chromium, copper, nickel and molybdenum can be added to the synthesis mixture leading to metal species located within the structure after calcination [3,4]. However, the location of the metal species and their state always remain uncertain, despite the employment of numerous different characterization methods comprising IR, NMR and ESR spectroscopy. The great variety of possible surface modifications offers wide applications of MCM-41 and MCM-48 in the field of catalysis.

Present address: Department of Chemistry. Chemical Technology. University of Kaiserslautern. P.O.Box 3049. D-67653 Kaiserslautern. Germany.

216 Catalysts based on copper/zinc mixed oxides are of great importance for industrial scale catalytic processes like low pressure methanol formation from synthesis gas and steam reforming of methanol yielding H2 and CO2. The commercially available catalyst for both reactions is the ternary system Cu-ZnO/Al203 [5]. In consequence of its success, the Cu-ZnO system has prompted a great deal of fundamental work devoted to clarify either the role played by each component and the nature of the active site. In the present work, AIMCM-41 materials with different nsi/ma-ratios were used as support for copper and zinc species, which were introduced during the synthesis of the mesoporous molecular sieve. Characterization of the metal-containing materials was primarily achieved by carbon monoxide adsorption and temperature programmed reduction. In particular the aim of this work was to distinguish between isolated copper species grafted on the wall of MCM-41 and/or or the formation of copper oxide clusters located in the channels.

2. E X P E R I M E N T A L SECTION

2.1. Synthesis Mesoporous MCM-41 materials were prepared from synthesis gels containing sodium waterglas (Merck, 27 wt.-% SiO2), tetradecyltrimethylammonimbromide (C~4TMABr, Aldrich), water and diluted H2SO4. Quantities of sodium aluminate (Riedel de Haen, 54 wt.-% Al), Cu(CH3COO)2 9H20 (Fluka) and ZnSO4 9H20 (Fluka) were added where applicable. In this series of samples the nsi/n~c-ratio was fixed to 30, while nsi/n.~a was 15, 30 and ~. Equal moles of copper and zinc were used for the samples containing both metals. The resultant gels were loaded into polypropylene bottles and heated to l l0 "C for 24 h. ,Aa~er synthesis the materials were recovered by filtration, washed with water and ethanol and finally calcined in flowing nitrogen up to 200 ~ and in flowing air up to 540 ~ for 18 h. 2.2. Characterization The chemical compositions of the samples were determined by atomic adsorption spectroscopy (AAS). X-ray powder diffraction patterns were recorded after synthesis and template removal on a Siemens D5000 diffi'actometer using CuK~ radiation. After calcination, nitrogen adsorption and desorption isotherms were measured on a Micromeritics ASAP 2010 sorption analyzer. 27A1MAS NMR spectra were recorded on a Bruker MSL 400 spectrometer using single pulse excitation with standard 4 mm rotors. The resonance frequency was c00/2x - 104.31 MHz for 27A1using a x/20 pulse and a 0.5 s recycle delay. A 0.1 M solution of aluminum nitrate in water was employed as the chemical shift reference. The TPR experiments were performed in an Altamira AMI1 instrument with a flow of 10 vol.-% H2 in At. A heating rate of 3 K / min and approx. 100 mg of sample were chosen to enhance resolution and avoid "hot spots". Prior to the reduction experiments, the samples were activated in a helium flow containing 10 vol.-% 02 up to a maximum temperature of 400 ~ at a rate of 5 K / min. The carbon monoxide adsorption isotherms were measured volumetrically at 25 ~ in a home-build all-steel apparatus. The samples were dehydrated at 250 ~ for 18 h prior to the adsorption measurements. ESR spectra were recorded on a Bruker ESP 300 spectrometer at 77 K.

217

3. RESULTS AND DISCUSSION 3.1. Characterization The chemical composition of the samples was determined by atomic adsorption spectroscopy (AAS) and is summarized in Table 1 for all copper-containing samples. Starting from ns]n.~a -- 15 and 30 in the gel, typically materials with lower ns/n~-ratios are obtained. Also the metal concentration (copper and zinc) is enriched in the aluminum-containing samples. However, the n~/nMr in the as-synthesized samples is almost identical to the gelcomposition for nsi/n.~ = 30 and aluminum is enriched in the samples with nsi/n.u = 15. The ncu/nzn ratio equals one in the samples containing both transition metals. Table 1 Metal and aluminum content of the synthesis ~el and the as-synthesized materials AIMCM-41 Sample nsi/n.v (Gel) ns,/ma (AAS) nsi/nx,e(Gel) nsi/nx,e(AAS) n.~a/nx,~ CuAIMCM-41-(15)

"

15

....

7

' "

30

i6

'

2.3

CuZnA1MCM-41-(15)

15

9

30

22

2.4

CuA1MCM-41-(30)

30

21

30

18

0.9

CuZnA1MCM-41-(30)

30

21

30

23

1.1

CuMCM-41

30

31

CuZnMCM-41

30 .

32 .

.

-

.

.

Table 2 Unit cell parameters and results from the nitrogen adsorption experiments for the copper and zinc containin~ AIMCM-4.! . _.... nsl/nal Sample

dl,~,~,

BET Surface / -~

(Gel)

.

m-g 1

Pore Volume ~' /

Pore Diameter /

cm-~g 1

nm .

. ,

.

.

.

.

CuA1MCM-41-(15)

15

31.41

850

0.58

2.3

CuA1MCM-41-(30)

30

32.54

890

0.65

2.4

CuMCM-41

-

34.38

1140

0.81

2.5

CuZnA1MCM-41-(15)

15

31.10

730

0.50

2.3

CuZnA1MCM-41-(30)

30

32.25

750

0.49

2.4

CuZnMCM-41

-

33.49

1060

0.70

2.4

ZnA1MCM-41-(15)

15

31.29

690

0.45

2.3

ZnA1MCM-41-(30)

30

32.83

700

0.46

2.2

-

31.97

1000

0.65

2.2

ZnMCM-41

.

.

a) The pore volumes and diameters were calculated from the desorption branch of the nitrogen isotherms using the BJH-model.

218 XRD and nitrogen adsorption studies reveal that AIMCM-41 can be synthesized in the presence of copper and zinc salts. While the addition of copper acetate to the synthesis gel up to a ratio ns~/ncu = 15 has no influence on the quality of the XRD pattern, the zinc-containing materials show XRD patterns with somewhat lower intensity. In agreement with the XRD powder patterns, the nitrogen adsorption is reduced in the zinc-containing samples, while copper introduction does not affect the adsorption capacity. Variation of the ns,/nv-ratio from 30 to 15 has no significant influence on the adsorption capacity. In Table 1, the surface area ABET, the pore volume Vp and the pore diameter dp, calculated from nitrogen adsorptiondesorption isotherms using (Brunauer, Emmett and Teller) BET and (Barrett, Joyner and Halenda) BJH analysis, are summarized. The pore diameter is virtually not affected by introduction of aluminum, copper and zinc. 53 ppm

(a)

"

,

.

~

~

(b)

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,

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(c) I

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120 100 80 60 40

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0

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-20 -40 -60 -80

CHEMICAL SHIFT / ppm Figure 1.27A1MAS NMR spectra of(a) CuA1MCM-41-(15) (20000 scans), (b) CuZnAIMCM-41(15) (8500 scans) and (c) ZnMCM-41-(15) (4000 scans). Figure 1 exhibits the 27AI MAS NMR spectra for copper- and zinc-containing AIMCM-41(15) after calcination. The spectra of the as-synthesized and calcined samples exhibit only a single line at 6 = 53 ppm, which is assigned to aluminum in tetrahedral coordination. The introduction of tetrahedrally coordinated aluminum into the walls of MCM-41 generates ionexchange sites, which might accommodate Cu z- or Cu- ions. In comparison to the zinc-

219 containing materials, the copper-containing samples exhibit a larger linewidth and a poorer signal to noise ratio indicating the presence of paramagnetic Cu2--cations near the aluminum sites in the channels of AIMCM-41. The ESR spectrum of CuAIMCM-4 l-(15) (Figure 2a) shows the presence of paramagnetic Cu2--cations with the typical hyperfine splitting of the Cu(H20)62 complex with g~ = 2.386 and g_ - 2.08 (A~ = 138 G). Evacuation at room temperature for 2 h (Figure 2b) does not result in a significant change of the spectral parameters, although the hyperfine lines of the perpendicular component are better resolved. A new species with g~ = 2.318 and g = 2.07 ( A~ = 168 G) develops upon evacuation at 250 ~ for 18 h (Figure 2c). Evacuation at higher temperatures up to 400 ~ shows no further change in the ESR parameters except for a decrease in intensity due to autoreduction of Cu 2- [6]. Similar results were obtained in AIMCM-41 after introduction of Cu 2- by liquid ion exchange [7,8]. Therefore, the ESR spectra confirm the presence of isolated Cu 2- ions after calcination, which are most likely located in ion-exchange sites in the MCM-41 channels.

( a ) - - - - - - ~~ ~ , glJ = 2 3 9

(b)~ ~ ~ ~ , o,,_ g•

f

Tt/ 2 07--

V

(c)

I

2000

'

!

'

!

'

I

'

I

2 5 0 0 3 0 0 0 3500 4000

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l

4500

'

I

5000

FIELD / G

Figure 2. ESR spectra at 77 K of CuA1MCM-41-(15) (a) fresh, hydrated sample, (b) evacuation at 298 K for 2 h and (c) dehydration at 250 ~ for 18 h.

220

3.2. Carbon monoxide adsorption Figure 3 shows the adsorption isotherms of carbon monoxide on MCM-41 samples with different concentrations of aluminum, copper and zinc. The isotherms of the only zinc containing samples, ZnMCM-41 and ZnAIMCM-41-(15) are straight lines, while the coppercontaining materials exhibit a initial curvature of the adsorption isotherm. Carbon monoxide is known to be much more strongly adsorbed in zinc- and copper-exchanged zeolites than in their sodium-containing precursor forms. This behavior has been attributed to the formation of strong complexes of CO with accessible Zn 2- and C u cations located within the zeolite structure [9,10]. The complex formation results in an initial steep rise of the respective adsorption isotherms. The almost linear behavior of the carbon monoxide isotherms of ZnMCM-41 and ZnAIMCM-41-(15) excludes the presence of strong adsorption sites. Therefore, the presence ofZn 2~ cations in the channels of MCM-41 can be excluded. Zinc is either present in the walls or as ZnO in the channels. However, the presence of large ZnO clusters was not observed by XRD, but the formation of microporous high silica zincosilicates has been reported [11 ]. A study concerning the state of zinc is in progress.

0.20

'

Tad s =

-I

'

l

'

w

25 ~

'

~

'

~

'

..

0.15 0

E E

0.10

u~

c-

0.05

0.00

50

100

150

200

250

300

p / hPa Figure 3. Adsorption isotherms of carbon monoxide at 25 ~ on mesoporous molecular sieves (m CuAIMCM-41-(15), i"! CuZnA1MCM-41-(15), 9 CuA1MCM-41-(30), O CuZnA1MCM41-(30), A ZnA1MCM-41-(15), A ZnMCM-41 ). In contrast, an initial steep rise of the adsorption isotherm is detected in all copper-containing samples indicating the presence of Cu- cations. Cu- is formed via autoreduction from Cu 2 during activation of the sample in a process analogous to the one proposed for zeolites [6]. The concentration of the copper(I) species detected increases with increasing copper and

221 aluminum content. The property of AIMCM-41 to stabilize C u has also been observed by Zecchina et al. employing IR-spectroscopy of adsorbed CO. They concluded that at low copper content atomically dispersed Cu- is anchored to the framework like Cu- in zeolites [12]. In CuAiMCM-41-(15) ca. 20 % of the copper cations are present as Cu- after mild activation (assuming nco/ncu = 1). This corresponds to a situation in which one out of ten charges present due to aluminum incorporation is balanced by Cu-.

3.3 Temperature-programmed reduction In Figure 4, the TPR patterns of CuMMCM-41 and CuZnAIMCM-41 with different ns,/n.~ratios are displayed. The samples with ns]n..~--> zc exhibit maxima at 250 and 197 ~ respectively (Figure 4a and d). In aluminosilicate MCM-41, the only copper-containing samples show a maximum of the reduction profile at 184 ~ while the maximum is shifted in the copper- and zinc-containing samples by ca. 20 ~ The introduction of zinc leads to a remarkable reduction of the peak halfwidth. Reduction temperatures in the range of 180 to 250 ~ are typically associated with the reduction of Cu 2- or CuO clusters. The presence of small amounts of Cu 2- in our samples has been detected by ESR spectroscopy (Figure 2). The copper oxide is formed during calcination and/or sample pretreatment. Reduction of CuO dispersed on this mesoporous molecular sieves has been achieved at substantially lower temperatures than on ~/-Al203 or SiO2 [4]. The reduction of CuO diluted with SiO2 is observed at 220 ~ [4]. Cu 2- ions stabilized at the surface of SiO2 or Al203 give rise to reduction peaks at 300 - 380 ~ while reduction of Cu 2- in X and Y zeolites is observed at 200 ~ [13]. After the TPR experiment, the samples exhibit a gray-red color, which is typical for copper metal clusters. The existence of large metal clusters after severe reduction was detected by XRD, which shows two reflections at 20 = 44.0 ~ and 59.5 ~ typical for copper metal. The structural integrity of the samples after TPR has been confirmed by XRD and nitrogen adsorption measurements. Nevertheless, the location of the CuO clusters and the copper metal clusters after reduction still remain uncertain. It has been shown previously that the channel diameter influences the cluster size at least in the first redox cycle [4]. Clusters initially located in the channels will, however, migrate to the outer surface after several redox cycles accompanied by agglomeration [13]. The synergistic effect of zinc or zinc oxide in reduction of copper is exploited for the commercial methanol synthesis catalyst (Cu-ZnO-Al203), but is yet not fully understood. In the pure siliceous MCM-41, the maximum reduction temperature Tm is reduced by replacement of copper by zinc. Additionally, the peak width is considerably narrowed (Figures 4d - f). Such a promoting influence by ZnO on the reduction of copper was also found in unsupported CuOZnO catalysts [14]. On the other hand, samples with ns]n.~a = 30 and 15 exhibit a delay in copper oxide reduction in the presence of ZnO. This effect is similar to that observed in CuZnY zeolites [15]. However, the TPR profiles are similar to the one observed for the commercial Cu-ZnO-Al203 catalysts, which underlines that the samples studied are potential model catalysts. Although there is some agreement that interaction between ZnO and CuO exists, the nature of the interaction is still unknown. The small concentration of Cu-, which was detected by CO adsorption (Figure 3), is believed to play a vital role in methanol synthesis and

222

methanol steam reforming [ 16,17]. However, a stabilization of Cu- in the presence of ZnO (introduction of Cu- into the wurtzite structure [18]) was not observed in this study.

'~

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Figure 4. TPR profiles of (a) CuMCM-41, (b) CuAIMCM-41-(30), (c) CuAIMCM-41-(15), (d) CuZnMCM-41, (e) CuZnAIMCM-41-(30) and CuZnA1MCM-41-(15).

223 4. CONCLUSIONS Aluminum-containing MCM-41 with different ns]n..~-ratio can be prepared in the presence of copper and zinc. The obtained materials are well ordered and of good quality as shown by the XRD patterns and nitrogen adsorption isotherms. The introduction of aluminum or zinc leads to materials with somewhat reduced quality, while the introduction of copper results in materials with comparable quality to pure silica MCM-41. Temperature programmed reduction reveals the presence of CuO clusters, which can be reduced to copper metal at 184 ~ in AIMCM-41. The low reduction temperature in these materials compared to amorphous silica or Al203 indicates the presence of small CuO particles. After mild activation, the presence of a small amount of Cu- has been detected by carbon monoxide adsorption. The synergistic effect of zinc addition has been shown to be effective in this class of materials, which makes them interesting catalysts for methanol synthesis or methanol steam reforming. A study concerning this aspect is in progress.

ACKNOWLEDGMENTS

Financial support from Deutsche l:orschungsgemeinschafi (DI:G) and l:onds der Chemischen Industrie is gratefully acknowledged. M.H. wishes to thank Prof. L. Kevan, University of Houston, for the permission to use his ESR instruments and the DAAD for a travel grant.

REFERENCES

1. J.S. Beck, J.C. Vartuli, W.J. Roth. M.E. Leonowicz. C.T. Kresge, K.D. Schmitt, C.T.-W Chu, D.H. Olson, E.W Sheppard. S.B McCullen, J.B. Higgins and J.L. Schlenker, J. Am. Chem. Soc., 114 (1992) 10834. 2. A. Corma, Chem. Rev., 97 (1997) 2373. 3. W.A. Carvalho, P.B. Varaldo, M. Wallau and U. Schuchard, Zeolites, 18 (1997) 408. 4. M. Hartmann, S. Racouchot and C. Bischof, Microporous and Mesoporous Materials, 27 (1999) 3 09. 5. K.C. Waugh, Catal. Today, 15 (1992) 51. 6. P.A. Jacobs, W. de Wilde, R.A. Schoonheydt, J.B. Uytterhoeven and H.K. Beyer, J. Chem. Soc., Faraday Trans. I, 172 (1976) 1221. 7. A. Poppl, M. Hartmann and L. Kevan, J. Phys. Chem., 99 (1995) 17251. 8. J.Y. Kim, J.S. Yu and L. Kevan, Mol. Phys., 95 (1998) 989. 9. M. Hartmann and B. Boddenberg, Microporous Mater., 2 (1994) 127. 10. B. Boddenberg and A. Seidel, J. Chem. Soc., Faraday Trans., 90 (1994) 1345 11. M.A. Cambler and M.E. Davis, J. Phys Chem., 98 (1994) 13135 12. A. Zecchina, D. Sacarano, G. Spoto, S. Bordiga, C Lamberti and G. Bellussi, in Microporous Molecular Sieves 1998, L. Bonneviot, F. Beland, C. Danumah, S. Giasson and S. Kaliaguine (Eds.), Studies in Surface Science and Catalysis Vol. 117, Elsevierl Amsterdam 1998, pp. 343-350.

224 13. M. Hartmann, unpublised results. 14. G. Fiero, M. Lo Jacono, M. Inversi, P. Porta, F. Coici, R. Lavecchia, Appl. Catal. A: General, 13 7 (1996) 327. 15. J.M. Campos-Martin, A. Guerrero-Ruiz, J.L.G. Fierro, Catal. Lett., 41 (1996) 55. 16. H. Agar/ts and G. Cerrella, Appl. Catal., 45 (1988) 53. 17. S. Wellach, M. Hartmann, S. Ernst and J. Weitkamp, in Proceedings of the 12th International Zeolite Conference, M.M.J. Treacy, B.K. Marcus, M.E. Bisher and 3.B. Higgins (Eds.), Materials Research Society, Warrendal, PA, 1999, pp. 1409-1416 18. R. G. Herman, K. Klier, G.W. Simmons, B.P. Fire, J.B. Bulko and T.P. Koleylinski, J. Catal., 56 (1979) 407.

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000 ElsevierScienceB.V.All rightsreserved.

225

On the applicability o f the H o r w a t h - K a w a z o e m e t h o d for pore size analysis o f M C M - 4 1 and related m e s o p o r o u s materials Mietek Jaroniec, a Jerzy Choma b and Michal Kruk a aDepartment of Chemistry, Kent State University, Kent, Ohio 44242, U.S.A. blnstitute of Chemistry, Military Technical Academy, 01-489 Warsaw, Poland

A series of good quality MCM-41 samples of known pore sizes was used to examine the applicability of the Horvath-Kawazoe (HK) method for the pore size analysis of mesoporous silicas. It is shown that the HK-type equation, which relates the pore width with the condensation pressure for cylindrical oxide-type pores, underestimates their size by about 2040%. The replacement of this equation by the relation established experimentally for a series of well-defined MCM-41 samples allows for a correct prediction of the pore size of siliceous materials but does not improve the shape of the pore size distribution (PSD). Both these versions of the HK method significantly underestimate the height of PSD. In addition, PSD exhibits an artificial tail in direction of fine pores, ended with a small peak, which may be interpreted as indicator of non-existing microporosity. 1. INTRODUCTION In 1983 Horvath and Kawazoe [1] proposed a simple method to derive analytical equations for the average potential in a micropore of a given geometry, which in fact relate the pore width w with the adsorption potential A = RT In (Po/P). The symbols P/Po, T and R denote the relative pressure, absolute temperature and universal gas constant, respectively. The aforementioned relation allows to express the amount adsorbed in fine pores as a function of the pore width and subsequently to calculate PSD by its simple differentiation. The Horvath-Kawazoe (HK) procedure is a logical extension of the pore size analysis based on the Kelvin equation to the micropore range [2,3], and represents an adaptation of the condensation approximation to the region of fine pores [4]. The HK method has been originally proposed for slit-like carbonaceous micropores [1] and often used for evaluation of the micropore size distribution of active carbons [3-6]. In 1991 Saito and Foley [7] extended this method for cylindrical and spherical pores. Although the HK method was originally proposed for microporous carbons [ 1], several authors have modified and used this method to determine PSDs of zeolite-type materials [8-11] as well as ordered mesoporous silicas (OMS) such as MCM-41 materials [ 12-18]. The applicability of the HK method for the pore size analysis of active carbons was questioned on the basis of adsorption isotherms obtained via density functional theory [19,20] as well as computer simulations [21,22]. The crudest assumption in this method is the use of the condensation approximation to represent the micropore filling, which in fact has a

226 more complex mechanism [19,21]. It was shown by computer simulations and density functional theory calculations that adsorption isotherms for larger micropores exhibit steps related to the surface film formation and surface-influenced capillary condensation. Consequently, the resulting HK PSDs show an extra peak that reflects the surface film formation, which is often incorrectly interpreted as indicator of non-existing microporosity [19,20]. Also, Kaminsky et al. [23] pointed out that simple mean-field approaches such as the HK method lead to polydisperse PSDs for adsorption systems which are in fact monodisperse in pore size. In addition, theoretical equations and/or parameters used to express the relation between the pore width and the condensation pressure for carbonaceous slit-like micropores have very limited applicability [19]. Their applicability is even more questionable for the MCM-41 materials, i.e., materials exhibiting a hexagonal ordering of cylindrical mesopores. It was recently pointed out by Galarneau et al. [24] that the HK equation for cylindrical pore geometry provides much less accurate characterization of MCM-41than that for slit-like pores, contrary to what is expected from the pore geometry. Since the HK method has been used by prominent researchers for the pore size analysis of the MCM-41 and related solids [12-18], it would be desirable to discuss its applicability for characterization of ordered mesoporous materials. The aim of the current work is to examine the HK method for a series of good quality MCM-41 samples of known pore sizes and discuss its usefulness for characterization of ordered mesoporous structures.

2. EXPERIMENTAL Nitrogen adsorption isotherms used to examine the HK method were measured at 77 K on a series of good-quality MCM-41 materials using an ASAP 2000 volumetric adsorption analyzer from Micromeritics (Norcross, GA). The MCM-41 samples of desired mesopore sizes were obtained using a synthesis procedure with surfactants of different length or postsynthesis hydrothermal treatment [25]. Details related to the synthesis of these materials, their characterization by X-ray diffraction (XRD) and nitrogen adsorption are given in our previous paper [25-27]. For each sample the pore width was calculated on the basis of pure geometrical considerations of the ordered honeycomb structure with input data such as the XRD spacing and the volume of primary mesopores. The following equation was used [26,27]: w - l . 2 1 3 d pVp / l + pVp

(1)

where d is the (100) interplanar spacing obtained from XRD, Vp is the volume of primary mesopores obtained from nitrogen adsorption and 9 is the density of mesopore walls, which in the case of pure siliceous materials is equal to 2.2 g/cm 3. The input data for equation (1) and the resulting pore widths are summarized in Table 1. In addition, PSDs for the MCM-41 samples studied were calculated by employing the pore size analysis method proposed by Kruk, Jaroniec and Sayari (KJS) [26]. The main idea of this method was the use of a series of good-quality MCM-41 materials to establish the Kelvin-type relationship between the pore width and condensation pressure and to derive the statistical film thickness for nitrogen on the silica surface. Next, these relationships were incorporated into the Barrett-Joyner-Halenda (BJH) algorithm [28]. The pore size distributions calculated according to the KJS method [26] are shown in Figure 1, whereas the corresponding pore widths are given in Table 1.

227

E .=

3.0

r162

&

2.0

9

3.1

~

2.8

[!

[I

46

5.5

,o ~." O

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Pore Width (nm) Figure 1. Pore size distributions calculated by the KJS method [26] for the MCM-41 samples studied. Table 1 Structural parameters of the MCM-41 samples studied. Sample d (nm) Vp(cc/g) 2.0 2.83 0.25 2.8 3.05 0.58 3.1 3.34 0.67 3.8 3.87 0.92 4.6 4.69 0.88 5.5 5.52 0.97 6.5 6.59 0.91

WXRD(nrl'l)

WKJS*(nlI1)

2.04 2.78 3.13 3.84 4.62 5.53 6.53

2.25 2.70 3.01 3.81 4.41 5.66 6.52

d - XRD (100) interplanar spacing, Vp - primary mesopore volume, WXRD - primary mesopore width calculated from equation (1), wKjs, -primary mesopore width at the maximum of PSD reported in [26].

3. RESULTS AND DISSCUSSION As shown in [3] the HK pore size distribution, J(w), where w denotes the pore width, can be expressed in terms of the adsorption potential distribution (APD), X(A), as follows: J(w) = - X ( A ) (dA / dw)

(2)

The X(A) function is a primary thermodynamic characteristics of a given adsorption system and can be easily calculated by differentiating the equilibrium adsorption isotherm with respect to the adsorption potential A = RT In (Po/P). Equation (2) shows that a simple

228

O

4.0 3.0

~D O

2.0

.

S e

'..

_

-%,

ZLZ

O

1.0 O

rae~


4.5 nm), the linear relation underestimated the pore size. When we estimate the pore volume from the area under the differential curve, the adsorption on the external surface is also included. In many cases, the external surface area is not important, compared to the surface of the pores (all samples in this study are falling in such cases). The inclusion of the adsorption by external surface causes no obvious deviation from the real pore volume. This is the reason that we can obtain good linear relation in Fig 7. The proposed approach inherits the reliability and conciseness of the comparison plots. The function of the comparison plots, t- and c~-plot is to compare the adsorption of the sample under test with that of the nonporous reference. The latter is expressed in the simplest form, a straight line passing through the origin. This brings about a significant advantage that deviations from such a line are readily to be recognized and linked to the adsorption of pores in the sample. It is known that micropore and mesopore fillings are based on different mechanisms. The attractive force from the micropore walls on adsorbate molecules is enhanced, compared with that from a non-porous surface. Therefore, micropores are filled by the adsorbate at low vapor pressure. Mesopores are generally filled by capillary condensation caused by the increase in the interface curvature between gaseous and adsorbed phases The comparison plot as well as its differential curve is not related to any specific underlying mechanism, but illustrates phenomenologically the pore filling processes and the difference between these processes from adsorption on non-porous surface. The fillings are always accompanied by steep increase in adsorption, and, the comparison plot of the sample will swing upward significantly, so does the differentials curve. After the filling, the surface of the pore walls is not available to further adsorption. The adsorption proceeds on much less surface area, giving substantially low differential values. The peak thus observed on the differential curve identifies the existence of pores The size and volume of these pores are reflected by the position of the peak and area under the curve as discussed above.

250 Conclusions Differential curves can be readily derived from comparison plots, which can be used to describe the adsorption process on micro- and meso-porous solids in concise and reliable way. Using the pore size data known by X-ray diffraction technique, we obtain a simple relation which allows us to convert the differential curve to a PSD curve. In contrast to conventional methods for calculating PSD from a nitrogen isotherm, there is no assumption limitation for this approach. This method is applicable over the range of micropores and mesopores. Besides, construction of such curves does not involve complicated and laborious calculations. For the purpose of deriving PSD from the adsorption isotherm, the approach proposed is a simple yet powerful means.

References

1. B.C. Lippens and J. H. De Boer, .l. Catal, 1965, 4, 319. 2. K. S. W. Sing, in Surface Area Determmattou, Proc. htt. Syrup., 1969, ed. D. H. Everett and R. H. Ottewill, Butterworths, London, 1970, p.25. 3 S. J Gregg and K. S. W. Sing, Adsorption, Smface Area and Porosity. 2nd Ed Academic Press, New York, 1982 4. R. S. H. Mikhail, S. Brunauer and E .E. Bodor, .L Uolloid and hlterface Sci. 1968, 26, 45. 5. H.Y. Zhu, X. S. Zhao, G. Q. Lu, and D. D. Do, Langmuir. 1996, 12, 6513. 6. H. Y. Zhu, G. Q. Lu, N. Maes and E. F. Vansant, .L ('hem. Soc. Faraday Trans., 1997, 93(7), 1417. 7. P. J. Branton, P. G. Hall, and K. S. W. Sing,, .L ('hem. Soc. Uhem. Commun. 1993, 1257-1258 8 E.P. Barrett, L. G. Joyner and P. H. Halenda, .LAmer. ('hem. Soc. I95 I, 73, 373. 9 M.M. Dubinin, in Progress m Surface and Membrane Science, ed. D. A Cadenhead, J. F. Danielli and M. D Rosenberg, Academic, London 1975, p. 1. 10. G. Horvath, K. Kawazoe, J. Chem. Eng. Japan, 1983 16(6), 470. 11. H. Y. Zhu, G. Q. Lu and X. S. Zhao, J. Phys. ('hem. B, 1998, 102, 477.

Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) 92000 Elsevier Science B.V. All rightsreserved.

251

Rotational State C h a n g e of A c e t o n i t r i l e Vapor on M C M - 4 1 u p o n C a p i l l a r y C o n d e n s a t i o n with the aid o f T i m e - C o r r e l a t i o n F u n c t i o n A n a l y s i s o f IR S p e c t r o s c o p y Hideki Tanaka, Akihiko Matsumoto*, Klaus K. Unger', Katsumi Kaneko

Physical Chemistry, Material Science, Graduate School of Natural Science and Technology, Chiba University, Inage, Chiba, Japan *Faculty of Engineering, Toyohashi University of Technology, Tempaku-cho, Toyohasi 441, Japan * Institute for Ingorganic Chemistry and Analytical Chemistry, Johannes Gutenberg University, Becherweg 24, D-55099 Mainz, Germany The infrared spectra of adsorbed acetonitrile on MCM-41 (porewidth = 3.2 rim) were measured at 303 K. In the CN stretching v2 region, two bands were observed at 2265 cm 1 and 2254 cm -1, assigned to hydrogen-bonded molecules on surface hydroxyls of MCM-41, and physisorbed molecules in mesopores, respectively. We designate here the 2265 cm -~ band as the v2ct band and the 2254 cm -1 band as the v2[~ band. The bandwidth of the fundamental transition Vzf[3, was obtained by removing the overlap with hot band transitions of the same mode, VzCt band, and other modes by least-squares fitting. Before capillary condensation, the relaxation time 9 obtained from the bandwidth of the yell3 band was smaller than that of the bulk liquid, indicating presence of weakly hindered rotation. After capillary condensation, 1: was slightly longer than that of the bulk liquid, suggesting that the motion of acetonitrile molecules condensed in mesopores is prohibited in comparison with that of liquid acetonitrile at the same temperature.

1. Introduction

Although capillary condensation theory has devoted to the determination of pore size distribution of mesopores, adsorption studies on regular mesoporous silica such as MCM-41 [1,2] or FSM [3,4] pointed that classical capillary condensation theory cannot explain the dependence of the adsorption hysteresis on the pore width. Also we have assumed that condensed states in mesopores have the same as bulk liquid. In case of molecules adsorbed in

252 micropores it was found that molecules in micropores form a molecular assembly whose structure is different from that of liquid. Hence the molecular states of molecules adsorbed even in mesopores should be different from those of bulk liquid. The band shape analysis of vibrational spectra provides a useful information about dynamics of condensed molecules. Since the original works of Gordon [5] and Shimizu [6] in which the infrared band profiles of dense gases, liquids, and solutions are represented by Fourier transformation of the time-correlation function of the vibrational transition moment, many studies have been reported on the molecular motion in condensed phase [7,8]. A molecule in the condensed state changes its temporal equilibrium orientation owing to the frequent collisions with its surroundings. The molecular reorientational relaxation in condensed phase causes the broadening of the bands. Also the band broadening stems from the vibrational relaxation, of which main process is vibrational dephasing. The dephasing process is the vibrational analogue of a ~-process in nuclear magnetic relaxation [7]. Thus, the bandwidths of infrared absorption band have the contributions of the two relaxation processes. However, an exact analysis of the adsorption band is not easy. In the preceding letter [9], we studied the rotational-vibrational relaxation of acetonitrile molecules confined in mesopores of MCM-41 and assumed the Gaussian curve for the absorption peak owing to hydrogen-bonded molecules with surface hydroxyls of MCM-41 in order to understand the molecular state of physisorbed molecules upon capillary condensation. In this work, we developed new band analysis for more reliable information on molecular states of acetonitrile in cylindrical mesopores of MCM-41 at 303 K. Acetonitrile is a symmetric top molecule and has a very large dipole moment (3.92 D), which plays a key role in the reorientational relaxation [ 10].

2. Experimental MCM-41

samples were prepared by Johannes Gutenberg University. The detailed

preparation procedure was given elsewhere [11]. The pore structure of MCM-41 was determined by N 2 adsorption at 77K. The surface area, pore volume, and pore width were 940 m2 g-~, 0.74 ml g-', and 3.2 nm, respectively. Acetonitrile of spectroscopic grade reagent from Wako Pure Chemicals was used. The adsorption isotherm of acetonitrile was measured at 303K using the computer-controlled volumetric apparatus [12]. The infrared spectra of acetonitrile adsorbed on MCM-41 were measured at 303K using an in situ IR cell with KRS-5 windows with the aid of an FT-IR spectrometer (Jasco FT/IR-550). The infrared spectrum was measured with the summation of 256 consecutive scans and a resolution of 1 cm -~. The

253 MCM-41 powder was uniformly coated on the KBr disk under the pressure of 5MPa for the ir measurement, which does not induce the destruction of pore structures [13].

3. Results and Discussion 3.1. Adsorption isotherm and infrared spectra. Adsorption isotherm of acetonitrile on MCM-41 at 303K was shown previously [9]. The adsorption isotherm had a sharp jump at P/P, = 0.3 without an adsorption hysteresis, indicating capillary condensation in regular mesopores. Also the adsorption isotherm had a well-defined plateau, which provides clear evidence for the upper limit of capillary condensation. The value of the BET monolayer capacity, nm, for acetonitrile was 4.5 mmol g-~. By assuming the surface area from nitrogen isotherm to be available for the adsorption of acetonitrile, we may calculate the apparent molecular area, am, of adsorbed acetonitrile from the value of n m. The value of a m for adsorbed acetonitrile (0.37 nm 2) was quite different from the value (0.22 nm 2) which was calculated from the liquid density by assuming the close packing as the bulk liquid. This result indicates that the BET monolayer cannot be regarded as a perfect close-packed monolayer and a specific adsorption of acetonitrile takes place. Fig. 1 shows the infrared spectra of adsorbed acetonitrile in the C : N stretching v 2 region over the range of P/Po = 0.05-0.37. The amounts adsorbed at P/P, = 0.05 and 0.15 are 70% and 98% of the monolayer capacity. Hence the absorption bands at P/P, = 0.05 and 0.15 are assigned to acetonitrile molecules in the monolayer. The band at 2265 cm ~ can be associated with the C - N stretching v 2 band of the molecule interacting with surface hydroxyls of MCM41, because the growth of the 2265 cm -~ band coincides with the disappearance of the absorption band of free surface hydroxyls at 3744 cm -~. According to Purcell [14] the C - N frequency increases, when acetonitrile forms a coordination complex with an electron acceptor molecule and the N2s orbital overlapping with the C2.~ and C2p,, orbitals is responsible for the observed strengthening of the C-:N bond upon coordination of the acetonitrile to Lewis acids. The C--N stretching v 2 band at 2265 cm -~ shifts upward by 11 cm -~ from the bulk liquid phase value. Consequently, this upward shift is due to increase of the C--N force constant of the acetonitrile molecule hydrogen-bonding with surface hydroxyls. In the case of decationized zeolite sample having OH groups, similar spectral features were reported [15]. Above P/Po = 0.3, a new band is explicitly observed at a low-frequency side of the 2265 cm -~ band.

This band

becomes

predominant

above

the adsorption jump

(after capillary

condensation). Also the band position of the lower frequency band agrees with that of the bulk liquid acetonitrile. This suggests that the band at 2254 cm -~ can be assigned to the

254

vibrational transition due to physisorbed molecules with non-specific interactions In order to assign the absorption bands of adsorbed acetonitrile exactly, the observed spectra in the C--N stretching v2 region were carefully analyzed. As a first step of the analysis of the v2 band, we got second derivative curves from the observed spectra in the 2320-2220 c m -I

range (Fig. 2). At P/P,,- 0.05, the second derivative curve has minima at 2298 and 2265

cm -1 which correspond to the band positions. The curve around 2298 cm ~ which originates from the band of the combination v3 + v4 transition is considerably symmetric, while the curve around 2265 cm -1 (v2 transition of the hydrogen-bonded acetonitrile) is slightly asymmetric owing to another component of the low-frequency side. Above P/P, - 0.05, the minimum at 2254 cm -l becomes quite apparent, indicating the presence of the physisorbed acetonitrile. Nevertheless the 2254 cm -1 band is smeared 0.7

out in the case of the infrared spectrum at

P/P

0.6

P/Po = 0.15, we can say that there are two

V

'"

"

p

kinds of the molecular states of hydrogen-

bonded and physisorbed acetonitrile above P/Po

0 15 at least (Fig. 2 (b)) o

,

We

;,"'~i I-?,, t

,7_, o.5

~0.4

designate here the v 2 band of hydrogen-

o.2 7.~k

bonded acetonitrile as the v,ot band and that

o. 1

of physisorbed acetonitrile as the v213 band.

0

2265 cm -z band at P/P, --- 0.05 cannot be attributed

to the physisorbed

However there

molecules.

is another possibility

as

o.2o

",,"::",',"k

i

o.o5

/

..

i

2280 2260 2240 -1 Wave number / cm

2300

Thus the low-frequency component of the

0.24

L , ~ ' . . .t

/

"

;;2)

F - ~ - - \ ,1.

,, + v

,~

()~-,

J ,t

E

.~ 0.3

q)

"~ 0.37 0.33

2220

Fig. l. Change of infrared absorption of acetonitrile adsorbed on mesopores as a function of

P/t;,

in the C -=

N stretching v_, region at 303 K.

described later. *...,

3.2. Band shape of liquid acetonitrile. It is well known that the v2 band of liquid

\.

/

=

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

,

% "

L_

"~''J

,

~

i r'~_j/".

b w

k

~, r~....

- -

acetonitrile is significantly asymmetric due to overlap of hot band transitions in the low

/

,)=., e=. ,m,,

C

9

j

frequency side. From a study of gas phase rotation-vibration

spectrum

[16], the hot

,

,~

.

i

. . . . . . . . .

2300

|

. . . . . . . . .

2250

i

. . . . .

2200

W a v e n u m b e r / crrr 1

band transition from the first exited state of

gig.2. Second derivative curves from the observed

the degenerate C - C - N bending vs mode, v~h~

spectra of adsorbed acetonitrile in the 2320-2220 cm ~

= v2 + v8 - vs, has its center at 4.944 cm -~

range at (a)

P/P,,

= 0.05, (b) 0.15 and (c) 0.20.

255

lower than that of the fundamental transition,

V2f. Also the existence of v~ " = v2 + 2vs - 2v~

transition is expected. The v~ band of liquid acetonitrile has been studied in detail by Hashimoto et al [10] in order to determine reorientational and vibrational relaxation times of liquid acetonitrile. They showed that the peak position and bandwidth of the hot band transitions were not the same as those of the fundamental transition, but those contributions to the fundamental transition can be corrected using the Boltzmann distribution; they succeeded to separate the component bands. In the preceding paper [9], we used their method to determine the molecular motion of acetonitrile in mesopores.

3.3. Accurate band shape analysis of adsorbed acetonitrile. As the hot band transitions should exist in both of the v~ band of hydrogen-bonded and physisorbed acetonitrile, we must get the accurate v_, band without the effect by the hot band transitions. We have to determine the analytical functions for fundamental transitions of vefot and

v2t'6 and for hot band transitions upon the least-squares procedure. We assumed that

the reorientational-vibrational relaxation processes of physisorbed acetonitrile could be described as a diffusion process like bulk liquid molecule, whose spectral density has a Lorentzian form. Accordingly it is supposed .

that the

,

9

.

.

,

.

'V2[~ band is reproduced as a sum of

.

.

,~'~

,

9

.

.

,

.

.

.

~

b

three Lorentzian curves of the v2fl3, v)Zl 3 , _ and

v2h26 bands. In the previous study [9], it was

", %'

assumed that the v2fot band has a Gaussian band shape and the hot band transitions could be ignored. In the present study we assumed

4-

V 4

/

i~

"

-

"

g ....j

that the v2ot band over the range of P/P,, = 0.15-0.37 was represented by the band profile measured at P/Po = 0.05, because there are

V

~


-

relation between the absorbance of the v2fl3 band and P/Po has a steep upward jump at P/Po - 0.3. This steep jump stems from

capillary gradual

condensation, increases

of

whereas the

other

absorbance

03 "~ ~02

'v2f[~ bands

'

9.:

,

9

0

increase. In this fitting procedure, each of

-,"

.'

0 1

correspond qualitatively to the adsorption the intensities of the

.... "

~,

9

_-4rjZ

0.1

0.2 P/P

0.3

0.4

over the

Fig.4. Changes in absorbance of the v,(t and x,2t~ bands

range of P/Po - 0.15-0.37, was smaller

with adsorption. Open and solid symbols denote the v2u

than

show the previous results.

that

of

previously

studied

vzf13

and v.,'l~ bands, respectively, and the plots with dashed line

intensities. This result suggests that the 4.5

intensity of the v2f13 band is overestimated in the previous fitting procedure because of ignoring the hot band transitions of the

,->

'~ r

= 0.15,

suggesting that the effect of

(,

--5

~t-species. Both of absorbance curves of the v2et band increase gradually above P/Po

40

3.5

,,

.,2

molecule

concerned.

This

is

also

evidenced by the fact that the absorbance of the O-H stretching band of hydrogen-

-O

3.0

adsorbate-adsorbate interaction is increases the dipole moment of the C - N bond of the

(

"'\~,

t~

200

j

ads

des

- - v m B_Fe203---v--

100

T/T c = 0.61 0

A

0.0

I

0.2

1

,

0.4

,

1

0.6

A

1

0.8

,

,..I

1.0

relative pressure P/P0 Figure 1. Nitrogen adsorption/desorption isotherms at 77 K for the pristine MCM-48 silica B and the host/guest compound B-Fe203.

Adsorbent

SBET Vpore [m2/g] [cm3/g]

dp(BJH) [nm]

Dh dp(SF) Vp(SF) [nm] [nm] [cm~/g]

Table 1. Characterization of the pristine MCM-48 silica B and the host/guest compound BFe203 with respect to specific surface area, pore size and pore volume using various methods (BET-specific surface area SBET, BJH-mode pore diameter dp(BJH), average pore diameter Dh = 4 Vpore/SBEv. In addition argon sorption isotherms at 87 K for both materials were analyzed with respect to pore size (dp(SF)) and pore volume (Vp(SF)) by applying the SaitoFoley method. In Figure 1 nitrogen sorption isotherms at 77 K for the pristine B and impregnated B-Fe2Os MCM-48 silica materials are shown. Both sorption isotherms exhibit similar shape, i.e reversible pore condensation at p/p0 < 0.4. The MCM-48 silica phases exhibit no microporosity as revealed by measurements in the low pressure region [13]. Different methods were used to analyze the nitrogen sorption isotherms to obtain surface and pore size

263

characteristics for the two MCM-48 systems. The results are summarized in table 1. The insitu formation of iron(III) oxide within the pores of the pristine MCM-48 silica phase results in a decrease of specific surface area, pore volume and pore diameter. Although the results obtained for the mode pore diameter by analyzing the nitrogen sorption isotherms at 77 K with the BJH-method and argon sorption isotherms at 87 K with the Saito-Foley (SF) method differ in absolute value, in all cases the pore diameter of the impregnated MCM-48 silica phase was lowered of about 0.3 nm compared to the pristine MCM-48 phase. A similar shift in the pore diameter was obtained by calculating the average pore diameter according to Dh = 4 Vpore/SBET, by assuming cylindrical pores. These results reveal still mesoporosity for the MCM-48 silica/iron(III) oxide system, accompanied by a reduction of the pore width, which is together with results from HRTEM, EDX and XAFS [14,15] a good indication for a coating of the inner surface of the silica walls. However, it should be noted, that methods like the BJH, which are based on the macroscopic Kelvin equation, provide not a reliable basis for the calculation of pore widths < 5 nm [ 11,16,17]. Compared with new methods that rely on microscopic descriptions like the density functional theory (DFT) and Monte Carlo computer simulation (MC), the macroscopic thermodynamic methods underestimate the calculated pore diameter by ca. 1 nm [11,17]. In addition, it is argued that in case of nitrogen as adsorptive the BJH and related methods based on the Kelvin equation cannot be applied below a relative pressure p/P0 = 0.42 because this relative pressure is considered as the limit of the thermodynamic stability of liquid nitrogen. Hence, pore sizes obtained by application of the BJH method should be regarded as apparent rather than real pore sizes [7].

3.2. Results of systematic sorption studies of Nitrogen, Argon and Krypton at 77 K and 87 K on different pristine MCM-48 silica materials N 2 / 77K

700 600 500

E

400

O

E 3oo o >

ads ---~

~

~-

200

--o--- C - - ~ T/T c = 0.61

100 k

0.0

des A-----~

,

I

0.2

,_

,

,

I

0.4

~

[

0.6

,

I

0.8

......

,

I

1.0

relative pressure P/P0 Figure 2. N2 sorption isotherms at 77 K on pristine MCM-48 silica phases A [dp,N2(BJH)" 2.67 nm], B [dp.N2(BJH)" 2.52 nm], and C [dp,N2(BJH)" 2.04 nm].

264

Ar / 87K

700

,.J

600 500

c~

E

'o

400

E

300

o>

200

ads

des

--~-- A - - - - - "--""~

B

~ A ~

____o_~ C _ . _ ~ _ - ~

100

f

0

!

T/T c = 0.58 ~

0.0

I

~

0.2

I

,

0.4

1

~

I

0.6

~

I

1.0

0.8

relative pressure P/P0 Figure 3. Argon sorption isotherms at 87 K on pristine MCM-48 silica A [dp,N2(BJH)" 2.67 nm; dp,Ar(BJH) = 3.0 nm], B [dp,N2(BJH): 2.52 nm; dp,Ar(BJH)= 2.81 nm], and C [dp,N2(BJH): 2.04 nm; dp,A~(BJH)= 2.52 nm].

Ar / 77K 700

- ._,.,,,L,,i.~e4s.-pO=aN4 4,,O-m'i H ~

600

"9

E

500

o,.=...,,

400

E

300

ads

des

~ O ~

A

.----.~

B

~ - - - -

C

- ~ .._..._.A~ @

0

>

200

r

T/T = 0.51 T/T = 0.92

100

0.0

L

019

._

,

I

0.4

a

I

0.6

J

i

0.8

~

I

1.0

relative pressure P/P0 Figure 4. Adsorption/desorption isotherms of argon at 77 K on the same MCM-48 silicas as in figure 3. In all cases pore condensation accompanied by sorption hysteresis is observed.

265

Ar / 8 7 K and 77K

700

77 K / ~ z ~ ~

600 ~o 500

E

~,

o

300

o

200

E

. ~ A (MCM-48)

400

t~~'~~cd~',~ ads < > o

1

87 K

des

87K

*

CPG

100

0

i

0.0

,

i

0.2

,

0.4

~

,

0.6

i

,77 K~

0.8

1.0

relative pressure P/Po Figure 5. Temperature dependence of sorption hysteresis for argon sorption on MCM-48 material A [dp,N2(BJH) = 2.67 nm] and for comparison on controlled-pore glass [dp,N2(BJH)= 15.7 nm].

Kr / 87K

700 -

~

600 500

~___~__~_l~------~~

/ -

'~

400

~'ll/ //~

'~

300

j

:E

I

tt

ads

--v--

/ ~ 1 1 ~ v

"-~ 200

~ &

des

--o--A --~--C

/g

i.d2J

.

v . ,, v .

v .

v v.

--'---'--

B-FezOs--v-.

,,

.

.

~7

~7~V

T/Tc = 0.41

100

oo

A&

'0'2

'o14'

o16'

o'8'

,'0

relative pressure P/Po Figure 6. Krypton sorption at 87 K (T/Tc = 0.41, i.e. T-Tc ~ 122 K; T/Tt = 0.75, i.e Tt-T ~ 28.5 K) on pristine MCM-48 silicas" A, C, B-Fe203. For A an overlay plot of two subsequently performed sorption isotherms is shown. The results for nitrogen, argon and krypton adsorption on pristine MCM-48 materials can be summarized as follows: (i) Argon sorption isotherms at 87 K (T/Tc = 0.58, where Tc is the critical temperature of the bulk fluid) reveal for all MCM-48 silica phases used in this study pore condensation but no hysteresis at relative pressures p/po < 0.4. With increasing pore size

266 the occurence of pore condensation is shifted to higher relative pressures as expected from classical theories of pore condensation. (ii) Argon sorption isotherms at 77 K (T/T~ = 0.51; TtT ~ 6.5 K, where Tt is the triple point temperature of the bulk fluid ) show for all MCM-48 silicas pore condensation and sorption hysteresis of type H1 (IUPAC classification). The width of the hysteresis loop increases slightly with increasing pore diameter. Nitrogen sorption isotherms at 77 K (T/Tc = 0.61) in MCM-48 silicas show however no hysteresis, but still pore condensation. (iii) Krypton sorption isotherms at 87 K (T/Tc = 0.42; Tt-T ~ 28.5 K) on MCM48 silicas show a phase transition accompanied with pronounced hysteresis. The width of the hysteresis loops increases with increasing pore size. These results indicate that the shape of sorption isotherms of pure fluids on MCM-48 silicas, i.e. the occurence of pore condensation and sorption hysteresis as well as details of the hysteresis loop depend on the pore size and temperature. The observed hysteresis loops are of type HI, indicating that networking effects are not dominant for sorption hysteresis in the MCM-48 silica materials studied here, despite the fact that MCM-48 consists of a unique three dimengional pore network. The reversible pore condensation at P/P0 < 0.4 observed for nitrogen sorption at 77 K on the MCM-48 silicas used in this study was also observed in MCM-41 silica materials of pore diameters 2 - 4 nm [11,12]. These observations are in accordance with the expectation that the lower closure point for nitrogen sorption hysteresis at 77 K is around P/P0 = 0.42, which was originally considered as the limit of thermodynamic stability of the liquid nitrogen meniscus [6]. Recent theoretical studies [18] and computer simulations [19] indicate, that pore wall roughness and details of the fluid-wall interaction may also be significant for the disappearance of nitrogen sorption hysteresis in M41S materials. In a comprehensive discussion on the lack of hysteresis in N2 isotherms at 77 K in MCM-41 [11] it was assumed, that in the limit of small mesopores or with increasing temperature the contribution of thermal fluctuations to the nucleation of the capillary phase becomes important, which may lead to the occurence of capillary condensation close to the equilibration transition, i.e. pore condensation without hysteresis. However, in larger mesopores (> 4 run) or at lower temperatures fluctuation effects are not dominant, i.e. hysteresis occurs, which is attributed to a delayed nucleation of the capillary phase. In accordance with these arguments it is also expected that sorption hysteresis disappears on approaching the critical temperature of the pore and (bulk) fluid [8]. The observed disappearance of sorption hysteresis in the temperature range from 77 K to 87 K for argon sorption on the MCM-48 silicas (Figures 3 and 4), is consistent with this picture. The difference in the occurence of hysteresis for nitrogen and argon at 77 K can also be explained as a consequence of the lower reduced temperature T/To of argon compared to nitrogen, where Tc is again the critical temperature of the bulk fluid. (T/Tc(Ar) = 0.51; T/Tc(N2) = 0.61). As indicated before the locus of the phase diagram of a confined fluid compared to the coexistence curve of the bulk fluid is of importance for the occurence of pore condensation and hysteresis, i.e. for the shape of the sorption isotherm. It is expected that the critical temperature and the triple point temperature will be shifted to lower values for a confined fluid compared to a bulk fluid, i.e. the smaller the pore width the lower the critical temperature and triple point temperature of the pore fluid [8,9,20]. Pore condensation occurs whenever the pore

267 condensation line is crossed, along either an isothermic or isochoric path. The pore condensation line reflects the locus of states (T-p) of the unsaturated vapor at which pore condensation will occur in pores of given size and shape. It terminates in a pore critical point at a temperature Tcp < Tc, where Tc is again the critical temperature of the bulk fluid [8,9]. Above the critical temperature Tcp of the pore fluid pore condensation and sorption hysteresis do not occur anymore. However, not well understood is so far the pore condensation behavior at temperatures near and below the triple point of the bulk fluid. In a recent study [20] of the phase behavior of CO2 in vycor glass (mean pore width ca. 4 nm) using positron and positronium annihilation spectroscopy, it was found that the pore condensation line terminates in a (quasi) pore triple point, which is shifted significantly to lower temperatures compared to the bulk fluid. Within this context the very different argon sorption behavior observed for MCM-48 silicas and controlled-pore glass at 77 K and 87 K (see figure 5) may be discussed in the following way: At 87 K pore condensation and hysteresis occurs for Ar in CPG, which indicates that the pore condensation line is crossed well below the pore critical temperature but above the triple point temperature of the pore fluid. The lack of pore condensation and hysteresis for argon in CPG indicates that there may be no extension of the pore condensation line down to 77 K, which is ca. 6.5 K below the triple point temperature of the bulk fluid; only adsorption exists in the pores without any phase transition until solidification of the bulk fluid occurs (in case of Ar sorption at 77 K the saturation pressure of Ar solidified in a special P0cell was chosen as reference P0, which was measured continuously during the sorption experiment). The sorption isotherms of Ar in MCM-48 reveal pore condensation and hysteresis at 77 K, indicating that here in contrast to the Ar/CPG system the pore condensation line extends at least down to this temperature. This implies that the triple point of the confined argon in MCM-48 silica of pore width < 4 nm is shifted more than ca. 6.5 K to lower temperature compared to bulk argon. Futher work is necessary to come to a more comprehensive understanding of the observed phenomena [13]. Another point of view is that one should use instead of the saturation pressure of solid argon at 77 K (as used in this study) the saturation pressure of the supercooled liquid. In this case one may argue that it is not possible to measure a complete argon isotherm at 77 K as bulk solidification occurs before the saturation pressure for liquid argon occurs, which would lead to a truncated isotherm without capillary condensation and hysteresis for argon in CPG at this temperature. Phase transitions of the pore fluid were also observed for krypton in MCM-48 silica materials at 87 K, which is 26.5 K below the bulk triple point [13]. Remarkably, the width of the hysteresis loop decreases with decreasing pore size, which may indicate that at 87 K the pore fluid of C is much closer to pore criticality as the confined fluid in A (in case the observed phase transitions for krypton in MCM-48 silica reflect still a gas-liquid phase transition). For krypton/A an even broader hysteresis loop is observed at 77 K compared to 87 K [13]. Recent work on MCM-41 of mean pore diameter 4 nm indicated a solidification of the krypton capillary phase at 77 K [21]. The observed phase transitions of krypton in the MCM-48 silicas will be investigated in more detail in further studies [13].

REFERENCES [1]

U. Ciesla and F. Schfith, Microporous Mesoporous Mater., 27 (1999) 131; A. Corma, Chem. Rev., 97 (1997) 2373; K. Moeller and T. Bein, Chem. Mater., 10 (1998) 2950

268

[2] [3] [4]

[5] [6] [7]

[8] [9] [10] [11]

[12] [13] [14] [15]

[16] [17]

[18] [19] [20] [21]

X. Auvray, C. Petipas, R. Anthore. I. Rico, A. Lattes, J. Phys. Chem., 73 (1989) 7458 J. S. Beck, J. C. Vartuli, W. J. Roth, M. E. Leonowicz, C. T. Kresge, K. D. Schmitt, C. T.-W. Chu, D. H. Olson, E. W. Sheppard, S. B. McCullen, J. B. Higgins, J. L. Schlenker, J. Am. Chem. Soc., 114 (1992) 10834 T. Abe, Y. Tachibana, T. Uematsu and M. Iwamoto, J. Chem. Soc., Chem. Commun., (1995) 1617 Z. Y. Yuan, S. Q. Liu, T. H. Chen, J. Z. Wang, H. X. Li, J. Chem. Soc. Chem. Commun., (1995) 973 S. J. Gregg, K. S. W. Sing, Adsorption, Surface Area and Porosity, Academic Press, London, 1982 F. Rouquerol, J. Roquerol, K. S, W. Sing, Adsorption by Powders & Porous Solids, Academic Press, London, 1999 R. Evans, J. Phys. Condens. Matter 2, (1990) 898 M. Thommes and G. H. Findenegg, Langmuir, 10 (1994) 4270; G. H. Findenegg and M. Thommes, in: Physical Adsorption: Experiment, Theory and Applications, J. Fraissard (ed.), Kluwer, Dordrecht, 1997 K. S. W. Sing, D. H. Everett, R. A. W. Haul, L. Mouscou, R. A. Pierotti, J. Rouquerol, T. Siemieniewska, Pure & Appl. Chem., (1985) 57 P. I. Ravikovitch, S. C. O. Domhnaill, A. V. Neimark, F. Sch~th, and K. K.Unger, Langmuir, 11 (1995) 4765; P. Ravikovitch. D. Wie, W. T. Church, G. L. Haller and A. W. Neimark, J. Phys. Chem. B 101, (1997) 3671 J. P. Branton, P. G. Hall, K. S. W. Sing, H. Reichert, F. Schfith, and K. K. Unger, J. Chem. Soc., Faraday Trans. 90, (1994) 2965 M. Thommes, R. K6hn and M. Fr6ba, Microporous Mesoporous Mater., 1999, submitted M. Fr6ba, R. K6hn, G. Bouffaud, O. Richard, G. van Tendeloo, Chem. Mater. (1999) in press R. K6hn, G. Bouffaud, O. Richard, G. van Tendeloo. M. Fr6ba, Mat. Res. Soc. Sym. Proc. 547, (1998), 81 Lastoskie, K. Gubbins, N. Quirke, J. Phys. Chem., 97 (1993)4786 K. E. Gubbins, in: Physical Adsorption: Experiment, Theory and Applications, J. Fraissard (ed.), Kluwer, Dordrecht, 1997 S. Inoue, Y. Hanzawa, and K. Kaneko, Langmuir 14. (1998) 3079 M. W. Maddox, J. P. Olivier, K. E. Gubbins, kangmuir, 13 (1997) 1737 H. M. Fretwell, J. A. Duffy, A. P.Clarke, M. A. Alam and R. Evans, J. Phys.: Condens. Matter, 8 (1996) 9613 J. P. Coulomb, Y. Grillet, P. L. Llewellyn, C. Martin and G. Andre, in: Fundamentals of Adsorption, F. Meunier (ed.), Elsevier, Paris, 1998

ACKNOWLEDGEMENTS RK and MF thank Prof. Armin Relier for his support. Financial support by the Deutsche Forschungsgemeinschaft (Fr 1372/1-1, Fr 1372/2-1, Fr 1372/4-1), the Wemer-Ranz Foundation, the Fond der Chemischen Industrie, and the University of Hamburg is gratefully acknowledged. MT thanks Gerd Scharschuh (Quantachrome GmbH) for technical support.

Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 9 2000 Elsevier Science B.V. All rights reserved.

269

Synthesis and characterization o f ordered m e s o p o r o u s M C M - 4 1 materials J.L. Blin, G. Herrier, C. Otjacques and Bao-Lian Su* Laboratoire de Chimie des Materiaux Inorganiques, I.S.I.S, Universite de Namur, 61, rue de Bruxelles, B-5000 Namur, Belgium

The synthesis of mesoporous materials has been investigated at various conditions. The nature, the pore size, the wall thickness, the channel array and the morphology of the obtained materials have been characterized by powder X-ray diffraction, BET and Scanning Electron Microscopy. The present work shows that in the studied conditions, the pore diameter remains relatively constant while the thickness of the walls increases significantly with increasing time and temperature, signifying that the condensation of the source of silicium around the micelles is enhanced. From the characterization results, a synthesis mechanism is postulated.

1. INTRODUCTION Since the discovery in the early nineties, mesoporous molecular sieves attracted much research attention due to a number of remarkable properties of these materials such as the adjustable pore size, the high surface area and pore volume, the high thermal stability and the ease of surface modification. These materials have been therefore widely used as catalyst and catalyst support in various reactions. These materials were synthesized based on the use of assemblies of surfactant molecules as framework templates. Surfactants are larger organic molecules with a hydrophilic head and a long hydrophobic tail of variable length. In aqueous solution, these molecules pack together to form first isolated spherical, then cylindrical micelles and finally higher-ordered phases, depending on solution conditions. The synthesis of pure siliceous mesoporous molecular sieves consists of the condensation and polymerization of an inorganic source of silicium around the micelles of surfactant. Electrostatic pathways, based on a supramolecular assembly of charged surfactants (S- or S) with charged inorganic precursors (I or I-) S-I, S ' X I (X = CI-, Br), S M I (M - = Na-, K*) [1-3] or neutral pathway S~ ~ [4-6] can be used for preparation of the mesoporous materials. The wall thickness, the pore diameter and the nature of the final structure : hexagonal MCM41, cubic MCM-48 or lamellar MCM-50, are affected by several physico-chemical factors such as kind of surfactant [ 1], silicium/surfactant molar ratio [ 1], pH value [7], crystallization time and temperature. The influence of the first parameters on mesoporous materials synthesis has been widely studied. In this work, we have investigated the effect of some physical variables such as crystallization time and temperature on the MCM-41 synthesis, on the pore

* Corresponding author

270 size and, in particular, the thickness of walls separating two pores of materials obtained using the Sq-pathway. The intermediate and final phases obtained at different crystallization temperature and time have been intensively characterized in order to find the optimal physical conditions for the synthesis of the mesoporous molecular sieve (Si)-MCM-41. 2. EXPERIMENTAL 2.1. Synthesis All syntheses were made according to the following scheme, H2SO4

]

Sodiumsilicate solution

~ 9 .

stirring I H2SO4 I

pHadjustment

stirring ~

A

/

/

J

~

/

Micellar solution of surfactant

+ l Gel F + Hydrothermal treatment at different temperatures and times

+

Solvant extraction

Drying

Powders Synthesis scheme of mesoporous molecular sieves (Si)-MCM-41. Cetyltrimethylammonium bromide (CTMABr) was dissolved in water at 40~ a clear micellar solution was obtained. Then sodium silicate was added to this solution and the pH value was adjusted with sulfuric acid. pH value and surfactant/silicium molar ratio were fixed at 10 and 0.62 respectively according to literature [8]. After stirring for several hours at room temperature, the homogenous gel with the molar composition of 1 CTMABr : 0.63 SiO2 : 102 H20 was sealed in Teflon autoclaves and heated. The crystallization temperature and time varied respectively from 80~ to 140~ and from 1 day to 11 days. The obtained solid phases after ethanol extraction with a Soxhlet apparatus were dried in vacuum at 100 ~ overnight.

271 2.2. Characterization Powder X- ray diffraction patterns of the obtained materials were recorded on Philips PW 170 diffractometer, using CuKa (1.54178 h) radiation, equipped with a thermostatisation unit (TTK-ANTON-PAAR, HUBER HS-60). Micrographs of the obtained intermediate and final phases were made from Philips XL-20 Scanning Electron Microscope (SEM) using conventional sample preparation and imaging techniques. Nitrogen adsorption- desorption isotherms were obtained from a volumetric adsorption analyzer AS AP 2010 manufactured by Micromeritics. The samples were degassed for several hours at 250~ The measurements were carried out at-196 ~ over a wide relative pressure range from 0.01 to 0.995. The pore diameter and the pore size distribution were determined by the BJH method [9].

3. RESULTS AND DISCUSSION 3.1. Identification of intermediate and final phase by XRD Figure 1 reports the XRD patterns of materials obtained at crystallization temperatures of80~ (a), 100~ (b), 120~ (c) and 140~ (d) after 1 (Fig. 1A), 4 (Fig. 1B), 6 (Fig. 1C), 8 (Fig. 1D) and 11 (Fig. 1E) days. It is well known that the XRD difffactogram of MCM-41 materials exhibits at least 3 peaks characteristic of the 100, 110 and 200 reflections in the small angle region. If the two last ones are not detected, the channel array of materials is disordered and not hexagonal [ 10]. For a well-ordered hexagonal MCM-41, the unit cell ao (= 2d100/(3)v2) is the sum of the pore diameter and the thickness of the wall separating two adjacent pores. From figure 1, it is obvious that 80~ is a too low temperature. An important amount of amorphous phase is detected in the range of 200 1 day at 140~ leads to the formation of a tri-phasic mixture. By comparing the XRD pattern of our sample prepared at 120~ for 11 days (figure IF) with that published by Huo et al [11 ], the hexagonal MCM-41, the lamellar MCM-50 (indicated by *) and the amorphous phase (the broad peak in the range of 200 11 days at 120~ and > 1 day at 140~ lead to the formation of a triphasic mixture (MCM-41, lamellar MCM-50 and amorphous phase). 3.2. The morphology of the intermediate and final phases determined by SEM Figure 2 depicts the variation of Scanning Electron Micrographs with crystallization time at different temperatures. At the beginning of the crystallization, the texture of obtained solid phase can be described as an agglomeration of fibrous (Fig. 2a, 2b, 2d). The 110 and 200 reflections are not present in the XRD pattern at this moment. When those reflections appear, the morphology characteristic of MCM-41 described by Tanev et al [6] or Elder et al [12] is detected (Fig.2e, 2f, 2h, 2j). Crystals have variable size and form and very porous surface. Finally when the triphasic mixture composed of hexagonal MCM-41, lamellar MCM50 and amorphous phase is detected (Fig. 2i, 2k, 21), crystals with a "sandy-rose like" structure and spheric grains are clearly observed. The "sandy-rose" crystals belong to the MCM-50 lamellar structure [13] and the spheric grains correspond to the amorphous silica phase. The presence of MCM-50 and amorphous silica is proved by XRD patterns.

Figure 2. Variation of the morphology of intermediate and final phases with crystallization time at different temperatures a : 4; b, c : 8; d : 0.33; e, f: 11; g : 0.25; h : 4; I : 11; j : 1; k : 6;1:11 (days).

274

3.3. Characterization by nitrogen adsorption-desorption Nitrogen adsorption- desorption isotherms of all obtained samples are type IV, characteristic of mesoporous materials according to the classification of BDDT [ 14]. Figure 3 depicts an adsorption-desorption isotherm of nitrogen (a) and the pore size distribution curve (b) determined by the BJH method for sample obtained at 120~ for 4 days. Isotherms can be decomposed in three parts :the formation of the Langmuir's monolayer, a sharp increase characteristic of the capillary condensation of nitrogen within the mesopores and finally the saturation. For crystallization time less than 8 days at 80~ or 4 days at 100~ the sharp increase due to the capillary condensation is not clearly observed and the volume of nitrogen adsorbed is low. This is due to the presence of an important quantity of amorphous phase in the sample. The same observations can be made for long crystallization time at higher temperatures (> 11 days at 120~ and > 1 day at 140~ For other samples (> 8 days at 80~ between 6 and 11 days at 100~ between 1 and 8 days at 120~ and 1 day at 140~ the capillary condensation step is quite evident and it occurs at the almost same relative pressure p/p0 (about 0.35). This indicates that samples are very homogeneous and that the-pore diameter remains almost constant for all samples obtained since the p/p0 position of the inflection point is related to the pore diameter. We can also see from figure 3b that the pore size distribution is very narrow and centered at about 2.6 nm. However, the X-ray diffraction results demonstrate that the dl00 spacing and a0 values, which are summarized in Table 2 and the wall thickness as well, increase significantly with crystallization time and temperature (Table 2). Since a0 is the sum of the pore diameter and the thickness of the walls separating two adjacent pores, the constant pore size obtained by the BJH method and the increase in ao value from XRD indicate that the wall thickness increases with the increasing crystallization time and temperature. This suggests strongly that the silica condensation is enhanced with increasing crystallization time and temperature.

O.lO~~]

Desorpt,on ~

"

.

~

0.08 -

250

~'~ 0.06-

i~

150

i

o.o4~

100 ;~

n.n2

50 0

j

012

,

014

,

016

,

1 08

,,

10

0.00

Relative pressure P/Po

Figure 3. Adsorption-desorption isotherm of nitrogen at-196~ (b) of obtained compounds.

5

!0

15 Pore Diameter (nm)

(a) and pore size distribution

275 Table 2 ao and dl00 values, calculated wall thickness and pore diameter of the samples obtained at different crystallization temperature (~ and time (days) Crystallization time (days) _

11

Crystallization temperature (~ ~

dloo (nm) by XRD .

ao (nm) by XRD

Pore diameter (nm) by N2 adsorption

Wall thickness (nm)

80 100 120 140

4.1 4.1 4.3 4.6

4.7 4.8 5.0 5.3

2.6 2.6 2.6 2.8

2.0 2.2 2.4 2.5

80 100 120

4.1 4.3 4.4

4.8 4.9 5.1

2.6 2.6 2.7

2.2 2.3 2.4

80 100 120

4.2 4.4 4.4

4.8 5.1 5.1

2.5 2.7 2.6

2.3 2.4 2.5

80 100 120

4.2 4.2 4.6

4.8 4.9 5.4

2.6 2.6 2.5

2.2 2.2 2.9

80 100

4.2 4.4

4.8 5.0

2.5 2.5

2.3 2.5

Figure 4 shows the variation of the specific surface area with crystallization time and temperature. From this figure, it is clear that at 80~ or at 100~ between 1 and 4 days of crystallization, only a small part of the gel is transformed into hexagonal MCM-41, the 110 and 200 reflections are not detected by XRD. Then at 100~ between 4 and 8 days the specific surface area increases up to 900 m2/g and the well-ordered hexagonal MCM-41 structure is clearly identified by XRD. At 120~ and 140~ the value of the surface area is high but it decreases very quickly when the crystallization time increases.

3.4 Proposed synthesis mechanism From the above results we can propose the following mechanism for hexagonal MCM-41 synthesis. At low crystallization temperature or short crystallization time a fibrous agglomerate structure is often observed by SEM on intermediate samples. The 100 and 200 reflections are not detected by X I ~ and the value of the specific surface area is low. This reflects the initial step of synthesis which is generally referred to the nucleation step in zeolite synthesis. After this step, the 100 and 200 reflections are present on the XRD diffraction pattern. The value of the specific surface area is between 700 and 900 m2/g. The fibrous agglomerate structure disappears and crystals of MCM-41 appear. This corresponds to the crystallization step. Finally if both the synthesis temperature and time are continuously raised, a triphasic mixture MCM-41, MCM-50 and amorphous phase is identified by XRD. The

276 specific surface area dramatically decreases and crystals with a "sandy-rose like" structure and silica spheric grains can be observed by SEM. This is due to the amorphisation of MCM41 and the transformation of MCM-41 to a more dense phase MCM-50. The proposed mechanism for MCM-41 synthesis is represented in figure 5.

1000

o.o

800

600

t~

400

.,..q

200

0

9

I

2

"

I

4

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I

6

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8

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1

12

C~stallization time (da}~) Figure 4. Variation of the specific surface area with crystallization time at different temperatures a 80~ b 100~ c. 120~ d 9140~ 4. CONCLUSION The intermediate and final solid phases obtained at different synthesis conditions have been extensively characterized by multitechniques. For the given composition and pH value, we have defined the following optimum crystallization temperature and time : between 6 and 8 days at 100~ or less than 4 days at 120~ The present work led us to postulate a synthesis mechanism which includes three steps, i.e. nucleation, crystallization and simultaneous amorphisation and transformation to more dense phase. ACKNOWLEDGEMENT 9 This work has been performed within the framework of PAI/IUAP 4-10. Gontran Herrier thanks the FNRS (Fond National de la Recherche Scientifique, Belgium) for a FRIA scholarship.

277

Figure 5. Proposed mechanism for MCM-41 synthesis. REFERENCES 1. J.S. Beck, J.C. Vartuli, W.J. Roth, M.E. Leonowicz, C.T. Kresge, K.D. Schmitt, C.T-W.

Chu, D.H. Olson, E.W. Sheppard, S.B. McCullen, J.B. Higgins and J.L. Schenker, J. Am. Chem. Soc., 114 (1992) 10834 2. C.T. Kresge, M.E. Leonowicz, W.J. Roth, J.C. Vartuli and J.S. Beck, Nature, 359 (1992) 710 3. Q. Huo, D.I. Margolese, U. Ciesla, P. Feng, T.E. Gier, P. Sieger, R. Leon, P.M. Petroff, F. Schtith and GD. Stucky, Nature, 368 (1994) 317 4. A. Sayari, Studies in Surface Science and Catalysis, 102 (1996) 1 5. P.T. Tanev and T.J. Pinnavaia, Science, 267 (1995) 865 6. P.T. Tanev and T.J. Pinnavaia, Chem. Mater., 8 (1996) 2068 7. K.J. Elder, J.W. White, Chem. Mater, 9 (1997) 1226 8. J.S. Beck, J.C. Vartuli, G.J. Kennedy, C.T. Kresge, W.J. Roth and S.E. Schramm, Chem. Mater. 6 (1994) 1816 9. E.P. Barret, L.G Joyner, and P.P. Halenda, J. Am. Chem. Soc., 73 (1951) 37 10. C.Y. Chen, S.O. Xiao, M.E. Davis, Microporous Mater., 4 (1995) 20 11. Q. Huo, D.I. Margolese and GD. Stucky, Chem. Mater., 8 (1996) 1147 12. K.J. Elder, J. Dougherty, R. Durand, L. Iton, G. Lockhart, Z. Wang, R. Whithers and J.W. White, Colloids Surfaces A : Physicochem. Eng. Aspects, 102 (1995) 213 13. Y.Z. Khimyak and J. Klinowski, Chem. Mater., 10 (1998) 2258 14. S. Brunauer, L.S. Deming, W.S. Deming and E. Teller, J. Am. Chem. Soc., 62 (1940) 1723

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Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 2000 ElsevierScienceB.V. All rightsreserved.

279

Textural and Spectroscopic Characterisation of vanadium M C M - 4 1 materials. Application to gas-phase catalysis. Philippe Trens", Agustin Martinez Feliu b, Ana Dejoz b, Regis D. M. Gougeon c, Michael J. Hudson" and Robin K. Harris c a Department of Chemistry, University of Reading, Whiteknights, Reading, Berkshire, RG6 6AD, UK b Instituto de Tecnologia Quimica, UPV-CSIC, Avenida de los Naranjos s/n, 46022 Valencia, Spain. c Department of Chemistry, University of Durham, South Road, Durham, DH1 3LE, UK. Highly ordered mesophases and calcined vanadium-containing (V-MCM41) materials have been synthesised using a quick (1 h) but reproducible method. The ordered, calcined materials may contain up to 10% vanadium(V), which is highly dispersed throughout as described by Laser Raman spectroscopy and confirmed by XRD. NMR studies indicate that V~Os-like particles develop on the surface of the walls during the formation of the mesoporous material. Upon calcination, they partly transform into tetrahedral species strongly bound to the silica walls. DR-UV-Vis shows that some V species could have migrated from the hexagonal tubular walls to the wall surface during catalysis. Catalysed oxidative dehydrogenation of propane yields better conversion than that obtained with conventional vanadium coated silicas, with a higher selectivity to propylene.

1. INTRODUCTION Solely siliceous materials only have a mild catalytic activity since the silanol groups are weakly acidic. [1] Therefore, since the discovery of the family of MCM41 materials by Mobil, there has been a considerable interest in the synthesis of new highly ordered mesoporous silicas with additional heteroatoms in order to confer, for example, greater acidities to some of the hydroxyl groups. [2, 3] These materials may contain metals such as aluminium, titanium(IV), zirconium(IV) or vanadium(V), with the heteroatoms directly incorporated into the structure. [4, 5, 6 7, 8] The metal oxides, such as vanadium oxide, have already found wide commercial application as catalysts for reduction, oxidation or dehydrogenation reactions. [9, 10, 11 ] For example, the conversion of low molecular weight paraffins into the corresponding olefins is an attractive process in the petrochemical industry which allows for upgrading of cheap feedstocks into higher value products. In this sense, the oxidative dehydrogenation (ODH) of short paraffins has been shown to be an interesting alternative to the classical dehydrogenations, which are strongly exothermic reactions and have to be carried out at temperatures above 600~ By constrast, in the ODH reactions, the hydrogen abstracted from the paraffin is oxidized, releasing heat of reaction, so they require

280 much lower reaction temperatures to achieve significant conversions [12]. Nevertheless, in order to obtain good yields and selectivities to the desired olefins, consecutive side reactions which lead to total oxidation products, CO and CO2, have to be minimized. Vanadiumsupported catalysts, particularly when supported on basic MgO, have been reported to be selective in the ODH reaction [ 13, 14, 15]. The catalytic performance of the V-catalysts for the ODH reaction strongly depends on, besides the V loading, the acid-base character of the support, which in turn affects the nature of the V species present on the surface [ 16].

2. EXPERIMENTAL

2.1. Synthesis The mesophase (uncalcined) materials for this study were prepared at room temperature within 1 h followed by calcination of the mesophase using a significant modification of the method developed by Grtin et al, for silica MCM-41 materials [17]. Solution A, which had been stirred for 30 min, contained cetytrimethylammonium bromide (CTAB, 2.4 g, Aldrich), doubly distilled water (120g) and ammonia (32%, 8ml, Merck). Mixture B contained silicon tetra-ethoxide (TEOS, 10ml, Aldrich) and the appropriate amount of vanadium (IV) as VOSO4.3H~O (Aldrich). Mixture B was added with vigorous stirring to solution A and the combined mixture was stirred at room temperature for 1 h. After this period of 1 h, the product was air-filtered, washed with doubly distilled water and dried in the oven at 80~ overnight. The dried materials were calcined in air starting from room temperature to 500~ for over 5 h, after which time the samples were allowed to cool to ambient temperature.

2.2. Analyses X-ray powder diffraction (XRD) patterns were taken on a Spectrolab CPS Series 3000 120 diffractometer, using Ni filtered Cu Kot radiation. The nitrogen adsorption isotherms were determined at 77 K by means of a Micromeritics Gemini 2370 surface area analyser. Surface areas were derived from the BET equation in the relative pressure range 0.05-0.25, assuming a cross-sectional area of 0.162 nm 2 for the nitrogen molecule [ 18]. 5~V, 29Si and ~H MAS NMR spectra were recorded at 78.75, 59.58 and 299.95 MHz, respectively, using a Varian Unity Plus 300 spectrometer, and a high-speed MAS probe from Doty Scientific. 5~V spectra were obtained by direct polarisation with a 0.4 ~s pulse duration (10 ~ pulse angle), at spinning speeds of 8 and 10 kHz. The recycle delay was chosen to be between 0.2 and 0.4 s. Following a pulse, the recovery time before the start of the acquisition was 9.9 laS. Silicon-29 NMR spectra were acquired by direct polarisation and a 4 ~ts 90 ~ pulse. Silicon-29 CP-MAS experiments were also obtained using ~H and 29Si field strengths equivalent to 62.5 kHz. All 29Si experiments have been carried out with proton dipolar decoupling. Chemical shifts were referenced to TMS and tetrakis(trimethylsilyl)silane for ~H and 29Si respectively. 5~V chemical shifts were indirectly referenced to VOCI3, through the chemical shift of the high-frequency peak of a sodium metavanadate solution (-574. 5 ppm/VOCl3). No second-order quadrupolar shift corrections have been made. For the dehydration experiment, some samples were left overnight in an oven at 90 ~ Then, prior to the experiment, the rotor was packed quickly without any other precautions.

281 Gas-phase catalysis was performed at a temperature of 550~ under atmospheric pressure. The composition of the gas before oxidation was 4% propane, 8% 02 and 88% of helium used as gas vector. The laser Raman spectra were recorded on a Bio-Rad spectrometer, model FT-Raman II, using the 1.064 nm line of a Nd:YAG laser for excitation. The Raman spectra were corrected for instrumental response using a white light reference spectrum.

3. RESULTS AND DISCUSSION 3.1. T e x t u r a l c h a r a c t e r i s a t i o n

The XRD patterns of materials having different vanadium doping percentages are shown, figure 1. One important feature is the similarity of these curves, for up to 10% vanadium content, to the curve for the pure silica (only) MCM41 material. This suggests that the vanadium species do not affect the overall long-range order of the silica framework. For each material with up to 10% V, there are three reflections, which can be indexed according to a hexagonal structure. The (100) sharp, well defined 4 reflection at 2.28 ~ (20) corresponds to a distance from one pore wall to an equivalent position in the adjacent wall of o ca.3.9 nm. The additional (110) and (200) ~3 2 reflections appear at higher 2 0 values and indicate some substantial degree of 1 ordering in all the samples. The absence of further higher Bragg reflections was o 0 5 10 15 20 attributed to small scattering domains [19]. Furthermore, there was no X R 20 (degrees) evidence for crystalline vanadium(V) Figure 1. Powder XRD diffractograms for the oxide for materials containing up to 10% MCM-41 with different vanadium contents. vanadium content. There is a slight shift (a) pure MCM-41, (b) 0.1%, (c) 0.5%, (d) 1%, of the reflections to the higher angles as (e) 5%, (f) 10%, (g) 20%. the percentage of vanadium increases, indicating a small shrinkage of the structures as the vanadium is incorporated. This shrinkage is somewhat similar to the influence of alkali species introduced during the synthesis of MCM-41 materials, as shown by Arnold and Holderich [20]. Above 10% V content, the materials prepared are not as well defined, since the [110] and [200] reflections, though present, are less intense and broadened. Furthermore, for the 20% V-material, there is only a broad reflection [ 100], indicating the significant disruption of the material. It was decided that only the 0.5% V-MCM-41 and the 5% V-MCM-41 materials would be further investigated as 5% seems to be a reasonable limit to retain the highly ordered hexagonal structure required for catalysis purposes. Raman spectra of the as-synthesized samples were performed at the Instituto de Tecnologia Quimica at Valencia, but are not presented here. The bands typically associated

1

282

with the presence of V205 crystallites (at 284, 404, 527, 702, and 994 cm -~) could not be observed even for the sample with high V loading, suggesting that V is highly dispersed in the silicate matrix of the as-made samples and confirming XRD results. The Raman spectra of the calcined materials could not be recorded due to low signal-to-noise ratios obtained with our equipment. The nitrogen adsorption isotherm for the calcined vanado-silicate materials for each of the materials corresponds to that for an ordered MCM-41 type material, figure 2. There is little or no hysteresis which could be associated with a broad range of mesopore diameters as seen in type IV isotherms [21 ]. All of the pores are filled and emptied at a 7(J0 relative pressure of c a . 0.33 as indicated by the 60O very steep uptake, suggesting a very narrow distribution of the pore diameter. At higher 2~ 500 relative pressures, after capillary condensation, "~ 40O the adsorption and desorption branches are flat, indicating that there is a negligible residual 300 E external surface area. Over the doping ranges used (up to 5%-V) the adsorption isotherms and 20o the pore volume plots remained substantially ,7. . . . . --o- 5%-V-MCM[ -~ < 1 O0 the same, indicating that there is no pore blocking by the vanadium-containing species. 0 The surface areas are each over 1000 m: g-~ and 0 0.2 0.4 0.6 0.8 1 the CBEXparameters range from 70 to 100, as is p/pO usually observed for mesoporous materials. However, the CBET values increased with the VFigure 2. Nitrogen adsorption isotherms at doping percentages, suggesting an affinity of 77K. the surface vanadium-containing species, such as >V-O or >VOH (> is used here to signify bound V), for the nitrogen molecules. The pore diameters calculated by the BJH method give values of between 2.5 and 2.9 nm. The difference between the pore diameters (BJH) and the 3.9 nm calculated from XRD above gives an estimated average wall thickness in the region of 1.0 to 1.2 nm. 3.2. MAS-NMR studies Figure 3 shows the e9Si MAS NMR spectra of the 5% V-MCM sample before and after calcination. For comparison, the spectrum of the uncalcined standard MCM-41 is shown, its synthesis route being described elsewhere. [22] These spectra consist of two lines with chemical shifts centred at -100. l and -108.7 ppm, together with a shoulder centred on ca. -90 ppm. The first two lines can be attributed to Q3 and Q4 silicon sites, respectively, and the shoulder to Q2 sites. No extra peak associated with Si-O-V environments is present, though overlap with one of the lines is in principle possible. A clear increase of the Q4/Q3 ratio is observed when going from the standard MCM material to the vanadium-containing one. The most likely reason for this increase is the incorporation of some vanadium into the structure during the synthesis. Two types of incorporation could occur, as observed in the case of the ZSM-12 [23]. The first incorporation involves the interaction of vanadium with silicon oligomers already at the beginning of the condensation process, leading to strongly bound

283 vanadium within the inorganic siliceous wall. The second incorporation concerns vanadium species that are not involved in the condensation process but which are trapped in the channels, weakly bound or unbound to the walls. In both cases of interaction, Q3 silicons are the most likely species from the siliceous, wall to interact with [24], thus decreasing their relative intensity with respect to that of the Q~s. It must be noted, however, that this assumption is made on the basis that Si-(OSi)30- H- (or CTAB-) and Si(OSi)4.nOV, species do not have the same chemical shift. Since the spectrum of the uncalcined vanadium-containing sample does not exhibit extra peaks to those of the standard sample, Si-O-V species cannot be clearly identified in the spectra at this point. Si-{ V } 2D-correlation experiments are currently implemented in order to investigate the presence of these species. Upon calcination, both the Q3 and Q4 signals seem to broaden, indicating a distribution of silicon environments in the structure. The ~H-29Si cross-polarisation time constants (Tsl,) associated with the Q3 species of both the 5% V-MCM and the standard MCM-41 calcined samples have been derived from variablecontact-time experiments. These values can be viewed as an indication of how fast the transfer of polarisation from protons to silicons occurs. The value for the 5% V-MCM sample is of the order of 0.15 ms, whereas for the standard sample it is 20 times greater, about 3 ms.

1.94

i

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9

i

-1 O0 29 S i /ppm

9

!

-1 5 0

Figure 3. 29Si MAS NMR spectra of the 5% V-MCM41 material. (A) Pure MCM41 - ( n o V) (B) 5% V uncalcined (C) 5% V calcined.

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1H / p p m Figure 4. ~H MAS spectrum of the calcined, dried 10% V-MCM sample

Since these are calcined materials, the only remaining protons within the structure that can be a source of polarisation are either V-OH, Si-OH, or H:O groups that would be rigid and close enough to a Q3 silicon. These three sources of polarisation are considered to be active in our material. Indeed, it has been shown that, under ambient conditions, silica-supported vanadium species are hydrated [25], therefore allowing water molecules bound to vanadium species to be close to Q3 silicons. On the other hand, V-OH is expected to be more acidic than Si-OH and therefore would have a IH NMR signal shifted to higher frequency compared to Si-OH, i.e. between 4 and 7 ppm [23]. Figure 4 shows the IH NMR spectrum of the calcined, dried 10% V-MCM material. It can be decomposed into two signals. The peak at ca. 1.9 ppm is

284 typical of Si-OH species. The broader signal forming the base of the spectrum, centred at ca. 6 ppm, falls in the region 4-7 ppm, and since the material has been dried, this signal can be assigned to V-OH species. Figure 5 displays the 5~V MAS NMR spectra of the 5% V-MCM sample, before and after calcination. For comparison, the spectrum of crystalline V:O~ is also shown. The spectra in this figure are presented without any baseline correction. Therefore, the baseline distortion observed in each spectrum arises from the instrumental dead-time prior to the acquisition and is more deeply pronounced for the V-MCM materials than for V205 due to the much weaker signal-to-noise ratio. Vanadium in V205 is in principle five-coordinated but is also considered to be in a distorted VO6 octahedral environment, one of the six bonds being significantly longer than the others. This distortion due to the inequivalency between the different V-O bonds is at the origin of a rather high chemical shift anisotropy (-~640 ppm), but a weak quadrupolar coupling constant (0.8 MHz) [26]. Only one Wsite can be detected in our 5% sample before calcination, with an isotropic chemical shift at -604 ppm. This is very close to the chemical shift of crystalline V205 (-610 ppm) and indicates that this is the only-NMR observable species in the as-synthesised material. The structure differs however, from the crystalline ./-610 compound, as indicated by the significantly different V 2 0 ~ spinning-sideband manifolds. As mentioned above, two types of incorporation of vanadium could occur during the synthesis. However, since strongly bound vanadium A, -565, -600 within the wall has not been detected in the assynthesised crystalline ZSM-12 material [23], it is all the more reason that it would not be detected in a noncrystalline MCM material. As shown by DR-UV/ ~---604 visible, such species is indeed observed in our assynthesised sample. The reason why it cannot be seen by NMR could be a too large distortion from tetrahedral symetry. Consequently, even if two types of vanadium 500 0 -500 -lO00 -1500 -2000 incorporation have occurred during the formation of our 5rV/ppm V-MCM material, 51V NMR only shows one of them, which is the species that is loosely or unbound. Figure 5.51V MAS spectra of the Consequently, these results indicate that (i) V2Os-like uncalcined and calcined 5% Vparticles develop on the surface of the walls during the MCM samples. For comparison, formation of the mesoporous material, (ii) since these of crystalline V205 is shown. particles are not detected by XRD, they are likely to be small clusters regularly spread over the entire inner surface, (iii) these particles do not have the same structure as V205, as indicated by their different spinning-sideband manifolds. i

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Upon calcination and under ambient conditions (hydrated), the spectrum changes to give rise to a second peak with an isotropic chemical shift of-565 ppm. The peak at -600 ppm then appears as a shoulder on the low-frequency side and can be correlated to the peak at -604 ppm in the non-calcined material. In hydrated samples, isotropic chemical shifts around -565 ppm have been attributed to tetrahedral V 5§ species, bound to the silica walls through one to three Si-V bonds, but

285 coordinated by water molecules to give square pyramidal or octahedral-like species, as observed in other vanadium-containing mesoporous materials [27], in vanadium-substituted silicalite [28] or in coated zeolites [29].

3.3. Diffuse reflectance UV-visible spectroscopy The UV-vis spectra of the as-made V-MCM-41 samples containing 0.5 and 5 wt% V are given in Figure 6. The two as-made samples show the bands at ca. 280 and 340 nm, assigned to the low-energy charge transitions (CT) between tetrahedral oxygen ligands and a central colourless V 5. ion. They are typical for framework V 5- ions in zeolites [29, 30, 31 ]. In the case of V-substituted MCM-41, the two V 5" bands at ca 280 and 340 nm have been assigned to different tetrahedral environments, the former to V 5+ inside the hexagonal tubular walls, and the latter to tetrahedral V 5+ on the wall surfaces [32]. This second species could be correlated with the one observed by 5~V NMR on the as-synthesised sample. Since vanadium is introduced as V 4+ during the preparation of the synthesis mixture, this indicates that most of the V 4+ is oxidized to V 5+ during the synthesis, according to previous observations in vanadium-substituted zeolites [33, 34]. 260 t~

380

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.,,.,,

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0.5%-V-MCM-41 l

200

300

v

r

400

500

600

700

Z/rim

Figure 6. DR-UV-Vis spectrum for the assynthesised materials

200

300

400

500

600

700

Z/rim

Figure 7. DR-UV-Vis spectrum for the hydrated calcined materials

Moreover, no adsorption band near 600 nm typical of VO 2. ions is observed in the spectra of the two as-made samples, although vanadyl cations in a square pyramidal geometry have been detected by ESR in V-MCM-41. This is probably due to the fact that d-d transitions in VO 2§ are generally 10-30 times weaker than those of CT transitions and therefore are undetectable by diffuse reflectance UV-vis [34]. However, a small band at ca 605 nm has been detected by Chao et al. [24] in the as-synthesized V-MCM-41 samples having Si/V = 30. This band is responsible for the pale violet colour of the as-made sample. Nevertheless, our as-made samples are white in colour, suggesting that VO 2. species should occur, if any, in very small concentration.

286 As observed in Figure 7, the calcined and hydrated samples present two broad absorption features centred at ca. 260 and 380 nm. A shoulder at ca. 410-450 nm can also be envisaged in the spectra of the sample with 5%V in Fig. 7. A 260 similar UV-vis spectrum was obtained for a calcinedhydrated V/Beta catalyst [35]. The slight shift to higher energy (lower ~) of the band at ca. 275 nm of the asmade sample suggests a greater distortion of the CM-41 tetracoordinated V 5 after calcination [35]. According to these authors the band at ca. 375 nm is attributed to square pyramidal or octahedral V species. The fact that the band at ca. 275 nm remains high in intensity upon calcination (although shifted to higher energies by distortion of the tetrahedra), while that of ca. 340 nm is shifted to lower energies in the calcined samples, 2~ 3~ 400 5~ 600 7~ )- nm suggests that only the V 5+ located in the surface of the hexagonal walls can achieve higher coordination than 4 and can carry out reversible red-ox cycles. Finally, the Figure 8. DR-UV-Vis spectrum for UV-vis spectra of the two V-MCM-41 samples after the calcined materials following being used in the ODH of propane were recorded in ODH use. order to observe possible changes in the state of V species. As an example, the spectrum of the sample with 5 wt%V content is given in Figure 8. It is seen by comparing this spectrum with that of calcined sample before the reaction (Fig. 7) that the same type of V species are present in the used samples, but it appears that relative intensity of the band at ca 375 nm (square pyramidal or octahedral V species on the surface walls) has increased with respect to the band at higher energies (~,= 260 nm). This suggests that some V species could have migrated from the hexagonal tubular walls to the wall surface under the reaction conditions.

3.4. Oxidative Dehydrogenation (ODH) of Propane The propane conversion against the contact time (W/F-- weight of catalyst/flow rate of C3 fed in g/h) for the two V-MCM-41 samples with different V loading and for the V/SiO2 (3 wt%V) used as a reference is shown in figure 9. It is seen that the activity of V-MCM-41 strongly increases when increasing the V content from 0.5 to 5 wt%, and that the V-MCM-41 sample with the highest V content is slightly more active than the reference V/silica. Moreover, when the selectivity to propylene is plotted against the propane conversion for the 3 catalysts (not shown here), it is observed that the V-MCM-41 catalysts are, at constant conversion, more selective than the V/silica, thus showing the advantage of incorporating vanadium into MCM-41 materials.

70 60

5% V-MCM-41 ~

3 % V-Silica

......

50

--*-0.5% V-MCM-41

4O

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:3 30 20

. . . . . . . . . . .

10 0 0

50

100

150

200

250

W F (h)

Figure 9. Propane conversion against time of contact

287 CONCLUSION This study shows that it is possible to synthesise ordered, mesoporous V-MCM-41 materials, with percentages of vanadium up to 10% without damaging the silica framework. The vanadium species are dispersed throughout the silica framework and are not aggregated as small crystallites. The textural properties of the materials are like those found for pure MCM41 silicas, i.e. specific surface areas above 1000 m 2 g-~, total pore volume above 1cm 3 g-~ and an average pore diameter of about 30A. 5~V NMR reveals that the vanadium species occurs in V-MCM41 with two different environments possible (pentacoordinated, or octahedral), suggesting that the vanadium is incorporated in two different sites. These could be either within the silica framework or on the siliceous wall surface, the only active species being located on the walls, which is consistent with UV-Vis specvtroscopy. NMR results also indicate that V2Os-like particles, weakly bound to the silica walls, develop during the formation of the material. Upon calcination, they transform to give tetrahedral vanadium species, which coordinate with water molecules under hydrated conditions. UV-vis. spectroscopy confirms these observations but also evidence the incorporation of vanadium within the silica walls already during the synthesis. Oxidative dehydrogenation of propane yields propene with a better conversion than that observed with a standard V- coated silica. Moreover, the V-MCM-41 catalysts are at constant conversion, more selective than the Vsilica, thus showing the advantage of incorporating vanadium into the high surface area MCM-41 material.

Acknowledgements. This work was carried out under the TMR Programme of the European Union - contract ERB FM RX CT 960084

References

1. R.K.Iler, "The Chemistry of Silica", John Wiley and Sons: New York, 1979. 2. C. T. Kresge, M. E. Leonovitz, W. J. Roth, J. C. Vartuli, J. S. Beck Nature 1992, 359, 710. 3. X. B. Feng, J S. Lee, J. W. Lee, D. Wei, G. L. Hailer ('hem. Eng. d. 1996, 64, 255. 4. M. J. Meziani, J. Zajac, D. J. Jones, J.Roziere, S. Partika, Langmuir, 1997, 13, 5409. 5. J.S. Reddy, P. Liu, A. Sayari ,4pp/. CataL ,4." General 1996, - 148. 6. S. Gontier, A.Tuel Microporous Mater. 1995, 5, 161. 7. Z. Luan, J. Xu, H. He, J. Klinowski, L. Kevan.L Phys. ('hem. 1996, 100, 19595-19602. 8. K.M. Reddy, I. Moudrakovsky, A. Sayari d. ('hem. Soc, ('hem. ('ommun. 1994, 1059. 9. H. Bosch, F. Janssen CataL Todc9,, 1988, 2, 369. 10. A. Corma, M. Iglesias, F. J. Sanchezd. ('hem. Soc., ('hem. ('ommun. 1995, 1635. 11 M.Sanai, A. Anderson d. MoL Catal. 1990, 59, 233. 12. T. Blasco, J.M. Lopez-Nieto, Appl. Catal. A: General 157, 117 (1997). 13 M.A. Chaar, D. Patel, H.H. Kung, J. Catal. 109, 463 (1988). 14. D.S.H. Sam, V. Soenen, J.C. Volta, J. Catal. 123,417 (1990). 15 A. Corma, J.M. Lopez Nieto, N. Paredes, J. Catal. 144, 425 (1993). 16 A. Galli, J.M. Lopez Nieto, A. Dejoz and M.I. Vazquez, Catal. Lett. 34, 51 (1995).

288

17. M. Grfin, K.K. Unger, A. Matsumoto, K.Tsutsumi, in "('haracterisatiou of Porous Solid~II.'" Eds. B. McEnaney, T.J. Mays, J. Rouquerol, F. Rodrigmez-Reinoso, K.S.W. Sing and K.K. Unger, Exeter 1996, Royal Society of Chemistry London 1997. 18. S. Brunauer, P. H. Emmett, E. Teller J. Am. Chem. Soc. 1938, 60, 309. 19. P. T. Tanev, M. Chibwe, T. Pinnavaia Nature, 1994, 3-1, 81. 20. B. J. A Arnold, W. Olderich in Studies in Surface Science aud Catalysis, vol 117, p399403, L. Bonneviot, F. Beland, C. Danumah, S. Giasson, S. Kiliaguine eds; Elsevier Sci 1998. 21. Sing, K.S.W. Everett, D.H. Haul, R.A.W. Moscou, L. Pierotti, R.A. Rouquerol J. Siemieniewska, T. Pure Appl. Chem. 1985 5- 603. 22. Same synthesis method as described in the experimental part, but without any vanadium source. 23. I.L. Moudrakovski, A. Sayari, C.I. Ratcliffe, J.A. Ripmeester, K. F Preston J. Phys. Chem. 1994, 98, 10895. 24. K.J. Chao, C.N. Wu, H. Chang, L.J. Lee, S. Hu J. Phys. Chem. B, 1997, 101, 6341. 25. N. Das, H. Eckert, H. Hu, I.E. Wachs, J.F. Waltzer, F.J. Feher, J. Phys. ('hem., 1993, 9-, 8240. 26. J. Skibsted, N.C. Nielsen, H. Bidsoe, H. J. Jacobsen Chem. Phys. Letters, 1992, 188,405 27. J.S.Reddy and A. Sayari, J. Chem. Soc. Chem. Commun., 2231 (1995) 28. J. Kornatowski, B. Wichterlov& J. Jirkovsk~,, E. Loffier, W. Pilz J. Chem. Soc., Faraday Trans. 1996, 92(6), 1067. 29. G. Catana, R. R. Rao, B. M. Weckhuysen, P. Van Der Woort, E. Vansant, R. A. Schoonheydt J. Phys. Chem. 1998, 102, 8005-8012. 30. G. Centi, S. Perathoner, F. Trifiro, A. Aboukais, C.F. Aissi, M.J. Guelton, Phys. Chem. 96, 2617 (1992). 31. M. Morey, A. Davidson, H. Eckert, G. Stuky, Chem. Mater. 8, 486 (1996). 32. Z. Luan, J. Xu, H. He, J. Klinowski, L. Kevan, J. Phys. Chem. 100, 19595 (1996). 33. G. Bellussi, M.S. Riguto, Stud. Surf. Sci. and Catal. 85, 177 (1994). 34. D.C.M. Dutoit, M. Schneider, P. Fabrizioli, A. Baiker, Chem. Mater. 8, 734 (1996). 35. S.Dzwigaj, M. Matsuoka, R. Franck, M. Anpo and M. Che, J. Phys. Chem. B 102, 6309 (1998).

Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) 92000 Elsevier Science B.V. All rightsreserved.

289

On the Ordering of Simple Gas Phases Adsorbed within Model Microporous Adsorbents N. Dufau a, N. Floquet b, j. p. Coulomb b, G. Andr6 c, R. Kahn c, p. Llewellyn a,* 8s Y. Grillet a a CTM

du CNRS, 26 rue du 141 eme RIA, 13331 - Marseilles cedex 3, France

b CRMC2_CNRS, Campus de Luminy, case 901, 13288 - Marseilles cedex 3, France c Laboratoire mixte CNRS-CEA Lron Brillouin, CEN-Saclay, 91191 Gif sur Yvette, France

Neutron diffraction and adsorption microcalorimetry have been used for the detection of the ordering of simple gases adsorbed within model microporous samples. This ordering would seem to be the result of the interaction of permanent or induced molecular moments within pore systems presenting either regular, long distance, crystallographic adsorption sites (silicalite-I, mordenite, A1PO4-11) or distinct cationic sites (5A and 13X). 1. I N T R O D U C T I O N

When the pore diameter of a solid is no more than half an order of magnitude larger than that of an adsorbed molecule, the properties of the confined fluid are considerably different to those of the bulk. Although the overall densities of the bulk and confined fluid are similar, it is their degrees of freedom that change [1 ]. Thus mathematical treatments such as Density Functional Theory and Monte-Carlo Simulation [2] agree that on the inside of such micropores, the local density of a confined fluid highly depends on the radial position of the adsorbed molecules. Consider now real materials with model micropores, that is to say with regular dimensions and whose pore walls consist of well-defined crystalline adsorption sites (including possible cationic sites). Such solids can be found within the realm of zeolites and associated materials such as the aluminophosphates. One can imagine the probability that a fluid adsorbed within such micropores may be influenced by the well-defined porosity and thus become itself "ordered". Such phenomena have already been highlighted with the aid of powerful but heavy techniques such as neutron diffraction and quasi-elastic incoherent neutron diffusion. The structural characterisation of several of the following systems was carried out with the aid of such techniques in collaboration with the mixed CNRS-CEA Lron Brillouin Laboratory at Saclay (France). The continuous thermodynamic analysis of the evolution of the differential enthalpies of adsorption at 77 K directly measured by isothermal microcalorimetry can quite easily highlight such phenomena that have thus far been overlooked.

corresponding author : [email protected],fr

290 In this present study, several examples relative to simple gas / zeolite systems have been chosen in which an ordering of the adsorbed fluid phase is shown to occur. 2. SYSTEMS STUDIED

It is probable that the organisation of the confined fluid phase of simple gases strongly depends on both the polar nature of the molecule and the extent of its polarizability. For this reason, we have chosen to study the following simple gases whose properties are recalled in Table 1. To allow an examination of the ordering of the fluid phase adsorbed within microporous materials, the first material studied is one, as we shall see further on, that has been previously been examined in detail (silicalite-1). This will allow a base from which it will be possible to highlight the influence of a distinct double pore size distribution (mordenite), of micropore curvature (ALP04-11) and of compensation cations (5A and 13X). Table 2 recalls several aspects of these solids. Table 1 Several properties of the simple gases used in the present work. Gas

kinetic diameter

polarizability / 10 .3 nm 3 [4]

Nitrogen

0.36

1.76

Carbon Monoxide

0.38

1.95

Methane

0.38

2.60

/nm[3]

dipole/ 10 -3~ [4]

0.39

quadrupole p0 at / 1 0 -4~ 2 77K [4] / kPa

p0 at 87K / kPa

enthalpy of liquefaction / kJ mol -~ [5]

-5.0

101

285

5.57

- 12.3

61

182

6.03

1.3

7

8.18

Table 2 Several properties of the microporous materials used in the present work. Solid

structure type [6]

Silicalite-I MFI

pore network

pore dimensions / n m [6]

framework composition (T atoms)

3D

0.53 x 0.56

Si- O

compensation cations

0.51 x 0.55 A1PO4-11

AEL

1D

0.39 x 0.63

A1- O - P

Mordenite

MOR

3D

0.26 x 0.57

Si - O - A1

H

0.65 x 0.70 5A

LTA

3D

0.41

Si - O - A1

Na, Ca

13X

FAU

3D

0.74

Si - O - A1

Na

291 3. RESULTS Although a number of systems were studied, we have chosen to show the results obtained with methane and carbon monoxide. Carbon monoxide, due to its larger permanent moment proves to highlight more the effects due to specific interactions with a solid. The manometric data is often presented in semi-log (log p/p0) form to highlight changes that may occur at very low relative pressures, as is the case during micropore filling. It is oten the case however, that filing occurs below the detection limit of the pressure gauges which is of the order of 0.1 Pa (i.e around p/p0 = 10-6 for carbon monoxide). This would explain the relatively high background noise levels for some of the manometric data at low relative pressures. The microcalorimetry results are plotted as the net enthalpy of adsorption with increasing coverage. Here we have used the term coverage, 0 = na/nap/po=o.1,i.e amount adsorbed relative to the amount adsorbed at p/p0 = 0.1. The manometric data is also plotted on the same curves for direct comparison. 3.1 Siliealite-I

The adsorption of simple probe molecules occurs simultaneously in both sets of channels of the silicalite-I micropore network. The isotherms obtained for both nitrogen and carbon monoxide are characterised by two sub-steps (Figure 1). The larger of these two sub-steps ("13") is the signature of a 1st order transition of the adsorbed molecules to a "solid-like commensurate phase" as characterised by neutron diffraction [7]. Although this step was quite easily detected using adsorption manometry [8,9], it was only ater the use of isothermal microcalorimetry that the much subtler first sub-step "or" was noted (Figure 2a and [10]). Neutron diffraction studies have suggested that this sub-step is the consequence of an ordering of the adsorbed fluid phase :"fluid" ~ "lattice fluid" [7]. It is thus possible to draw a phase diagram of the adsorbed fluid : this is shown for the first time for the carbon monoxide / silicalite-I system (Figure 2b). 35 ]

Ar

Kr

~o= 3 0 1 S 25

i.~

[

CO

N2

~ ~

}substep"I3" H4

.,,,, 7/

2o

.Q

I I- = 0 0

1

2

3

log (p / pO)

Figure 1 : Adsorption isotherms for simple probe molecules on silicalite-I at 77K.

292

Non-polar molecules such as argon and krypton also give rise to a phase transition of the a "solid-like commensurate phase" [11] (Figure 1). However, methane does not undergo such a transition [11 ] and gives rise to an isotherm of purely Type I character indicating micropore filling (Figure 1). This behaviour may result from the weakness of interactions between the hydrogen atoms of neighbouring methane molecules in this confined geometry.

type "fluid" ~

12

10 v "EL

0.05

107

0.045

1

0

6

~

3D hquJd

OO4

0.035

8

0.03 i... 0.025 EL ._ "~ (9 0.015 n,'

Pa

10a

IO~

X,~

"~ ~

101 ~ , , ~ o O i l e 100

- "~jlocal,zed

~

adsorpt,on)

-~~

adsorptmn'~

Imat~le~.~ P~tlon~~ . Substep 13

filling step

0.02

.,,..., (9 Z

0.01

2

0.005 -

0

0

, 0.2

. 0.4

, 0.6

--" 0.8

e =Coverage

0 1

12

10"4"

',7.

10-710

11

12

13

14

15

16

1000 / T. K 1

(a) (b) Figure 2 9Carbon monoxide adsorption in silicalite-I" (a) net enthalpies and isotherm at 77K, (b) Clapeyron phase diagram. Further studies into the adsorption of simple molecules on MFI-type zeolites in which some silica is partially substituted with aluminium [7,11] or iron [12] or where the pore system is partially blocked withpre-adsorbed species [ 13] have been carried out to explain the nature of these transitions. The studies suggest that both a "perfectly structured pore system" (without significant defects, cations, preadsorbed molecules...) and a parametric compatibility between the host structure and guest molecule are required to observe such rare adsorption phenomena. 3.2 Mordenite Mordenite is a zeolite with two distinct types of micropores formed by tings of 12 T-atoms (0.65 x 0.70 nm) and 8 T-atoms (0.26 x 0.57 nm) (Table 2). Neutron diffraction has been used to follow the adsorption of methane within this zeolite (Figure 3). At low and medium adsorption uptakes, the intensity of the peaks observed in the region 0.05 < Q / nm -~ < 0.08 decrease strongly. It would seem that the methane first adsorbs at the entrances of the smaller pores connected to the larger ones in what can be described as "side pockets". This is translated by a decrease in the [200] peak whilst the [ 110] peak, correlated to the larger micropores, remains constant in intensity. Only after filling of these side pockets, would it then seem that the methane adsorbs into the larger pores. The same phenomenon was also recently reported for the argon / mordenite system at 80 K [15]. After total filling of all the microporous volume, a modification of the diffraction pattern is observed in the region 0.15 < Q / nm -1 < 0.20. An increase of peaks in this region would seem to be due to a partial ordering of the adsorbed phase ("lattice fluid"). The relatively high value of the polarizability of the methane molecule may explain such a phenomenon.

293

(a) methane (b) carbon monoxide Figure 4 : Differential enthalpies and isotherms at 77K for adsorption on mordenite. The differential enthalpies of adsorption directly measured by microcalorimetry confirm these three steps of pore filling for methane (Figure 4a). These three pore-filling steps are even more clearly visible from the results obtained for the adsorption of polar molecules such as nitrogen or carbon monoxide (Figure 4b). However, the isotherms obtained via adsorption manometry, even using continuous, quasi-equilibrium, high resolution techniques with very sensitive pressure gauges are not able detect this stepwise pore filling and ordering of the adsorbed phase. It would seem that it is the mordenite pore structure influences the ordering of the simple gases adsorbed. The ordering of the adsorbed phase is slightly influenced by the polar character of the individual molecules. It would seem that the more polarizable or more polar the molecule, the more the adsorption phenomena are enhanced.

294 3.3 AIPO4-11 The aluminophosphate AIPO4-11 consists of unidirectional pores whose cross section is elliptical. Incoherent quasi-elastic neutron diffraction has previously been used to study the translational mobility of methane adsorbed in A1PO4-11 at 78 K [15]. On the contrary of what is usually observed (e.g. for A1PO4-5), the translational mobility of the fluid phase is seen to increase with the amount of methane adsorbed. The initial molecules of methane adsorbed, characterised by a relatively weak translational mobility, would seem to be attracted to structural sites at the more curved parts of the pores forming a relatively ordered "lattice fluid". It is only then would it seem that the methane fills the larger central section of the pores corresponding to the increase in translational mobility. Moreover, the variation in the differential enthalpies of adsorption with methane uptake (Figure 5a), clearly show these two stages of pore filling. The first step is characterised by a constant net enthalpy o f - 1 3 kJ.mol -~ whereas the second step is characterised by a constant differential enthalpy o f - 8 . 5 kJ.mol -~. Again, this second step is more marked with molecules having a permanent moment (N2 & CO, Figure 5b) thus suggesting that the fluid adsorbed during this step is still relatively ordered, whilst still being more mobile than the initial molecules adsorbed. 16

1

16 14

14

12

,4 >' 10 _ca. t.-

6)

u) 0.01

8

g

-..,=

e-

6 4

Z

ca.

~

001

10

0001

2 g 8

2 0

9

0

0.2

..,

~

0.4

0.6

~

,

0.8

1

0 = Coverage

I

r

oo s

00001

._

"~

o

1

.~

0 00001 0.001

, 0.0001 .2

~ .,,... 6) Z

4

0 000001

2

,,.

0

0"2

0.4

.

0.6

,...

0 8

0 . ~ 1

,

1

2

e = Coverage

(a) methane (b) carbon monoxide Figure 5 9Differential enthalpies and isotherms at 77K for adsorption on A1PO4-11. Once again in the present case, it would seem that the elliptical pore structure of A1PO4-11 governs the unusual ordering behaviour of the adsorbed fluid phase. Here also, the ordering of the adsorbed phase is enhanced by the polar (and polarizable) nature of the individual molecules.

3.4 Zeolites 5A & 13X The study of relatively simple solid / gas systems such as those previously outlined, allow a better understanding of more complex systems such as zeolites with cationic sites. A prior study of the adsorption of nitrogen at 77 K on 5A and 13X zeolites using quasiequilibrium, isothermal, adsorption microcalorimetry experiments at 77K [ 16] has detected a step in the differential enthalpies of adsorption, towards the end of micropore filling. At the time, this was interpreted as a consequence either of the adsorbate-adsorbate interactions, or

295 of a phase change within the cavities. The present study has detected the same phenomenon for both methane and, even more so, for carbon monoxide. We know now that this latter step corresponds to the delocalised adsorption of mobile molecules as the u-cages are almost full [17]. 25

0.9

16

0.8

14

-5

--5 12

"~

0.6 ~ ~

"" ~

| ,=

~'~ 04 ~

~ ~,

o~

0.~

15

m "~

.,~9

0.2

5

Z

0

0.2

0.4

0.6 0 = Coverage

08

_J 1

0 1.2

0001

8 0 0001

._

~ ~

0.00001

"~ Z

o

001

10

0.000001

2 0

0 0000001 0

0.2

0.4

06

0.8

1

12

0 = Coverage

(a) carbon monoxide / 5A (b) methane / 13X Figure 6 9Net enthalpies and isotherms at 77K for the adsorption of (a) carbon monoxide on 5A and (b) methane on 13X. It would thus seem strongly probable that this atypical variation in the differential enthalpy of adsorption corresponds to the presence of an ordered fluid. This could result from the interaction of the cationic field with the permanent moments of nitrogen or carbon monoxide and even with the induced dipole of the methane molecules. 4. CONCLUSION

A variety of different adsorbate-adsorbent systems have been taken in which an ordering of the adsorbed fluid phase occurs. Such atypical phenomena would seem to be inherent of the sample pore systems taken. Furthermore, the use of well-crystallised samples helps their observation. This ordering can depend on a variety of factors : the presence of regular, long distance, crystallographic adsorption sites (double pore size distribution, micropore curvature ...) and the presence of cationic sites. In each case, however, the permanent or induced moment of the molecules adsorbed would seem to play a role. It would seem that the stronger the polarisability or the stronger the permanent moment, the more distinct the ordering behaviour becomes. Although the structural characterisation of such changes requires relatively costly and extremely specialised techniques such as neutron diffraction, the present study has highlighted that such ordering effects can be detected using microcalorimetry. Whilst being far more sensitive than adsorption manometry, adsorption microcalorimetry experiments have the advantage of being relatively easy to carry out and rapid (~ 10 hours) when compared to neutron diffraction. It is thus an ideal tool for the detection of such subtle adsorption phenomena. Nevertheless, these two approaches are complementary : thermodynamic (microcalorimetry) and structural (neutron diffraction).

296 5. REFERENCES

1. 2. 3. 4. 5.

J.M. Prausnitz, Fluid Phase Equilibria, 150-151 (1998) 1-17. E. Kierlik, Y. Fan, P. A. Monson & M. L. Rosinberg, J. Chem. Phys., 102 (1995) 3712. D.W. Breck, "Zeolite Molecular Sieves", Wiley & Sons, New York (1974). T. Kihara, "Intermolecular Forces", Wiley & Sons, Chichester (1978). R. C. Reid, J. M. Prausnitz & T. K. Sherwood, "The Properties of Gases and Liquids", McGraw-Hill, New York (1977). 6. W. M. Meier & D. H. Olson, "Atlas of Zeolite Structure Types", 3rd Edn., ButterworthHeinemann, London (1992). 7. P. L. Llewellyn, J.-P. Coulomb, Y. Grillet, J. Patarin, G. Andr6 & J. Rouquerol, Langmuir, 9 (1993) 1852-6. 8. P.J.M. Carrott & K. S. W. Sing, Chem. & Ind., (1986) 786. 9. U. MiJller & K. K. Unger, Fortschr. Mineral, 64 (1986) 128. 10. U. Miiller, H. Reichert, E. Robens, K. K. Unger, Y. Grillet, F. Rouquerol, J. Rouquerol, D. Pan & A. Mersmann, Z. Anal. Chem., 333 (1989) 433-6. 11. P. L. Llewellyn, J.-P. Coulomb, Y. Grillet, J. Patarin, H. Lauter, H. Reichert & J. Rouquerol, Langmuir, 9 (1993) 1846-51. 12. P. L. Llewellyn, Y. Grillet & J. Rouquerol, Langmuir, 10 (1994) 570-5. 13. Y. Grillet, P. L. Llewellyn, M. Kenny, F. Rouquerol & J. Rouquerol, Pure and Appl. Chem., 65 (1993) 2157-67. 14. L. A. Clarck, A. Gupta & R. Q. Snurr, in "Proceedings of the 12th Int. Zeolite Conf.", Eds. M. M. J. Treacy, B. K. Markus, M. E. Bisher & J. B. Higgins, MRS, Warrendale, Pennsylvania (1999), 51-58. 15. J.-P. Coulomb, C. Martin, Y. Grillet & R. Kahn, "Proceedings of the 12th Int. Zeolite Conf.", Eds. M. M. J. Treacy, B. K. Markus, M. E. Bisher & J. B. Higgins, MRS, Warrendale, Pennsylvania (1999), p.51-58. 16. F. Rouqu6rol, S. Partyka & J. Rouqu6rol, in "Thermochimie", CNRS Ed., Paris (1972) p.547-54. 17. D. Amari, J. M. Lopez Cuesta, N. P. Nguyen, R. Jerrentrup & J. L. Ginoux, J. Therm. Analysis, 38 (1992) 1005-15.

Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) 92000 Elsevier Science B.V. All rights reserved.

297

T e x t u r a l a n d F r a m e w o r k - c o n f i n e d P o r o s i t y in S+I - M e s o p o r o u s Silica Patrik Agren, a Mika Linddn, a Philippe Trensb and Stefan Karlsson a aDepartment of Physical Chemistry, ,~bo Akademi University, Porthaninkatu 3-5, FIN-20500, Turku, Finland bDepartment of Chemistry, University of Reading, Box 224, Whiteknights, Reading, RG6 6AD, United Kingdom. 1. I N T R O D U C T I O N The surfactant templated MCM-41 materials consists of hexagonally ordered cylindrical pores, where the pore sizes may be varied between 2 and 10 rim.[1,2] These frameworkconfined mesopores are usually the only mesopores reported to be present in MCM-41-type materials. For catalytic, biofiltration and chromatographic purposes it is important to have an easy access to the small framework-confined mesopores. Tanev e t a/.[3,4] have synthesized molecular sieves, denoted HMS, consisting of both framework-confined and textural mesopores where the latter originate from the voids between agglomerated silica particles. These textural mesopores are about one order of magnitude larger than the frameworkconfined mesopores and therefore allow a better access for guest molecules to the frameworkconfined mesopores. Furthermore, the small particles (< 100 rim) reduce the flow time for guest molecules in the mesoporous channels, making the material more attractive for catalytic purposes. The HMS molecular sieves were prepared by using long-chain amines as the template. The same authors also used CnTAB (n = 8-18) as the template but did not achieve as high a textural porosity as for the amine. We hereby report the synthesis of mesoporous silica possessing both framework-confined and textural mesoporosity prepared using an ionic (S+I-) synthesis route with a total porosity similar to those of the HMS materials or higher. 2 EXPERIMENTAL

2.1. Sample preparation The materials were prepared at room temperature (30 ~ from water, TEOS, C16TABr and NH3. The molar composition was 148.66 H:O : 1.0 TEOS : 0.15 C16TABr. Two different synthesis routes were used. For the samples denoted P01-05 (see table 1) the NH3 concentration of the aqueous solution was varied between 0.1 and 0.5 M. The reaction was started by adding TEOS to a mixture containing all the other components. For T00-04 samples, on the other hand, the NH3 concentration was kept constant at 1 M. Here, the TEOS was prehydrolyzed in a mixture of water and NH3 for 0 to 240 minutes, after which a solution of equal volume containing water, CI6TABr and NH3 was added. The formed materials were aged with stirring for 1 hour and subsequently filtered. While the T00-04 and P04 materials gave a precipitate of large, ill-defined particles, the P01-03 synthesis compositions resulted in

298 a gel-structure. After filtration, the materials were dried at 90 ~ for 24 h and calcined for 5 h at 550 ~ (heating rate 1 ~

2.2. Sample characterization The N2 isotherms reported here were determined at 77 K by using a Micromeritics ASAP 2010. Samples were outgassed at 423 K for 12 hours before measurements. The X-ray diffraction (XRD) patterns were recorded with a 2~ step size of 0.02 ~ on a PHILIPS PW3710 diffractometer (Philips, Almelo, The Netherlands) using Cu K~ radiation. High-resolution transmission electron microscopy (TEM) images were obtained on a Philips CM20 transmission electron microscope, operating at 200kV. Samples were prepared by extensive grinding of the sample in methanol. The slurry obtained, was deposited on lacey carboncoated copper grids and dried in air before analyses. 3. RESULTS AND DISCUSSION

3.1. Sorption properties The adsorption-desorption isotherms in Fig. 1 show the measured adsorption isotherms of samples P01, P03 and P05. Sample P05 showed a typical isotherm for MCM-41 materials consisting of framework-confined mesopores, while the other samples showed a more complex nitrogen isotherm indicating the existence of both framework-confined and textural mesopores. Sample P01 possessed the highest value of the total pore volume of all those reported on here, exceeding 2 cm3/g. It is evident that the material possesses both frameworkconfined and textural mesoporosity. The BET surface area was about 1000 m2/g, which is a typical value for MCM-41-type materials. There were two marked uptakes in the isotherm. The first uptake between p / p o = 0.2 and p / p o = 0.4 is characteristic of framework confined mesopores. The second uptake together with a hysteresis loop appeared around p/po = 0.8 1.0, due to the presence of textural mesopores. However, the presence of a fraction of smaller, textural mesopores is apparently the reason why the uptake around p / p o = 0 . 2 - 0.4 is not as steep as generally observed for MCM-41 materials, probably due to the fact that adsorption to textural mesopores coincides with adsorption to framework-confined mesopores. The uptake around p / p o = 0.2 - 0.4 was steeper for all other samples as shown in Fig. 1. Generally, the larger the fraction of textural porosity the less well defined the uptake between p/p~, = 0.2 and P/po = 0.4. Table 1 includes the sorption properties of the materials prepared at different pH. The major difference between the samples was the total amount of N2 adsorbed at high relative pressures. This is indicated by the ratio Vte• where Vfr is the volume adsorbed between p / p o = 0 and P/po = 0.4 attributed to framework-confined mesoporosity, and Vtex = Vtot- Vfr and attributed to textural porosity. There is a clear correlation between the synthesis pH and the textural porosity; the lower the synthesis pH the higher the textural porosity. Especially for the synthesis carried out at low NH3 concentrations there is a marked decrease in pH during synthesis as indicated by pHini, the pH measured prior to addition of TEOS, and pHfin, the pH measured 1 hour after the addition of TEOS. Most of the decrease occurs during the first minutes after the addition of TEOS due to traces of HCI in the TEOS. Furthermore, the buffeting ability of NH3 is becoming much weaker as its concentration becomes lower and that allows the pH to decrease. It is clear that the increased fraction of textural porosity as the synthesis pH decreases is coupled to the formation of a gel-structure.

299

Table 1 pH, physisorption, XRD and TEM data for samples P01-05. ,

.,

,,,,

Sample _

.,

CNH3 [mol/dm 3]

,,.,,

,

,

P01 P02 P03 P04 P05 ,

,

,

,

.

.

pHini ,,,..,

,

0.1 0.2 0.3 0.4 0.5

,,.,,

1400

,

,

.

.

.

.

.

.

.

pHil. ,,

.,,.

,

.

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

SBET [m2/g]

. . . . . . . . . . .

11.3 11.3 I 1.5 11.6 11.6

,

,,

9.3 9.7 9.9 10.1 10.3

.

,,

..,

Vtot [cm3/g]

_

,

1018 1083 970 1028 1091

,

,

,

,

. . . . . . . .

ooo- % ,001/ 800-. > ,oo~ ~.o

0.2

.

,

dl00 [nm]

2.23 1.21 O.85 0.36 0.16

4.68 4.58 4.58 4.57 4.15

....

2.01 1.56 1.18 0.97 0.89

900

.0.6

08

800 " 700 600 500 i 400 300 200 100 4tT03 700

/',/

i I 0.4

,

.

~ 5oo~:-

600" 400 -

,, ,,

Vtex/Vfr

. . . . . . . .

1200. ~ 3oo

,t

10

.t~lm

P/Po 43x:a-Q"n~..~o -~i~e~D~

HI

,,o, ,,,,' Q-,,~r-~ g---~=@--~'u'-

9

9

5~

a. 800 F- 700 1 o9 '-" 600 ~500 400

o6~

,

/

200 -" ~ , " ~ ' ~ 900 P01 . . . . . . . . . . . . . .

6~a"

'i|

9

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

~" 600 500 ~" 400 E o. 300

~ 300 >

~,

el

> ~ 200 i' 100

200 100 600 -

-4

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

.

.

.

T01

600

.

500

500

400

4O0

300

3OO

200 ,,

2O0 i'

100

100

0 P05 0.0

'

i

0.2

' .....

I ....

T'

I

0.4 p/po 0.6

9

I'

0.8

'

'

0 TOO 1.0

Figure 1. The N2 adsorption-desorption isotherm at

77 K for samples P01, P03 and P05. Solid symbols denote adsorption and open symbols denote desorption. Inset: Zoom of the sorption isotherm associated with framework-confined mesoporosity.

"

0.0

" .....

.

.

.

I

0.2

.

'

'

" I'

'

"

' i .....

0.4 p/P00.6

~ '

'

I.

08

'

~

'-

1.0

Figure 2. The Nz adsorption-desorption isotherm at

77 K for samples TOO,T01 and T03. Solid symbols denote adsorption and open symbols denote desorption.

Some textural porosity was also observed for the T00-04 samples where the TEOS was allowed to hydrolyze for different periods of time before surfactant addition as shown in Table

300 2. Fig. 2. shows nicely that the longer the prehydrolysis time the higher the amount of textural porosity. All T00-T04 samples showed three reflections in the XRD, although the reflections at higher angles were poorly resolved for the T01-04 samples. More interestingly, for those samples that were allowed to prehydrolyze (T01-04) the d-spacing increased with prehydrolysis time although the p/po-interval where the marked uptake originating from adsorption into framework-confined mesopores remained the same. This could be indicative of the formation of thicker pore walls. The longer the prehydrolysis times the wider will the distribution of silicate oligomers in the solution be and also the degree of internal condensation in the oligomers. If more silicate is incorporated into the walls, the effective number-ratio of silicate species to surfactant molecules in the solution will decrease and the formation of smaller particles could be rationalized as a concentration effect. Table 2 Mixing time, physisorption and XRD data for samples T00-04. ,

Sample

Mixing Time [min]

SBE'r [m2/g]

Vtot [cm3/g]

Vtex/Vfr

dl00 [nm]

TOO T01 T02 T03 T04

0 15 30 120 240

1200 1104 1075 1015 1014

0.90 0.96 1.06 1.17 1.11

0.08 0.21 0.38 0.63 0.51

3.84 4.57 4.82 5.07 5.28 ,,

3.2. T E M analysis The textural porosity in these gels will depend on the particle size and the packing of the particles. An estimation of the particle size has been made by recording transmission electron microscopy TEM micrographs of the samples. Fig. 3 shows representative TEM pictures of sample P03. The material consists of loosely aggregated particles with a mean particle size of roughly 50 nm. The framework-confined mesopores are visible as small dots in the particles. No non-porous, amorphous particles were observed. The corresponding particle sizes were approximately 25 nm and 90 nm for sample P01 and P04, respectively. These results are in line with the fact that sample P01 had the highest fraction of textural mesopores in the series while sample P04 had the lowest. Samples P01 and P02 showed only a single low-angle reflection in the XRD. Samples P03, P04 and P05 showed two additional low-intensity reflections, which could be indexed assuming a two-dimensional hexagonal symmetry, although the higher angle reflections were poorly resolved for sample P03. Therefore one may conclude that the long-range order decreased with decreasing pH as did the particle size. Both these effects will have a detrimental effect on the quality of the diffractogram. If the synthesis of P01 was carried out in the presence of inert salt (KBr), the textural porosity decreased with increasing salt concentration. TEM analysis revealed that the addition of KBr had yirtually no influence on the particle size which indicates that the primary particles in the gels formed were packed more densely in this case. These results are in agreement with the well-known dependence on pH and ionic strength of the particle size and of gelation in silica sols.[5,6]

301

Figure3. TEM micrographof sample P03. Scale bar = 50 nm. 4. CONCLUSIONS Two different S+I- synthesis paths for making mesoporous silica possessing both framework-confined and textural mesoporosity has been presented. In the first synthesis path, adjustment of the reaction pH resulted in a gel-structure consisting of smaller particles and larger fraction of textural mesopores compared to ordinary MCM-41 materials. The lowest reaction pH resulted in the smallest particle size and highest amount of textural mesopores. In the second synthesis path, TEOS was allowed to prehydrolyze for different periods of time before surfactant addition. Longer prehydrolysis times resulted in a higher fraction of textural porosity and thicker pore walls.

Acknowledgements The authors would like to acknowledge Philip Llewellyn, Renaud Denoyel, Yves Grillet, Philip Pendleton and Jarl B. Rosenholm for fruitful discussions. EU project ERB-FMRX CT96-0084, the Ministry of Education (Finland), Graduate School of Materials Research and MATRA project are acknowledged for financial support.

References 1. a) C.T. Kresge, M.E. Leonowicz, W.J. Roth, J.C.Vartuli, Nature. 359 (1992) 710; b) J.S. Beck, J.C. Vartuli, W.J. Roth, M.E. Leonowicz, C.T. Kresge, K.D. Schmitt, C.T.-W. Chu, D.H. Olson, E.W. Sheppard, S.B. McCullen, J.B. Higgins, J.L. Schlenker, J. Am. Chem. Soc., 114 (1992) 10834. 2. Q. Huo, D. I. Margolese, U. Ciesla, P. Feng, T. E. Gier, P. Sieger, R. Leon, P. M. Petroff, F. Schtith, G. D. Stucky, Nature, 368 (1994) 317. 3. P. T. Tanev, and T. J. Pinnavaia, Chem. Mater., 8 (1996) 2068. 4. P. T. Tanev, M. Chibwe and T. J. Pinnavaia, Nature, 368 (1994) 321. 5. R. K. Iler, The Chemistry of Silica, A Wiley-Interscience Publication, 1979. 6. C. J. Brinker, and G. W. Scherer, Sol-Gel Science, Academic Press, San Diego, 1990.

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Studiesin SurfaceScienceand Catalysis128 K.K. Ungeret al. (Editors) 92000ElsevierScienceB.V.All rightsreserved.

303

Use of immersion calorimetry to evaluate the separation ability of carbon molecular sieves C.G. de Salazar, A. Sepfilveda-Escribano and F. Rodriguez-Reinoso Departamento de Quimica Inorgfinica. Universidad de Alicante. Apartado 99. E-03080 Alicante, Spain

Two series of carbon molecular sieves have been prepared from coconut shells, with different pore size distribution. They have been characterised by carbon dioxide adsorption at 273 K and immersion calorimetry into liquids of different molecular sizes. The results have been related with the ability of the CMS to separate the components of O~q2, COJCH4 and n-C4H4/i-C4H4 gas mixtures.

1. I N T R O D U C T I O N Carbon molecular sieves (CMS) are carbonaceous materials characterised by a very narrow micropore size distribution, this producing a high adsorption selectivity. These materials are receiving great attention because of their practical interest in fields such as catalysis [1-3] and gas mixtures separation [4], where they show some advantages over zeolites (greater thermal stability in nonoxidising atmospheres, higher chemical stability and larger adsorbate packing density in their slit-shaped micropores). Because of their narrow microporosity, the textural characterisation of CMS is not easy. Gas and vapours adsorption, especially nitrogen adsorption at 77 K, may be kinetically hindered, and large equilibrium times are needed to obtain the adsorption isotherms. In this way, immersion calorimetry emerges as a powerful technique for the characterisation of pore size distributions in CMS. By choosing liquids with different molecular sizes, the micropore volumes can be obtained as a function of their size by applying the relationship obtained by Stoeckli and Kraehenbuehl [5]: -AHi (Jg-1) - [[3 Eo Wo (1+aT) ~1/2] [ [2Vm] - hi Se

(1)

In this equation, a and Vm are the thermal coefficient of expansion and the molar volume of the liquid, respectively, 13 is the affinity coefficient a n d - h i is the areal enthalpy of wetting (Jm -2) of the external surface area.

304

This paper reports the characterisation of CMS with different pore size distribution by means of immersion calorimetry into different liquids. The data obtained are related with the separation ability of these samples towards gas mixtures such as O2/N2, CO2]CH4 and n-C4Hlo]i-C4H]o.

2. EXPERIMENTAL The starting material used for the preparation of CMS was coconut shell. It was crushed and sieved (particle size: 2-2.8 mm), and washed with deionized water (Series CW) or diluted sulphuric acid (Series CS). After drying in air at room temperature, the material was carbonised under a nitrogen flow (80 cm3min 1) at 850~ for 2 h, with a heating rate of 2~ -1. The mean yield obtained from this process was 30.1 + 0.2 %. Activation was carried out with carbon dioxide (120 cm3min -1) at 750~ during 2-72 h, with a heating rate of 5~ The ash content of samples was determined by X-Ray Flourescence (XRF) and Atomic Absorption Spectroscopy (AAS). Carbon dioxide adsorption at 273 K was carried out in a volumetric automatic system (Autosorb 6, Quantachrome). The enthalpies of immersion into liquids with different molecular sizes (dichoromethane, benzene, cyclohexane, 2,2-dimetylbutane and a-pinene) were measured at 30~ with a Tian-Calvet type calorimeter (C80D, Setaram). The samples (about 0.15-0.20 g) were placed in a glass bulb with a brittle end and degassified at 250~ and 10 -~ Torr for 4 h; then, the bulb was sealed and placed into the calorimeter cell containing 7 cm 3 of the wetting liquid. Once the thermal equilibrium was achieved in the calorimeter block, the brittle end was broken and the liquid allowed to enter into the bulb and to wet the sample, the heat flow evolution being monitored as a function of time. Thermal effects related with the breaking of the bulb and the evaporation of the liquid to fill the empty volume of the bulb with the vapour at the corresponding vapour pressure were calibrated by using bulbs of different volumes. Adsorption kinetics of different gases (CO2, CH4, N2, 02, n-C4H10 and i-C4H10) on the CMS prepared were determined at 25 ~ in a volumetric system, at 760 Torr initial pressure, after sample degassification in high vacuum at 250~ for 4 h.

3. R E S U L T S AND D I S C U S S I O N The two series studied have been prepared from chars with different ash contents, as a result of the acid- and water-washing treatments at which the starting material was submitted. The inorganic matter is constituted mainly by potassium salts and, to a lesser extent, also by sodium and calcium salts, which are known catalysts for the carbon gasification reaction with CO2. Figure 1 plots

305 the different burn-offs achieved as a function of the activation time at a given t e m p e r a t u r e for the w a t e r - w a s h e d (CW) a n d acid-washed (CS) series. Burn off(%)

50 40 30 20

cw

cs/

10 0

0

20

40

I

I

60

80

1oo

Time (h) Figure 1. Burn-off of samples from both series as a function of activation time. n aOm'ol g" 1)

n a(nlml g-1)

5 9 CW-1 9 CW-2

b)

51" f 9 4l 9 10 |

4_W CW-4

* ..- 9 -**~',-% "

9 CW-8 # CW-16

v

O

CS-2 CS-4 CS-8 CS-16

a) ~~-- ~

V-

2 1 .

0

.

.

.

.

.

.

.

0.01

.

.

.

.

.

.

0.02

P/Po

0.03

0

0

0.01

0.02

0.03

P/Po

Figure 2. CO2 adsorption i s o t h e r m s at 273K on CMS from series CS (a) and CW

(b).

306 Figure 2 presents the CO2 adsorption isotherms obtained at 273 K for samples of series CS (a) and CW (b). The amount of carbon dioxide adsorbed increases, for both series, with burn-off. Isotherms are rather similar for samples with low burn-off (CS-2 to CS-8 on one hand, CW-1 and CW-2 on the other) what makes it difficult to distinguish them only with these measurements. When plotted in Dubinin-Radushkevich (D-R) coordinates, these isotherms become straight lines as corresponds to samples with a narrow and uniform homogeneous microporosity. The micropore volumes of the different samples, obtained by application of the D-R equation to the CO2 adsorption data are reported in Table 1. Micropore volumes increase from 0.22-0.23 cm3g 1 in the less activated CMS to 0.32 cm3ff I in samples with the highest burn-off in each series although, due to the different reactivity of the starting materials, they are obtained after very different activation times (16 h for CW series and 70 h for CS series).

Table 1 Micropore volume (CO2 273 K, D-R) (cm 3 g-l) and specific enthalpies of immersion of CMS into different liquids at 303 K (J g-l) Sample V0 (CO2) AHi AHi AHi AHi hHi CH2 CI~ C6H6 C6H,2 2,2-DMB (z-Pinene CS-2 0.23 7.74 . . . . . . . . . . . . . . . . CS-4 0.25 23.12 . . . . . . . . . . . . . . . . CS-8 0.24 42.68 3.71 . . . . . . . . . . . . CS-16 0.26 52.39 19.8 . . . . . . . . . . . . CS-32 0.27 98.11 90.35 20.84 3.34 .... CS52 0.30 103.16 102.15 86.00 9.35 .... CS-70 0.32 116.49 106.03 98.35 33.09 6.51 CW-1 0.22 82.30 66.84 5.27 ........ CW-2 0.23 82.76 71.92 6.55 2.99 .... CW-4 0.25 88.56 79.14 15.90 6.96 .... CW-8 0.26 95.08 92.04 73.14 15.98 3.34 CW-16 0.32 117.19 109.92 103.54 79.81 29.31

Table 1 also reports the specific enthalpies of immersion (J if1) of the different CMS into liquids with different molecular size: dicholomethane (CH2C12, 0.33 nm), benzene (C6H6, 0.37 nm), cyclohexane (C6H12, 0.48 nm), 2,2dimethylbutane (2,2-DMB, 0.56 nm) and a-pmene (0.70 nm). These values can be analysed in different ways to obtain the pore size distribution of the CMS. On one hand, the areal enthalpy of wetting (per square meter of surface) of a given liquid for a carbon surface can be obtained by using a nonporous carbon of well-known surface area as reference. Theoretical and experimental evidence has been given to support the assumption that the immersion enthalpy is simply proportional to the surface area available to the immersion liquid, irrespective of the micropore

307

size [6]. In this way, the pore size d i s t r i b u t i o n of a c a r b o n a d s o r b e n t can be e s t i m a t e d from the i m m e r s i o n e n t h a l p i e s into liquids of different m o l e c u l a r sizes [6,7]. In t h i s s t u d y a g r a p h i t i s e d c a r b o n black, V3G, h a s b e e n u s e d as a reference; it h a d a B E T surface a r e a (N2, 77K) of 62 m e if*. The surface a r e a s accessible to the different liquids used in t h i s s t u d y for the CMS of both series are plotted in F i g u r e 3.

grama (m2g-I) f {

1000 t

800

m 9 9 9 # 0 Vl

'

~

!

',,'

1

600 i

~

i

"

\ '\

!

CS-2 ~ CS-4' CS-8 CS-16: CS-32, CS-52~ CS-70

'

Sun m (m2g-l) r

a)

[]

9 9 9 O

' , 1000 ~ 800 ~ , "*---, 600 ,~-

CW-I CW-2 CW-4 CW-8 CW-16

&,

m',, ,,

400~ ,\ i

, ,

I

\\

",

'

200i A

I,. i

0~ 0.3

400 -

,

',

,:' '/,?

"

9 ,

200 ~

"

,

~.

6_

9

.......

0.4

"

0.5

*

d min (rim)

----.

0.6

0.7

- ~

O

..........

0.3

0.4

0.5

0.6

0.7

d min (nm)

F i g u r e 3. Surface a r e a accessible to liquids w i t h different m o l e c u l a r kinetic d i a m e t e r , o b t a i n e d by i m m e r s i o n c a l o r i m e t r y .

It can be seen t h a t , for a given CMS, the accessible surface a r e a s d e c r e a s e as the m o l e c u l a r size of the i m m e r s i o n liquid increases, the d e c r e a s e being more i m p o r t a n t in s a m p l e s w i t h low burn-off. However, the evolution of the pore size d i s t r i b u t i o n w i t h the burn-off is not the s a m e for both series. For e x a m p l e , s a m p l e s CW-1 a n d CW-2, w i t h a b o u t 2% burn-off, h a v e a surface a r e a accessible to d i c h l o r o m e t h a n e of a b o u t 750 m 2 g-l, w h e r e a s the surface a r e a accessible to cyclohexane is v e r y small. This m e a n s t h a t t h e s e two s a m p l e s are CMS of a b o u t 0.5 nm. On the o t h e r h a n d , s a m p l e CS-8, w i t h 2.4% burn-off, h a s a surface a r e a accessible to d i c h l o r o m e t h a n e of only 400 m e g-I, a n d the one accessible to b e n z e n e is n e a r l y nil. In o t h e r words, it is a CMS of a b o u t 0.35 n m pore width. D a t a from i m m e r s i o n e n t h a l p i e s into liquids whose v a p o u r is a d s o r b e d according to the D u b i n i n - R a d u s h k e v i c h (D-R) e q u a t i o n can also be a n a l y s e d following the a p p r o a c h s u g g e s t e d by Stoeckli a n d K r a e h e n b u e h l [5]. T h e y showed t h a t the i m m e r s i o n e n t h a l p y of a solid m t o a given liquid is r e l a t e d to the

308 micropore volume accessible to the liquid according to equation (1). The last term in t h a t equation, -hi Se, corresponds to the enthalpy of wetting of the external surface area of the solid which, in essentially microporous solids such as the CMS under study, should be much lower t h a t the enthalpy of wetting of the internal surface. With this assumption, this term could be ignored in equation (1). If a given liquid is taken as a reference, the AHi/AHi ref ratio is proportional to the EoWo]Eo refW0 ref ratio, as shown by equation (2): (2)

AHi/AHi ref -- (~/~ef)(E0Wo/Eo refW0 ref)[(l+aT)Vm red/[( lq-o~refW)Vm] w h a t can be converted to:

(3)

EoWofEo refW0 ref =(AHi/AHiref)[~ref(1 +O~refW)Vm/~(l'}'aW)Vm red

For convenience dicholoromethane, the liquid with the smallest molecular size, is chosen as the reference. In this way, EoWo/Eo refW0 ref values can be obtained from the experimental AHi/AHi ref values with the help of p a r a m e t e r s listed in Table 2.

Table 2. Data of the t h e r m a l expansion coefficient a (10 -3 KI), affinity factor and molar volume of the liquid-like adsorbate, Vm (cm 3 tool1). Liquid CH2C12 C6H6 C6H12 2,2-DMB ~x-pinene

(z 1.34 1.24 0.96 1.44 1.02

13 0.66 1.00 1.04 1.12 1.7

Vm 64.02 88.910 108.10 132.80 158.85

Figure 4 represents the evolution of the EoWofE0 refW0 ref ratio for the different carbon molecular sieves of the two series, as a function of the molecular size of the immersion liquid, and using CH2C12 as a reference. A decrease of this ratio as the size of the immersion liquid increases indicates t h a t the accessibility of the porosity is limited. It can be seen t h a t the pore size distributions obtained by this method are comparable to those shown in Figure 3, corresponding to the surface area accessible to the different immersion liquids. In conclusion of this pore-size analysis, a variety of CMS with different pore size distribution, but always smaller t h a n 0.7 nm, have been obtained. CMS with the narrowest pore diameter are prepared from the acid-washed precursors, i.e., without ashes able to catalyse the gasification reaction.

309 EoWo/Eo refWoref

EoWo/Eo refW0ref 1

0.8

9 9 0 0 U]

a)

I/

,,

\\

CS-8~ CS-16, CS-32 CS-52 CS-701

b) 0.8 ~-I

:i'i~\~-~--~-~''\

,

0.6

i/

',

i /

\

0.4 -

"2 \

'\

0.2 0 0.3

CW-2 CW-4 CW-8 CW-16

\\ \

",,

CW-1

9 9 9 0 \

'k' '(\ ,

0.4

9

x

~i',",

,,

\ o

0.2 '7

\,

\ 9

~,t ~O

0.4

0.5

0.6

d rain (nm)

0.7

O

,

_ .

0.3

.

.

.

~_

0.4

0.5

0.6

0.7

d min (nm)

Figure 4. Micropore size distribution of carbon CMS derived from eq. (3). Series CS (a) and CW (b).

The aim of this work was to evaluate the separation ability of CMS by means of their pore size distribution obtained from immersion calorimetry measurements. In this way, adsorption kinetics of different gases (N2, O2. CO2, CH4, n-butane and i-butane) on the CMS prepared have been carried out at room temperature and 760 Torr initial pressure. The most illustrative results are reported in Figure 5. Figure 5 (a) plots the adsorption kinetics of N2, 02, CO2 and CH4 on CMS CS2. Data in Figure 3 shows t h a t this CMS has a very narrow porosity, with a small area accessible to dicholoromethane, the enthalpy of immersion in benzene being nearly nil. This means t h a t it contains pores smaller t h a n 0.37 nm. The molecular size of benzene, 0.37 nm, is closer to t h a t of m e t h a n e (0.38 nm) and, accordingly, the adsorption of m e t h a n e on this sample is nearly nil. The kinetic selectivity, defined as the ratio of adsorbed CO2 and CH4 after 2 minutes, is then infinite. On the other hand, the NdOe kinetic selectivity is about 11. The next sample in the series, CS-4, presents a higher surface area accessible to dichloromethane, about 200 m2g-1, the one accessible to benzene r e m a m i n g very low. In turn, methane adsorption is still too low as compared to t h a t of CO2, thus indicating t h a t both gases can be separated with these CMS. On the other hand, the Nz/O2 kinetic selectivity decreases to 6. An increase in the activation time (sample CS-8, Fig. 5 (c)) produces a small pore widening; the surface accessible to dichloromethane is about 400 m2g-1 and a small fraction of it is now accessible to benzene. As a result, the a m o u n t of CO2 adsorbed at equilibrium increases with

310 regard to samples CS-2 and CS-4, but m e t h a n e is also adsorbed to a little extent, this decreasing the COdCH4 kinetic selectivity to 29.5. n a (nrml g-l)

n a (rm~l

a)

1.4

g-l)

b)

1.4

1.2

1.2 ~C O 2

1J

0.8/-

C02f~J

i

....................... N 2 . . . . . . . . . .

j

_~.

I

0.8

f-

0.6

0.6

0.4 I

/

0.2 ~-j ' /

0.4 ~

N2

, _ j r

J"

....

02

f Jr

0 a~

0

0.2-

200

400

c]-t,~ 600

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

0 ~ ............

0

~ 02

200

t(s)

1.4 '

1 CH4

o.8~

/

0.6

/" // /"

I/ i/

0.2 ~/ f f

N2 02

......

CH4

0 ~~ ~ ~ :

0

1.2

......

/

0.6 i 0.4~

C02

9

o.8~ i

d) J

cQ 1/---j

i

....

600

n a (n'n~l g-l)

c)

1.2 l

_

400

i

t(s)

n a (rrr~l g-l) 1.4 i

...........

200

4OO t(s)

600

0.4

N2

0.2

Q ....

0

200

400

600

t (s)

Figure 5. Adsorption kinetics of CO2, CH4, N2 and 02 in CS-2 (a),CS-4 (b), CS-8 (c) and CW-2 (d).

311 Then, it can be concluded from these results that the smaller the surface area or micropore volume accessible to benzene, the higher ability of the CMS to discriminate between CO2 and CH4. On the other hand, the N2/O2 kinetic ratio also decreases (3.6 for CS-8), as can be expected from the widening of the porosity as determined by immersion calorimetry. These results already anticipate the expected behaviour for samples from series CW. Sample CW-1 contains a porosity that is accessible to both dichloromethane and benzene in a similar extent, and even also to cyclohexane (0.46 nm). Then this sample, and also its counterpart CW-2, is expected not to discriminate between CO2 and CH4. This is confirmed by data in Figure 5 (c) (CMS CW-2), where it can be seen that the adsorption rate is similar for both gases. It can be concluded that microporosity in CMS prepared from the waterwashed precursors is too wide, even after low activation times (low burn-off), as to separate N2 from 02 or CO2 from CH4. However, they can be used to separate other mixtures of gases with larger molecules, such as n-butane (0.43 nm) from ibutane (0.5 nm). Figure 6 compares the adsorption kinetics of these two gases on samples CW-1, CW-2 and CW-4. Micropore size distributions of these samples indicate t h a t their microporosity is narrower than 0.6 nm, with a higher surface area or micropore volume accessible in CW-4. Corresponding to this, the amounts of n-butane and i-butane adsorbed are higher for CW-4. Samples CW-1 and CW-2 behaves similarly, as expected from their pore size distribution. Their porosity is hardly accessible to cyclohexane (0.46 nm) and then, the amount of i-butane (0.5 nm) adsorbed is very low.

n. (nm~l g-~) 2

w.4]

1.5

n-butan

CW-I CW-2

',

0.5 ~ 0

t

a

n

200

e 400

600

t(s) Figure 6. Adsorption kinetics of n-butane and i-butane on CW-1, CW-2 and CW-4.

312 4. CONCLUSIONS Immersion calorimetry can be apply successfully to the characterisation of CMS to evaluate their pore size distribution and, in this way, their ability to separate gas mixtures as a function of their molecular size. On the other hand, carbon molecular sieves can be prepared from coconut shells by activation with CO2. These materials can be used for the separation of gas mixtures such as O2/N2, CO2/CH4 and n-C4H10]i-C4H10. A c k n o w l e d g e m e nts This work was supported by DGICYT (Project No. PB94-1500). C.G. de Salazar acknowledges a grant from M.E.C. (Spain).

REFERENCES

1. H.C. Foley, Microporous Mat., 4 (1995) 407. 2. J.L. Schmitt, Carbon, 29 (1991) 743. 3. M.S. Kane, L.C. Kao, R.K. Mariwala, D.F. Hilscher and H.C. Foley, Ind. Eng. Chem. Res., 35 (1996) 3319. 4. T.D. Burchell, R.R. Judkins, M.R. Rogers and A.M. Williams, Carbon, 35 (1997) 1279. 5. H.F. Stoeckli and F. Kraehenbuehl, Carbon, 19 (1981) 353. 6. R. Denoyel, J. Fernhndez-Colinas, Y. Grillet and J. Rouquerol, Langmuir, 9 (1993) 515. 7. M.T. Gonzhlez, A. Sepflveda-Escribano, M. Molina-Sabio and F. RodriguezReinoso, Langmuir, 11 (1995) 2151.

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000 ElsevierScienceB.V.All rightsreserved.

313

Molecular simulation and measurement of adsorption in porous carbon nanotubes E. Alain, Y. F. Yin, T. J. Mays * and B. McEnaney Department of Materials Science and Engineering, University of Bath, BATH BA2 7AY UK Imerest in carbon nanotubes as potential adsorbents has been stimulated by a claim that they might be useful for hydrogen storage at room temperature. Open ended carbon nanotubes are potemially powerful carbon adsorbems with cylindrical micropores or mesopores, depending upon their diameter. Additionally, the interstices in arrays of nanotubes may provide supplementary microporous or mesoporous adsorption spaces. Grand canonical Mome Carlo molecular simulations of adsorption of nitrogen at 77 K use gas-solid potemials that have been developed for exohedral and endohedral adsorption in model singlewall nanotubes. Simulations have been carried out on individual and square arrays of nanotubes. Experimental measuremems of adsorption of nitrogen at 77 K have been performed on single-wall and multi-wall nanotubes. 1. INTRODUCTION Since their discovery in 1991 [1 ], carbon nanotubes have been the subject of considerable study from both a fundamental and an applied viewpoint. Generically two different types of carbon nanotubes exist, depending on whether the tube walls are made of one layer (singlewalled carbon nanotubes: SWCNT) or more than one layer (multi-walled carbon nanotubes: MWCNT). MWCNT are usually prepared by electric-arc discharge between two graphite electrodes in an helium atmosphere [2, 3], while SWCNT are prepared using the same method by simply introducing catalyst species (like Ni and Y) in the anode [4]. Another way for producing SWCNT is the laser evaporation technique [5]. A modified version of the arc discharge method is used to make doped multiwalled nanotubes with boron (BCNT) in which BC3 domains are incorporated in the hexagonal carbon network [6]. The benefit of boron doping is that it assists the graphitization process and promotes the yield of long nanotubes. Catalytic decomposition of hydrocarbon gases by catalytic particles of transition metals (Co, Fe) has been also used to produce nanofibres [7, 8]. Recently a new development in nanotube forms has lead to the preparation of packed nanotubes in films [9]. However, whatever the method used for the synthesis of nanotubes, the samples obtained are usually not pure: nanoparticles, catalyst metals and/or amorphous carbon accompany the nanotubes. There are a number of ways to purify nanotubes: one method is to oxidise the nanotube sample by heating it in the presence of air or oxygen [10, 11] or carbon dioxide [12]. This method suffers from the disadvantage that more than 95% of the original material is destroyed during oxidation. Purification by oxidation in acidic solutions (nitric acid for instance [13, 14]) gives better yields, depending on the starting material. * Corresponding author: Tel/Fax: +44 (0)1225 826588 / 826098; E-mail: [email protected]

314

Carbon nanotubes contain narrow central channels and the idea that it is possible to store atoms in these cylindrical microporous or mesoporous adsorption spaces has attracted much attention. One highlight to date is the demonstration that tubes can be opened by oxidation because of the higher reactivity of their end caps which contain pentagonal rings [12] and subsequently filled with a variety of materials [12. 15, 16, 17]. In this context, both theoretical [19-23] and experimental [17,18] studies have been carried out in order to determine the suitability of carbon nanotubes for gas storage. Nanofibers have been also regarded as a potential media for gas storage [24-26]. However, only limited attention has been paid to the experimental study of adsorption in carbon nanotubes [27-29]. In this paper we report results from grand canonical Monte Carlo (GCMC) molecular simulations of nitrogen adsorption at 77 K in isolated SWCNT of different tube diameters, and in square arrays of unidirectional SWCNT of different tube diameters and separations. Both closed and open nanotubes arrays are considered. Results of an experimental study of nitrogen adsorption at 77 K on different kind of carbon nanotubes are also given to compare with the simulations data. 2. MODEL NANOTUBES The model used in simulations for isolated carbon nanotubes is shown in Figure 1. The tubes consist of n coaxial graphite sheets separated by a distance A. The inner diameters of the tubes are D which are measured as internuclear distances. The number of carbon atoms per unit area in the tube wall is Oa. All distances relative to the tube are expressed as r, which is the distance from the position of concern to the tube axis. These tubes are then assembled together to form nanotube arrays. For simplicity, only single wall carbon nanotubes and square arrays are considered here. In such a model, parallel single wall carbon nanotubes are placed at comers of squares. A cross-section view of a part of such an array is shown in Figure 2. In addition to the parameters described above for isolated carbon nanotubes, a parameter G is introduced to describe the tube separations in the array: G is the internuclear distance between two adjacent tube walls, see Figure 2.

n graphite sheets k

.......

'~

"(f

D=2R tube axis ._I"

A

--~

A

]

Pa atom s

per unit area

Figure 1. Model of an isolated carbon nanotube.

315

Figure 2. A cross-section view of square single wall carbon nanotube arrays.

Figure 3. Potential derivation.

In the case of isolated carbon nanotubes, if the tubes are closed, only exohedral adsorption can take place; if the tubes are open, then both exohedral and endohedral adsorption will occur. In the case of tube arrays, if the tubes are closed, then only interstitial adsorption can take place; if the tubes are open, then both endohedral and interstitial adsorption will occur. 3. SIMULATIONS

3.1. Adsorption potentials The Lennard-Jones 12-6 pair potential [30] is commonly used to describe the interaction between simple molecules or atoms and it has been widely used in previous molecular simulations for both fluid-fluid and fluid-carbon interactions. If d is the internuclear distance between two interacting atoms or molecules then the LJ 12-6 pair potential, u, may be written as:

u =4~;

-

(1)

where e is an energy parameter (the depth of the potential well) and ~ is a length parameter (the collision diameter). Equation (1) applies to interactions between two atoms in the bulk fluid phase, in which case the potential energy, and the energy and distance parameters refer to fluid-fluid interactions and are denoted by u ff, err and ~fr. Assuming that the solid atoms in the pore wall are uniformly distributed and characterised by the number of atoms per unit area, Pa, then the interaction between a fluid molecule and an area element, dA (see Figure 3), in the tube wall my be written as"

dusf = 4~;sf Pa

-

dA

(2)

where the subscript sf refers to solid-fluid interactions. The total interaction between a fluid molecule and the tube may be obtained by integrating Equation (2) over the area of the tube [23, 31] as follows:

316 [(~)12

Usf = 4~ Pa A~

-

(-~)61 dA= ~ { 2n:esfPa~sf2 I ( ~ / } , 'i - (G6(s)/1 i=l I_~, R*i ) R*6i

--

where R, i - R + (i 1)A ands i Cysf

(3)

r

R + ( i - 1)A

In Equation (3) G!2 and G6 are complicated functions of s~ involving elliptic integrals. Unlike previous equations, [22, 32, 33], this equation can be applied both to endohedral and exohedral adsorption. Potentials calculated according to Equation (4) for inside and outside nanotubes, using established parameter values for carbon structure and carbon-nitrogen interactions [22], are shown in Figures 4 and 5 respectively. Figure 4 shows that potentials inside nanotubes are strongly enhanced. This enhancement increases with decreasing tube diameter and the maximum enhancement is more than three times over a fiat surface. Figure 5 shows that the depth of the potentials outside nanotubes increases with increasing tube diameter, due to the negative curvature of the external surface. This will certainly affect endohedral and exohedral adsorption behaviour. The differences between endohedral and exohedral adsorption potential minimum for a single nanotube are illustrated in Figure 6, where a horizontal line representing the potential of a fiat surface is also shown. Examination of the potentials for SWCNT arrays indicates enhancement of the potentials in the interstitial spaces between the tubes due to the summing of exohedral potentials from neighbouring tubes. ! li:

:ii

i i. : 0 _ ' '.: ] t . . . . . . . . . . . . .

/

/

'

b-,-10

't

,,, ,; l, ,~

9

.-" ~ i,-!-:~.....t-!-. i : |

.~ ,L~ ''

:alt' ': ,.~ i: :, '."

'!,.'"',X. '.l f 9

.i:

ii, . .,

1i,. i,':

9 ~!:

,~ :1 .

i

.~

r

~1; I .i

0"

,' t n

"

,!

} o

....,. !

:

',

! .

~ t~ ,,,1. i r it I : : i ! ":t

,~ ',,

!i i~

'

~, ,

! I " :' i i : I . .~, :! ! 9 ,'1

!i i!

-20

i .

;' :] ,. ',

1,,

9

D= 7.5 A ....... D=12.0 A ........... D=17.8 A

4~D -a

-30

........... D=22.0 A ............. D=28.6 A .............. D=47.8 A

-40 -:20 ' - 1 0 '

0 ' 1'0 ' 2'0 ' 3'0

distance from pore centre / A Figure 4. Nitrogen adsorption potentials inside single-walled carbon nanotubes as functions of tube diameter.

--*-4 "fi-6

D=7.5 A D=10 A D=13.7 A D=30 A D=200 A

b

~ ' - 8

i

-10 -12

2

.

'

'

'

l'O

'

1'2

'

1'4

distance from tube wall / A

Figure 5. Nitrogen adsorption potentials outside single-walled carbon nanotubes as functions of tube diameter.

317

-10

--... ...........................................

-12

exohedral

flat surface

-14 -16

i'

/

f

f

s

/

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

endohedral

/ /

:E -18

I I

.,-~

O

I

I

-20

I I I I

-22

I I

-24 -26

I

10

1'5'2'0'2'5 ' 3'0 ' 3'5 ' 4'0 ' 4'5 '5'0

tube diameter, D / A Figure 6. Endohedral and exohedral potential minima for nitrogen in single-walled carbon nanotubes as a function of tube diameter. 3.2. Simulations General details of the GCEMC molecular simulations, including values of carbon structure and LJ parameters, have been reported elsewhere [34-36], and are only summarised here. For isolated nanotubes, a cylinder was used as the simulation cell. The length of the cell varied from 10.0~fr to 30.0~fr depending on the tube diameter, where c~ is the LJ length parameter for nitrogen-nitrogen interactions. For tube arrays, the simulation cell was rectangular, with square cross-section, see Figure 2. The Peng-Robinson equation of state [37] was used to calculate the chemical potential of nitrogen. Gas phase intermolecular potentials were cut off at a distance r = 5.0cr~r. In each simulation run, of the order of 10 6 configurations were allowed for equilibration. Average numbers of adsorbed nitrogen molecules in simulation cells were subsequently determined over blocks o f - 1 0 5 configurations. Parameter values used in the simulations are: ~fr/k = 93.98 K, ~f~= 3.572 A, ~sf/k = 53.52 K, ~sf = 3.494 A, (k is Boltzmann's constant), and Pa = 0.3818 atoms A -2 (which is the value for perfect graphite). It may be noted that the potentials used in the simulations are approximations, and that the selected equation of state for N2 is only applicable over restricted ranges of pressure and temperature. Like many other authors we have used these simple approximations to reveal broad patterns ofbehaviour. However, we are currently exploring more realistic models (e.g., multi-site LJ potentials) to explore the detail of adsorption in nanotubes.

4. EXPERIMENTAL

Three samples have been received for investigation: MWCNT, which were made by the arc discharge method, BCNT made by the arc discharge method by using a BC composite anode and a graphite cathode (both of these samples have been provided by W. Hsu et al. from the University of Sussex, UK) and SWCNT originating from an arc discharge experiment using a mixture Ni/Y as a catalyst material in the graphite anode (sample provided

318 by W. Maser et al. from the CSIC in Zaragosa, Spain). SWCNT can be found in a spongiform "collaret" around the cathodic deposit and in carbonaceous webs that range from the cathode to the reactor walls. The samples were characterised by scanning electron microscopy (SEM JEOL 6310), transmission electron microscopy (TEM JEOL 2000FX) and nitrogen adsorption at 77 K. Prior to gas adsorption, the samples were degassed at 10.3 bar at 200 ~ for 24 hours. Nitrogen isotherms at 77 K were measured for the as received nanotubes without further purification, using a volumetric adsorption apparatus (ASAP 2010. Micromeritics Instrument Corporation). SEM images show that the supplied MWCNT and BCNT consist of balls of loosely aggregated nanotubes with lengths often exceeding 10 ~m. The nanotubes represent 60 to 80 vol. % of the whole sample. The porous aspect of the collaret can be observed for the SWCNT sample, where tangled fibril structures can be seen. SWCNT represent about 80 vol. % of the total sample. Table 1 summarises the observations of the different nanotubes samples made by TEM. HRTEM observations show that the SWCNT comprise bundles of few tens of tubes arranged in a triangular lattice having a parameter of about 17 A. We assume that all the nanotubes samples studied here are made of closed tubes even if the ends of the SWCNT have been hardly observed (assumption supported by the model proposed for the growth of the SWCNT [38]). Table 1 Characteristics of the different nanotubes samples obtained by TEM MWCNT Diameter (nm)

3-40

SWCNT Bundle: 5-20 SWNT: 1.4

Length (lain) Tips

3-20 Closed

>10 Assu~med to 'be closed

BCNT 10-50 10-80 Ciosed

5. RESULTS AND DISCUSSION 5.1 Simulation results Simulated isotherms for nitrogen at 77 K adsorbed inside isolated SWCNTs are shown in Figure 7. As previously reported, isotherms for small tubes are of type I and tubes are filled with nitrogen at very low pressures. Larger tubes yield type IV isotherms where both monolayer completion and condensation take place. Exohedral adsorption isotherms however are rather of type II than of type I as shown in Figure 8, though in some cases there are steps associated with monolayer completion. The surface coverage increases with increasing tube diameters. For an open isolated SWCNT, endohedral and exohedral adsorption can take place at the same time. For such a system, the isotherms are shown in Figure 9, where the isotherm labelled Exo is for exohedral adsorption, Endo is for endohedral adsorption and Total for the sum of the two. There are three shoulders in the total isotherm, corresponding to endohedral monolayer completion, exohedral monolayer completion and endohedral condensation respectively. It is also interesting to note that at low pressures, endohedral adsorption has higher surface coverage than exohedral adsorption; while at high pressures, exohedral adsorption has the higher coverage. This may indicate that in applications of carbon nanotubes such as gas storage, exohedral adsorption might be more important than endohedral, where the usable gas stored is the difference between the amount of gas stored at a higher pressure and that at a low pressure.

319 r | . 0 -

i

o
I(0).

l(ll) witl~ 0 t'r the a(I-

normalized by use of the I (0) values r carbon sa~nples

s~rl)ti~

without adsorbed water in vacuo. The 1(0) ~f t~IT-5

t l~e cloister i~ ~nicr()l)r

the fiwn~aticm r

decreases gradually as increases 0. T h e 1(0)~s. 0 pl,,ts

()t" 1(0) ab(,ve O - ().7 sl~()~l(I indicate t l~at t l~e vaca~t

Iwa~('i~ ~f t~I'I'-2I)i~r

(l"ig~re 5(I~,)). The steep (lr()p

for adsorption m~d desorption bra~mhes aJ'e ~werlapl)e~l

p~we st)ace r

each other over the wlmle 0 region. On lhe r her hm~(l.

tots and limit n~erging.

the I(0) of the wider pore system (I'I"I'-20) i~wreases

(lewes n~t change u~til 0 - O. 1 r

with the increase of 0 until 0 - 0.7 and then drops

gests ll~e ~mifiwn~ evap~walicm of water ~n~lem~les (Vig-

above ~ -

0.7 for adsorption.

T h e I(0) ~.~. 0 t )lr

,)wi~g t~, fi~nnati,)~ ~)f larger cl~sItr

tile l(I)) ~s. 0 plr

ure 5((')). llence, waler ~r

(tescwt)t i~m. This sugfr

ads(wpli(n~. |)~l desr

t h a n t h a t fiw the adsorption branch above. ~) -- 0.1

,~n,lec~lar evai)r

and it. coincides with t.hat, fiw adsorption branch bel(~w

()~ tl~e c~mtrar)', the I(()) ~;s. 0 pl~t. ['r t)]'I'-h indicates

0-

0.1. Accordingly, t.he I(0) ~)s. 0 ph)ls fi-w ads~wpt i~m

prr

tl~e clusters on

for desorption brmmh is situated at a lower p(~sit.io~

Ihr~gh

i~m in case ~)f l~l'l'-21) (u'

lhe u~if~,r~ adlaver ~r

unifiw~n 1. l ~ n ) .

The ~nicrop~we walls

and desorption branches form an explicit. !r I) wl~r

~,f A('t" are llv~lr,,l)i~t,ic, as sh~,wn in i i~ a~is~wl)ti(m

closing 4) agrees with t h a t of the adsorpti~m hysteresis.

isr

(l"ig~re 1). Acc, w(li~gly, water nl~lec~lles call-

359

Figure 5: Schematic diagram of eleclron density flucluation and water adsorption on carbon lnicropore. lot form the uniform adlaver on the pore walls. "l'llen. we presume that water molecules form slnall unit clus-

ln()le('ui(~ ill tile gas t)hase.

Thus, in silu SAXS ex-

aminati(m c~l elucidate I he dependence of adsorpt.i()n

ters whose size is assumed to be about 0.Snm. Those

m(whal~isn~ ()f water in hydrophobic microp()res with

unit clusters behave ,as if they were a single molecule.

tim pore wi(lth.

The Ulfit clust, ers form uniform adlayer in s~nall micropore of Plq'-5. Hence, formation of the adlayer are

4

Acknowledgment

continuous and I(0) does not increase with adsort)tion.

The aulh()rs tllank [)rofe,~or K. Nishikawa ('lliba

tlere, water clusters can form a unit'onn layer struc-

l.niversit v f(>r her ('(>mments ()n t he SAXS analysis. T.

ture in the hydrophobic space, as suggested by tim

Iiyalna was sut)p~)rle(l by t{ese~u'ch Fe.ll~wship ()f.lapan

recent, molecular simulation [23]. Thereby m()le('ules

S()cielv f~r the l)r~ml()ti(m of Science f(~r Y(nlng Scien-

eva, porat, e at, the int.erface upon desorpti(m as well as

tists.

desorption in PIT-20, giving no change in I(0) with

the (~rant-in-Aid fr Scientific I{ese.ar(:tl ()I~ [)riCwitv Ar-

Lhe progress of de~orpt.ion.

eas ( ( ' a r b o n Alloys)(ff ,lat)anese (-]()vel'lllllo,nl..

The adsorption is(~therm

\Ve ackn(~wle(lge the Nlinistry (~f [';ducat|on f()r

of PIT-5 does not steeply rise, which in(ticates that small clusters have the size disl ribution such as dimers to pentamers.

If water molecules desorb in tl~e fi)rm

of slnail clusters having the size distributi(m, the desorption isotherm can be close to the adsorption one. as

Refferences Ill ['~. l)efay, I,. [)igogine, A. Bellemans and I). |1. l~verret, SuTfac; "l'eT~mon and A&o77Jt.m~z (Long|nan, l,on(t~m, 19(;6) p.251

observed. As the serious geomel rica] rest ricl ion f(w f(w-

121 .1. l:. Quinson, .l. l)umas and ,1. Serughetti, J. No',.Cr.qsL Soh& 79 (l.086) 397,

mat|on of the ordered structure in micropores of l)I'I'-5

{;q .M. Xl. l)ubinin, (;hem. Hey. 60 (1,()(;6) 215.

produces a defective solid-like structure ml(! the inter-

Ill S. S. I:;arion, Xl..I. l~. Evans, ,I. lt()llan(t and .I. 1{. K()resh, Carbon, 85 (198-1) 265

cluster binding is not strong, the small clllster can be detached fl'om lhe adsorbe(l phase t() (liss(wiale itdo

[51 K, Nanok(), N. Kosugi and It. t(uroda, J, (:hem. So(: l'hmday 7}'an,~. 1 85 (1989) 8(;9.

360

[61

T. Iiyama, K. Nishikawa, T. Otowa and K. Kaneko, J. Phys. Chem.. 99 (1995) 10075.

I71

C. L. McCallum, T. J. Bandosz, S. C. McGrother, E. A. Miiller and K. E. Gubbins, Langmuir 15 (1999) 533.

[~1

J. W. Patrick, Porosity in Carbon.s (Edward Arnold,

[91

M. Ruike, T. Kasu, N. Setoyama, T. Suzuki and K. Kaneko, Y. Phys. Chem.. 98 (1995) 9594.

[101

A. Nakayama, K. Suzuki, T. Enoki, C. Ishii, K. Kaneko, M. Endo and N. Shindo, Solid S'ate Commun. 34 (1995) 323.

[11] [121

K. Kaneko and C. Ishii, Coll. Surf 67 (1992) 203.

[131

K. Nishikawa and T. Iijima, Bull. Chem. Soc. Jpn. 57 (1984) 1750.

[141

T. Iiyama, K. Nishikawa, T. Suzuki and K. Kaneko, (',hem. Phys. Lett. 274 (1997) 152.

[1~1

T. Iiyama, T. Suzuki and K. Kaneko, (:hem. Phys. Lett. 259 (1996) 37.

[161

T. Iiyama, K. Nishikawa, T. Suzuki, T. Otowa, M. Hijiriyama, Y. Nojima and K. Kaneko, J. Phys. Chem.. B 101 (1997)3037.

I171

T. Ohkubo, T. Iiyama, K. N~shikawa, T. Suzuki and K. Kaneko, J. Phys. Chem. t3 103 (1999) 1859.

[1~1

T. Ohkubo, T. Iiyama and K. Kaneko, Chem. Phys. Left. in press.

[191

K. Kaneko, Y. Fujiwara and K. Nishikawa, J. CoUozd Interface Sci. 127 (1989) 298.

[201

Y. Fujiwara, K. Nishikawa, T. Iijima and K. Kaneko, J. Chem. Soc. Faraday 7~718. 87 (1991) 2763.

[211

T. Iiyama, M. Ruike and K. Kaneko, Chem. Phys. Left. to be submitted.

1221

H. E. Stanley, Introduction to Phase 7~an.,ition.s and Critical Phenomena (Oxford University Press, Oxford,

[23]

K. Koga, X. C. Zeng and ti. Tanaka, Phys. Rev. l, ett. 79 (1997) ,5013.

London, 1995).

K. Kaneko, C. Ishii, M. Ruike and H. Kuwabara, Carbon 30 (1992) 1075.

1971).

Studies in Surface Scienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScience B.V. All rightsreserved.

361

Ultra-thin Microporous Carbon Films R. Petri~evid ~, H. Prgbstle and J. Fricke u ~Bavarian Centre for Applied Energy Research, bphysikalisches Institut der Universit/it Wfirzburg, Am Hubland, D-97074 Wiirzburg, Germany Ultra thin microporous carbon films are derived via the pyrolysis of phenolic precursors. The latter can be prepared from resorcinol-formaldehyde resins using a base catalyst. After several hours at 50~ of curing, the solution forms a stable polymeric film. Followed by a solvent exchange and ambient pressure drying, the film is pyrolysed in argon atmosphere at temperatures above 800~ The result is an electrically conducting polymeric carbon film, the structure of which resembles the organic precursor, but shows microporosity in addition. Hereby, films with thicknesses of _> 5 microns and sufficient mechanical stability can be made. For characterization of the micro structure small angle X-ray scattering (SAXS) experiments were carried out. The gas permeability was determined by measuring the stationary gas flow for helium and nitrogenwhich gives important information about the gas transport mechanisms. The electrochemical behaviour was studied by cyclic voltammetry and impedance spectroscopy. 1. I n t r o d u c t i o n Glassy carbon and carbon aerogels are intensively studied materials, the synthesis of which is described elsewhere [1,2]. With respect to the physical and structural properties ultra thin carbon films are to be arranged in between glassy carbons [2] and carbon aerogels [1,3]. Since microporous carbon films can be prepared with very low thicknesses down to ~ 5 #rn their properties are interesting for filter devices and supercapacitor applications. From a fundamental point of view, microporous carbon films represent an interesting material to study the development in microstructure during pyrolysis and electrochemical oxidation. Small angle X-ray scattering (SAXS), gas permeability measurements, cyclic voltammetry and impedance spectroscopy were employed for the characterization of the porous structure. SAXS is a sensitive tool for analyzing inhomogenities on a length scale > 1 ]t, which typically appear in a large number of carbons (e.g. activated carbons, glassy carbon [21, nanofibres, and carbon aerogels [4]). The permeability measurements allow to investigate the fraction of pores available for gas transport and the transport mechanisms. Cyclic voltammetry and impedance spectroscopy are used to study the electrochemical behaviour and to quantify the performance of the films as double layer capacitor in aqueous electrolyte [5].

362

2. Porosity and pore size distribution from small-angle X-ray scattering In the two-phase model [6], the material is assumed to consist of randomly distributed micropores surrounded by a matrix, mainly consisting of amorphous carbon. From the scattered intensity, the scattering cross section dcr/df~ as a function of the scattering vector can be obtained, if correlation effects between the scattering entities are neglected. Thus, for randomly distributed pores with uniform sizes the scattering cross section is related to the number Np of micropores and the contrast ~r/2 between the pore phase and the carbon matrix [7]" (1)

dcr/df~( @ - NpAr/2Vp2S(@,

where I/p and S(q-) are the volume and tile scattering function of a single micropore, respectively. The contrast ,'.Xr/2 for such a two-phase medium can be written as follows

[s]. ANt/2 - 0(1 - r

(2)

r = P/Ps is the ratio between macroscopic and matrix or "skeletal" density. For light elements C = (NA/M~)Zre = 8.504. 1011 m/kg is a constant, including the classical electron radius re, the atomic number Z, the molar mass M~, and Avogadro's constant NA. By normalizing eq. 1 to the illuminated mass rn = pV and considering the cross section at q = 0, one obtains for the specific cross section:

(3) If the scattering is homogeneous for small scattering vectors, this equation allows to determine the porosity via: (1 - b) - v/m-idE/df~(O)(p, C2~l~)-i.

(4)

For this evaluation, an intensity calibration in absolute units (here" crn2(g 9srad) -1) is necessary. In the case of polydisperse pores (in particular of spherical shape) a size distribution P(R) must be taken into account"

do/df~(q)- NpArl 2

S(R,q)-

[

/0

P(R)Vp2(R)S(R,q)dR,

]2

with

/o

P(R) d R - 1.

(5)

(6)

3(sinqR-qRcosqR)/(qR) 3

is the single-sphere scattering function with radius R. Eq. 5 can be fitted to the experimental data. With the fitted distribution, mean values for the volume Vp, surface area Sp and radius /~p of a single pore can be determined" ~-p- (4~r/3)

')C

P(R)R 3 dR,

fO~176

o•0 P(R)R

R, -

fO ~

P(R)RdR.

(7)

363 3. E x p e r i m e n t a l Tile organic polymer precursor was prepared from a ,'esorci,lol:formaldelude (R F) resin with a molar ratio of 1"2 and a base-catalyst labeled C5. Tile 1qF-resiIl was i~oured between glass plates (4 x 4 crlz 2) with catalyst impregnated sllrfaces and tllerl sealed i~l order to avoid an evaporation of the liquid. Subsequentl\'. the t)l'ecursor was cured for se\'eral hours at S0~ until polymerization was complete. Tllis was controlled via a referetlce glass vial filled with the same resin. After tile curiIlg tile "'saIldwictles'" were ot)elled carefully and the organic film put in a bath of acetone, in order 1o IlliIlimize ttle surface lellsioil of the liquid and to avoid a collapse of the film (turiIlg t tie dryiIlg process. ['t)oil air-di'viilg of the film warping due to the shrinkage was observed. To kee t) it in plaIlar sllape rile film was put between two porous ceramic plates. Pyrolysis ll~lder inert atmospt~ere was applied to transform the organic film in a carbon film. Agaiil ceramic plates were used to avoid a warping upon pyrolysis. The thickness of the resllltiIlg (:aI'l~oll film \'arie(1 t)eween 5 and 10 /zm.. SAXS experiments were carried out at tlle beamliIle JI'SIF.\ [61 at It:\SYI~:\I~. I)ES'~'. Hamburg. A q-range between 0.1 1~1~-~ an(t S ~,~,~-~ co~ld t)e covered l)\" ~si~l,,,, lwo ~tifferent detector-sample distance geometries (3635 ~ m a~(t .~1:~5~nm) a~(t a corrr162 energy tune for each geometry, ~a~nely l a k e \ for ~],e s],o,-I ~tisla~ce a~l 7 keN" f(~r t]~e long distance. The thickness of the measured tilm was 10 t~n. For permeability measurements tt~e sample was mect~a~tically s~pI~orl e(t b\" a peter,s ~ e m braise which t~ad no influence o~ tl~c t~crmeat)ility. 13ot}~ were glued o~to t t~e sai~I)le ]~older witt~ machinable epoxy resin a~d sealed tt~orougt~ly. \Vil}~ tt~e rim of the samI)le t~older being evacuated, tt~e leakage of t.l~e ct~amber witt~ iI~slalled sa~nt)let~older a~(t san~I~le was minimized to < 6 • 10 -~ m b a r / s , wt~ict~ limits t h e w o r k i ~ g ra~geoftt~eal)l)al'at~s. Tt~e permeability of the carbon film was deteI'ini~ed, as reporte~t i~ [.q]. al~t~lyi~g a i~ressure pulse ~ p to one side of the sample. On l t~e low pressure side l]~e i~crease of t~ress~re was recorded in a calibrated volume 1 t)3" a capacita~ce m e ~ t , r a ~ ' t)r('ssure tra~s~t~cer (ravage 0.1-1000 Pa) until stationary t)ressuI'c increase was rca(l~e(t. ]t~is i)rocedure was I'~,l)eated tbr various mean pressure levels betwee~ 5 a~(t 50 t't)a. Cyclic v o l t a m m e t r y and ilnpeda~lce st)e,ctros(ol)y xV~'l'~, t)~,rfol'~nc(l i~l a glass cell using I molar s~lfuric acid as electrol\'te. :\~t .-\g/-\g('l, . ~ rt'l'ere~'~' ~'lectrode and a 1)latinum counter electrod were used i~ tt~e tt~rt'e e'lectro~tr arra~geme~t, l't~e i~\'estigate~l sami)le (working electrode) with a r geo~letr\" was attacl~e(t 1o a t)rass saml)le t~ol(ter. I~ order to avoid a sigI~al of lt~e sanipleholdeI" ilself, oI~ly lt~e sa~iI)l(' was dit)pe .~ 0.1, multilayer adsorption takes place on the external surface and on the walls of any mesopores (width-~ 2 - 50nm) before they are filled by capillary condensation [ 1-3]. The nitrogen isotherms discussed in this paper were determined on two representative porous carbons with the aid of commercial automated equipment and the manufacturer's software was used for the pore structure analysis. This approach has provided a basis for a critical appraisal of a number of readily available data processing procedures. 2. Experimental The two representative adsorbents were new samples of carbon cloth, which had been activated under conditions designed to give different ranges of pore size. A Micromeritics

422 ASAP 2010 Analyser was used to determine the adsorption-desorption isotherms of nitrogen at the temperature of liquid nitrogen (77.4 K). To ensure reproducibility of the adsorption data, especially at low pressures, it was necessary to take a number of critical factors into account. These include the conditions of outgassing, the choice and calibration of the various pressure gauges, the minimisation of leaks in the manifold and the verification of adsorption equilibrium. During the outgassing, the residual pressure was maintained at 3 x 10.2 mbar while the sample temperature was slowly raised to 400~ and held at this level for 16 hours (i.e. the procedure used in Sample Controlled Thermal Analysis). The gas pressures were measured with the aid of three calibrated gauges over the ranges of 0 - 1 mbar, 0 - 10 mbar and 0 1000 mbar. Fixed incremental doses of gas were introduced to construct the initial part of the isotherm and thermal transpiration corrections were applied. In the region of very low pressures it was found necessary to allow several hours for each point to attain equilibrium.

3. Results and discussion The nitrogen isotherms for the two carbons are shown in Figure 1(a) in the conventional form of amount adsorbed, n a, vs the relative pressure, p/pO, and in Figure 1(b) in the semi-log form of n a vs log p/pO. In a new extended isotherm classification [1 ], the isotherm given by sample A is of Type Ib and that by sample B is a composite isotherm of Types Ib and IVb. From the isotherm shapes in Figure l(a), we can tentatively conclude that sample A has a wide range of micropores and that sample B is both microporous and mesoporous.

Figure 1 : Adsorption isotherms of nitrogen at 77.4 K on carbon cloth samples A and B The semi-log plots in Figure 1(b) reveal that the two isotherms are of similar shape at very low p/pO. It can be seen that significant amounts are adsorbed at p/pO < 10-5. However, because of the very slow rate of equilibration, we must be cautious in the interpretation of the adsorption data at these low pressures. The next step is to consider which of the available data processing procedures would appear to be the most suitable for the quantitative interpretation of the two isotherms. As is well

423 known, the Langmuir model involves an ideal localized monolayer mode of adsorption, which is not compatible with either monolayer adsorption on a heterogeneous surface or with pore filling. For these reasons, we have not used the manufacturer's software to construct Langmuir plots. Although the BET theory is also based on an unrealistic model, we have followed the generally accepted convention [1,2,3] of applying the BET-nitrogen method to obtain the values of apparent surface area, a(BET), in Tables 1 and 2, where the ranges of linearity of the BET plots are also recorded. In our view, it is inadvisable to use the software to fit the 'best' straight line over a predetermined p/pO range. Instead, we have employed several consistency tests to ensure that the C value is positive and that an unambiguous range of plot is obtained [1]. The short BET ranges and the high C values are consistent with the microporous nature of the two samples. Table 1 9Micropore analysis of sample A Property

t

~s (Vulcan) ~S (EIftex 120) DA

a (ext) / m 2 g-i

14

92

90

a (mic) / m 2 g-1 *

1652

506 *

566 *

Vp(mic) / cm 3 g-1

0.68

0.62

0.56

0.33 ~

0.26 *+

Wp range / n m

-

HK

DFT

1490-1670

-

1400

0.63 - 0 . 7 0

0.64

0.58

1.6 - 1.7

0.4 - 0.8

0.5 - 1.4

* BET-area = 1666 m e g t - linearity of BET plot" 0.015 < p/pO < 0.058, CBET = 493 * Effective supermicropore area [a (s, mic)] *~Effective ultramicropore volume [vp (u, mic)] Table 2 9Micropore analysis of sample B t

(XS (Vulcan)

(XS (Eifiex 120)

a (ext) / m 2 g-i 9

130

94

99

a (mic) / m 2 g-i

928

473 *

543 *

982 - 1126

vp (mic) / em 3 g-i

0.37

0.35

0.32

0.38 - 0.44

0.41

0.46

0.24 ~

0.18 ~ 1.5 - 1.6

0 . 4 - 2.0

0 . 6 - 1.2

wp range / n m

-

DA

HK

DFT

Property

860

* BET-area = 1058 m 2 g-l_ linearity of BET plot" 0.005 _

SANS data

%

0.4 0.2

isotherm

0.0 0.0

0.2

0.4

0.6

0.8

1.0

P/Po Figure 1. Comparative presentation of experimental H2O adsorption isotherm and the reconstructed, from the SANS data, isotherm.

431 SAS can detect the presence of non-accessible to vapor pores, which cannot be detected by the intrusive methods, such as sorption. If no such pores exist, a good agreement is expected between the intrusive sorption and the non-intrusive SANS, as illustrated in Fig. 1 where, an experimental water adsorption isotherm on a mesoporous alumina membrane, made by compressing non-porous spherical particles, is compared to the corresponding one reconstructed from the SANS data.

1.1.2 Network Model based on Random Packing of Equal Spheres A three dimensional capillary network model has been developed, aiming to the simulation of sorption by several model mesoporous adsorbents, such as the one mentioned in the previous section. The model offers realistic simulation conditions and is able to provide satisfactory. prediction of adsorption-desorption isotherms of CC14 and C5H~2 for different porosities, temperatures and adsorbates. The expected desorption branch hysteresis is estimated as a two component summation of the thermodynamic (single pore) and the network hysteresis. Similarly, the overall sorbed volume is the two component summation of the volume due to multilayer adsorption and to the volume due to capillary condensation. 1.2 Dynamic Methods 1.2.1 Membrane modeling Dynamic methods rely on the study of fluid flow properties of porous membranes, which are extremely sensitive functions of the pore structural characteristics like the pore size distribution, f(r) and the pore connectivity, z. The resulting data, if analyzed in combination with other measurements obtained by equilibrium methods, can offer important structural information, regarding the membranes performance evaluation. The most widely used representation of a porous structure is as a bundle of tortuous capillaries with radii obeying the pore size distribution f(r) and effective length Left, along the flow axis. The model is completely defined by f(r) and the tortuosity factor, ~=(Len/L)2, where L is the straight distance in the flow direction. Alternatively, the capillary network model constitutes a significant improvement over this tortuosity model, since it can provide realistic modeling, especially for systems involving membranes partially blocked by condensed vapors. In this model the degree of connectivity of the pores, z, is replacing the less tangible factor. 1.2.2 Gas relative permeability Gas relative permeability, PR, is defined as the permeability of a fluid through a porous medium partially blocked by a second fluid, normalized by the permeability when the pore space is free of this second fluid. This property diminishes at the "percolation threshold", at which a significant portion of the pores are still conducting but they do not form a continuous path along the flow direction. It is obvious that only the network model, can provide a satisfactory analysis of the percolation threshold problem. Nicholson et al. [3] introduced a simple network model, and applied it on gas relative permeability [4]. For the gas relative permeability, an explicit approximate analytical relation between the relative permeability and the two network parameters, namely z and the first four moments of, f(r), has been developed, based on the Effective Medium Approximation (EMA) [5]. If a porous

432 solid is in equilibrium with bulk vapor at a vapor relative pressure 1" t'o the adsorbate consists of a capillary condensed liquid, filling the pores with radii smaller than the Kelvin radius, rh(subcritical pores, r=rx) and an adsorbed layer of thickness t coveting the walls of the supercritical pores (r>rx). For the classic case of N2 sorption on a mesoporous medium at 77 K, the following expressions have been employed [6]: 1

r ln(Ppo

t- -

(2)

C1

r~ = ~ + t

(3)

where C1, C2 are constants, characteristic of the particular adsorbate. The flux expression for an open cylindrical pore (bond) of the network connecting two nodes (sites), i and./, in the Knudsen regime can be written as follows: (4)

2~rx'j3 (8RgT'] ''= (Pg'-P~)

where x~j=ro-t is the open core radius of a capillary partly filled with adsorbate of thickness t, Rg is the universal gas constant, 7 is the ambient temperature, M is the molecular weight of the non-adsorbed gas (e.g. He) and l is the length of the capillary pore (assumed to be the same for all network pores). The material balance equation at each pore junction, results in a set of linear algebraic equations which can be solved for the nodal pressures using successive over-relaxation methods. The network permeability is then determined from the total flux, J, obtained for a given pressure drop across the network, [4]. The above computation scheme is repeated for a range of values of P Po between zero and unity and the relative permeability is determined as a function of the relative pressure t" t'o or the normalized adsorbed volume Vs. Alternative to the network model is 1

l

. . . . .

0.8-

0.8 -

0.6

0.6 - -

NETWORK - - - - EMA ~=8

~" 0 . 4 - -

~0.4

0.2--

0.2

, nT=6 7 ' ~ I~~,,,,L ]

0 0

0.2

0.4

V~

0.6

0.8

Figure 2a. Relative permeability vs adsorbate volume, for 3D network and EMA models

0 0

,

,

0.2

0.4

fb

,

I

,

0.6

0.8

1

Figure 2b. Relative permeability vs open pores fraction, J~, for 3D network and EMA models

433

the effective medium approximation (EMA) model [7]. Application of EMA for the determination Of PR requires the solution of an integral equation which is easily solved [8]. In Fig. 2 relative permeability curves computed by the network model are plotted for ==4,6 and 8 and are compared with EMA results. As z increases the I'R curve becomes broader as it approaches the percolation threshold, V~,. In all cases EMA is in good agreement with the network solution, except in the neighborhood of Vsc. In that region, the EMA predicted I"R curve decreases linearly with I(s., while the network solution exhibits a non-linear behavior and reaches a higher percolation threshold, Vsc. This is because Vs~: predicted by the network model, corresponds to the theoretical fbc predicted by percolation theory ~ c - 1 . 5 / z , [9]), while Vs.(, found by EMA corresponds to fbr [10]. A similar picture is presented in figure 2b, where t'R is plotted as a function of the fraction of the open pores,./~. It can be seen that for all -, near the percolation threshold, EMA shows a linear decrease of 1"~ with.[~,. On the other hand, network results indicate that, in the same region, Pn decreases with ]b according to a power law. For an infinitely large network percolation theory states:

where t is a universal critical exponent that depends only on the dimensionality of the network [ 11 ]. For a three dimensional lattice E1.87. For a network of size LxLxL, finite size scaling effects are expected to influence the above behavior [12]. However, a standard approach is employed for the case of finite size networks in order to apply percolation theory and to determine critical exponents [11]. According to this, eq. (5) is replaced by the following:

(6) where v is another universal critical exponent, with v=0.88 for three dimensional lattices [13] and g(x) is a scaling function, which varies from lattice to lattice but has a common asymptotic behavior:

g ( x ) -~

1; x r0 1

j =(32" n'T~ 2 .(r_t)3. APg ~R.

j = 2"n'r'z2"R'T APg

l

Pm.C~.S~

Capillary Enhanced Jc-zt'r4"pl

8. n~

r-

Flux (rk -> r > tO _

" l(r

=

8-n I

(10)

" !

Liquid Poiseuille Flux (r< t) 7t - r 4 . p j APg

Jl

(9)

l

(11)

1

Figure 4. Different flow regimes developed inside the individual pores, depending on the specified pressure gradient across the network.

436 steady state viscous condensate flux, Jc, is assumed to obey Poiseuille's formulation and is given by the eq. (11), where fil is the liquid density and nl is the viscosity of the fluid. Eq. (10), when compared to Poiseuille's law, is characterized by an enhancement factor ((r-t)Z/rZ)filRT/MPm, which is physically attributed to capillary pressure gradients [15]. Indeed, an additional driving force occurs due to the difference in the curvatures of the menisci that are formed between nodes and bonds filled with condensate. This capillary action is gradually diminishing as the mean pressure increases for a given bond. The reason is that the menisci begin to flatten as the pressure is raised above Kelvin equilibrium conditions. Experimental data from the literature [15] concerning freon 113 permeability on a vycor glass membrane were simulated by the 3D network model. An average effective length of each pore was selected in a way that the (non-condensing) helium permeability predicted by the network matches the experimental values, and at the same time gives a porosity and surface area close to the experimental ones. Subsequently, the pore size distribution obtained from porosimetry and the effective pore length were used for the simulation of the condensable vapor permeability. The agreement between the experimental points and the theoretical results is excellent, for two different temperatures, as can be observed from Figure 5. This agreement is attributed mainly to the narrow pore size distribution of the vycor membrane, as well as to the shape of the pores for vycor which appear to be well represented by cylinders.

2.2 Experimental Measurements The membrane characterization data reported in this section have been obtained by means of a home-made apparatus which is made of stainless steel and can operate from high vacuum up to 70 bars [17]. It is characterized by the unique capability of performing a broad range of porous membrane characterization and evaluation measurements, namely equilibrium isotherms, absolute (integral and differential) and relative gas and condensed vapor permeabilities and selectivities. Two pellets, of porosities 0.41 and 0.48 respectively, were made by means of coaxial compaction of Alumina powder consisting of non porous spherical particles of size ca. 200.~ in diameter. Each pellet consists of 11 sections, and the compaction pressures of those sections were selected in such a way that no macroscopic porosity inhomogeneities would be present on the final pellet. The BET specific surface area of the pellets was calculated 100 + 15 m2/gr. Experimental results of water vapor adsorption, Helium relative permeability, PR, and water vapor permeability, Pe, for the two alumina pellets are presented in figures 6a and 6b, for water relative pressures up to unity. As the amount of water adsorbed starts to rapidly increase with P/Po, due to capillary condensation, a significant increase of its permeability may also be observed due to the resulting capillary enhancement of flow. At a certain value of P/Po where V~ is close to unity, all pores of the membrane are in the capillary condensation regime and thus follow the capillary enhanced type of flux. At this point water vapor permeability reaches its maximum value while, helium relative permeability decreases rapidly and falls to zero well below the point of saturation. This may be attributed, according to percolation theory, to the fact that in a simple cubic lattice, if ~75% of the pores are blocked by capillary condensate, the system has reached its percolation threshold and helium

437 can no longer percolate through the membrane. The point where helium ceases to percolate through the membrane is closely related to the point where water permeability starts becoming "super-conducting" due to capillary enhancement effects. The maxima regions in 0.00004 -o EXPERIMENTAL 9 EXPERIMENTAL

% 0.00003--

fl/~

"/

\

r~

~

~T

T--194~

'.' 0.00002-_

-K

o.ooool

r~

5OC

--

I

I

I

,

0.2

0.4

0.6

0.8

P/Po Figure 5. Comparison of network (solid lines) and experimental results [19] of Freon 113 permeability on Vycor glass membrane the condensed phase permeability figures, are very important in assessing the conditions for maximum permeability and selectivity of the membrane.

.,.)"

m! Om"

0.8

~

0.8

0

O

-.

G

,m [~

D

m

i

i I

0.6

~, 0.6

ii

----4,---- Adsorption -

0.4

-

-m-

- Water

_"2

Isotherm

~

Permeabihtv

Relative

'

Perm.

~

9 .t 0

0.2

,~._---04

~m,,mm

0

0.2

i ,

m

,

.

~-.0.4

0.6

0.8

P/Po Figure 6a. Experimental results for Alumina membrane c=41%

i i I

.Im o

-

0

m m

Isotherm

. ,

. Water Permeability Relatnve perm

~1~0

9

1

I'm

9 9

, ,

9IO

, , m, Q

u mm m u mm am,m . m

0.4

Adsorption

0.2

!

v-

0

9

,

0

4',

.

o, mm

.~

,

,

~ , am'

4

m . . . . -'i 0 " . -.'" "" "'. J'.. J.

0.2

0.4

0.6

0.8

P/Po Figure 6b. Experimental results for Alumina membrane c=48%

1

438 Since the dominant feature of packings of spheroidal particles is the constrictions between the tetrahedral cavities formed by the Alumina microspheres, a more realistic model is required, based on the random sphere packing models. Such models are obviously more complex. Conversely, they permit a more realistic representation of the pore space among the spheroidal particles. A preliminary model has been reported for sorption [20] and relative permeability PR [21 ]. A more realistic model described above to predict the sorption properties in such systems is currently developed to predict also permeability, given the porosity and the spheroidal particle size distribution.

REFERENCES

.

4. 5. .

.

.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

J.D.F. Ramsay, Advances in Colloid and Interface Sci., 76-77 (1998) 13 A.Ch. Mitropoulos, T.A. Steriotis, F.K. Katsaros, K.P. Tzevelekos, N. K. Kanellopoulos, U. Keiderling, S. Sturm and A. Wiedenmann, J. Membr. Sci., 129 (1997) 289 D. Nicholson, J. K Petrou, and J. H. Petropoulos, Chem. Eng. Sci., 43 (1988) 1385 D. Nicholson and J. H. Petropoulos, J. Chem. Soc., Faraday Trans., 80 (1988) 1069 T. A. Steriotis, F. K. Katsaros, A. Ch. Mitropoulos, A. K. Stubos and N. K. Kanellopoulos, J. of Porous Mat., 2, (1995) 73 S.L.Gregg and K.S.W. Sing, Academic Press (eds.) Adsorption, surface area and pororsity, New York, 1982 J.H. Petropoulos, J.K. Petrou and N.K. Kanellopoulos, Elsevier Publishers B.V. (eds), Characterisation of Porous Solids, Amsterdam 1988 Kainourgiakis M.E., Kikkinides E.S., Stubos A.K. and Kanellopoulos N.K. Chem. Eng. Sci., 53(13), (1998) 2353 V.K.S. Shante and S. Kirkpatrick, Adv. Phys. B, 28 (1971) 307 S. Kirkpatric, Rev. Mod. Phys. 45 (1973) 574 M. Sahimi, B.D. Hughes, L.E. Scriven and H.T.Davis, J. Chem. Phys., 78, (1983) 6849 D. Stauffer, Taylor and Francis (eds), Introduction to percolation theory, London 1985 M. Sahimi, A.I.Ch.E.J., 39(1993) 369 P.C.Carman and F.A.Raal, Proc. Roy. Soc., A209 ( 1951 ) 38 K.H. Lee and S.T. Hwang, J. Colloid. Interf. Sci., 110 (1986) 554 R.J.R. Uhlhorn, K. Keizer and A.J. Burgraaf, J. Membr. Sci. 66 (1992) 259 D.P. Sperry, J.L. Falconer and R.D. Noble, J. Membrane Sci., 60 (1991 ) 185 P.B. Weisz, Bunsegres Phys. Chem., 79, (1975) 798 K.P. Tzevelekos, E.S. Kikkinides, A.K. Stubos, M.E. Kainourgiakis and N.K. Kanellopoulos, Advances in Colloid and Interface Sci., 76-77, (1998) 373 N. K. Kanellopoulos, J. K. Petrou, and J. H. Petropoulos, J. Colloid Interf. Sci., 96 (1983)90 N. K. Kanellopoulos, J. K. Petrou, and J. H. Petropoulos, J. Colloid Interf. Sci., 96 (1983) 101

Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) o 2000 Elsevier Science B.V. All rights reserved.

439

S A N S c h a r a c t e r i s a t i o n o f m e s o p o r o u s silicas h a v i n g m o d e l structures

J.D.F. Ramsay a, S. Kallus a, E. Hoinkis

b

aLaboratoire des Mat6riaux et des Proc6d6s Membranaires, UMR CNRS 5635, Universit6 Montpellier II, France bHahn-Meitner-Institut, Bereich Strukturforschung, NI, Glienickerstr. 100, D- 14109 Berlin, Germany

The mechanisms of the adsorption and condensation of benzene in a mesoporous silica gel having a model pore structure have been investigated by SANS. Measurements have been made in situ during an adsorption/desorption isotherm (310 K) cycle using contrast matching conditions for the condensed fluid. The SANS of the evacuated silica showed low angle diffraction features corresponding to a cylindrical pore structure (diameter 6 nm) oriented in an ordered hexagonal array. Changes in the SANS on adsorption of benzene can be ascribed to a process of multilayer formation and condensation process in such a model pore geometry. The existence of much larger pores (> 0.1 gm) corresponding to the inter granular silica structure was readily distinguished by SANS.

1. INTRODUCTION Structural details of porous materials on a scale covering a range from-~ 1 to -- 100 nm may be determined from measurements of the small angle scattering (SAS) of both X-rays (SAXS) and neutrons (SANS)[1-4]. SANS arises from variations of scattering length density, Oh, which occur over distances exceeding the normal interatomic spacing. Such variations occur when solids contain pores, and details of the porosity and surface area can be obtained from measurements of the scattered intensity, I(Q), where 4zt sin0 Q=~

(1)

The appropriate angular range (20) where this information is contained is defined by Q and the size of the pore, d. Thus an analysis of the scattering in the range 0.1 < Qd < 1 provides details of the size and form of the scattering object (pores); information of surface properties and structure may be obtained at larger angles (Qd >> 1). A recent and important development of SANS in the characterisation of porous solids has been the application of the contrast variation technique. In this development, SANS measurements are made in situ during the adsorption of a gas in a porous solid for example.

440 Thus, for a two phase system, I(Q) is proportional to the contrast, i.e. the square of the scattering length density difference between the two phases: I ( Q ) - K [pb(1)-Pb (2) ]2 = K (AOb)2

(2)

For an evacuated solid, where Oh(l) = Pb (solid), the situation is simple, since pb(2) = 0. However, more detailed information may be derived if the pores are filled, or partially filled, with an adsorbed vapour. Thus, scattering from pores filled with a condensed liquid adsorbate may be eliminated if the scattering length, Pb is chosen to be the same as that of the solid, viz., (Apb)2 0. This feature may be used, for example, to distinguish open and closed porosity, the latter being inaccessible to the adsorbate. In contrast matching experiments with SANS there is a wide flexibility in the choice of adsorbate (e.g., water, hydrocarbons, etc.) due to the control in lob which can be achieved by an isotopic substitution of H for D in the molecule. Several applications of the contrast variation method have been reported. These have included SANS investigations of lhe growth of adsorbed multilayers and capillary condensation processes in porous glasses and oxide gels [5-8]. Other important developments have been made using SAXS and SANS to probe the structure of the surfaces of porous materials which have a fractal character [9-12]. The majority of these earlier studies were made with samples which were pre-exposed to a fixed adsorbate pressure before the scattering measurement. This procedure, although simple, is limited for several reasons. Firstly, because of uncertainties in the P/P0, secondly, due to problems of reproducibility between different samples, and thirdly, the impossibility of making non-equilibrium and kinetic adsorption measurements. These limitations have recently been overcome with the development of a special apparatus [13], which allows in situ measurements on thermostated samples under controlled relative vapour pressures of different adsorbates. This equipment, which has enabled the contrast matching method to be applied in more demanding situations, has recently been used to investigate the process of capillary condensation of benzene in a mesoporous silica gel having a defined and regular structure [8,14]. Here detailed SANS measurements corresponding to the adsorption/desorption states in the isotherm hysteresis loop, were required. From this investigation the processes of multilayer formation and subsequent capillary condensation in the porous network were analysed. These results were in accord with a pore structure formed by the regular packing of uniform spherical colloidal particles. We have now extended these investigations to another type of mesoporous silica, having a different pore geometry, as reported in the present paper. The present silica contained uniform cylindrical pores (diameter -6 nm), arranged in an aligned periodic structure, as described by Stucky et al. [15]. This pore geometry is similar to that ofMCM-41 type materials [ 16]. =

2. E X E R I M E N T A L

Materials The ordered mesoporous silica (pore diameter - 6 nm) was kindly provided by Dr. Ulla Junges and was prepared as described previously by G.D. Stucky et al. [15]. A commercial triblock copolymer (Pluronic-123| was used in the synthesis process. This polymer comained ethylene oxide/propylene oxide/ethylene oxide blocks, which formed a hexagonal mesophase in the synthesis mixture during the hydrolysis of the silicon alkoxides.

441 Techniques SEM measurements were performed using a field emission microscope (Hitachi $4200). Adsorption isotherms of nitrogen (77 K) and benzene (310 K) were measured gravimetrically at NCRS, Demokritos, Athens, Greece. SANS measurements were made using the V4 spectometer at the HMI, Berlin. A specially designed apparatus was used for in situ measurements on a thermostated (310 K) sample under closely controlled relative vapour pressures of benzene (59 % C6D6), which was contrast matched with the silica, as described previously [ 14]. SANS measurements (~, = 6 A) were made at three sample-detector distances (1.4, 4 and 16 m). 3. RESULTS AND DISCUSSION

3.1 Scanning Electron Microscopy A typical SEM image of the silica powder, obtained using the field transmission technique, is illustrated in Figure 1. This shows an aligned porous structure within grains having a uniform geometrical shape. These grains are probably the pseudomorphs of the original liquidcrystalline structures formed by the tri-block copolymer molecules, during the synthesis of the silica gel. The size of the grains is remarkably similar (Figure 1.(a)): the width being of the order of 0.25 lam and the length in a range ---0.8 to 1.2 ~tm. The aligned pores run parallel to the facetted surfaces of the grains and have a periodicity o f - 1 2 nm (Figure 1.(b)). The diameter of the pores, which can be estimated from the image at the end faces of the grains, is very uniform and is approximately - 6nm.

Figure 1. Field emission scanning electron micrographs of ordered mesoporous silica powder. The SEM at lower magnification, Figure 1.(a), shows rhombohedral grains with a uniform size and shape. These grains have a highly regular and aligned porous structure, as revealed at higher resolution in Figure 1.(b).

3.2 Adsorption isotherms Nitrogen The adsorption isotherm of nitrogen (77 K) for the porous silica is shown in Figure 2. This has a type IV character in the IUPAC classification [ 17], exhibiting a hysteresis loop with a shape corresponding to a capillary condensation process in cylindrical pores [18]. The v

442

adsorption and desorption branches of the hysteresis loop are almost vertical, indicating a very narrow pore size distribution. A pore radius, ra, of 3.2 nm was derived from the desorption branch by the standard procedure [ 18] using the Kelvin equation. This value is in good agreement with the size of the pores observed by SEM. The specific surface area, ABET, obtained using the BET method was 827 m2gt and the pore volume, Vp, was 1.01 cm3g~. When the cylindrical pores have been filled by capillary condensation at P/P0 ~- 0.7, there is a small but progressive uptake which cominues to very high P/P0. This cominuing uptake can be ascribed to adsorption on the external pore surface of the grains of the porous silica. Further details of the structure of the mesoporous silica can be obtained by an analysis of the isotherm using the Ors method [18] using the standard isotherm data on non porous silica. Thus the total area, AT (844 m2g~), can be calculated from the slope of the as plot in the monolayer region while the corresponding value of the external area, AExt, (--~ 60 m2gl), can be derived from the slope of the plot corresponding to high P/P0. The external area, AExt, is relatively small, as would be expected, since the grains of porous silica are approaching micron size.

"7,E~ -

0

35

25

"13 9

20

0 ~

15

~

10

0

5

E

adsorption desorplJon

30

E E

00.0

o~

~~

9

ee

0

II

oo

0.2

o~

00

0.4

0.6

0.8

1.0

P/Po

Figure 2. Nitrogen adsorption isotherm (77 K) for mesoporous silica. Benzene The adsorption isotherm of benzene (310 K) (Figure 3) has similar characteristics to that of nitrogen: It is of type IV and again shows three regions corresponding to (i) monolayer multilayer adsorption, (ii) capillary condensation in the cylindrical mesopores, and (iii) adsorption on the external surface of the silica grains. There are however significant differences in the region of initial adsorption. Thus for nitrogen a steep uptake at P/P0 < 0.1, corresponding to strong interaction of N2 with the surface during the formation of a monolayer, was observed. Such behaviour is typical for N2 adsorption on oxides and reflects a strong interaction of the molecule with the surface [18]. However for benzene the interaction is weaker, as is reflected by the ill-defined "knee" in the isotherm. The hysteresis loop has a similar shape but is displaced to lower P/P0. This is expected due to the different fluid properties of benzene compared to nitrogen. The Kelvin radii ,rk, for benzene and N2 are however similar. Thus the value of rKbenzene(2.7 rim), derived from the desorption branch, is in close agreement with that of rKN2 (2.5 nm) obtained from the N2 isotherm. To determine the

443 pore size, rp, from the desorption branch requires a knowledge of the statistical thickness, t, of the benzene multilayer which remains after the loss of capillary condensate. The value for Vp of 0.91 cm3g l, again derived using the bulk liquid density, is in satisfactory agreement with that obtained from the N2 isotherm (0.89 cm3g-l).

'7 O

14

12

E E 10 -o 8 o

or) "O t-

o E 111

adsorption desorption

~

o

o o

oo

~ 1 7 6Q

6 4

eO

2 0 ~ 0.0

0.2

0.4

0.6

0.8

1.0

P/Po

Figure 3. Benzene adsorption isotherm (310 K) for mesoporous silica. 3.3 Small angle neutron scattering (SANS) The SANS for the evacuated sample is illustrated (Figure 4) on a logarithmic scale to highlight features both at low Q and high Q. In the higher Q range ( 3xl 0 .2 to - 3xl 0 ~ A~), a well-resolved diffraction peak, at Q = 6.5 x 10.2 A -~, together with a secondary maximum, at -~ 1.3xl 0 l A J, are observed. These can be ascribed to the (100) and (200) reflections associated with a hexagonal pore structure (space group p6mm) as described previously by Stucky et al [15] from XRD analysis (cf. Figure 5). The (100) peak corresponds to a d-spacing of-~ 96 A indicating a large unit-cell parameter (a0 - 111 A). Other very much weaker peaks at higher Q (210, 300 etc.), which were reported by Stucky [15], using XRD are not detected by SANS. This can be attributed firstly to the polychromatic nature of the neutron beam (A~./~. -10 %), which limits resolution, and secondly the significant background at high Q. In the low Q range (< 3x10 2 to -~3x103 A -~) the SANS exhibits a marked increase corresponding to a power law: I(Q) ..Q-4 (3)

This is typical of Porod law scattering [20] and indicates a scattering contribution from other objects, which are considerably larger than the regular cylindrical pores. Thus Porod law scattering is normally observed in the tail of a SAS curve when Qd > 4. This would imply here that the dimension, d, of such objects was > 103 A. This Porod behaviour can therefore tematively be ascribed to scattering from the grains of the porous silica, a conclusion which is substantiated by the changes in the SANS after adsorption of benzene as described below.

444

I(Q)

1000

~

Q-4

II B

100 10

0 A

0.1 0.01

'

'

'

'

'

'

'

I

0.01

'

'

'

'

'

'

'

I

0.1

Q I A -1 Figure 4. SANS curve obtained for the evacuated mesoporous silica.

000 ao

d(loo)

Figure 5. Schematic representation of the pore structure of mesoporous silica, depicting the cylindrical pores in a regular hexagonal array. The sequential process of multilayer film formation and capillary condensation in this structure are illustrated. The SANS for the evacuated sample, and after in-situ equilibration with benzene (59 % C6D6) at different relative pressures (P/P0, 0.22, 0.50, 0,80) during the adsorption isotherm (310 K), are compared in Figure 6. This shows that there is a dramatic suppression of the diffraction feature in the interval of P/P0 between 0.50 and 0.80, which can be ascribed to a filling of the cylindrical mesopores. This behaviour accords with the adsorption isotherm (Figure 3) earlier described, which exhibited capillary condensation in a narrow range of P/P0 f r o m - 0.55 to 0.6.

445

(a)

(b)

(c)

(d)

10000 1000

.. 9

"..

~00

0

".

:

'.

v

.

m

0.1

X,

-

0.01

.

.

.

.

.

.

.

0.01

.

.

.

.

0.1

.

.

.

.

.

-

0.01

0.1

0.01

0.1

0.01

0.1

Q I A -1 Figure 6. Evolution in the SANS of mesoporous silica in situ, atter isothermal (310 K) equilibration with matched (59 % C 6 D 6 ) benzene at progressively increasing relative pressures, P/P0" (a) evacuated, (b), 0.22; (c), 0.50; (d), 0.80. The changes in the main diffraction peak, following progressive stages of adsorption, are more clearly seen in Figure 7, where I(Q) is plotted on a linear scale. Here equilibrium data for additional values of P/P0 in the interval between 0.50 and 0.80 are shown (these were only measured for the S/D distance of 4.0 m). These results also show that on initial adsorption (P/P0 = 0.20) there is an increase in the intensity of the diffraction peak; thereafter little change occurs until the onset of capillary condensation. This initial increase can be tentatively ascribed to the adsorption of the matched benzene on the surface of the cylindrical pores. This will result in an effective "thickening" of the pore walls. (a)

(b)

(c)

(d)

(e)

(f)

10 _

eo

9e

9

I(Q) 6~

"

9

9

"

"

9

% _

9

9

9

9 9

o 9

9

9

oeeoo

0 ......... ~ ........ 0.06 0.08 0.06

0.08

0.06 0.08

0.06 0.08 0.06 0.08

0.06 0.08

QIA-1 Figure 7. Evolution in the diffraction peak (100) of mesoporous silica in situ after isothermal (310 K) equilibration with matched benzene at progressively increasing P/P0: (a) evacuated; (b), 0.22; (c), 0.50; (d), 0.54; (e), 0.62; (f), 0.80.

446 When the pore walls are thin, as is the case here, such a process can be shown to lead to an enhancement of I(Q). From further quantitative analysis, which will be described subsequently, information on the pore wall structure and the effective thickness of the benzene film in the monolayer/multilayer region can be derived. A schematic mechanism for the progressive uptake of benzene in the organised cylindrical pore structure is illustrated in Figure 5. The abrupt onset of the capillary condensation which occurs at P/P0 > 0.54 can be followed kinetically by SANS as depicted in Figure 8. Here data were accumulated at intervals of 130 s after increasing P/P0 from 0.54 to 0.62. It will be noted that equilibrium is almost reached after 17 minutes. Such kinetic measurements were also performed on the desorption branch of the hysteresis loop although these are not shown here. Further analysis of these results, although not possible here, can yield information on the mechanisms of formation and release of capillary condensate within the pore network. Such an analysis is feasible when there is contrast matching between the condensed fluid and the porous matrix, as discussed earlier. It is however of interest to note that other workers [21,22] have observed qualitative changes of the (100) peak intensity of MCM-41 following the adsorption of deuterated molecules (e.g. CD4, D20) during in situ neutron diffraction experiments. As the aim of these earlier investigations was to determine the structure of the adsorbed phase from wide angle diffraction, contrast matching conditions were not required, (incoherent scattering from protons in the adsorbate molecule would have been undesireable). Consequently a direct comparison with the present results is not possible. We now consider the SANS behaviour in the low range of Q during in situ adsorption. From Figure 6 there is very little evidence of change: Porod scattering behaviour is still observed up to the highest P/P0 measured (P/P0 = 0.80). This implies that the interstices between the silica grains are still unfilled at this pressure. As the sizes of these interstices (or pores) are of the same order of magnitude as the grains (> 0.1 ~tm) (cf. Figure 1.(a)) this behaviour is expected. Slight changes in the SANS in the Porod region were however noted on adsorption of benzene, although these are not evident in Figure 6. Such changes corresponded to an increase in the relative intensity on progressive adsorption. These effects, which can be ascribed to the filling of the cylindrical mesopores within the grains, will not be considered further here however.

8 t i 6

~4 2

0

-~

Q/A'I

Figure 8. Kinetic evolution of the diffraction peak (100) of mesoporous silica during capillary condensation of benzene (59 % C6D6),corresponding to the incremental increase in P/P0 from 0.54 to 0.62. (Time interval between measurements is 130 s.)

447

4. CONCLUSIONS The process of adsorption and condensation of benzene in the model pore system of a mesoporous silica gel have been investigated by SANS. This has been achieved by following the scattering in situ at different stages of an adsorption/desorption cycle. Such isothermal measurements have been performed using contrast matching conditions for the solid matrix and adsorbed fluid. Although a detailed theoretical analysis is not given here, the results can be ascribed to a process of multilayer formation and capillary condensation within the uniform cylindrical pores of this regular structure. The pore diameter of the present silica is sufficiently large (6 nm) for behaviour to be consistent with the condensation of benzene having bulk fluid properties. The SANS technique also highlights the existence of a secondary system of larger pores between the grains of the mesoporous silica. Future investigations can be envisaged with MCM-41 type silicas, which have smaller pore diameters, to test the limits of validity of theories which assume bulk thermodynamic behaviour of condensed fluids.

5. REFERENCES

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

A. Guinier and A. Foumet, Small angle Scattering of X-rays, Wiley, New York, 1955. P.W. Schmidt, Stud. Surf. Sci. Catalysis, 39 (1988) 35. J.D.F. Ramsay, Stud. Surf. Sci. Catalysis, 39 (1988) 23. J.D.F. Ramsay, Stud. Surf. Sci. Catalysis, Adv. Coll. Int. Sci., 76-77 (1998) 13. J.C. Li, D.K. Ross, M.J. Benham, J. Appl. Cryst. 24 (1991) 794. J.D.F. Ramsay and G. Wing, J. Coll. Interface Sci., 141 (1991) 475. J.D.F. Ramsay and E. Hoinkis, in "Proceedings of Characterisation of Porous Solids IV", Royal Society of Chemistry, London, 1997, p33. 8. J.D.F. Ramsay and E. Hoinkis, Physica B 248 (1998) 322. 9. D.W. Hua, J.V.D. Souza, P.W. Schmidt, D. Smith, Stud. Surf. Sci. Catalysis, 87 (1994) 255. 10. C.J. Glinka, L.C. Sander, S.A. Wise, N.F. Berg, Mat. Res. Soc. Proc., 166 (1990) 415. 11. A.Ch. Mitropoulos, P.K. Makri, N.K. Kanellopoulos, U. Keiderling A. Weidenmann, J. Coll. Interface Sci., 193 (1997) 137. 12. E. Hoinkis, Adv. Coll. Int. Sci., 76-77 (1998) 39. 13. E. Hoinkis, Langmuir, 12 (1996) 4299. 14. J.D.F. Ramsay and E. Hoinkis, J. Non. Cryst. Solids, 225 (1998) 200. 15. D. Zhao, J. Feng, Q. Huo, N.Melosh, G.H. Fredrikson, B.F. Chemelka, G.D. Stucky, Science, 279 (1998) 548. 16. C.T. Kresge, M.E. Leonwitz, W.J. Roth, J.C. Vartuli, J.S. Beck, Nature, 359 (1992) 710. 17. 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 (1985) 603. 18. S.J. Gregg and K.S.W. Sing, Adsorption, Surface Area and Porosity, 2 nd Edn. Acad. Press, London, 1982. 19. M.M.L.R. Carrott, P.J.M. Carrott, A.J.E. Candeias, K.K. Unger and K.S.W. Sing, in "Fundametals of Adsorption VI", Elsevier, Paris, 1998, p. 69. 20. G. Porod, Kolloidn. Zh., 124 (1951) 83. 21. J.P. Coulomb, C. Martin, Y. Grillet, P.L. Llewellyn, G. Andr6, Stud. Surf. Sci. Catalysis, 117 (1998) 309. 22. N. Floquet, J.P. Coulomb, S. Giorgio, Y. Grillet, P.L. Llewellyn, Stud. Surf. Sci. Catalysis, 117 (1998) 583.

448 6. ACKNOWLEDGEMENTS We are indebted to Dr. U. Junges, for kindly providing the mesoporous silica sample, to Mr. G. Nabias for the SEM measurements and to Drs. Th. Steriotis and E.S. Kikkinides for nitrogen and benzene isotherm data. Technical support and access to facilities at BENSC, Berlin are gratefully acknowledged, as supported by the European Commission under the TMR/LSF Access Programme (contract no. CT950060).

Studies in Surface Science and Catalysis 128

K.K. Ungeret al. (Editors) 92000 Elsevier Science B.V. All rights reserved.

449

PORE-SCALE COMPLEXITY BY TIME-CONTROLLED

OF A CALCAREOUS MATERIAL MERCURY POROSIMETRY

Adrian CEREPI*, Louis HUMBERT*, Ren6 BURLOT* *Institut EGID-Bordeaux 3, UniversitO Michel de Montaigne, Bordeaux 3 tel.." (33) 05 56 84 80 72; email ."[email protected]

1. I N T R O D U C T I O N The mercury porosimetry technique constitutes a well established three dimensionel petrophysical tool for characterization of porous media. Hg-injection and withdrawal capillary pressure curves transformed into dimensionless capillary pressure function can be used to predict the behavior of other fluid pairs, such as oil and water, during pressure changes in pore systems of reservoir rocks. Reservoir engineers, petrophysicists and exploration geologists are interested in how permeability and porosity relate to pore aperture size and pore-aperture size distribution in order to evaluate the sealing capacity of cap rocksl. The aim of this paper is to purpose and describe a new quantitative dynamics method determining the pore-scale complexity from time-controlled mercury porosimetry data. New parameters characterized the complexity are defined from the curve of capillary pressure and volume versus time. The theorical basis of porosimetry is defined by Laplace's law which explained that the work required to expand a non-wetting fluid surface (mercury) of principal radii of curvature R 1 and R 2 is equal to the work done to the concave side of the surface. Washburn (1921) linked to Laplace's equation by using a capillary model where the porous medium is assimilated to a bundle of conic or cylindric capillary tubes (Fig. 1). (conic capillary tubes) Pc = (cylindric capillary tubes)

Pc =

2plcos(0 + qb)l Rc

2p cos 01 --Rc

(l) (2)

Rc Zz,,,-,,. ~ - ' _ Pore wall R , : R'~_ =R= cos(0+~) :.~'i::'~ - " -

~

............................ ..i......:.::......

Flow direction

P! ........

0 ~

.....

Figure 1: Average pore radii of a conic capillary tube.

where Pc is the capillary pressure (MPa); Rc is the the average pore-throat size (A) and 0 is the angle between mercury menisc and pore wall (for mercury 9=0.480 N/m, 0=140~ Two classical experimental modes of data acquisition in mercury porosimetry exist. A) Pressure-controlled mercury porosimetry procedure ~'2. It consists of recording the injected mercury volume in the sample each time the pressure increases in order to obtain a quasi steady-state of the mercury level as P,+l-Pi >dP>0 where Pi+l, Pi are two successive experimental capillary pressure in the curve of pressure P versus volume V and dP is the pressure threshold being strictly positive. According to this protocol it is possible to calculate several petrophysical parameters ~3 of porous medium such as: total porosity, distribution of pore-throat size, specific surface area and its distribution. Several authors estimate the permeability from mercury injection capillary pressure data. Thompson 4 applied percolation theory to calculate permeability from mercury-injection data.

450 He used three length scales derived from mercury-injection data to characterize a porous medium. He defined thresholds pressure as the pressure at which mercury forms a connected pathway across the sample and indicated that the measured threshold pressure corresponded graphically to the inflection point on a mercury injection plot. This protocole is often insufficient to characterize the porous space and to describe completly the phenomena in mercury injection. Experiments often show that between two successive experiments points the decrease of capillary pressure can be important and during this time the volume of injected mercury can be 50% of the total volume. Indeed, it observed sudden falls of pressure corresponding to the spontaneous redistribution of mercury in porous network. For similar porosity of samples we have unexplained different mercury saturation time of pore network. B) Volume-controlled porosimetry procedure "~'6'7'8. A constante mercury volume (Vi+lVi=dV=c st) is injected. It obtains the value of corresponding pressures Pi+l, Pi. Several researchers have tried to interpret these data and observed that capillary pressure fluctuates during volume-controlled displacement. Haines 9 gives the primary trait of fluid interface motion with so-called the which results from unstable configurations. In a during injection a Pc fluctuations occurs that depends on two factors. One is the volume spontaneously occupied (or evacuated) by mercury. The other is the capacity of the system to supply (or absorb) mercury globally. Morrow l~ clearly demonstrated in simple experiments the _0

Then, among the experimental points Pk corresponding to the decreased capillary pressure we compute the local maxima such as :

Pk -Pk-I >0 t k --tk_ 1

( =>

Rk- Rk-!

1

(t k - t k _ l ) . R k _ I-R k 2p']COS0[ > 0

Pk-Pk+i > 102/~. Further analysis of these preliminary SANS results is complex and can only be outlined here. The treatment takes as its basis, a model composed of an array of parallel cylindrical objects, length, 1and cross-sectional radius, a [14]. When such a system is oriented, where 7 corresponds to the angle between Q and the cylindrical axis, two specific cases can be defined for the scattering behaviour. For the first, where the vector Q is parallel to the cylindrical axis (~/ = 0) the scattering will be only a function of the axial length. Thus for a single isolated cylinder

I(Q,y = 0)--K/OoV sin(Q1 ~2)3 2 QI/

(3)

Where 90 is the scattering-length function and V is the cylindrical volume. This situation corresponds to the SANS in Figure 11.(b) corresponding to I(Qv). Secondly, if the Q vector is perpendicular to the cylindrical axis, the scattering will be a function only of the radius. In this case I(Q,7 = n/2)--- K(2p0V J'(Qa)/2 Qa }

(4)

Jr(x) is the first order Bessel function of the first kind. This situation corresponds to the SANS in Figure 11.(a) for both I(QH) qnd I(Qv) and also in Figure 11.(b) for I(QH). The origin of the anisotropy in the SANS behaviour observed is thus evident.

465

(a) 10

9 9 0

@'.

" I(QH)

9i(Ov)

o

0 @.

0

0 @. O0

@@ 9

0.1

9

-4

CY 0.01 1E-3

00

~

1 E-4

IE-5

'

'

'

'

'

I

w

0.01

. . . . . . .

I

,

o11

QIA" (b)

10"ID

9

9l(Qv)

o

9I(Qv)

0.1 o

0.01

o ~ oo

1E-3

~

Q_4

000% o

o

1E-4 1E-5

,

,

,

,

,

,

w

0

~176 '

9

0.()1

9

@@

@.

Q',

o 0o '

'

'

--I

'

'

'

0.1

O/A-' Figure 11. Anisotropic SANS results for an oriented alumina membrane (Anodisc, A20). In (a) the orientation is perpendicular and in (b) parallel to the incident neutron beam respectively. I(QH) and I(Qv) correspond to scattering along the horizontal and vertical axes of the 2D detector, respectively.

466 4. CONCLUSIONS The highly anisotropic porous texture of alumina membranes containing monodispersed cylindrical pores has been characterised using a combination of three techniques: SEM, mercury porosimetry and SANS. The SANS technique is a promising and very sensitive method for the analysis of such anisotropic pore structures. Further quantitative analysis of these membranes, which contain uniform macropores, will require SANS measurements at much lower Q.

5. REFERENCES

1. 2. 3. 4.

T.P. Hoare and N.F. Mott, J. Phys. Chem. Solids, 9 (1959) 97. J.P. O'Sullivan and G.C. Wood, Proc. Roy. Soc. Lond. A, 371 (1970) 511. A.W. Smith, J. Electrochem. Soc., 120 (1973) 1068. G.E. Thompson, R.C. Fumeaux, G.C. Wood, J.A. Richardson and J.S. Goode, Nature, 272 (1978) 433. 5. R.C. Fumeaux and M.C. Thorton, Brit. Ceram. Proc., No. 43 (1988). 6. A.J. Burggraaf and K. Keiser, in "Inorganic Membranes: Synthesis, Characteristics and Applications", R. Bhave (ed.) Van Nostrand Rheinhold, New York, 1991, pp. 10-63. 7. J.D.F. Ramsay and P. Lindner, J. Chem. Soc., Faraday Trans., 89 (1993) 4207. 8. A. Guinier and G. Foumet, "Small Angle Scattering of X-rays", Wiley, New York, 1955. 9. G.G. Kostorz, in A Treatise on Materials Science and Technology, H. Hermann (ed.), Academic Press, New York, 1998, p. 227. 10.J.D.F. Ramsay, Adv. Colloid Interface Sci., 76-77 (1998) 13. 11 .M.H. Stacey, Stud. Surf. Sci. Catalysis, 62 (1991) 165. 12.A. Matsumoto, K. Kaneko and J.D.F. Ramsay, in Studies in Surface Science and Catalysis, 80 (1993) 405. 13. J.S. Rigden, J.C. Dore and A.N. North, Stud. Surf. Sci. Catalysis, 87 (1994) 263. 14. J.D.F. Ramsay, S.W. Swanton and J. Bunce, J. Chem. Soc. Faraday Trans., 79 (1990) 3919.

6. ACKNOWLEDGEMENTS

We are indebted to Mr. E1 Mansouri for the measurements of Hg porosimetry, and the CNRS for access to neutron scattering facilities at LLB. S.K. acknowledges financial support by the European Community under the Industrial and Materials Technologies Programme (Contract No BRPR-CT96-313).

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) o 2000 ElsevierScienceB.V. All rightsreserved.

467

ZEOLITE M E M B R A N E S - CHARACTERISATION AND APPLICATIONS IN GAS SEPARATIONS

S. Kallus a, P. Langlois a, G.E. Romanos b, Th. Steriotis b, E.S. Kikkinides b, N.K. Kanellopoulos b and J.D.F. Ramsay a a Laboratoire des Mat6riaux et des Proc6d6s Membranaires, UMR CNRS 5635, Universit6 Montpellier II, France b NCSR DEMOKRITOS, Institute of Physical Chemistry, 15310 Ag. Paraskevi Attikis, Greece

Silicalite-1 membranes, supported on porous alumina ceramic discs, have been prepared by two different routes. In the first the zeolite membrane has been formed by in situ hydrothermal synthesis. Secondly a layer has been formed by controlled filtration of zeolite colloids. To optimise membrane stability, conditions have been established in which penetration of zeolite into the support sublayer occurs. The pore structure of these membranes has been characterised by a combination of SEM and Hg-porosimetry. The permeabilities of several gases have been measured together with gas mixture separation behaviour.

I. INTRODUCTION Because inorganic membranes have good thermal stability and a resistance to corrosive environments, they are of considerable interest in many new technical applications [ 1-3]. More recently this field has been further stimulated by the development of zeolite membranes [4,5]. As zeolites are crystalline microporous materials with defined structural properties, such membranes have potential in highly selective size separation processes, particularly involving gas separation and catalytic reaction processes for example [6-8]. Several processes have been reported for the synthesis of such zeolite membranes [9,10]. These frequently involve the growth of zeolites as films or layers on a substrate (ceramic, metal). The synthesis of continuous, defect-flee zeolite membranes, has been attempted extensively but has proved to be a considerable task. Most work has been generally confined to zeolites with the MFI structure (ZSM-5 and silicalite-1) [11,12]. In our previous work we have discussed the advantages of forming zeolite membranes which are supported on meso and macroporous ceramic substrates [13]. Such membranes can also be obtained by incorporating the zeolite phase within the porous structure of the ceramic to give a continues zeolite layer which is remarkably stable. Examples of this concept are demonstrated here. In the first the zeolite is formed in situ, by contacting an alumina ceramic support with a silicate oligomer solution under hydrothermal conditions. The structure of the zeolite membrane is determined by the hydrothermal synthesis conditions and the pore characteristics an alumina ceramic support.

468 Secondly the membrane is formed by the filtration and retention of a colloidal zeolite precursor. The characteristics of the pore structure of these membranes is described here, together with some of the gas permeation properties.

2. EXERIMENTAL Silicalite-I membrane Synthesis 2.1 Hydrothermal Synthesis The synthesis solution for silicalite-1 was obtained by dissolving pyrogenic silica (SiO2, Aerosil 380, Degussa) in an aqueous solution of tetrapropylammonium hydroxide (Aldrich) to give a molar composition of 1 SiO2 : 1 TPAOH : 56 H20. This mixture was aged for 4 days at room temperature to give a clear homogeneous solution of oligomeric silica species. Syntheses were carded out by heating the synthesis mixture with the support in 50 ml teflon lined stainless steel autoclaves at different temperatures (in a range between 130 and 190 ~ and various times (from a few days to several weeks). After crystallisation of zeolite the membranes were rinsed with distilled water, dried and further characterised. Before gas permeation experiments, the organic template was removed by calcination up to 500 ~ under controlled conditions to avoid the formation of defects in the membrane. 2.2 Colloidal Filtration This novel route involves the retention of colloidal dispersions of zeolites (silicalite-1 described here) onto the surface of macroporous ceramic substrates. Silicalite-l colloids were synthesised as described by Schoemann [14]. These were characterised by SEM and filtered through ceramic alumina discs.

3. RESULTS AND DISCUSSION Macroporous ~-alumina supports The porous supports, in disc or tubular shaped form, were produced commercially (Velterop Company, Netherlands). The discs (25 mm in diameter and 2 mm in thickness) were available with different macropore sizes (0.08, 0.15, 2 and 9 ~tm). These macropores, which were formed between the sintered alumina grains are shown typically for a disc in Figure 1. The tubes with an outer diameter of 14 mm and a wall thickness of 3 mm were manufactured with pores of 2.5 lam and 9 ~trrL The macropore structure of these different types of supports was analysed by mercury porosimetry. Changes in the porosity which occurred after the hydrothermal treatment were also monitored. Figure 2 shows the highly uniform pore structure of a series of supports with different nominal pore sizes.

469

Figure 1. surface of the a-alumina support having a mean pore diameter of 0.08 ~tm.

b)

a) 0.20

.

.

.

.

.

.

.

.

.

c)

d)

.

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10 0

l o -~

-]0 ~

lo o

10-~

~o ~

~o o

~0-~

~o ~

lo o

10 -~

Pore diameter / ~tm

Figure 2. Shows the highly uniform pore structure of a series of supports with different nominal pore size: a) 0.08 ~tm, b) O.15 ~tm, c) 2 ~tm and d) 9 ~tm.

Silicalite-I Experiments were undertaken to optimise the conditions for the formation of defect free silicalite-1 membranes. In the first set of experimems the influence of the ceramic support on the growth of the zeolite film was studied by SEM and mercury porosimetry. Syntheses were performed with the different porous ceramic supports using fixed temperature/time conditions. The crystallinity of the zeolite layer was confirmed by X-ray diffraction. When the synthesis temperature was kept for 6 days at 190 ~ for all the different porous alumina supports, extensive growth of a silicalite-1 layer on the support surface occurred. This is illustrated by the micrograph in Figure 3 showing a cross-section through the membrane. This layer shows a dense region near the substrate and a rugged structure on the top which is formed by individual crystals growing out of the dense phase. In addition to the layer formation on the surface of the

470 ceramic, there is evidence of penetration and a pore filling inside the support. The thickness of the outer layer varied between 30 and 80 lam. Synthesis conditions were established which either favoured the growth of a well-crystallised zeolite layer on the surface of the ceramic support or the preferential formation of a zeolite phase within the macropores of the alumina sub-layer. To obtain defect-free and stable zeolite membranes, growth within the sub-layer is preferred. We will briefly illustrate the formation of these two distinct membrane structures here. In the case of the ceramic support with the smallest pores (diameter- 0.08 ~tm) the most homogeneous layer was obtained in contrast to the surface layer on the 9 lam tubular support. The surface of the layer on this tube had a thicker rugged region and thinner dense region, the boundary between the layer and the support being ill-defined. In order to increase the penetration frontier inside the pores of the support and to minimise extensive surface growth of zeolite, kinetic investigations at lower temperatures were carried out. Hg porosimetry provided a detailed insight into the mechanism of the growth of zeolite phase in the macropore structure of the alumina support. Investigations were made using supports with different pore sizes for different reaction conditions (time, temperature). Typical results showing Hg porosimetry before and after synthesis at two different temperatures (150 and 190 ~ are shown in Figures 3. These results clearly demonstrate different zeolite growth processes. At the lower temperature filling of the support macro-pores occurs resulting in a decrease in the total pore volume. (Some reduction in the macropore size of 0.15 lam also occurs). At 190 ~ however a growth of a zeolite layer results in the development of larger macropores (> 10 tam) and an overall increase in porosity.

Figure 3. SEM showing a cross-section of a silicalite-1 membrane on a porous support oralumina having a mean pore diameter of 2 lam.

471

.,r-

L E

0.3

a)

b}

c}

--.,.

O3

E

=0

0.2

r

s L._

.~ [1.1 ._. E =

o

0.0

10 2 101 10~ 10 -1 10-2

10 2 101 10 0 10-1 10.2

10 2 101 100 10-1 10-2

Pore diameter / pm

Figure 4. Intrusion of mercury as function of the synthesis temperatue on a support having O.15 ~tm pores: a) support untreated, b) atter 24 h at 150 ~ and c) after 24 h at 190 ~

Colloidal Filtration The formation and growth of colloidal zeolites has been described by Schoemann [14] and Bein [ 15]. Synthesis involves the controlled nucleation and crystallisation under hydrothermal conditions. Routes have been described for the synthesis of several different zeolites (silicalite1, zeolite-A and zeolite-J3). Our experiments have been directed to silicalite-1 synthesis. The SEM's in Figure 5 illustrate the size and morphology of these colloids. Thus the colloidal particles are approximately spherical with a diameter of~ 100 nm which is remarkably uniform. At higher resolution (Figure 5b) it appears that these colloids are formed by the clustering of smaller units (_< 10 nm). In the colloidal filtration process the size of the support pore size was selected to be slightly larger than that of the colloidal particles. This was to give retention but also some penetration into the surface of the support. An indication of the surface layer pore structure was obtained by performing Hg porosimetry measurements before and after filtration. This is illustrated in Figure 6. Thus for the support (nominal pore size 0.15 ~tm) there is no significant porosity for pores < 0.1 ~tm in size. Aider filtration with the silicalite-1 colloid described above a slight (~ 0.1 ml, g l) reduction in porosity (pore size > 0.1 ~tm) is observed. However the presence of much smaller pores is observed (0.1 to 4,10 .3 ~m). The volume contribution of these smaller pores is nevertheless very low (~ 0.005 ml, gt). This additional porosity can be ascribed to the pores between the packed zeolite colloids in the surface layer on and also within the sub-surface of the ceramic support.

4'/2

Figure 6. Difference in mercury intrusion for alumina supports (having 0.15 ~tm pores) before (a) and after (b) treatment with the colloidal zeolite solution.

Gas Transport behaviour Single Gas Permeation The membranes were analysed by single gas permeability measuremems in order to characterise their properties. The results reported here are restricted to experiments undertaken with silicalite-l membranes. To ensure that the developed membranes were defect flee, gas relative permeability experiments were conducted. In these experiments the membrane was initially strongly equilibrated by a strongly adsorbed gas (CO:) and subsequently a non-adsorbable gas such as He permeated through the membrane. It was found that as the pre-adsorbed amount of CO2 increased there was a sharp drop in He permeability, compared to the corresponding value on a clean zeolite membrane. At a certain partial pressure of CO2, He could no longer permeate

473

through the membrane, indicating that CO2 had blocked the small zeolitic cavities, responsible for gas permeation. Additional permeation experiments with a larger probe molecule, such as perfluoro-n-butylamine have shown almost no permeation of the vapour through the membrane, indicating defect free membranes. Typical permeability measurements were conducted for a variety of gases (He, N2, CO2, CH4, C2H6, C3Hs) at different temperatures. Activation energies have been determined assuming an Arhenius behaviour and are summarised in Table 1. In the same Table, the permeability ratio of each gas over N2 permeability is shown and compared to the inverse square root of the ratio of molecular weights of these gases, which corresponds to the permeability ratio under Knudsen flow conditions, at constant temperature. From these results it is clear that the developed membrane show activated permeation properties that cannot be predicted by single Knudsen flow. Gas " N2 He CO2 CH4 C2H6 C3H7 Activation Energy 5.9 6.2 12.7 6.9 6.8 11.5 (kJ/mol) (MW/MW(N2)) -1/2 1 2.65 0.80 1.32 0.97 0.80 lq/H(N2) 1 6.10 2.25 1.60 0.77 _ 0.6 Table 1. Activation energies and permeability ratia for permeation of different gases m a silicalit-1 membrane on a alumina support (pore size 0.15 ~tm).

Mixture Selectivity Experiments A gas mixture of n-hexane/2.2,DMP was used to test the membrane's ability to separate linear from branched paraffins. Selectivity results are shown in Table 2. As can be seen from the above results a selectivity between 16 and 28 is obtained by varying the temperature from 90 to 108 ~ It is important to observe that an increase in temperature results in a decrease in the mixture selectivity. This is because the branched paraffin (2,2,DMP) is activated at high temperatures resulting in higher permeation rates and thus in a decrease in selectivity of n-hexane over 2,2,DMP. Experiment

Ambient Pressure (atm)

T(K) ....

363 373 381 Table 2. Selectivity of n-hexane/2,2,DMP on a silicalite-1 membrane. .

.

.

.

.

Mixture Selectivity (n-he_xane/2,2,DMP) 28 20 16 .

4. CONCLUSIONS The synthesis and characterisation of silicalite-1 membranes on porous alumina ceramic supports have been described here. The growth of the silicalite-1 membrane could be optimised by controlling the hydrothermal synthesis conditions. It has been shown that by comrolling the synthesis conditions it is possible to optimise the growth and structure of silicalite-1 membranes. Thus at lower synthesis temperatures (150 ~ the growth of silicalite inside the macro-pores of the ceramic support is favoured. At higher temperatures (190 ~ thick, well crystallised zeolite layers develop from the surface of the support. A more stable membrane is

474 obtained if the zeolite phase is formed predominantly inside the pores of the support. Furthermore, the zeolite layer structure and the penetration depth depend on the type of macro-porous support used for the synthesis. A more homogeneous silicalite-1 film, together with a lower degree of penetration, was obtained for the alumina support having the smaller macropores (0.08 lam) compared to the more rugged film on the surface of the support having larger pores (9 lam). To obtain defect free membranes it is again preferable to have zeolite growth inside the support sub layer. To achieve this, a control of the formation of the gel phase which precedes the nucleation of the zeolite is necessary. The same principal of forming a subsurface layer of zeolite by the controlled filtration of zeolite colloids is also described. The characterisation of these relatively thin surface layers has been achieved using a combination of Hg porosimetry and scanning electron microscopy. It was confirmed fi'om initial gas permeability experiments that the silicalite-1 membranes were free of cracks and defects. From measurements made with a range of single gases, activation energies for transport have been estimated. Large separation factors for gas mixtures which are currently under investigation are expected to be achieved with these membranes.

5. REFERENCES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

R.R. Bhave, Inorganic Membranes, Synthesis and Applications, Van Nostrand Rheinhold, New York, 1991. A. Larbot, J.P. Farbre, C. Guizard and L. Cot, J. Membrane Sci. 39 (1988) 203. A. Larbot, J.P. Fabre, C. Guizard, L. Cot and G. Gilot, J.Amer.Ceram.Soc. 72 (1989) 257. J.C. Jansen, D. Kashiev, A. Erdem-Seatalar, Stud. Surf. Sci. Catalysis, 85 (1994) 215. D. Uzio, J. Peureux, A. Giroir-Fendler, J.A. Dalmon, J.D.F. Ramsay, Stud. Surf. Sci. Catalysis 87 (1994) 411. W.J.W. Bakker, F. Kapteijn, J. Pope, J.A. Moulijn, J. Membrane Sci. 117 (1996) 57. W.J.W. Bakker, L.J.P. Van den Broeke, F. Kapteijn, J.A. Moulijn, AIChE J. 43(1997) 2203. J.G. Tsikoyiannis, W.O. Haag, Zeolites, 12 (1992) 126. Y. Yan, M.E. Davis, G.R. Gavalas, Ind. Eng. Chem. Res. 34 (1995) 1652. S. Mintova, J. Hedlund, B. Schoeman, V. Valtchev, J. Sterte, Chem. Commun. (1997) 15. H. van Bekkum, E.R. Geus, H.W. Kouwenhoven, Stud. Surf. Sci. Catalysis, 85 (1994) 509. M.-D. Jia, B. Chen, R.D. Noble, J.L. Falconer, J. Membrane Sci. 90 (1994) 1. G.E. Romanos, E.S. Kikkinides, N.K. Kanellopoulos, J.D.F. Ramsay, P. Langlois, S. Kallus, in "Proceedings of Fundamentals of Adsorption 6", Elsevier, Paris, 1998, 1077. B. Schoeman, O. Regev, Zeolites, 17 (1996) 447. S. Mintova, N.H. Olson, V. Valtchev, T. Bein, Science, 283 (1998) 958.

6. ACKNOWLEDGEMENTS

We are indepted to Dr. Velterop and Mr. Weierink for kindly providing the ceramic supports. This work was funded by the European Community under the Industrial and Materials Technologies Programme (Brite-Euram III; Contract No BRPR - CT96 313).

Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) o 2000 Elsevier Science B.V. All rights reserved.

475

A MODIFIED HORVATH-KAWAZOE METHOD F O R M I C R O P O R E SIZE ANALYSIS

Christian M. Lastoskie Department of Chemical Engineering Michigan State University East Lansing, MI 48824-1226 USA ABSTRACT The Horvath-Kawazoe (HK) method is a semi-empirical, analytic model of adsorption in micropores that is commonly used for determining the pore size distributions (PSDs) of microporous materials. The HK method is a substantial improvement over classical adsorption models (e.g. Kelvin-based methods) in that the adsorbate potential interactions with the adsorbent surfaces are explicitly accounted for. One of the principal shortcomings of the original HK method, however, is that the mean potential energy change due to adsorption is calculated from an unweighted average over position within the micropore. It is known from molecular simulation studies of adsorption at subcritical temperatures that the local density of the adsorbate in the pore varies strongly with position due to fluid layering near the pore walls. The omission of this structure dependence from the original HK model leads to an overestimation of micropore filling pressures relative to the exact filling pressures calculated from molecular simulations. In this paper, a modified HK method is presented which accounts for spatial variations in the density profile of a fluid (argon) adsorbed within a carbon slit pore. We compare the pore width/filling pressure correlations predicted by the original HK method, the modified HK method, and methods based upon statistical thermodynamics (density functional theory and Monte Carlo molecular simulation). The inclusion of the density profile weighting in the HK adsorption energy calculation improves the agreement between the HK model and the predictions of the statistical thermodynamics methods. Although the modified Horvath-Kawazoe adsorption model lacks the quantitative accuracy of the statistical thermodynamics approaches, it is numerically convenient for ease of application, and it has a sounder molecular basis than analytic adsorption models derived from the Kelvin equation.

1. I N T R O D U C T I O N Gas sorption porosimetry is a standard method for the characterization of the pore size distribution (PSD) of porous solids. To interpret the experimental isotherm and obtain the adsorbent PSD, one must adopt a model for the pore structure, and a theory that estimates the adsorption that will occur in pores of a particular size. If the porous solid is represented as an array of independent, noninterconnected pores of uniform geometry and identical surface chemistry, then the excess adsorption, /-(P), at bulk gas pressure P is given by the adsorption integral equation

476

Hmax V(P)=

~V(P,H)f(H)dH

(1)

Hmin where/-(P,H) is the excess adsorption for an adsorbent in which all the pores are of width H; and f(H) is the pore size distribution of the material. The integration endpoints Hmin and Hmax correspond to the minimum and maximum pore widths present in the adsorbent. The adsorption integral of equation (1) is written in terms of a distribution of slit pore widths, a geometry frequently used to approximate the pore structure of activated carbons. For porous glasses, oxides, silicas, and other mineral adsorbents, the adsorption integral may be recast in terms of a distribution of pore radii f(R) for a model porous solid composed of noninterconnected cylindrical pores. Within the constraints imposed by the assumed geometric model for the pore shape, the accuracy of the PSD obtained by the solution of equation (1) depends on the realism of the adsorption model/-(P,H) that is adopted to describe the local isotherm. A variety of pore filling models have been proposed for representing the local isotherm. The classical approach has been to assume that the Kelvin equation, or a modified form of it, correctly predicts capillary condensation as a function of pore width [1]. It is known from experiments [2], and from comparisons with exact molecular simulation results for a variety of pore geometries [3-7], that the Kelvin and modified Kelvin (MK) equations predict pore filling pressures that are too large (see Figure 1). Consequently, Kelvin-based adsorption theories, when inserted into equation (1), give pore sizes that are too small. The error is significant for pore sizes below about 7.5 nm [2,5], and it becomes very large for micropores (i.e. pores smaller than 2.0 rim). In microporous adsorbents, dispersion interactions between the adsorbate and the atoms of the porous solid are greatly enhanced. Because the Kelvin-based adsorption models do not account for these enhanced gas-solid interactions, PSD analysis methods based upon the Kelvin equation are unreliable for the characterization of microporous solids. An alternative to the classical thermodynamic model of pore filling is to use methods from statistical thermodynamics, such as density functional theory (DFT) [6,8] or Gibbs ensemble Monte Carlo molecular simulation (GEMC) [7,9] to calculate local isotherms for simple pore geometries (e.g. for slits or cylinders). These methods explicitly incorporate the gassolid potential interaction into the adsorption calculation, and hence they yield more realistic local isotherms for modeling adsorption in micropores. Several independent studies have demonstrated that DFT is superior to the Kelvin equation for micropore PSD analysis [6,10-11]. Because detailed morphologies of porous adsorbents like activated carbons are usually not known, molecular simulation results for ideal model adsorbents are frequently used as the standard for evaluating other pore filling models. One such comparison is shown in Figure 1 for nitrogen adsorption on model carbon slit pores at 77 K. The modified Kelvin method (MK) severely overestimates the micropore

4'//

1 E+00 1E-01

Figure 1: Relation between filling pressure and pore width predicted by the modified Kelvin equation (MK), the Horvath-Kawazoe method (HK), density functional theory (DFT), and molecular simulation (points) for nitrogen adsorption in carbon slits at 77 K [11].

n n

o

M

-

1 E-02 -

o 1E-03 -

DFT

P 1 E-04 u~ O L

1 E-05 -

GEMC

o. 1 E - 0 6 O~

=-9 1E-07-

u. 1 E - 0 8 1E-09 1E-10

"ill

)

i l J , l l l I

5

I

10

l l i l l l l I

15

, i l l l l l i l I I

20

111

25

Pore Width

Ill I

30

l l l i i l l I

35

lllillll

40

III

45

50

(/~)

filling pressures, whereas the DFT method yields a pore filling correlation in close agreement with the "exact" results computed from GEMC molecular simulation [7]. The principal drawback of the DFT method is that it is computationally intensive relative to the classical adsorption models, although it is still much less compute-intensive than full Monte Carlo molecular simulation. A semianalytic adsorption model that retains computational efficiency while accounting for gas-solid potential interactions in micropores was originally proposed by Horvath and Kawazoe [12]. In the Horvath-Kawazoe or HK method, a pore filling correlation is obtained by calculating the mean heat of adsorption qt required to transfer an adsorbate molecule from the gas phase to the condensed phase in a slit pore of width H: (2)

ln(Pc /Po) = ~(H)/RT

In equation (2), P, is the bulk gas saturation pressure; Pc is the pore filling pressure; R is the gas constant; and T is the temperature. In the original HK method, the mean heat of adsorption is computed from an unweighted average of the gas-solid interaction potential taken over the accessible volume of the pore"

-

r --

[U-osr .' O'sf

-

sf H - 2o r

(3)

478 In equation (3), ~bis the gas-solid potential for an adsorbate molecule located at position z in a slit pore of physical width H; i.e. a pore in which the nuclei of the surface layer solid atoms are located at z-0 and z=H. The effective gas-solid molecular diameter, Crsf, is calculated from the arithmetic mean of the diameter of the adsorbate molecule and the adsorbent surface atom. The pore filling correlation predicted by the original HK equation for nitrogen adsorption in carbon slit pores at 77 K is shown in Figure 1. It is seen that the HK method gives improved micropore filling predictions compared to Kelvin-based methods. However, the HK model still substantially overestimates the micropore filling pressures given by molecular simulation. The original HK methodology of equations (2) and (3) was subsequently modified for cylindrical [13] and spherical [14] pore geometries, with essentially the same result: the HK model is superior to the Kelvin equation for micropore characterization, but inferior to DFT or simulation methods [ao, aa]. The failure of the HK method, as originally formulated, to accurately predict micropore filling pressures can be understood by considering the gas-solid potential ~z) in a carbon slit pore, and the local adsorbed fluid density profile ,o(z) that arises in the pore on account of this potential. In Figure 2, the gas-solid potential ~b~' = ~bj/j~'ff for three different slit pore widths H*

= H/crffis shown in Figure 2 for nitrogen adsorption in a carbon slit pore at 77 K; ~ffand o-flare the Lennard-Jones well depth and molecular diameter for nitrogen pairs. The gas-solid potential is shown as a function of the center-of-mass position z* = z/off of the nitrogen molecule, where z=0 is the centerline of the slit pore. For each case, the gas-solid potential is calculated using the 10-4-3 potential [151 to represent the interaction between the nitrogen molecule and the graphite slabs that bound the slit pore. It can be seen from Figure 2 that a large potential well is present in the pore at a distance of one molecular diameter from either pore wall. It is at this location that the contact layer (monolayer) of adsorbate will form within the slit. The region of the slit pore near the centerline may also have a negative (i.e. attractive) gas-solid potential, depending upon the width of the pore. For supermicropores (e.g. H*=4), the gas-solid potential is attractive throughout the entire accessible pore volume; for ultramicropores (e.g. H*-2), the two potential minima coalesce into a single, deeper potential well. Because of the presence of strong potential wells for adsorption at low temperatures, the adsorbed fluid adopts a highly structured local density profile, as shown in Figure 3 for argon adsorption in a carbon slit pore of width H*=6. The local density profile p*=pcrff is computed from DFT and exhibits strong monolayer peaks near z*=l and z*=5. Secondary peaks in p(z) form at positions z*=2, 3 and 4 due to structuring of the condensate adjacent to the monolayer. Similar condensed-phase density profiles are observed in slit pores of other widths. The structure of the local density profile given by DFT has been validated against molecular simulation calculations and has been found to be quantitatively accurate over a wide range of pore sizes and bulk gas pressures. In the original HK method [12], the mean heat of adsorption ~b is calculated from an unweighted average of the gas-solid interaction potential measured over the accessible volume of the pore. This prescription implicitly assumes that the adsorbate density is

479 Gas-solid interaction potential ,,,,,

Figure 2: Gas-solid potentials for nitrogen adsorption at 77 K in carbon slit pores of different width.

-5-

~*-10 --

--8

-15 -20 H*=2

-25 -4

-3

-2

-1

0

Z*

1

2

3

4

D e n s i t y Profile in a Slit Pore o f W i d t h H*=6

Adsorbate

10 9 DFT _ Original HK 8

. l

Figure 3." Adsorbed jquid density profile for argon adsorption in a carbon slit pore of width H*=6 at 77 K and 229 torr.

6

9

9"

O

9

9

0 4

.

~ 9

"

2

0

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00

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uniform everywhere in the accessible region of the slit pore, as shown schematically by the solid line in Figure 3. However, it can be clearly seen from the DFT results of Figure 3 that the adsorbed fluid density profile is not uniform, but is in fact highly structured and contains peaks and troughs resulting from the monolayer adsorption well and fluid layering. By neglecting the high degree of ordering in the adsorbed fluid, and in particular by undercounting the adsorbate density in the mort 9 region, the HK method, as originally posed, underestimates the mean heat of adsorption computed by equation (3), and thus overestimates the micropore filling

480 pressures calculated from equation (2). This leads to PSD analysis results obtained for the HK model in equation (1) that are less accurate than those given by DFT or molecular simulation.

2. THE MODIFIED HORVATH-KAWAZOE METHOD The neglect of adsorbed fluid structuring principally accounts for the shortcomings of the original HK method, and also suggests a corrective measure. If the density profile, or a reasonable representation of it, were to be included in the calculation of the mean heat of adsorption ~b, then the HK pore filling correlation would more closely agree with the molecular simulation/DFT results. Thus, in our modified HK method we seek to evaluate the mean heat of adsorption from the density-weighted integral

__

q~-

"CYsf

I2 r-ere tg(z)dz sf

(4)

and use this result for ~b in equation (2). One difficulty in doing this is that a full statistical thermodynamics treatment is needed to obtain the adsorbate density profile in the slit pore. To retain the computational efficiency of the HK approach, we seek a mathematical function that realistically represents ,o(z) in accordance with the DFI" results, so that we can evaluate equation (4) for other probe gas/adsorbent systems without having to repeat the DFT calculations. The sharply peaked, highly structured density profile that is observed in Figure 3 is characteristic of adsorption at low temperature, and suggests that a sum of Gaussian distributions might satisfactorily represent the adsorbate density profile. The number of Gaussian distributions required for a pore of a given size is equal to the number of peaks that appear in the condensed fluid density profile of the pore. For pore widths that have density profiles with more than two peaks (e.g. the H*=6 pore in Figure 3), we have the option of fitting the height and variance of each Gaussian distribution separately. Also, we could in principle fit the Gaussian parameters for the density profile at each pore width independently of the other pore widths. However, this would lead to a large and unwieldy parameter set, and would make a corresponding states-type generalization of the modified HK method for other adsorbate/adsorbent systems very difficult. Therefore, the local density profile is modeled as an n-modal Gaussian distribution, where each mode i of the distribution has the same height a and variance r, but a different mean position ,u, in the slit pore:

,, I-(z- /12l

p{z) = a'y' exp

i=l

2r

2

(5)

481 Although this choice of fitting function somewhat diminishes the overall accuracy of the Gaussian fits to the DFT density profiles, it simplifies the model to a manageable number of parameters. An additional simplification is achieved by spacing the mean positions of the Gaussian distributions exactly one adsorbate molecular diameter crffapart; i.e. / ~ = Crsf + (i -

1)off

(6)

for each additional Gaussian distribution inward from the monolayer peak to the pore centerline. This placement strategy is consistent with the peak positions observed for DFT density profiles in pores of different size. To implement the modified HK method, we therefore need only find the pair of (a, z-) values in equation (5) that give the best fit to the adsorbate density profiles over the range of micropore widths of interest for PSD analysis.

3. RESULTS AND DISCUSSION Sorbed argon density profiles from DFT were fit for a set of 15 different graphitic carbon slit pore widths spanning the pore size range H* from 2 to 6 (0.68 to 2.04 nm). All of the density profiles were calculated from DFT for supercooled liquid argon at its saturation pressure of 229 torr at 77 K, using a spacing interval of 0.01crff for the solution of ,o(z) at each pore width. Details of the DFT calculations are reported elsewhere. The optimal value of the uniform Gaussian peak height a was constrained so as to give the best agreement with the monolayer peak height (e.g. the peak centered at z*=l in Figure 3) in the set of density profiles. A sum-ofsquares error criterion was then used to determine the best value of the variance r to represent the 15 density profiles according to equations (5) and (6). The number of Gaussian distributions n used to fit each density profile was determined from the formula

(* + 0 5 ) - 1

n=intH

(7)

where int(x) is the rounded integer value of x. Equation (7) assigns an additional Gaussian distribution to the fitting function whenever the dimensionless pore width is greater than or equal to half of a molecular diameter, so that n=l for H* 30 nm that predominate the pore size distribution. The higher the portion of smaller mesopores and the less distinct the maximum is, the higher is C ~~ In fig. 4, the modified C-parameters are plotted versus the average pore diameter D~ve indicating the lower values of C ~~ for D~ve >_ 13 nm. 5. D I S C U S S I O N

Owing to the variation in Vacac and NH3 contents of the starting solution and the subsequent different shrinkage rates upon CO2-drying, aerogels with a broad range of densities and average pore sizes have been obtained. The values for lp derived from SAXS and D~veobtained from N2-adsorption agree remarkably well, while the specific surface areas differ by about 100 m 2 g-1. BET theory assigns an area and a volume to each gas molecule adsorbed that corresponds to the space they occupy in a close packing. In small micropores, however, such a close-packing cannot be realised owing to

571

55

,

~

50L_ O

~

i D,

,

\

--~

i

i"

--w

9 .....

"\

45 40 35

'

1

1

i

i

i

10

9

I

i

I

"

15

Gve (rim)

Figure 4. Modified C-Parameter C ~~ of aerogel samples V33 in dependence of the average pore size. To emphasize the tendency of the data points, a function 40(1 + a exp(bx)) has been fitted.

the geometrical proportions of pores and molecules. Thus, both area and volume arising from micropores might be underestimated in comparison with values from SAXS, resulting in smaller specific surface areas while their influence on the average pore size might, by chance, be cancelled owing to a specific pore size distribution because Dave is proportional to the ratio of pore volume and surface area. The t-plot in the range 0.30 nm _< t _< 0.50 nm turns out to be a good method to determine the part of smallest micropores responsible for an increased adsorbate-substrate interaction. Carrott and Sing [14] distinguish accordingly between primary and secondary micropore filling. The transition between the two processes is found around P/Po ~ 0 . 0 2 w h i c h corresponds to a statistical film thickness of t - 0.4 - 0.5 nm. The total micropore volume, however, must be considered as being underestimated by the t-plot method. The higher the density is, the smaller the mesopores. A clear separation between micro- and mesopore distribution, which is the basic requirement for the determination of the total micropore volume with a t-plot, is then not even approximately given. C c~ from BET analysis after subtraction of $~ot might be a helpful test for the reliability of the total pore volumes determined. Their comparison is only reasonable if C c~ is close to the "true" C-parameter of the non-microporous material. Though this value is not known for the material under investigation here, the accumulation of C c~ around 41 might indicate a sufficiently good estimation of the total micropore volumes for the corresponding samples. 6. CONCLUSION Vanadia-doped silica aerogels with densities between 200 kg m -3 and 400 kg m -3 w e r e investigated via helium pycnometry, nitrogen adsorption and small angle X-ray scat~ tering. While evaluating the scattered intensity with the two-phase-media model, the

572 size of the nitrogen molecule was taken into account to get results that are comparable to the ones obtained from the gas measurements. Good agreement was found for skeletal densities and average pore sizes, however, specific surface areas were found to differ by about 100 m 2 g-1 or about 10%. The C-parameter from BET analysis was found to correlate with the volume of primary micropores.

ACKNOWLEDGEMENTS We would like to thank Dr. P. L6bmann, Fraunhofer-Institut f/Jr Silicatforschung, W~rzburg, for performing the He-pycnometry measurements.

REFERENCES 1. J. Fricke and T. Tillotson, Thin Solid Films, 297 (1997) 212-223. 2. M. del Arco, M. J. Holgado, C. Martin and V. Rives, Langmuir, 6 (1990) 801-806. 3. D.C. Dutoit, M. Schneider, P. Fabrizioli and A. Baiker, Chemistry of Materials, 8 (1996) 734--743. 4. G. C. Bond and K. Br/ickman, Faraday Discussions of the Chemical Society, 72 (1981) 235--246. 5. K. Tran, M. A. Hanning-Lee, A. Biswas and A. E. Stiegman, Journal of the American Chemical Society, 117 (1995) 2618-2626. 6. A. E. Stiegman, H. Eckert, G. Plett, S. S. Kim, M. Anderson and A. Yavrouian, Chemistry of Materials, 5(11) (1993) 1591-1595. 7. G.W. Scherer, Journal of Non-Crystalline Solids, 225 (1998) 192-199. 8. A. Emmerling and J. Fricke, Journal of Non-Crystalline Solids, 145 (1992) 113-120. 9. S.J. Gregg and K. S. W. Sing, Adsorption, Surface Area and Porosity, Academic Press, London, 1982, 2 edn. 10. R. K. Iler, The chemistry of silica, John Wiley & Sons, New York, 1979. 11. J. H. de Boer, B. C. Lippens, B. G. Linsen, J. C. P. Broekhoff and A. van den Heuvel, Journal of Colloid and Interface Science, 21 (1966) 405-414. 12. E. P. Barrett, L. G. Joyner and P. H. Halenda, Journal of the American Chemical Society, 73 (1951) 373-380. 13. U. Klett, Herstellung und Charakterisierung von Vanadiumoxid-dotierten SilicaAerogelen, Ph.D. thesis, Universit/it WLirzburg (March 1999). 14. P. J. M. Carrott and K. S. W. Sing, in K. K. Unger, J. Rouquerol, K. S. W. Sing and H. Kral (eds.), Characterization of porous solids, 1988 pp. 77-87.

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) o 2000ElsevierScienceB.V. All rightsreserved.

SHEAR STRENGTH

573

OF MINERAL FILTER CAKES

O. OZCAN, Istanbul Technical University, Chemical Engineering Department, Maslak 80626, Istanbul-TURKEY M. RUHLAND, W. STAHL, Ins. Mechanische Verfahrenstechnik und Mechanik der Universit~.t Karlsruhe, Karlsruhe-GERMANY

ABSTRACT

This study covers the shear strength measurements of very fine pressure filter cakes of TiO2, calcite fractions, labosil, kaolin and synthetically prepared glass spheres. The shear strength behavior of all these cakes at the full range of saturation, i.e. from S=0.0 to S=I.0, showed the same tendency as in the case of Schubert's diagram for the tensile strength of the mineral filter cakes. The dependence of the shear strength of the filter cakes on the used pressure, particle size and shape has been analyzed. The effect of a surfactant (Lutensol TO3) treatment on the shear strength of the cakes was also investigated. It has been found from the laboratory scale experiments that the shear strength of all analyzed materials is strongly dependent on the applied filtration pressure: the higher the pressure the greater the shear strength. The shear strength also increases with the decreasing particle size. The shape of the particles has also a very large effect on the shear strength of the cake. The surfactant treatment, on the other hand decreased the shear strength of the cakes very sharply. Although the surfactant helps the filtration operation giving less residual moisture contents in the cakes, it was not possible to obtain saturation degrees higher than 50 and 60 % for kaolin and calcite when using the surfactant.

1. INTRODUCTION The consistency of the filter cakes for the final treatments such as transportation and storage is very important. In general, the filter cakes of slimes are finally stored without any thermal application. In order to obtain the slime storage with enough stability, the filter cakes have to have some certain solidity characters such as the tensile strength, compressive strength, shear strength etc (1, 2). Schubert's studies on the tensile strength of very fine calcite filter cakes (3, 4) showed that the volume and the porosity of the cake decreases by the application of pressure. As a result the consistency of the cake is also changed.

574 The aim of this study is to show the dependence of the shear strength of different very fine mineral filter cakes on the pressure, particle size and shape and the surfactant treatment.

2. EXPERIMENTAL

2.1. Materials and methods

TiO2, kaolin, t w o calcite fractions (juraperle BS and schwarzsiegel)), quartz fraction (labosil) and synthetically prepared glass spheres were used in the experiments. The average particle sizes of these minerals are given in Table 1.

Table 1. Average particle sizes of the. minerals used in the experiments Mineral

Particle size, x

Manufacturer

Otto)

,,

Quartz fraction (Labosil)

0.33

Not known

TiO2

0.65

Firma Tioxide, (Grimby, GB)

Calcite fraction (Juraperle BS)

3.60

E. Merkle GmbH und Omya GmbH, (Germany)

Glass sphere

3.80

Not known

Kaolin Calcite fraction (Schwarzsiegel)

.

6.00 .

.

10.0

.

Stid-Chemie AG, MiJnchen ...

E. Merkle GmbH und Omya GmbH, (Germany)

The filter cakes were obtained in a laboratory pressure filter (5, 6). The diameter of the filter cake obtained was about 46 mm and the height of the cake was approximately 10 mm in each experiment. The filtration of the prepared suspensions consisted of two stages: First, the filter cake was formed by applying 2 bar air pressure for 2 to 5 minutes on top of the suspension in the filter cell. In the second stage, the formed cake was pressed using a latexbellows produced in the laboratory under 4, 15 or 32 bar pressurized air for half an hour. The cakes obtained on these conditions were fully saturated with water, i.e.

575

S =1. These cakes were then dried for a definite time in the open atmosphere in the laboratory to obtain partially saturated cakes. The required time to reach a definite saturation degree was determined experimentally. The shear strength measurements of the produced cakes were made then using a Fischer test apparatus (6,7) shawn in Fig. 1. All experiments (production and the shear strength measurements of the cakes) have been done at room temperature. The surfactant used in the experiments was a polyethylen glycol ether of B ASF company with the trade name Lutensol TO3. General structure of the reagent is RO(CH2 CH20)x H where R is iso-C~3 H27 and x is 3,5,7,8,12.. The reagent has a nonionic character and does not give much froth in water. It was used as 500 g/t of solid material in the suspension. Shear strength, T (N/m 2) was calculated from the following equation: X,h~,, = F/(Dr * he)

(I)

where, F is the measured force in the Fischer test apparatus and Dc and h~ are the cake diameter and height, respectively. The saturation degree, S is defined as the ratio of the liquid volume (V~) to the pore volume (Vp) in the cake and it is calculated as follows

(6)

{7)

(11)

13)

L-18)

~

t"l 9) (10}

(1) fixed support (2) fixed shear punch (3) filter cake container (4) filter cake

(5) movable shear punch (6) movable support (7) apparatus shell (8) hydraulic cylinder

(9) hydraulic cylinder (10) manometer (11 ) crank driver

Figure 1. Fischer test apparatus used in the shear strength measurements.

576

(2)

S = Vi/Vp = V!/(V e) = (l-e)/e *Xm *(PJP0

Where, V is the total volume (solid volume + pore volume), x, (or RM in some literature) is the residual moisture, e is the porosity of the cake and p,, p~ are the densities of the solid and the liquid, respectively. The porosity of the cake is defined as the ratio of the space volume to the total volume (solid volume + space volume) of the cake and was calculated from the following equation (6) using the mass of the dried cake m, and the density of the solid material p,:

(3)

= ] - ( m, I (p, * ~:14 * Dc 2 * h~))

where, Dc and h~ are the diameter and the height of the cake, respectively.

3. RESULTS AND DISCUSSION

All minerals subjected to the shear strength measurement have been compressed for half an hour at varying pressures to obtain a stable cake height. This compression time (half an hour) has been chosen according to the typical compression kinetics of TiO2 as an example given in Fig.2. As it is seen in Fig.2, the cakes have reached to a constant height in 3-5 minutes by compression at 4-20 bar and therefore to make sure 30 minutes has been taken as the compression time in each experiment. 15

14 o a x

13 E E

w

~

12

p=/~bar p= llbar p =16 b~r p = 20 b ~

11

w II

10

1

3

5

7

9

Ti~m, w .

Figure 2. Compression kinetics of TiO2 pressure filter cakes at different pressures.

577 3.1. The effect of pressure and particle size on the shear strength

The results of the experiments carried out at 4, 8 and 15 bar for Juraperle BS are given in the Table 2. Graphical representation of these data is also given in fig.3. As it is clear from the table 2 Fig.3 that, shear strength of juraperle BS increases with the increase in saturation at a given pressure. The measured shear strength values of calcite fraction juraperle BS at the saturation about S-0 % and pressures 4, 8 and 15 bars are 17212, 41229 and 51222 N/m 2, respectively. For S=99-100 % saturation degree these values are 70324, 109020 and 207060, respectively. When plotting the shear strength values versus the applied pressure at a definite saturation range, for example S=0-3% and S=99-100 % a linear relation is obtained between the shear strength and the pressure as seen in Fig. 4. The shear strength increases linearly with the applied compression pressure in the bridging and capillary regions.

Table 2. Shear strength values of Juraperle BS measure d at differen t pressures 4 bar 8 bar 15 bar Saturation, Shear Saturation, Shear Saturation, 'Shear Strength, Strength, Strength, % % % N/m 2 N/m 2 N/m 2 17212 51222 4i229 1 14319 26201 42136 62 175233 52 188239 189655 45 73 145279 69 129533 57 162842 79 186903 77 108324 81 220037 92 198127 231986 94 232446 90 100 70324 207060 99 109020 100 ....

, .

....

.

.

.

.

.

..

O&

2OOOOO 9

z

&

0

0

l~xx)o 0 1.. i._

1OO0O0

0

5O00O ~ ' r - -

0 o 4 bar

& 8 bar

10

20

30

915 bar } J

40

50

60

70

80

90

100

Saturation, %

Figure 3. Shear strength changes ofjuraperle BS versus saturation at 4, 8 and 15 bar.

578

For the saturation range, S = 60-70 % (which is the transition region) on the other hand, there is a minimum for the three pressure applications. This tendency is seen better in the Fig.3. Although the tendency of the curve in Fig.3 seems to be the same as the Schubert's diagram for the tensile strength-saturation curve of calcite mineral filter cakes (3,4), there is a decrease in the shear strength in the saturation region about 60 % (It can be defined as a breaking in the curve). The shear strength is increasing linearly with the saturation in the bridging region ( 0 % < S < 30 %) up to S= 40 % and beginning to decrease and reaching a minimum value around the saturation S= 60 %. Then it increases again and gives the maximum value near 90 % saturation and decreases again. The reason of the breaking of the shear strength-saturation curve in the region S = 60% is not clear yet with the present data. The studies are continuing on the subject.

250000

E 200000

Z

i .,

15oooo

*" w

100000

ot c

tm

r

@

J=

50000 e'--" . . . . . . . . . . . . r

J _ 9S=O-1%

2

9S=lO0 % j

7

T

12

Compression pressure, bar

Figure 4. The changes of the shear strength of juraperle BS cakes with the compression pressure for the saturation about S = 0-1% and 99-100 %.

The experiments carried out on TiO2 have shown the similar results as given in the Table 3 and Figs.5 and 6.

579

As it is clear once more in Fig.5 that, the changes of the shear strength of TiO: with the saturation at 8, 15 and 32 bar showed the same tendency with the calcite fraction (juraperle BS) and also Schubert's diagram for the tensile strength. The maximum value of the shear strength is about at 80-90 % saturation region for the three pressures; and in the saturation region S = 50-60 % there is a minimum. The cake weakens in the saturation region 50-60 % and then the shear strength increases sharply with the increase of saturation.

Table 3. Shear strength of TiO2 filter cakes at different compression pressures 8 bar 15 bar 32 bar Saturation, Shear ' Saturation, Shear Saturaiion, Shear Strength, Strength, Strength, % % % N/m 2 N/m 2 N/m 2

..

3 11 33 50 65 70 83 90 99

.,

..

,.

30000 95000 260000 170000 215000 370000 425000 440000 210000

3 " 30 60 75 85 87 90 95

103500 159015 150113 405700 532507 255316 ..... 135214 132107

' 9 16 34 53 65 77 - 85 90 96

.,

100000 210000 270000 250000 400000 690000 650000 530000 260000

8000CX)

7ooooo ~, c,txx~ r-"

& 9 9

5OOOOO A

~

:301:1000 9

tt~

9 o

100000

i~ 9

0 ~015bar

08bar

9

10 9

0

!

r

T

v

20

30

40

50

9 "

0

0 O

0

9

c

9 9

w

w

60

70

Saturation.

0

w

80

!

90

1O0

%

Figure 5. Shear strength changes of TiO2 with the saturation at different pressures.

580 Similar to the calcite results, the shear strength of TiO2 increases linearly with the increase of the pressure for the saturation S=0-1% and S= 99-100 % as shown in Fig.6. For the maximum value of the shear strength at about S = 85-90 % saturation, this relation is also valid.

70OOO0 E 600000 Z

500000 4oooo0 300000 200o0o

r

IO(XXX)

!

9s = o - l o %

1-

1

t

t

I

9

14

19

24

29

.......

Pressure, bar

n oo-90~ .... ' }

Figure 6. Shear strength changes of the TiO2 cakes with the pressure at different saturation regions.

Similar studies have been done for schwarzsiegel, glass sphere, kaolin and labosil. The results are given in the following.

Table 4. Shear strength values of schwarzsiegel and glass sphere at 4 and 15 bars Scfiwarz Glass sphere siegel 15 bar 4 bar 4 bar 15 bar Shear st., Saturat., Shear st., Saturat., Saturat., Shear st., Saturat., Shear st., % N/m 2 % % % N/m 2 N/m 2 N/m 2 38784 12178 2 18756 2 19317 2 39577 55685 26784 23 32157 52 4 42974 47 48 79620 64 56288 35 35152 31917 57 60 64998 63 64411 77 38360 75367 72 72 47160 82 78550 83 50414 71375 88 31547 94 93089 76368 88 96 44265 93 51214 98 76831 98 100 7865 _

,..

, .

. . .

,,

581

8O000 ~E

7OO0O

~ saaoo

0

JE

,*' 4(X)O0 P

I/1

0

9

O 9

o

10000 0 915bar

i

.

,

T

20

40

60

80

100

Saturation, %

o4bar {

Figure 7. Shear strength changes of schwarzsiegel with saturation at 4 and 15 bar.

1OOOOO

?7 aoooo

9

x:" 7OOOO

9 o

o

oo

~ 6ctx~ ,~ 5oooo ~_ 40(X)0 U)

c"

tn

3oooo o 20000 'e 10OOO 0 0

[ O4bar

|

l

!

,

20

40

60

80

100

Saturation, %

e15bar I

Figure 8. Shear strength changes of glass sphere with saturation at 4 and 15 bar.

Table 5. Shear strength values of kaolin_and labosil at Kaolin 4 bar 15 bar 4 bar Saturat., Shear st., Saturat., Shear st., Saturat., % % % N/m 2 N/m 2 0 85000 3 184717 0 2 109305 10 190269 30 39 98330 54 44 239103 62 47 127783 6O 231586 63 58 43604 63 240760 92 100 63856 87 222032 ..

..

,..

..

4 and 15 bar Labosil 15 bar Shear st., Saturat., % N/m 2 192260 159614 196506 73280 15115 104918

17 30 75 79 87 89 93

Shear st., N/m 2 260983 295183 405849 184843 288375 580873 330326 116669

582

700000 6(xxxx) E z 5(XXXX)

C~4

p 4ooooo P t_ rO

300000

o

o

200000

o

tn

10OOOO J 0 Io4bar

9 n

v

v

10

20

30

ol5barl

v

1

v

40 50 60 Saturation, %

v

w

i

70

80

90

100

Figure 9. Shear strength changes of labosil versus saturation at 4 and 15 bars.

3OOOOO

~E

25OOOO

Z

,_-20(~

,.=,..,, Ill

0 0

0o

0

150000 100000

c-

u~

50000 0

0 {e4 bar 015 bar I

10

i

l

l

l

v

i

v

i

20

30

40

50

60

70

80

90

1O0

Saturation, %

Figure 10. Shear strength changes of kaolin versus saturation at 4 and 15 bars.

Among all the figures (Figs.3-10) which show the changes of the shear strength of the different minerals with the saturation at different pressures there is only one exception: The appearance of the curve of kaolin at 15 bar in Fig. 10. The change of the shear strength of kaolin with the saturation is almost constant for 15 bar pressure application. The value of the shear strength is about 200000-230000 N / m 2 in all the saturation region from S=40 % to S= 100 % at 15 bar. This behavior of the kaolin cake is due to its sheet structure in the crystal lattice and the saturation does not effect so much the shear strength compared to the other minerals. From the Figs.3-10 it is clearly seen that schwarzsiegel (another calcite fraction), glass sphere, labosil and kaolin at 4 bar show also the same behavior as juraperle BS and TiO2 in their shear strength changes with the saturation and pressure.

583 In order to see the effect of the pressure and the particle size on the shear strength for all these minerals for a given saturation degree, the data given in the Tables 2-5 can graphically be represented as in the Fig. 11. Fig. 11 shows the effect of the pressure and the particle size on the shear strength more clearly. Shear strength increases with the increasing compression pressure without exception for all six investigated minerals. The particle size is also effecting the shear strength in a large extent. The highest value for the shear strength was obtained for labosil whose particle size, 0.33 l.tm is the lowest among all minerals. Calcite fraction, schwarzsiegel has the lowest shear strength value at 4 and 15 bars with the highest particle size, 10 pm. The relation between the shear strength (x) and the particle size (x) was obtained from the curve in Fig. l I as follows: Shear strength, x oc K/x ~ Here, K is the constant and covers the pressure, saturation, shape factor, porosity and surface tension. This relation is similar to the relation between the tensile strength-particle size relation for the filter cakes given by Schubert (4). Kaolin has the second highest shear strength values at two pressures opposite to its highest particle size, 6 microns. This is due to the sheet structure of kaolin and this structure makes kaolin stronger than the other cakes and this effect appears as f (shape factor) as in the case of tensile strength equations defined by Schubert ( 3 , 4 ) for the calcite cakes.

3OOOOO

E Z

25oo(~

114 bar

2OOOOO

I_

m

15OOOO

alsm I

I

ill

c-

t/)

I

1ooooo ,5oooo - -

Labosil

i

I__ -

Kaol~1

x

-

-

TK)2"

JurapedeBS Oass~ere ~ e g e ~

Figure 11. Dependence of the shear strength on the compression pressure and the particle size of the minerals at about 0 % saturation region (TiO2* " The values for TiO2 are for the pressures 15 and 8 bar).

584

3.2. Effect of surfactant The surfactant (lutensol TO3) used in the experiments has drastically effected the shear strength of the cakes. The shear strength of the four investigated minerals were decreased about half of the values measured in the absence of the reagent. The results at 15 bar with the reagent treatment are given in the Table 6 and Fig. 12.

Table 6. The shear strength values of TiO2, calcite, kaolin and quartz (labosil) at 15 bar in the presence of the surfactant, lutensol TO3 Calcite TiO2 Quartz (labosil) Kaolin Saturat., Shear st., Saturat., Shear st., Saturat., Shear st., Saturat., Shear st., % % N/m 2 % % N/m 2 N/m 2 N/m 2 0 3502 1 47306 2 148820 4 116309 20 49713 60 150124 13 137308 5 263885 23 34253 68 395333 40 375204 32 129721 49 41048 84 241370 43 351896 38 92000 63 75963 91 130093 48 319739 44 100958 65 43911 96 130271 50 358492 45 117053 58 75599 46 69155

400000

CM

E 35O000 Z

r" ~XIO00 t_ L

~ 15oooo 1-

~

0

9

o

0

10O0OO

10

20

30

40

50

60

70

80

90

9

100

Saturation, % 9Ti02

o Kaolin

9Labosil (quartz)

9Juraperle BS (calcite) I

Figure 12. Shear strength changes of juraperle BS (calcite), TiO2, kaolin and labosil (quartz) with the saturation in the presence of surfactant (lutensol TO3) at 15 bar.

It is clear from the data given in Table 6 and in Fig. 12 that, calcite, quartz and kaolin are drastically affected with the addition of the surfactant and their saturation degrees decreased down to 60 % maximum. It was not possible to obtain for these three minerals the saturation higher than 65 % and the cakes were dry. TiO2, on the other hand was the exception and it was possible to obtain about 100 % saturation for this

585 mineral even in the presence of the surfactant. It is also clearly seen from the comparison of the Tables 2,3,4 with the Table 6 that, the shear strength values for all the four minerals were decreased about two times in the presence of the surfactant compared to the values obtained in the pure medium. The tendency of the shear strength curve of the minerals in the case of surfactant treatment is also different from the tendency of the curves without reagent (see the figs. 2,3,4,7). While the maximum shear strength values for all minerals in the case of pure medium (without surfactant treatment) were obtained at about 80-90 % saturation region, this maximum is disappeared for calcite, kaolin and quartz and shifted to about 70 % for TiO2. It can be so concluded from table 6 and fig. 12 that, the surfactant changes the shear strength behavior of the cakes and causes to weaken them.

4. CONCLUSION

The shear strength of very fine mineral filter cakes are dependent on the compression pressure, particle size and shape and surfactant treatment. The higher the applied pressure the greater the shear strength for all type minerals. As the particle size decreases the shear strength increases very sharply. The relation between the shear strength and particle size is: Tshear = K,/x 0"6

The surfactant causes to weaken the shear strength of the minerals. Although the tendency of the shear strength curve is the same as the Schubert's tensile strengthsaturation diagram, there is a weakening around the saturation S = 60 % for all of the minerals. The maximum value of the shear strength was obtained in the saturation region, about S = 90 % for all the investigated minerals.

REFERENCES 1. Bumdenumweltministerium, TA Siedlungsabfall, Bonn, Juni 1993 2. Deutsches Institut fiar Normung, DIN 4096, Mai 1980 3. H. Schubert, Untersuchungen zur Ermittlung von Kapillardruck und Zugfestigkeit von feuchten Haufwerken aus k6migen Stoffen, Dissertation, an der Universitat Karlsruhe, 1972. 4. H. Schubert, Kapillarit~t in por6sen Feststoffsystemen, Springer-Verlag, Berlin, 1982. 5. O. Ozcan, M. Ruhland, W. Stahl, Scherfestigkeit von Pressfilterkuchen Einfluss von Tensiden und Pressdruck-, Wiss.Abschulussberichte, 31. Internationales Seminar der Univ. Karlsruhe, Juli 1996. 6. G. Barthelmes, Einfluss der Entwasserunsbedingungen auf das Festigkeitsverhalten von feink6rnigen Filterkuchen, Diplomarbeit Nr. 842, Institute ~ r MVM der Univ. Karlsruhe, 1995. 7. O. Ozcan, Changing of the shear strength behavior of very fine mineral filter cakes using a surfactant, paper submitted to Int. J. Minr. Processing, 1998.

This Page Intentionally Left Blank

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) o 2000ElsevierScienceB.V. All rightsreserved.

587

A frequency-response study of diffusion and adsorption of C~-C5 alkanes and acetylene in zeolites Gy. Onyesty~.k, a J. Valyon a and L. V. C. Rees b alnstitute of Chemistry, Chemical Research Center, Hungarian Academy of Sciences, H-1525 Budapest, P.O.Box 17, Hungary. bDepartment of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, Scotland, UK.

The dynamics of methane, propane, isobutane, neopentane and acetylene transport was studied in zeolites H-ZSM-5 and Na-X by the batch frequency response (FR) method. In the applied temperature range of 273-473 K no catalytic conversion of the hydrocarbons occurred. Texturally homogeneous zeolite samples of close to uniform particle shape and size were used. The rate of diffusion in the zeolitic micropores determined the transport rate of alkanes. In contrast, acetylene is a suitable sorptive for probing the acid sites. The diffusion coefficients and the activation energy of isobutane diffusion in H-ZSM-5 were determined. 1. INTRODUCTION A number of methods are used for studying the sorption of basic probe molecules on zeolites to learn more about zeolite acidity. A common disadvantage of all the examinations is that adsorbed basic probe increases the electron density on the solid and, thereby, change the acidic properties of the sites examined. From this aspect it seems advantageous to probe the acid sites with a weak base, e. g., with a hydrocarbon. It was shown that adsorption of alkanes is localized to the strong BrOnsted acid sites of H-zeolites [1, 2]. However, recent results suggest that usually the diffusion in the micropores controls the rate of hydrocarbon transport [3-5]. Obviously, the probe suitable for the batch FR examination of the sites has to be nonreactive and the sorption dynamics must control the rate of mass transport. The present work shows that alkanes can not be used because, due to their weak interaction with the H-zeolites, the diffusion is the slowest step of their transport. In contrast, acetylene was found suitable to probe the zeolitic acid sites. The results are discussed in comparison with those obtained using ammonia as probe. Moreover, it is demonstrated that fundamental information can be obtained about the alkane diffusivity in H-zeolites. 2. EXPERIMENTAL A detailed description of the batch type FR system used in the present study has been given previously [6]. The FR functions measured were fitted by in-phase and out-phase characteristic

588

functions which were derived from a theoretical model involving all the possible kinetic processes in the FR system [7, 8]. The general model can be replaced by relatively simple degenerate models if only one resistance controls the transport of a single component. The models used in this study are (a) the model for micropore diffusion [7], (b) the sorption model [7], and (c) the model for macropore diffusion [8]. Dynamic parameters, such as the time constant of the rate determining process step of a consecutive process or the time constants of parallel processes, were determined from the best-fit characteristic function. Bed effects were avoided by dispersing the zeolite particles in the FR chamber in a plug of glass wool. When it was necessary sample was ground to reduce the effect of particle-size heterogeneity. If it is not stated differently the FR measurements were carried out at 373 K temperature and 133 Pa sorbate pressure. Samples were pretreated in situ by 1-h evacuation at 673 K. 13X powder and beads manufactured from the powder were obtained from Lancaster Syntheses, U. K. The characteristics of the H-ZSM-5 samples studied are given in Table 1. Table 1. The Identification and Characterization of the ZSM-5 Sb.mples Sample ID Composition of the unit cell Size, ~m Z15a H5.77Na0.03AI5.80Si90.20192 3-10 Z23b H3.91Na0.16A14.06Si91.60192 0.1-0.4 Z34~ H2.53Na0.25AI2.79Si93.20192 3•215 Z57a_ H1.60Na0.06AI 1.65Si94.40192 10• 10• 'Parent sample obtained as a giR from the Zentralinstitut fllr Physikalische Chemie, Berlin, GDR. Si/AI=15. Sample was prepared from parent Z15. The template was first burned offat 823 K then the template-free material was ion exchanged at 298 K using a 1N aqueous solution of N~C1. t'The sample was provided by Degussa, Germany with an identification CAZ 49. A detailed characterization of the sample is given in refs. [9, 10]. 47 % of the total A.l-content is present as extra-framework species. ~I'he sample was provided by Degussa, Germany with identification CAZ 36. A detailed characterization of the sample is given in refs. [9, 10]. 25 % of the total Al-content is present as extra-framework species, dThe sample was synthesized at the Imperial College by Prof. S. Z. Chen in 1987 [ 11 ].

The size-distribution and the shape of the zeolite crystals and crystallite agglomerates were analyzed by scanning electron microscopy (SEM). 3. RESULTS AND DISCUSSION Rate spectra recorded with different sorptive molecules for commercial 13X powder and 0.3-ram radius pellets are shown in Figure 1 demonstrating the potential of the FR method. The diffiasivity of propane in the pellets was calculated to be 4.3 x 10.8 m2 s"t. It was found invariant to pressure in the 0. I-1.0 kPa range suggesting that Knudsen diffusion is involved. The diffusivity of isobutane, in accordance with its larger molecular mass and branched structure, was about one order of magnitude lower than that of propane. If diffusion in the macropores is controlling the rate of transport the time constant of the process must be in linear correlation with the square of the pellet size. This correlation was found valid for the time constants obtained by the FR method for the beads using isobutane, propane or ammonia. Thus, independent of the basicity of the sorptive, the rate of mass transport was limited by transport in the macropores. It seems unlikely that active sites of the pellets can be tested by a dynamic method. However, if the diffusion resistance of the macropores is eliminated, e. g., by using well-dispersed powder, the nature of the rate limiting process step could be associated with the strength of the acid-base interaction. Thus, for weak base alkanes micropore diffusion

589

1.0~=*~,.~ _ o ~ N 0.59

a , ~

A I (Figure l a, b) and for the strong base 1.0 ammonia sorption (Figure l c ) w a s found to 0.5 be the rate-controlling step of transport. It can be shown that the deviation from the 0.0 .... 0.0 true values of diffusivity can be reduced by o.5. b B o.5 selecting a model which allows for a distribution of particle sizes and shapes. It is 8 I advantageous to use samples of uniform ~~ . ~~ particle size and shape. For such samples the parameters of the dynamic processes can be 120 obtained by simulating the experimental FR 1.5 data with a relatively simple model. The 1.0 o.5 crystals of sample Z57 are of the same shape ol Ol 1 10 001 Ol 1 10--1(~ ~ and size (Figure 2A, B). However, it is not Frequency/Hz always easy to find the appropriate model. Figure 1. FR spectra of (a, A) isobutane, (b, For example, sample Z34 consists of regular B) propane, and (c, C) ammonia in 13X crystals but the crystals are of various sizes powder (a, b, c) and beads (R=0.30 mm) (A, and are aggregated to form larger particles B, C). (Fig. 2C), or the crystals of the Z15 sample are irregular both by shape and size (Fig. 2D). ~

97

m

A: Z57 500x

B: Z57 2500x

/

A: Z23

100x

B: Z23 500x

r

*o

.

"I

,.~')

.r , ."Jr

D: Z15 2500x

.

C: Z34 2500x

Figure 2. Scanning electron micrographs of ZSM-5 samples Z57 (A,B), Z34 (C), and Z 15 (D). The magnification is 500 for (A) and 2500 for (B, C, and D).

l.

D: Z23 30000x

C" Z23 500x

Figure 3. Scanning electron micrographs of the original (A,B,D) and the ground (C) ZSM-5 sample Z23. The magnification is 100 for (A), 500 for (B and C) and 30 000 for (D).

In Figure 3 SEM pictures are presented for the H-ZSM-5 sample Z23. The pictures show that sample Z23 is texturally quite different of those in Figure 2. 100-200-~m size particles are

590

built of very small intergrown crystallites (Figure 3A, B). A higher magnification shows that these particles are aggregates of 0.1-0.4-~tm size crystals (Figure 3D). In order to reduce the effects of particle-size heterogeneity on the measured FR spectra sample Z23 was ground to get particles smaller than about 20 I.tm (Figure 3C). 1.o. The FR spectrum of the ground Z23 sample shows a definite in-phase step and an out-of-phase peak (Figure 4, open ~ A ~= symbols). These data can be fitted by characteristic FR o.5 ~ functions (Figure 4, continuous lines). The data and the -' different profiles of the component curves, one set asymptotic 0.o a . __ and the other intersecting, demonstrate that the transport of the o " ~~*~ B I~ gases proceeds with about the same time constant, but follow ,,~1.o i~..%,~~~. ].~ different rate controlling mechanisms. The micropore diffusio n a: 0.5 ~ and the adsorption models were used to fit the FR spectra of ....... " isobutane and ammonia, respectively (Figure 4A and B). 0.o- . ~ - " X,_~ Measurements with the parent Z23 sample give broad, o.ol Frequency o.1 1 / Hz lo loo featureless FR spectra (Figure 4, solid symbols). Transport in Figure 4. The FR spectra of the macropores probably control the rate of transport in these the (A)isobutane and 03) large aggregated particles. The broad spectrum suggests that ammonia interaction with processes with various time constants are involved. parent (solid symbols) and In the temperature range of 373-573 K no transformation of ground (open symbols)Hthe C~-C5 alkanes occurred on the H-ZSM 5 samples. The ZSM-5. Spectra were adsorption of the small methane molecules was very weak, recorded using about 50 mg while the large neopentane ~.o of sample Z23 at 373 K and molecules could not enter the 133 Pa. narrow zeolitic channels. Thus, 0.5 the response to the applied pressure modulation was too small to record meaningful FR 0.01.Oo"~---............ spectra with these molecules. For propane and isobutane the FR results suggest that diffusion in the micropores is the rate limiting process of transport over the entire temperature range. The measured responses were fitted using the characteristic function of micropore diffusion in isotropic spherical particles of uniform size (see the symbols for the measured responses and rr C the best fit curves in Figure 5). The larger the deviation of the 0.5 _.x~ data from the best fit the wider is the particle-size distribution (cf. Figures 2 and 5). 0.01 0.1 1 10 10 The temperature and pressure dependence of the FR Frequency / Hz responses was determined using sample Z57, which consists of nearly identical crystals. The transport diffusion coefficients (D) Figure 5. The FR spectra of were calculated assuming that particles are spheres of 10-t.tm the isobutane/H-ZSM-5 diameter. The apparent activation energy of diffusion (E,) of systems at 373 K and 133 isobutane obtained from the Arrhenius plot was 21 kJ tool ~ Pa: (A) Z57; (B) Z34 and (Figure 6, open symbols). This value is about three times higher (C) Z 15. The sample than that obtained for the diffusion n-butane [12]. At 373 K and amount was 50 mg. 133 Pa the calculated D was 6 x 1012 m2 sl. If the pressure was increased to lkPa the value of D increased by about 10 %. The D and E, obtained are compared with corresponding data determined by other methods; e.g. Supported Membrane (MEMBRANE) and Quasi-Elastic

~ oo

I

....

591

1E-IO-

Neutron Scattering (QENS) [13], and Temporal-Analysis of Products (TAP) [14] (Figure 6, solid symbols). The isobutane diffusivities determined by the Q macroscopic methods, such as MEMBRANE, TAP, and FR show reasonable agreement. The self-diffusivity fxl coefficient derived from QENS is about E 1E-11 one order of magnitude lower. The E, values of 34 kJ mol "~ and 25 kJ tool "~ obtained by the MEMBRANE and the TAP methods, respectively, are higher than those determined by methods where the conditions of the mesurements correspond to sorption equilibrium or quasi-equilibrium, such as QENS (17 kJ 1E-12 550"5()0 450 " 4130 " 350 mol "l) or FR (21 kJ mol'l). It can be shown that the frequency, Temperature, K where the out-of-phase characteristic FR Figure 6. The temperature dependence of the function of diffusion is a maximum, isobutane diffusivity (D) in the micropores of H- depends on the particle geometry [7, 8]. ZSM-5 zeolite. Transport D values were Consequently, the diffusion coefficient calculated from FR results assuming that particles are spheres of 10-~tm diameter (O) Data 2I A I determined by the MEMBRANE (A), TAP(O), and QENS (11) methods were taken from refs. 13 1............... and 14 and are given for comparison. I ~'-'~_ t obtained from an FR spectrum also varies with the particle ~ o ~ geometry adopted for finding the parameters of the best-fitting ~, B characteristic function. In a model the real crystals are substituted with equivalent particles of simple geometry, such as, spherical, ~" 1i %, cubic, or orthorhombic. Different criteria of equivalency can be l .,/r selected; for instance, the equivalency of critical dimensions, o volume, or surface. The particles of the Z57 sample are virtually o.o~ Frequency o.~ ~ / Hz~o ~oo uniform in size and shape but they are definitely not spherical and Figure 7. The FR spectra isotropic (cf. Figure 2). The diffiasivity of isobutane in the of acetylene sorption on micropores of the Z57 sample was calculated using model H-ZSM-5 at 273 K and particles of various shapes and satisfying different equivalency 133Pa (A)Z57 (B)Z15 criteria. While E, was invariant to the model selection the ' " The sample amount was diffusion coefficient was found to vary within one order of 50 rag. magnitude. Obviously, the numerical values deduced by modeling must be evaluated with consideration on the limitations of the model. Under the conditions applied the dynamic parameters for the transport of the weak base C~-C5 alkanes are diffusion controlled and do not tell us anything about the dynamics of sorption, i. e., about the sorption sites. Stronger base olefins cannot be used as the sorptive for probing strong acidity since they are easily converted. Acetylene is quite inert to acid catalyzed transformation and its sorption is stronger than that of the alkanes. However, a full proton

592 transfer to the sorbate acetylene could not be substantiated below room temperature by IR spectroscopy [15]. It is conceivable that adsorbed acetylene is modifying the strength of the acid sites to a smaller extent than the strong base ammonia. The intersecting profile of the inphase and the out-of phase components of the FR spectra suggests that sorption is the ratecontrolling process of the acetylene~-ZSM-5 interaction at 273 K, suggesting that acetylene is an excellent hydrocarbon sorptive for probing the acid sites (Figure 7). Further research is needed, however, before the acidity of zeolites can be routinely characterized by the dynamic FR method. ACKNOWLEDGEMENTS The international cooperation was supported by the scholarship of the Royal Society CEE project grant and the Hungarian Academy of Sciences. Thanks is due to Dr. Katalin Papp (IC CRC, HAS) for the SEM pictures. REFERENCES 1. F. Eder, M. Stockenhuber, and A. J. Lercher, Stud. Surf. Sci. Cat., 97 (1995) 495. 2. F. Eder and A. J. Lercher, Zeolites 18, (1997) 75. 3. T. Masuda, Y. Fujikata, T. Nishida, and K. Hashimoto, Micropor. and Mesopor. Mat. 23 (1998) 157. 4. L. Song and L. V. C. Rees,Micropor. Mat. 6 (1996) 363. 5. L. Song and L. V. C., Rees, in Proc. of 12th IZC, Baltimore, USA, 1998, Materials Research Society, Warrendale, Pennsylvania, p67. 6. L. V. C. Rees and D. Shen., Gas. Sep. Purif 7 (1993) 83. 7. Y. Yasuda, Heterog. Chem. Rev., 1 (1994) 103. 8. R. G. Jordi, and D. D. Do, Chem. Eng. Sci. 48 (1993) 1103. 9. H. G. Karge, M. Laniecki, M. Ziolek, Gy. Onyestyak, ,~,. Kiss, P. Kleinschmit and M. Siray, Stud. Surf. Sci. Cat., 49 (1989) 1327. 10. L. C. Jozefovicz,.H.G. Karge, and E. N. Coker, J. Phys. Chem. 98 (1994) 8053. 11. S. Z. Chert, K. Huddersman, D. Keir and L. V. C. Rees, Zeolites 8 (1988) 106. 12. W. Heink, J. Karger, H. Pfeifer, K. P. Datema and A. K. Nowak, J. Chem. Soc. Faraday Trans. 88 (1992) 3505. , 13. B. Millot, A. Methivier, H. Jobic, H. Moueddeb and M. Bee, J. Phys. Chem. B 103 (1999) 1096. 14. O. P. Keipert and M. Baems, Chem. Eng. Sci. 53 (1999) 3623. 15. S. Bordiga, G. Ricchiardi, G. Spoto, D. Scarano, L. Camelli, and A. Zecchina, J. Chem. Soc. Faraday Trans., 89 (1993) 1843.

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScienceB.V. All rightsreserved.

593

Novel M n - b a s e d M e s o p o r o u s M i x e d Oxidic Solids V.N. Stathopoulos a, D.E.Petrakis a, M.Hudson b, P.Falaras c, S.G.Neofytides d and P.J.Pomonis a'. Department of Chemistry, University of Ioannina, Ioannina 45110, Greece. b Department of Chemistry, University of Reading, Reading RG6 2AD, UK. c Institute of Physical Chemistry, NCSR "'Demokritos", 15310 Ag. Paraskevi Attikis, Greece. d FORTH-ICE/HT, P.O. Box 1414, 26500 Patras, Greece.

a

Manganese-based high surface area mesoporous and/or microporous mixed oxidic solids AMnOx, where M = A1, La and Fe, have been prepared via controlled hydrolysis of a water sensitive tri-nuclear manganese complex [Mn30(CH3COO)6(pyr)3]C104 in aquatic microenvironment (drops). The specific surface area of the obtained solids heated at 300 ~ was found to be 711 mZ/g for A1MnOx, 247 m2/g for LaMnOx and 199 mZ/g for FeMnOx while the mean pore diameters were 3.6, 4.6, and 3.8 nm respectively. The surface composition of the solids was determined using XPS while their texture was checked using AFM. A mechanism of formation of the porous oxidic systems is proposed via hydrolytic attack of water molecules in the acetyl bridges of the complex followed by adsorption of Acations on the Mn(OH)x groups formed and diffusion limited aggregation (DLA) of the resulting clusters towards larger particles. 1.1NTRODUCTION Microporous and mesoporous manganese oxides are prepared via a variety of routes. The most important of them can be classified in the following categories (1) (I) Precipitation, Ionexchange and hydrothermal processing, which usually involves red-ox reaction of MnO 4 and Mn +2 salts for the formation of Mn +4 precursors. Typical manganese oxidic materials obtained include birnessites and hausmanite (2-6) (ii) Sol gel techniques, where the reduction of MnO 4 takes place using various organic reductants like acids, polyols and sugars (7-12). In such cases microporous layered structures (birnessites, cryptomelanes) are obtained with interlayer distance around 5-7A depending on preparation mixtures and the added heterocations. (iii) A third general route is through solid state reactions at high temperatures. Such methods provide small crystallites and porous phases (12) but often different crystal phase are present in the final material. The materials obtained by the above methods possess usually layered (13) or microporous tunnel structures (12, 14, 15). The pore size distribution of such microporous solids is rather broad (6-9A) (16) but such materials show high adsorbing capacity, up to 20g of absorbate / 100g of adsorbent, which rivals that of zeolites (3). Manganese oxide mesoporous solids (MOMS) of both hexagonal and cubic phases have been recently prepared via incorporation of surfactant micelles and partial oxidation of *Corresponding Author

594 Mn(OH)2 (17) followed by oxidation of Mn § "m Mn +4 and Mn +3 and removal of surfactant by calcination. Such materials are thermally stable with mesoporous diameter 3.0nm. Nevertheless the surface area of such solids is not particularly high and found around 50-170 m2g-1 for the samples fired at 600~ Other kinds of mesoporous manganese based materials have been also reported by transformation of layered birnessite (18). Finally amorphous microporous manganese oxidic materials prepared by the reaction between KMnO4 and oxalic acid and incorporation of hetero-cations like Cu +2, Cr +2, Nt +2 and Zn +2 in them have been recently prepared and tested as catalysts (19, 20). From the above literature it seems that there is no method readily available for the preparation of high surface area mesoporous manganese based solids. Nevertheless the development of such materials is highly desirable for two main reasons: First, it is well known since some time that manganese is a first choice catalyst for oxidation reactions (21) often operating at temperatures significally lower than comparable noble metal based catalysts (22). The literature on the catalytic activity of manganese based compounds, often containing additional cations is quite extensive and some recent work since 1995 can be found in refs (23-33). Second, manganese oxides are very important solids for applications both in aqueous and non-aqueous batteries, both of rechargeable (24-31) and of non-rechargeable (32, 33) nature. The present work describes a general route for obtaining large surface area, mesoporous and/or microporous manganese based oxidic systems based on the hydrolysis of trinuclear manganese complex [Mn30(CH3COO)6(pyr)3]C104 and it is a follow-up of some other relevant papers published by the same group (34-36). 2. EXPERIMENTAL AND RESULTS 2.1 Preparation of the [Mn30 (CH3COO)6(pyr)3]CIO4Complex The trinuclear manganese complex [Mn30(CH3COO)6(pyr)3]C104 (Fig.l) was prepared according to the original report of its synthesis (37). Briefly, 2g of Mn(CH3COO)24H20 (6.15mmol) were dissolved in a mixture of 20ml ethylalcohol, 3ml pyridine and 12ml glacial acetic acid. In this mixture 1.14g (3.15mmol) of N-nBu4MnO4 was added under vigorous

~N 0~@ Mn

Mn

~'~'~

j.~Mn.-._ ~. ~ , ,

Figure 1 Molecular shape of the cation of the trinuclear complex [Mn30(CH3COO)6(pyr)3]C104

595 stirring, where N-nBu4MnO4 is "tetra butyl-permanganate" prepared by mixing aqueous solutions of KMnO4 and N-nBu4Br. Addition of 0.69g (5.65mmol) of NaC104 resulted in the precipitation of a brown mass of the complex which was subsequently filtered and washed with acetone. The brown solid obtained was examined for its IR spectra, which was found similar to those reported in (37).

2.2 Hydrolysis procedure The trinuclear complex, henceforth referred as Mn3, is readily soluble in warm acetone, but instantly hydrolyzed in water. A weighted amount of Mn3 was dissolved in acetone and put in a 3-neck spherical flask, equipped with a reflux system used to avoid the escaping of acetone vapor. Then, an aquatic solution of one metallic ion in its nitrate form was added dropwise into the acetonic solution kept at 50 ~ In a typical example, in 250ml of Mna/acetonic solution containing 0.01 moles of Mn3, 250ml of Al(NOa)a/H20 solution (0.141 M) was added dropwise and slowly during 2h. Then the obtained precipitate was filtered, dried at room temperature and fired at 300~ and 500~ under atmospheric conditions. Samples prepared in this way are in Table 1 with some of their characteristic properties. 2.3 Surface Area and Porosity The specific surface area (ssa) of the solids (m2g1) obtained after hydrolysis and drying at various temperatures was measured routinely by multi-point BET method at 77K by N2 adsorption in a Fisons Sorptomatic 1900 system. From these isotherms the BET ssa's were determined and the corresponding pore size distribution was also found. Typical results including the adsorption-desorption isotherms as well as the corresponding pore size distributions are shown in Fig.2 O

R (A) 10

100

4001

' '' ..... I

9

1000 ' ....... I

100 ........

i

1000 ........

i

Mn-La-O / 300~

100 ........

I

1000 ' .......

Mn-Fe-O/ 300~

0.16

350

0.14 300 0.12 ,~

250 0.I0 ! 200 0.08 150

0.06

100

0.04

50 0

0.02 i

,

|

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0.00

P/Po Figure 2 Adsorption-desorption isotherms (N2 - 77 K) and the corresponding pore size distributions of Mn-based oxide materials

596

2.4 Surface composition (XPS) The surface composition of the three manganese based solids is shown in Table 1 and was determined by means of X-ray Photoelectron Spectroscopy (XPS). The powders were pressed firmly into carved stainless steel holders so that they could be introduced into the Ultra High Vaccum (UHV) chamber. The UHV system (base pressure 8x10 -1~ consists of a fast entry assembly and the preparation and the analysis chambers. The latter was equipped with a hemispherical analyser (SPECS LH-10) and a twin-anode X-ray gun. The unmonochromatized MgKa line at 1253.6 and a constant pass energy mode (97 eV) for the analyser were used for the analysis measurements. A typical spectrum is shown in Fig.3 for Mn-A1-O. The calculations of the various components composition of the solids shown in Table 1 were based on the spectra of the Mn2p, A12p, Fe3p, La4d and O ls photoelectrons. The sensitivity factors (I) o f the above photoelectron spectra are also given in Table 1, were reproduced from Wagner et al. (38). These empirically derived atomic sensitivities are applicable to other spectrometers with the same transmission characteristics. 25000 A/

20000

Mn2p I

4.=.) .1-.( ra~

01s

15000 10000

5000

Al s /•12p

Cls I

1000

'

I

800

'

I

600

9

I

400

'

I

200

'

I

I

0

200

Binding Energy, eV Figure 3. A typical XP Spectrum of the Mn-A1-O solid. 2.5 AFM The texture and morphology of the Mn-based oxides were investigated by atomic force microscopy (AFM Nanoscope III, Digital Instruments) in the tapping mode. Observations were performed on thin films of these materials deposited on microscope glass slides by solvent evaporation of aqueous dispersions (2gll), homogenized by ultrasounds (30 min). The three dimensional images, Fig. 4, clearly showed that the Mn-AI-O and Mn-La-O films are composed of large domains of features of different heights, probably resulting from a rather random particle deposition (39).). On the contrary, for the Mn-Fe-O films, Fig. 2(c), we observed the presence of a more robust and organized structure which consists of well defined rocks of different sizes on the top of a continuous background. The grain size analysis revealed that the grain diameter of the lanthanum containing Mn oxide is significantly lower than that of the corresponding aluminum and iron one's, Table 1. Furthermore, the roughness analysis indicated that the standard deviation of the difference between the highest and lowest

597

Figure 2. AFM images of (a) Mn-A1-O, (b) Mn-La-O and (c) Mn-Fe-O solid.

598 points (Rms) which directly reflects the height of surface features (40), is significantly higher in the case of the Mn-Fe oxide. Finally, the geometric complexity of the material surfaces was evaluated by a more detailed fractal analysis (41, 42) The results, Table 1, although they confirmed the presence of a more complex surface topography for the iron containing material, they did not show very clear and significant differences. Especially for the Mn-A1-O material, the results are consistent with the existence of an open network of interconnected particles forming features of medium height with no preferential scheme and orientation. Such a porous and disordered structure could be at the origin of the extremely high surface area value. Table 1: Mesoporous Manganese based solids Properties Calcined (~ Mn-A1-O Surface area (m2/g) 300 711 500 310 Mean pore diameter(nm) 300 3.6 500 3.8 Crystal Structure (XRD) 500 Amorphous ............................................................................................................................

Mn:A in hydrolysis bath Surface Composition

.

.

.

.

.

.

.

.

.

.

.

500

0.85 0.28:0.11:0.61

Sample Mn-La-O 247 166 4.8 5.1 Amorphous

Mn-Fe-O 199 62 3.8 9.4 Mn203-Fe203

1.70 0.33:0.05:0.62

0.85 0.26:0.09:0.65

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

Roughnes s/AFM(nm) Particle size/AFM(nm) Fractal dimension/AFM Sensitivity factors (I) : O ls-1,

300 9.76 300 20 300 2.22 La4d-2, Fe3p-0.26, A12p-0.28, and

13.53 10-15 2.29 Mn2p-3.93

41.79 20-25 2.30

3. DISCUSSION The obtained mesoporous and/or microporous materials A1MnOx, LaMnOx and FeMnOx are produced via hydrolysis of the trinuclear Mn30 complex, existing in the acetonic solution. The process of hydrolysis is generated by the gradual addition of aquatic drops containing the A-cation (A = A1, La, Fe) in its nitrate form. The sequence of events, which leads to the products, can be envisaged according to the following steps (Fig.5: A, B, C, D, E and F).

G

,,2-----2

'~,. ~ -~/ "- .'~_~j ~, 21., I "I I

NO3

n

" ~

r]rt

\

N(~'3 N O ~ ~ A +" 3A+,Q....,'-'~

~ ' ...0. _a~ . ~n il,

0

o Fig.5; Step A: The aquatic drop containing metal cations A n+ and anions NO3- is placed into an acetonic solution containing the starlike Mn3-complex cations.

,o.'14"o

Fig.5; step B: The water of the drop starts to be counter diffused towards the acetonic solution while acetone is diffused towards water. Both solvents carry with them the chemical species they contain.

599

Fig.5; step E: Cations A n+ are adsorbed in the vicinity of Mn hydrolysis products and bond to Mn via Mn-O-A bonds. The rate of adsorption depends on the concentration of A.

Fig.5; step F: As the concentration of Mn-O-A groups increases, they form larger species via Diffusion Limited Aggregation (DLA). The gel-type species form upon drying high surface area and porosity solids.

Which might be the reasons differentiating the specific surface area of the final products? We feel that this is related to the hydrolytic paths of the cations A +n, originally in the aquatic drops (step 5A), as soon as they find themselves in the buffered microenvironment created by the acetic and pyridine groups (step 5C). In a previous study (36) it was shown, that the gradual addition of Mn3-complex into aquatic solution containing a variety of cations, always leads to a final solution with pH=4.75 corresponding to the pK of CHsCOOH. In the same study (36) the nanoparticles obtained possessed relative high surface area 100-200 m2/g depending on the presence of heterocations and the heating temperature, but did not show any internal porosity as indicated by the absence of hysterisis loop in the adsorption desorption isotherms. The primary pore-free nanoparticles thus obtained were estimated to have a size of around 5-30nm, were amorphous after heating at 300 ~ and had the Mn203 structure at 700

600 ~ Such tiny hydrolytic products MnOx(OH)y should be formed immediately after the hydrolytic destruction of Mn3-complex (step 5C). Although the situation is further complicated here, with the presence of acetone, we shall make the working hypothesis that the micro-aquatic environment in which a particular cation A § is confined, is affected by this buffered pH - 4.75 as in (36). The nitrate solutions of Al(NO3)3, Fe(NO3)3 and La(NO3)3, fed dropwise into Mn3/acetone have initial pH equal to 2.65, 1.5 and 4.80 respectively. The Fe +3 ions when found themselves in pH = 4.75 suffered quick hydrolysis and precipitation, possibly together with the manganese nano-entities. This quick precipitation results in the lowest surface area without much porosity (Table 1). On the other hand the La § does not suffer any kind of hydrolysis at pH = 4.75 and remains in the form of monomers La+3(H20)x species (43, 44). These species are sparingly adsorbed on the MnOx(OH)y entities (step 5E) and remain largely dissolved in the solution. Therefore the final product contains a very low quantity of La (see XPS results in Table 1). Finally the A1§ ions have the advantageous behaviour in forming oligomeric species at this pH region, among them the well-known Keggin ions [AlI3Oa(OH)24(H20)I2]+7. Such species can be adsorbed on the MnOx(OH)y nano-entities and increase the surface area of the final product, resisting sintering. To summarize, the Mn-A1-O system has the highest Al-loading because the A1+~ forms oligomeric species, the Mn-La-O system has the lowest La-loading because the La § ions do not form any oligomers but remain monomeric while the Mn-Fe-O system suffer early precipitation resulting in the lowest surface area. Finally in Fig.6 we have use plots of the form lnVads = f (ln[In(Po/P)] in order to determine the dimensionality D of the surfaces as sensed by the adsorbed N2 molecular species. This method has previously applied to similar systems (36, 45), As seen in Fig.6, at high pressures (left hand part-plot line) the N2 is adsorbed in 3D fashion i.e. as liquid. At the low pressure (right hand part in Fig.6) the average dimensionality of the solids, as measured by the "stick" of N2 molecules is D = 2.34 for Fe-Mn-O, D = 2.49 for La-Mn-O and D = 2.47 for the A1Mn-O. These values should be compared with the fractal dimensions determined by the AFM (Table 1). For the A1-Mn-O and La-Mn-O the D values determined by N2 adsorption are larger by an amount equal to 0.25 and 0.22 dimensional units respectively, indicating the degree of finest structural details sensed by N2 as compared to the AFM probe. On the contrary the difference for the Fe-Mn-O solid is only 0.04 dimensional units. In other words the smaller N2 stick does not senses much more details in Fe-Mn-O solids, as compared to AFM stick, because of the lack of extended internal porosity, while it does senses a lot more details in A1-Mn-O and La-Mn-O because they possess internal surface area, accessible only to N2 species. A final observation is in line relative to the plots referred to A1-Mn-O and LaMn-O in Fig.6. The straight line in the right hand part of these plots can be actually divided in two regions of data. The low pressure points show D = 2.53 and 2.57 - very porous solids indeed. The higher pressure points show D = 2.36 and 2.35 respectively - corresponding to rather "blocked" porous system, reminding the Fe-Mn-O one for which D = 2.34. It is clear that the initially adsorbed N2 molecules block the small pores, probably the micropores, and fill the larger pores, i.e. the mesopores, at higher pressures sensing at these later adsorption steps a more "fiat" surface. For the Fe-Mn-O system such a distribution is not possible because of its low microporosity. The bending points in the icons of Fig.6 correspond to P/Po=0.25 for A1-Mn-O and P/Po=0.45 for La-Mn-O. A comparison with the adsorptiondesorption isotherms in Fig.2 shows that these are roughly the regions where adsorption on mesoporous starts. So this methodology provides a tool for distinguishing between the adsorption fractal characteristics in structural and textural levels of scrutiny in porous solids.

601 6.5

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ln[ln(Po/P)] Figure 6. Linear plots of In Vads as a function of ln[ln(Po/Po)] for the surface fractality of the solids

Acknowledgements: Part of this work was supported by EU TMR project (MESOP-ERB 4061-PL95-1357). REFERENCES 1. S.L.Block, N.Duan, Z.R.Tian, O.Givaldo, H.Zhou and S.L.Suib, Chem. Mater. 10 (1998) 2619. 2. J.Luo, S.L.Suib, J. Phys. Chem., B 101, (1997) 10403. 3. Y.F.Shen, R.P.Zerger, R.DeGuzman, S.L.Suib, L.McCurdy, D.I.Potter, C.-L.O'Young, Science 260 (1993) 511. 4. Q.Feng, E.-H.Sun, K.Yanagisawa, N.Yamasaki, J.Ceram.Soc.Jpn. 105 (1997) 564. 5. Q.Feng, E.-H.Sun, K.Yanagisawa, N.Yamasaki, J. Ceram. Soc. Jpn. 104 (1996) 897. 6. Q.Feng, K.Yanagisawa, N.Yamasaki, Chem. Commun. (1996) 1607. 7. S.Bach, M.Henry, N.Baffier, J.Livage, J.Solid State Chem. 88 (1990) 325. 8. S.Ching, J.A.Landrigan, M.L.Jorgensen, N.Duan, S.L.Suib, C. -L.O'Young, Chem. Mater. 7 (1995) 1604. 9. N.Duan, S.L.Suib, C. -L.O'Young, J. Chem. Soc., Chem. Commun. (1995) 1367. 10. S.Ching, J.L.Roark, N.Duan, S.L.Suib, Chem. Mater. 7 (1997) 750. 11. S.Ching, D.J. Petrovay, M.L.Jorgensen, S.L.Suib, Inorg. Chem. 36 (1997) 883. 12. P.Boullay, M.Hervieu, B.Raveau, J. Solid State Chem. 132 (1997) 239. 13. C.N.R.Rao, A.K.Cheetham, R.Mahesh, Chem. Mater. 8 (1997) 2421. 14. T.Rziba, H.Gies, J.Rius, J. Eur. J. Mineral. 8 (1996) 675. 15. A.R.Armstrong, H.Huang, R.A.Jennings P.G.Bruce J. Mater. Chem. 8 (1997) 255. 16. L.O'Young, R.A.Sawicki, S.L.Suib, Microporous Mater. 11 (1997) 1. 17. Z.R.Tian, W.Tong, J.Y.Wang, N.G.Duan, V.V.Krishnam, S.L.Suib, Science 276 (1997) 926. 18. J.Luo, S.L.Suib, Chem. Commun. (1997) 1031. 19. J.Chen, J.C.Lin, V.Purohit, M.B.Cutlib, S.L.Suib, Catal. Today 33 (1997) 205. 20. J.C.Lin, J.Chen, S.L.Suib, M.B.Cutlib, J.D.Freihaut, J. Catal. 161 (1996) 659.

602 21. M.Shelet, K.Otto, H.Gandhi, J.Catal. 12 (1968) 361; M.Shelet, Chem.Rev. 95 (1995) 209. 22. Kirk-Othmer Encyclopedia of Chemical Technology, 4th ed., Plenum Press, New York, 1991, Vol. 15. 23. B.Dhandapani, S.T.Oyama, Chem. Lett. (1995) 413. 24. T.Nagaura, 4th International Rechargeable Battery Seminar, Deerfiled Beach, FL, 1990. 25. J.R.Dahn, U.Von Sacken, M.R.Jukow, H.A1-Janaby, J. Electrochem. Soc. 138 (1991) 2207. 26. S.Hossain in Handbook of Batteries, 2"d ed., D.Linden (ed.), McGraw-Hill, New York 1995, Chapter 36. 27. R.Koksbang, J.Barker, H.Shi, M.Y.Saidi, Solid State Ionics 84 (1996) 1. 28. P.Le Goff, N.Baffier, S.Bach, J.P.Pereira-Ramos Mater. Res. Bull. 31 (1996) 63. 29. F.Leroux, L.F.Nazar Solid State Ionics 100 (1997) 103. 30. G.Pistoia, A.Antonini J. Electrochem. Soc. 144 (1997) 1553. 31. C.S.Johnson, M.F.Mansuetto, M.M.Thackeray, Y.Shao-Horn, S.A.Hackney J. Electrochem. Soc. 144 (1997) 2279. 32. C.C.Liang in Encyclopedia of Electrochemistry of the Elements, Vol. 1, A.J.Bard (ed.) Marcel Dekker, New York, 1973. 33. T.N.Andersen in Modem aspects of Electrochemistry, R.E.White, B.E.Conway, J.O'M.Bockris (eds.), Plenum, New York, 1996. 34. C.S.Skordilis, P.J.Pomonis in Preparation of Catalysts VI, G.Poncelet et al. (eds.), Elsevier Science B.V., 1995. 35. C.S.Skordilis, P.J.Pomonis J. Colloid Interface Sci. 166 (1994) 61 36. A.D.Zarlaha, P.G.Koutsoukos, C.S.Skordilis, P.J.Pomonis J. Colloid Interface Sci. 202 (1998)301. 37. J.B.Vincent, H.R.Chang, K.Folting, J.C.Huffman, G.Christou and D.N.Hedrikson, J.Am.Chem.Soc., 109, 5703 (1987). 38. C.D. Wagner, L.E. Davis, M.V. Zeller, J.A. Taylor, R.H. Raymond and L.H. Gale, Surf. Interf. Anal., 3 (1981) 211. 39. P. Falaras and F. Lezou, J. Electroanal. Chem., 455 (1998) 169. 40. P. Falaras, I. Kovanis, F. Lezou, and G. Seiragakis, Clay Minerals, 34 (1999) 223. 41. P. Falaras, Solar energy materials and solar cells, 53 (1998) 484. 42. A. Provata, P. Falaras, A. Xagas, Chemical Physics Letters, 297 (1998) 484. 43. J.Kragten in Atlas of Metal-Ligand Equilibria in Aqueous Solutions, Ellis and Horwood J.Willey, New York-London 1978. 44. C.F.Baes and R.E.Mesmer, Hydrolysis of Cations, Krieger Publishing Co., Florida, reprint edition 1986. 45. (a) M.Jaroniee, Langmuir, 11 (1995) 2316; (b) M.Sahoudi, S.Blacher and F.Brouers in Characterization of Porous Solids -COPS IV, Eds. B.McEnauey, T.J.Mays, J.Rouquerol, F.Rodriguez-Reinoso, K.S.W.Sing and K.K.Unger, The Royal Society of Chemistry, 1977.

Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScienceB.V. All rightsreserved.

603

Mercury porosimetry applied to precipitated silica. Ren6 Pirard and Jean-Paul Pirard Universit6 de Li6ge, Laboratoire de G6nie Chimique, Institut de Chimie (B~t. B6a), B-4000 Li6ge, Belgium Some materials, among the most porous, show a large volume variation due to mechanical compaction when submitted to mercury porosimetry. High dispersive precipitated silica shows, as low density xerogels and carbon black previously experimented, two successive volume variation mechanisms, compaction and intrusion. The position of the transition point between the two mechanisms allows to compute the buckling constant used to determine the pore size distribution in the compaction part of the experiment. The mercury porosimetry data of a high dispersive precipitated silica sample wrapped in a tight membrane are compared with the data obtained with the same sample without membrane. Both experiments interpreted by equations appropriate to the mechanisms lead to the same pore size distribution. I. INTRODUCTION Methods allowing the study of porous materials in order to obtain the pore volume distribution in relation to the pore size are infrequent. The nitrogen adsorption-desorption isotherm analysis gives a good knowledge of distribution in micropore and small mesopore domains. Thermoporometry gives also a volume distribution in the small mesopore domain. Small angle X-ray scattering (SAXS) and small angles neutron scattering (SANS) allow to obtain valuable information, constituent particle sizes and fractal dimension of the particle aggregation geometry, however the interpretation of the curve of scattered intensity versus wave vector does not allow generally to obtain a pore volume distribution versus pore size with an acceptable precision. In the macropore and large mesopore range, mercury porosimetry is the only method which allows to obtain a detailed pore volume distribution versus pore size. The interpretation of the mercury porosimetry data in terms of pore size distribution is based on the assumption that the mercury intrudes the pore network and on the use of the Washburn equation L = 47' cosO

(1)

in which L is the diameter of cylindrical assumed pores, 7' is the surface tension of mercury, 0 is the contact angle and P is the applied pressure. However, it has been shown that some materials, among the most porous have a mechanical apparent bulk modulus K very weak and

604 that these materials are easily compacted by the mercury isostatic pressure. In some cases, the deformation can be so large that any volume variation recorded during the mercury porosimetry experiment must be attributed to the mechanical compaction and not to the mercury intrusion in the pore network. In that case, the Washburn equation cannot be used to interpret the mercury porosimetry data in terms of pore size distribution. Experiments made on silica aerogels [1,2] or silica-zirconia aerogels [3] showed that these materials compact under the mercury isostatic pressure and do not allow any intrusion of mercury in the pore network. Because the volume variation is largely irreversible at high pressure, it is possible, using aerogel samples compacted at various pressures, to study the effect of pressure on pore size distribution measured by nitrogen adsorption-desorption isotherm analysis [3] or by small angle X-ray scattering [2]. These studies showed that volume variation observed during the pressure increase is due to the disappearance of the largest pores present in the material by collapse while the pore size distribution stays unaltered in the smallest pore domain. Numerous publications on aerogels showed that the texture of these materials is made of particles aggregated into filaments which in turn form a three dimensional crosslinked structure [4]. In such a texture, pores are largely interconnected in such a way that the surface separation between pores is undefined. In very porous materials, pores can be only defined as the space located inside polyhedra and only the edges of the polyhedra are materialized by aggregates (or filaments) of particles. Indeed, such a texture may be evidenced from examinations of very low density aerogels by scanning electron microscopy. When a material exhibiting such a texture is submitted to an isostatic pressure, it results a set of forces, mostly compressive, in the direction of lines joining two successive summits of polyhedra which define the pores. In the hypothesis of an isotropic matter which means that the size of pores is roughly the same in all directions, the intensity of forces in a polyhedron edge is proportional to the square of the polyhedron size. Filaments submitted to axial compressive forces are bent and buckled. According to Euler's law, the force which causes instability is proportional to the inverse of the square of the filament length for a constant filament cross section. This model leads to predict the disappearance of pores of size L by buckling of their edges at a pressure P given by equation L = ke/P ~

(2)

in which ke is a constant value with regard to pore size and varying with the filament cross section, the stiffness of the links between filaments and the shape of regular polyhedra which are used to model the pores. The value of constant ke cannot be determined theoretically. It must be determined experimentally by any method (nitrogen sorption, electron microscopy or small angle X-ray scattering) allowing to measure the size of largest pores which are subsisting after application of a determined compaction pressure. In a previous study [5], we showed that some materials, in particular the low density silica xerogels, exhibit a remarkable behavior when submitted to mercury porosimetry. At low pressure, the volume variation observed is entirely due to a crushing mechanism, generally irreversible with sometimes a weak elastic component. At high pressure, these xerogels are invaded by mercury which intrudes the pore network. The transition from the crashing mechanism to intrusion is sudden at a pressure Pt, characteristic of the material. This particular point can be easily located on the curve of cumulative volume versus logarithm of pressure by

605 a sharp slope change. The behavior of these materials is particularly interesting because it allows to determine the value of the ke constant of the equation (2) without other independent measurement. Indeed, at the pressure of transition P,, the pores of size L, which just resist to collapse are the first which are invaded by mercury. The collapse equation (2) and the intrusion equation (1) are simultaneously valid at P, and both give the value of the pore diameter ke

L , - p O.25 _

4-y'cos0 p,

(3)

which allows to determine the ke constant ke

- -

--

4-y-cosO pt o.75

(4)

Such a hybrid behavior has been noted on various materials amongst the most porous and is not peculiar to low density xerogels. It is the case of carbon black [6] and of some silica precipitated from alkaline silicates. The fumed silica synthesized in gas phase exhibits, depending on their bulk density, either a collapse behavior similar to the one of aerogels or a hybrid behavior similar to the one of low density xerogels [7]. In the present study, we show that the same pore size distributions obtained on the one hand, by the interpretation of an intrusion curve by the Washburn equation (1) and, on the other hand, by the interpretation of a crushing curve by the buckling equation (2) that we propose, are identical. These results are obtained on samples of industrial high dispersive precipitated silica.

2. EXPERIMENTATION The bulk density of materials was measured by Hg pycnometry from independent measurements of the mass and the volume of monolithic samples. The geometrical volume of the sample is determined fi'om the weight difference between a flask (calibrated volume) filled up with mercury and the same flask filled up with the sample and mercury. As mercury is a non-wetting liquid and as no pressure is exerted, mercury does not enter in the porosity of the sample or crush it. Mercury porosimetry experiments were performed on a Carlo Erba Porosimeter 2000 allowing measurements in the pressure range 0.01 - 200 MPa. The sample of high dispersive precipitated silica was synthesized and provided by Prayon-Rupel S.A, Belgium. The first step of this study consists in distinguishing whether the volume variation is due to intrusion of mercury into the pore network or to crushing of the sample under the isostatic pressure. This distinction can be done by a careful examination of the sample after a complete experiment including pressurization and depressurization. The sample is separated in advance from the liquid mercury which is easy if the sample is monolithic with large enough pellet size of about 0.2 to 0.3 cm3. The mercury intrusion up to the center of a monolithic sample at a given pressure takes some time to be completed. A slow enough pressurization velocity must be employed to reach a permanent quasi static equilibrium. One can periodically verify that the equilibrium is reached observing that the volume variation as a function of time is null at constant pressure. Using the minimum pressurization velocity available on the porosimeter, the

606

pressure reaches 200 MPa after 150 minutes. It was verified that the porosimetry curve is the same for a pressurization velocity 25 times slower obtained by a manual driving. For the depressurization, it is necessary to use a depressurization velocity below 0.1 MPa/minute, especially in the pressure domain where the volume variation is driven by an elastic crushing mechanism. Mercury porosimetry experiments have been also carried out on samples wrapped in an airtight membrane (Parafilm| Before sealing tightly the membrane, vacuum was done using a syringe needle connected to a vacuum pump. The goal of the membrane use is to prevent any mercury intrusion into the pore network without preventing the crushing of the sample by the isostatic pressure. 3. RESULTS Figure 1 shows mercury porosimetry curves on high dispersive precipitated silica and on a low density xerogel previously examined [5]. The volume variation as a function of logarithm of pressure shows the same behavior. On both curves, one can see a sharp increase of the curve slope for a characteristic transition pressure Pt. The value of this transition pressure is 45 MPa for precipitated silica and 27 MPa for the low density xerogel sample. The value of transition pressure Pt is dependent of the compressive strength of the sample. In order to identify the volume variation mechanisms on the precipitated silica sample, experiments were performed at various maximum pressure below and near the point of slope change Pt..A monolithic smnple of high dispersive precipitated silica was weighted and its specific volume (2.04 cm3/g) was determined using mercury pycnometry. It has been submitted to mercury porosimetry until a pressure (40 MPa) just below the characteristic transition _

i i

r

i[i

-+- Precipitated Silica

0'3

-4,- Silica Xerogel ......................

O

i

J

c)

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....

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.

.

.

.

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.

.

.

.

1O0

1

1000

Figure 1. Mercury porosimetry curves (cumulative pore volume versus pressure) obtained on high dispersive precipitated silica and on low density silica xerogel.

607

pressure of slope change Pt (45 MPa). Figure 2 (curve a) shows the pressurization and depressufization curves. The cumulative volume recorded at 40 MPa is 0.65 cm3/g and after the return to atmospheric pressure the residual cumulative volume is 0.36 cm3/g (point A on figure 2). After the experiment, the sample is weighted again and the mass is found identical to the initial one. This evidences that the cumulative volume (0.36 cm3/g) recorded after pressurization and depressufization does not correspond to entrapped mercury. This latter observation is confirmed by optical microscopy examination which shows also that no mercury is entrapped in the pore network. The mercury pycnometry measurement performed on the sample after mercury porosimetry experiment shows that the specific volume of the sample is equal to 1.67 cm3/g. The variation of specific volume measured by mercury pycnometry before and after pressurization and depressurization cycle is 0.37 cm3/g. This value is very close to the one observed by mercury porosimetry (0.36 cm3/g). This analysis evidences that the volume variation recorded below the characteristic transition pressure P, is due to a mostly irreversible compaction by the isostatic mercury pressure. The curve of a sample submitted to the maximum available mercury pressure (200 MPa) is given on the figure 2 (curve b). It shows that above the characteristic transition pressure P,, the volume variation is due to the mercury intrusion into the pore network which has been not completely destroyed at pressure below 45 MPa. During depressufization, the mercury extrudes with an hysteresis and a certain quantity of mercury remains entrapped. Back at the atmospheric pressure, the recovered sample initially white became gray and the microscope .6 ...................................................... 1.4 -+- P max = 40 MPa

fi~ 1.2

-o- p max - 200 MPa o

0.8

T

o ;>

0.6

=

0.4

B

0.2 0

I

:=

0.01

O. 1

1 10 Pressure (MPa)

1 O0

1000

Mercury porosimetry curves (Cumulative pore volume versus pressure) Figure 2. obtained on high dispersive precipitated silica samples at maximum experimental pressure 40 MPa (curve a) and 200 MPa (curve b).

608

, 6

-

- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Sample without membrane 1.4 1.2 ~~

1

- r! . . . . . . . . . . . . . . . . . . . . . . .

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- ~ Sample with membrane o Sample with membrane (corrected data)

1

"~

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o 0.8

ooOOOO

l

o

/

0.6

"~ 0.4 ~ 0.2

0.01

.

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0.1

1 10 Pressure (MPa)

100

1000

Figure 3. Mercury porosimetry curves (Cumulative pore volume versus pressure) obtained on high dispersive precipitated silica wrapped in a tight membrane and the same material without membrane. examination shows that it contains a large amount of entrapped mercury. This mercury entrapmem is confirmed by the large mass increase of the sample. The mass increase divided by the mercury density (13.5 g/cm 3) and by the initial sample mass gives a specific volume variation of. 0.17 cm3/g. This value is identical to the specific volume variation (0.17 cm3/g) obtained by difference between the points A and B on mercury porosimetry curves (figure 2). A monolithic sample of precipitated silica wrapped under vacuum in a parafilm| membrane was measured by mercury porosimetry until a 200 MPa pressure. Figure 3 shows the volume versus pressure curve compared to the curve of the sample without membrane. The mercury porosimetry curves of a sample wrapped in a tight membrane and the same material without membrane are identical between 1 and 40 MPa. It confirms that the mechanism of volume variation in this pressure domain is truly crushing without intrusion. At pressures above 45 MPa, the two curves are very different as expected because the two mechanisms are different; for the sample wrapped in a membrane, the only possible mechanism is the crushing whereas it has been shown that the sample without membrane is invaded by mercury at pressures above 45 MPa. The weak difference between curves observed between 0.1 and 1 MPa can be attributed to a lack of suppleness of the membrane which cannot fit the rough surface of the monolithic sample of precipitated silica from the lowest pressures. The volume differences between the two curves which appear progressively below 1 MPa corresponds to the volume comprised between the surface of the sample and the membrane. This volume is

609 not a part of the sample. It has been deducted from the experimemal curve of the sample wrapped in the membrane to give the corrected curve shown in figure 3. 4. D I S C U S S I O N

Below 45 MPa, the high dispersive precipitated silica sample with or without membrane collapses without mercury intrusion. The buckling mechanism of pores edges can be assumed as in the case of low density xerogels. Consequently, equation (2) can be used to interpret the mercury porosimetry curve in this low pressure domain. The constant k~ to be used in equation (2) can be calculated from the Pt value using equation (4). With a mercury surface tension y 0.485 N/m, a contact angle 0 = 130 ~ and Pt - 45 MPa, one obtains ke = 86.3 nm MPa ~ Figure 4 shows the cumulative pore volume versus the pore size. Above 33 nm, this last value corresponding to the 45 MPa pressure, both distributions obtained from samples with and without membrane are obviously identical because it corresponds to two sets of data quasi identical analyzed by the same equation : the buckling equation (2). In the pressure domain from 45 to 200 MPa, the pore network of the sample without membrane is progressively intruded by mercury. These data can be interpreted using the Washburn equation (1). Whereas the sample wrapped in a membrane undergoes compaction and the data can be again interpreted by the buckling equation (2). As shown in figure 4 both sets of data adequately interpreted lead to a same pore volume distribution 1.6 ell

~

1.4

i

\

Cha~ge-of mech~ nism . . . . . . . .

1.2-

10

0.8 -~

\

O I:L

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-o- Sample with membrane

= 0.40.2O0

25

50

t

F

75 Pore size (nm)

100

....... ~. . . .

125

*

150

Figure4. Cumulative pore volume distribution versus pore size obtained on high dispersive precipitated silica wrapped in a tight membrane and the same material without membrane.

610 0.05 .................. Change ot' mechanisr

0.045 -

/1

0.04t~

eD

o

I

0.035-

--~ Sample without membrane

0.03 -

~

-o- Sample with membrane

$I

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t

0.02 -

'

t

0.015o

>

0.01 -

o

a~ 0 . 0 0 5 -

f

L

_

25

50

75 Pore size (nm)

100

125

150

Figure 5. Pore volume distribution versus pore size obtained on high dispersive precipitated silica wrapped in a tight membrane and the same material without membrane. Figure 5 shows the differential distributions versus pore size for the two sets of data. They are obtained by numerical differentiation of cumulative curves given on figure 4. They confirms more finely the identity of pore size distributions obtained from the two different curves by the adequate interpretation. The exponents which act on the pressure in the two equations (1) and (2) have also an effect on the pore size range concerned. For pressure varying from 45 to 200 MPa, intrusion mechanism gives access to pore diameters from 33 to 7.5 nm. In the same pressure range, the buckling mechanism collapses only pore sizes from 33 to 23 nm. 5. CONCLUSIONS High dispersive precipitated silica submitted to an increasing pressure in a mercury porosirneter shows successively a collapse mechanism of porous texture followed by a mechanism of mercury intrusion in the part of pore network which has resisted to the collapse. Such a behavior has been previously observed on low density xerogels and on some carbon black. Both mechanisms can be clearly distinguished by a sharp variation of slope of cumulative pore volume curve versus pressure. The pressure value Pt at the point of change of mechanism allows to calculate the strength resistance constant ke which links the pore size to the fourth root of pressure in the buckling equation. The use of this buckling equation (2) in the pressure domain where the material collapses and the Washburn equation (1) in the pressure domain where intrusion occurs allows to obtain a correct pore volume distribution in the whole pressure domain investigated.

611 Using a tight membrane wrapping the sample, it is possible to avoid any mercury intrusion into the sample. Then the collapse mechanism is responsible of all volume variation in the whole experimental pressure domain. The set of data obtained can be interpreted calculating the pore size from pressure using buckling equation in the whole pressure range. The pore size distribution obtained in that way is identical to the pore size distribution obtained from the sample pressurized without membrane by calculating pore size using the equation appropriate to the relevant mechanism in each pressure domain. This experiment confirms the good identification of successive mechanisms responsible for the volume variation. It confirms also that equation (2) proposed to interpret a mercury porosimetry curve when the sample collapses leads to a pore size distribution identical to which obtained from Washburn equation when mercury intrudes the pores.

Acknowledgments Authors thank "le Fonds National de la Recherche Scientifique, les Services de la Programmation de la Politique Scientifique and the Minist~re de la Rrgion Wallonne, Direction grnrrale des Technologies et de la Recherche" for their financial support.

RI~FI~RENCES 1 G.W. Scherer, D.M. Smith, and D. Stein, J. Non-Cryst. Solids. 1995, 186, 309-315. 2 T. Woignier, L. Duffours, J. Phalippou, P. Delord, V. Gibiat, J. Sol-Gel Sc. Technol. 1997, 8, 789-794. 3 R. Pirard, S. Blacher, F. Brouers, and J.P. Pirard, J. Mater. Res., 1995, 10, 2114-2119. 4 C.J. Brinker and G.W. Scherer, Sol-Gel Science (Academic Press, New-York, 1990) 5 R. Pirard, B. Heinrichs, J.P. Pirard, "Mercury porosimetry applied to low density xerogels" in "Characterisation of Porous Solids IV " B. McEnaney, T.J. Mays, J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger eds. The Royal Society of Chemistry, Cambridge, UK (1997) pp 460-466 6 R. Pirard, B. Sahouli, S. Blacher and F. Brouers "Sequentially compressive and intrusive mechanisms in mercury porosimetry of carbon black" in press ;J. Colloid Interface Sci. 7 D.M. Smith, G.P. Johnston and A. J. Hurd, J. Colloid Interface Sci. 1990, 133, 227-237

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Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000 ElsevierScienceB.V.All rightsreserved.

SYNTHESIS AND TEXTURAL SILICA-ALUMINAS

613

PROPERTIES

OF AMORPHOUS

C. Rizzo, A. Carati, M. Tagliabue, C. Perego EniTecnologie S.p.A., via Maritano 26, I- 20097 San Donato Milanese (MI) ITALY Since early 90's amorphous silica-aluminas with a narrower pore size distribution have been described by several research groups (1-4). Their application as acid catalysts has been described and also related to their textural properties (5-7). In the present paper silica-aluminas with controlled porosity in the region of micro- (ERS8 (3), SA), (micro)/meso- (MSA (2)) and meso- (MCM-41 (l), HMS (4)) pores have been synthesized by sol-gel method using different gelling agents. The textural properties of these samples have been determined by physisorption of N2 at 77.4 K and Ar at 87.3 K and evaluated by different models, comparing their effectiveness.

1. INTRODUCTION Porous materials have found great utility as catalysts for industrial applications. Textural properties are important in the field of catalyst design for heterogeneous catalysis. Surface area and pore size determine the accessibility to active sites and this is often related to catalytic activity and selectivity in catalysed reactions. Therefore textural properties are often a target of catalyst design. Molecular sieves (e.g. zeolites, alumino-phosphates) are interesting as catalytic materials and are characterized by a very narrow pore size distribution in the micropore region and by a crystalline structure. Amorphous silica-alumina materials represent an important class of porous inorganic solids which have not long-range order and usually have a wide distribution of the pore size, in the micro and mesopore region. They show outstanding catalytic behaviours in several acid catalysed reactions (5, 6). Since the materials are amorphous no structural data related to pore size can be obtained. Nevertheless information about the pore structure of these amorphous materials can be obtained by physisorption isotherms, that are able to discriminate between micro and mesoporosity and associated border line situations. Recently a strong synthetic effort has been devoted to developing amorphous silicaaluminas with controlled porosity, simultaneously new models for description of pore architecture have been studied. MSA (2) is an amorphous silica-alumina prepared via sol-gel from alkaline free mixture in presence of tetraalkylammonium hydroxide (TAA-OH). The pore size distribution is very narrow and centred at -~ 40 A mean pore width. The amount or the kind of T AA-OH plays a key role on textural properties of amorphous silica-alumina: pore size distribution can be modulated from meso (MSA) to microporous

614 (ERS-$) (3, 8). The latter is characterized by a broad peak in the low angle region of XRD pattern attributed to a very low structural order. MCM-41 (1, 9) has a hexagonal array of uniform mesopores, that is reflected in a set of peaks in the low angle XRD spectrum (2-10 of 20). The pore size can be systematically varied from 15 to 100 A. MCM-41 is generally prepared from alkaline synthesis using a selfassembled liquid crystal as templating agent. A similar material named HMS (4) was described and prepared using a primary alkylamine as a template. Object of this work is to compare samples of the amorphous silica-aluminas above described. All samples were prepared by sol-gel synthesis in alkali-free medium via a polymeric gel route involving alkoxide hydrolysis and condensation, catalysed by base or acid. Similar reactant mixtures were used in all preparations and only the type of gelling agent was changed. 2. EXPERIMENTAL SECTION

2.1. Catalyst preparation All samples were prepared via sol-gel from Si(OC2H5)4 (Dynasil A, Nobel), AI(i-OC3H7)s or Al(sec-OC4H9)3 (Fluka), ethyl alcohol (EtOH) and water. The gel formation was catalysed by aqueous alkali-free gelling agent (cetyitrimethylammonium hydroxide (CTMA-OH) or tetrapropylammonium hydroxide (TPA-OH) or tetrahexylammonium hydroxide (THA-OH) or dodecylamine (DDA)) or by acidic medium (HNO3). The gelling agents play several roles: they act as fillers, mineralised agents and counterions of AIO2 groups. After calcination, their decomposition produces H* as counterion of aluminum in tetrahedral coordination giving rise to material with acidic properties. All syntheses were performed at molar ratio SiO2/Ai203 = 100. The main synthesis parameters are summarized in Table 1. MSA: 2.7 g of AI(i-OCsH7)3 was dissolved at 60 ~ in 109.6 g of TPA-OH (12 wt % in aqueous solution). The solution was cooled to room temperature, then 138.8 g of Si(OC2H5)4 in 245.4 g of EtOH was added. After about 5 minute the monophasic clear solution was transformed in a homogeneous lightly opalescent gel. After 15 hour ageing at room temperature, the gel was dried at 100 ~ and calcined 8 hour in air at 550 ~ Table 1 Reagent mixture and product compositions Samples

Gelling agent (a) R/SiO2 ~a) (R) (molar ratio) ERS'8 (C6H13)4NOH 0.08 SA HNO3 0.01 MSA (C3H7)aNOH 0.09 MCM-41 (CH3)3CI6H33NOH 0.11 HMS C12H25NH2 0.27 Grace J63 9 (a) reagent mixture, SIO2/A1203--100 in all syntheses; (b) product

SIO2/AI203 0~) (molar ratio) 100 100 100 39 75 100

615 ERS-8 1.2 g of Al(sec-OC4H9)3 was dissolved at 60 ~ in 52.0 g of Si(OC2H5)4. The solution was cooled to room temperature, then added to 42.4 g of THA-OH (17 wt % in aqueous solution) and 92 g of EtOH. After about 24 hour the monophasic clear solution was transformed in a transparent gel. After 15 hour ageing at room temperature, the gel was dried at 100 ~ and calcined 8 hour in air at 550 ~ MCM-41 2.7 g of AI(i-OC3HT)3 was dissolved at 60 ~ in 149 g of CTMA-OH (15 wt % in aqueous solution). The solution was cooled to room temperature, then 138.8 g of Si(OC2H5)4 in 245.4 g of EtOH was added. The original solution gave rise to a progressive flocculation. After 15 hour ageing at room temperature, the sample was filtered, washed, dried at 100 ~ and calcined 8 hour in air at 550 ~ HMS: A solution of 34.7 g of Si(OC2H5)4, 25 g of EtOH and 0.9 g Al(sec-OC4H9)3 was added to dodecylamine (8.3 g) dissolved in EtOH (51. l g ) and H20 (13.5 g). A progressive flocculation was observed. After 15 hour ageing at room temperature, the sample was filtered, washed, dried at 100 ~ and calcined 8 hour in air at 550 ~ SA 1.5 g of Al(NO3)3*9H20 was dissolved in 72 g of an aqueous solution of HNO3 0.015 M. Then 41.7 g of Si(OC2H5)4 was added. After about 72 hour at room temperature the clear solution was transformed in a transparent gel. After 15 hour ageing at room temperature, the gel was dried at 100 ~ and calcined 8 hour in air at 550 ~ The synthesized materials were compared to a commercial silica-alumina gel, having 100 as SIO2/A1203 molar ratio, delivered by Grace (Grade J639).

2.2. Physico-chemicai characterization Textural characterization. The nitrogen and argon isotherms were obtained at liquid nitrogen and liquid argon temperature by using a Micromeritics ASAP 2010 apparatus (static volumetric technique). Before determination of adsorption-desorption isotherms the samples (--- 0.2 g) were outgassed for 16 h at 350 ~ under vacuum. The specific surface area (SRET) has been evaluated by full 3-parameters BET equation and 2-parameters linear BET plot in the range p/p~ 0.01-0.2. The total pore volume (VT) has been evaluated by Gurvitsch rule and by density functional theory (DFT) method. The micropore volume (Vm) has been determined by DFT, Dubinin-Radushkevich (D/R) and HorvathKavazoe (H/K) (Saito-Foley) equations at p/pO < 0.168. Pore size distribution has been calculated using DFT method for all materials. Indeed, DFT, based on molecular statistical approach, is applied over the complete range of the isotherm and is not restricted to a confined range of relative pressure or pore sizes. Pore size distribution is calculated by fitting the theoretical set of adsorption isotherms, evaluated for different pore sizes, to the experimental results. For instance Figure l shows the N2 experimental isotherm together with the DFT best fitting isotherm for MSA sample. BJH method, based on the Kelvin equation, was applied only for mesoporous materials in order to evaluate pore size distribution. 3. RESULTS AND DISCUSSION The chemical composition of the catalysts, determined by chemical analysis, is reported in Table I. The materials obtained by gelation (MSA, ERS-8, and SA) show the same SIO2/A1203 molar ratio of the reagent mixtures, according to the complete hydrolysis of the alkoxides and to the absence of separation phase during the preparation.

616 600

5OO

9 Experimental --

i-..

E

i

D F T t'~ting

4O0

0 lo ,,r r 2O0 = o

E
400 ~ ix. ~) 2 0 0 0"-

-

f L

_j~/i

800

c

o

E800

.....

.--~--9 Silica xerogel --0.-- Silica-alumina hydrogel --0~- Silica-alumina xerogel

-

IZ

-o 4 0 0

:

-

"0

200

; II

-

. . . . .

0

5 10 Pore radius (nm)

15

Figure 1 C 9 o m p a r i s o n o f the texture o f silica and

silica-alumina (hydrogels and xerogels) from cumulative volume curves

0

5 10 Pore radius (nm)

15

Figure 2 9Comparison of the texture of silica and silica-alumina (hydrogels and xerogels) from pore size distribution curves.

It can already be noted that the texture of silica gels (hydrogel and xerogel) is characterized by a very narrow pore size distribution while silica-alumina gels have a wider pore size distribution.

3.1.Effect of stirring ." The gels are maintained under stirring throughout the preparation process. The influence of stirring on the gel texture has been evaluated from the comparison of the texture of gels obtained with stirring or without stirring (except for the initial mixing of reactants), all others operating parameters remaining constant. The results summarized in table 1 are related to fresh hydrogels (one day) or to aged hydrogels (7 days). The continuous stirring during silica gelation has a weak influence on the texture of silica hydrogel, a slight broadening of the pore size distribution is only observed. So, the silica hydrogel obtained with continous stirring can be assimilated to a suspension of small pieces of the monolith which would be obtained without stirring, and each piece has a texture quite similar to that of the monolith.

626 Table 1 9Effect of stirring on the texture of fresh and aged silica hydrogels ' Stinted hydrogel Hydrogel ageing (days) Pore volume (mm3/g) Mean pore radius (nm) Pore surface(m2/g) Pore range(nm)

1 460 3 388 2.3-3.7

7 653 3.1 517 2.2-4.2

Non stirred hydrogel 1 496 2.7 491 2.1-3.1

7 537 3 459 2.2-3.5

..

,.

It is noteworthy that ageing has the same effect on the two kinds of gel (stirred or non stirred) : increasing of pore volume, surface and mean diameter, and broadening of the pore range. As a consequence, to avoid these undesirable texture modifications, thermoporometry measurements must be carried out as soon as possible after the preparation of hydrogel samples (within 24 hours).

3.2.Effect of silica gelation pH: The gelation pH of silica is well known to be effective on gel texture [ 1]. Table 2 allows to compare the texture of monolithic silica gels prepared in acidic (pH=5.4) or basic (pH=l 0.5) gelation conditions. Table 2 9Effect of gelation pH on the texture of monolithic silica hydrogels. ,,.

.

10.5

5.4

Pore volume (mm3/g)

i339

1936

mean pore radius (nm)

4.5

6.6

Pore surface (mZ/g)

614

,

pH

..,

602

1

,,

The effect of gelation pH on silica texture is complex. A low pH value favors the formation of small elementary particles of silica, which would lead to the formation of small pores in the resulting gel. But, when the pH of the sol-gel transition has the neutral pH value the silica gelation is very fast, the silica particles exhibit a broad size distribution and the resulting gel network has a wide open porosity (large pore volume and mean diameter). On the other hand, textural modifications observed in table 2 are not only attributable to the pH change. To obtain silica gelation at pH 5.4 the preparation procedure should be changed by inversing the adding order of reactants : while basic pH is obtained in pouring sulfuric acid in the silicate solution (initial pH 12.5), acid pH is obtained in pouring silicate solution in acid solution. In this way instantaneous gelation at neutral pH is avoided. Intrinsic effects of pH change on gel texture are described by results of table 3 which gives the main textural characteristics of silica and silica-alumina hydrogels prepared at two basic pH according to the same preparation procedure 9acid is poured in silicate under continuous stirring. The main effect due to a pH decrease is an increase of pore volume and radius. Another interesting fact appears in table 3 : textural modifications induced in silica hydrogel texture still exist in silica-alumina hydrogels.

627 Table 3 9Effect of pH gelation on the texture of stirred silica and silica-alumina hydrogels. Silica

Silica-alumina

pH

10.5

9.5

10.5

9.5

Pore volume (mm3/g)

516

687

1380

1450

mean pore radius (nm)

2.9

3.5

5.5

6.6

Pore surface (m2/g)

452

451

421

389

, - .

3.3.Effect of gel ageing: The slurry obtained after gelation of silica is maintained under moderate stirring during an ageing step. R.K. Iler [ 1] described several modifications of the silica gel network occuring during this period. Table 1 and curves of figure 3 show the texture evolution of a silica hydrogel aged in presence of its mother-liquor. It appears that pore radius, pore surface and pore volume increase with ageing time. This behaviour has been attributed to the phenomenon of dissolution and precipitation of silica. These phenomena, due to the presence of convex and concave curvatures in the silica gel network, strongly modify the gel texture. In presence of water (or aqueous salt solution) the silica phase is not stable.

1400

T

....

/

1200 -I/

-

I

......

. . . . .

I! ~

....

_--looo

&

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_

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E

"0

800 +

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1 day

' 3 days

7 days 152 days

II , ';

600

'

~, 4oo t"

:-.~ !/~ '/

II/'1/,,, :

0

I

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-------

,, ',

--

--

i --

3

day-i days

- - - - - - 7 days,

I

. . . . . . . ~"

0

2

4 6 Pore radius (nm)

8

10

Figure 3 : Effect of ageing time on texture of a silica hydrogel.

0

30 10 20 . Pore radius (nm)

40

Figure 4 : Effect of ageing time on the texture of a silica-alumina hydrogel.

As shown by curves of figure 4, the texture of a silica-alumina hydrogel, kept in suspension in its mother-liquor, does not change during ageing. This stabilising effect of alumina would be due to the blocking of intermicellar junctions of the silica gel network by incorporation of A10 4" tetrahedrons between SiO 4 tetrahedrons. This blocking phenomenon suggests that the textural evolution of silica hydrogels, observed during ageing, would be due to mass transferts through the grain boundaries. These transfers lead to an increasing of mean particle radius and mean pore radius. These results point out that ageing step offers a simple way to strongly modify the texture of silica hydrogels. A further precipitation of alumina in the aged silica gel stops the

628 modifications and leads to a mixed gel whose structure, and as a consequence the texture, is much more stable than the silica one.

3.4.Effect of alumina precipitation in silica hydrogel : A qualitative effect of alumina incorporation in silica has been described : alumina is a stabilizing agent for silica hydrogel texture. Thus, it is also interesting to study the effect of alumina content on the texture of silica-alumina gel. This alumina content is modified by adjustement of the amount of aluminium sulfate and, therefore, of the ammonia amount needed to precipitate the aluminium sulfate at constant pH (-~ 6). Table 4 and figure 5 depict the results obtained when alumina content increases up to 60 wt%. Table 4 : Effect of the alumina content on the texture of silica-alumina hydrogels Alumina content (wt%)

Pore v0'iume mm3/g

Mean pore radius nm

Pore surface m2:g

0 (pure silica) 5 9 25 36 60

516 768 1018 1380 1700 1007

2.9 3.4 3.2 5.5 4.8 6.1

452 523 533 420 367 284

H,..

,,,..

1000 8oo

E

- ~ 0 ~ Pure silica - . . . . . 5 wt% alumina -- .13-- lOwt% alumina 25 wt% alumina I" 36 wt% alumina - - . - X m 6 0 wt% alumina

I | ,, I I '; ! ~1; '~ I1~ ', t~,,

600

B

~~'400

I[

'

-

-

-

200 0 0

2

4

6

8 10 12 Pore radius (nm)

14

16

18

Figure 5 : Effect of the alumina content on the pore radius distributions of. silica-alumina hydrogels Precipitation of increasing amounts of alumina in the silica hydrogel leads to drastic modifications of the gel texture. Up to 10 wt% of alumina, silica-alumina texture is related to that of silica, although pore volume, pore radius and pore surface are more or less increased.

629 Above 10 wt% of alumina the pore size distribution broadens, pore surface decreases and pore volume reaches a maximum value for 36 wt% of alumina. Whatever the alumina content silica-alumina texture differs from that of silica gel. A NMR study of the incorporation of alumina in silica (not detailed in this paper) points out the existence of two aluminium species, A1TM and A1v~, and leads to the following conclusions [8]: for low alumina contents (< 10 %) alumina precipitation results in an isomorphic incorporation of A 1 0 4 tetrahedrons between the SiO4 tetrahedrons forming the elementary silica particles which constitute the gel network. That isomorphic substitution (A1TMspecies) does not induces important textural changes but creates surface acid sites of silica-alumina. for alumina content between 10 % and 40 %, part of alumina is not incorporated in the silica network but precipitates on the silica skeleton. The upper limit of incorporated alumina (A1TM) is reached for a total alumina content (A1~v and A1v~) near to 40 % and is found egal to 25 %. - for alumina content greater than 40 % precipitation of free alumina (A1w species) occurs in the cavities of the gel network. The silica-alumina gel is not only made up of a silica gel network in which A 1 0 4 tetrahedrons are incorporated. Indeed it results on the mixture of a silica-alumina framework partly covered with alumina bonded to silica and free alumina clusters. The silica hydrogel is a compliant material whose network building-up is not completed when alumina is added. So, alumina precipitation can easily modify the silica gel structure and induce drastic texture modifications. -

-

3.5.Effect of gelation temperature . The formation of silica from a sol-gel transition is a low activation energy reaction. Thus, it was only expected a slight effect of the preparation temperature on the gel texture (silica-alumina as well as silica). However, as shown in table 5, the effect of preparation temperature on the texture of silica and silica-alumina hydrogels is important. Table 5 9Effect of gelation temperature on hydrogel texture.

Pore volume (mm3/g) mean pore radius (nm) Pore surface (m2/g) ,,,,,,

20 ~

Silica 40 ~

353 2.7 342

516 2.9 452

60 ~

20 ~

691 4.4 358

1073 4.8 387

,,,

S il ica-alumina 40 ~ 60 ~ 1380 5.5 421

1476 5.6 387 ,,,

As temperature is increased from 20 ~ to 60 ~ pore volume and mean radius of silica and silica-alumina gels are increased, while pore surface remains quite constant. This can be explained from the increase of the diameter of elementary particles of silica (silica sol) induced by the temperature increase [1]. As a consequence, the mean pore radius increases (pores are cavities in the gel network and between the particles), the number of elementary particles decreases (solid content is constant) resulting to the increasing of the pore volume. The weak variations of pore surface could be due to compensating effects.

3.6.Effect of drying 9 Thermoporometry measurements allow to evidence the effects of operating parameters of the preparation process on the texture of hydrogels of silica and silica-alumina. As the aim

630 of our work is to prepare xerogels usable as supports of heterogeneous catalysts the hydrogels must be dried. Thus, two questions arise" 1. what is the effect of drying on the gel texture ..9 2. do the texture changes obtained on hydrogels still exist after the drying step ? Thermoporometry applying also on xerogels can give the answers. The effects of three drying modes on gel texture have been studied and compared : tray drying : 15 hours, in air at 125 ~ after drying xerogel water content is 21.3 wt%. This drying mode leads to very hard pieces which must be ground. freeze drying : 24 hours, under vacuum (pressure : 10 Pa) at -48 ~ xerogel water content is 20.4 wt%. A powder, constituted of polyhedric particles, is obtained. spray drying : 20 seconds, air temperature : 125 ~ ; xerogel water content is 27.1 wt %. The spray drying provides powders constituted of well shaped particles. -

-

-

Results concerning drying of silica gels are summarized in table 6, while results concerning silica-aluminas are in table 7. Comparison of curves of figure 1 and 2 also illustrates the effect of the drying on gel texture.

Texture

Table 96 .Effect of drying on the texture of silica gels. Hydrogel Spray drying Tray drying Freeze drying

Vp(mm3/g) Rp (nm) S (m2/g)

Texture

516 2.9 452

176 2.3 230

141 2.3 179

215 2.2 291

Table 7 9Effect of drying on the texture of silica-alumina gels. Hydrogel Spray drying Tray drying Freeze drying

Vp (mm3/g) 1380 Rp (nm) 5.5 S (m2/g) 420 Radius range (nm) 4.1 - 11

425 2.9 359 2.3 - 4.1

236 2.3 161 2.4 - 5.5

793 3.1 414 2.8 - 11.2

Whatever the drying mode and the hydrogel type (silica or silica-alumina) the drying induces a large shrinkage of the gel 9mean pore radius, total pore volume and pore surface are strongly reduced. However, the extent of textural modifications depends on the drying mode 9 the freeze drying is the less altering technique while the tray drying is the worst one. Texture modifications occur mainly during the first step of drying (the constant rate period) and are related to the visco-elastic properties of the gel network [6]. During the second step of drying (the falling rate period), liquid water leaves the capillaries and the pore walls can be damaged by forces linked to the existence of liquid-gas meniscus [6, 7]. In the absence of a liquid-gas meniscus, as it is the case for freeze drying (sublimation of ice), the solid-gas interface tension is weak and the porous volume decreasing due to the drying is smaller. When a meniscus exists at the liquid-gas interface in the pores, the observed textural evolutions agree with a shrinkage produced by capillary forces [7]. This case is well illustrated by the tray drying which conjugates a high drying duration, and a large and thick sample in which water concentration is heterogeneous during the drying. In the case of spray drying, liquid-vapor menisci also exist in the pores, but the material is divided in very small particles (d ~ 150 gm) leading to a very short drying duration (20 to 30 seconds), which, combined to a low drying temperature (solid temperature-90 ~ results into less detrimental shrinkage effects.

631 The drying mode and drying operating parameters must be carefully chosen to minimize the gel texture modifications. Table 8 depicts the effects of the preparation temperature on the texture of hydrogels and xerogels of silica and silica-alumina. As the preparation temperature is increased the pore volume and the mean pore radius of hydrogels as well as xerogels, are increased. Table 8 9Effect of gelation temperature on the texture of hydrogels and xerogels of silica and silica-alumina. Temperature Silica hydrogel Silica xerogel Silica-alumina Silica-alumina ~ hydrogel xerogel Vp R V~ R ... Vp R Vp R 60 809 4.1 487 2.2 2170 7.8 897 3.8 ,,,,

20

568

3

141

1.7

1751

5.6

554

2

From these results it can be concluded that the modifications generated in the silica hydrogels are altered by the drying step, but they still exist in the silica xerogels. They are also observed on the silica-alumina hydrogels and, finally, on the silica-alumina xerogels. Although undesirable changes can occur at each step of the preparation procedure of silica-alumina, textural modifications deliberately generated in the silica hydrogels can be preserved. 4. CONCLUSION As thermoporometry is suitable for hydrogel as well as for xerogel materials, it has been possible to study the effects of the operating parameters of the preparation process on the texture of silica and silica-alumina and to follow the changes carried out by each step of the process. Large textural modifications occur during the precipitation of alumina in silica hydrogels and during the drying step. It has been demonstrated that the texture modifications generated at the beginning of the process (silica hydrogel formation) still exist in the dried end-product (silica-alumina xerogel). The knowledge of the influence of each preparation step allows a better mastering of the texture of the end-product. The silica hydrogel network constitutes the framework of the silica-alumina gel. From a textural point of wiev, a silica-alumina xerogel seems to be an "image" of the starting silica hydrogel. Depending on the alumina content the silica-alumina gels exhibit predominantly a silica-like texture or an alumina-like texture. REFERENCES 1. R.K. Iler in "The Chemistry of Silica" (John Wiley and sons, New-York 1979). 2. C.J. Planck and C.L. Drake, J. Colloid. Sci. 2 (1947), 399. 3. S.A. Mitchell, Chem. Ind. (1966), 924. 4. A.G. Forster and J.M. Thorp in "The Structure and Properties of Porous Materials" (D.H. Everett and F.S. Stone Eds., Butterworths, London 1958), 227. 5. J. Dumas, J.F. Quinson and J. Serughetti, J. Non Crystal. Solids, 125 (1990), 244. 6. C.J. Brinker and G.W. Scherer, Sol Gel Science (Academic Press, San Diego 1990), p.454. 7. G.W. Scherer, J. Amer.Ceram. Soc. In Sol-Gel Science (Academic Press Inc; Boston 1990), pp 453-513. 8. I. Bia7, Thesis, Paris VI l Jniversitv, 1999.

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Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) ,92000 ElsevierScienceB.V. All rightsreserved.

633

COMPARISON OF SPECIFIC SURFACE AREAS OF A MICRONIZED DRUG SUBSTANCE AS DETERMINED BY DIFFERENT TECHNIQUES

M. Sautel, H. Elmaleh and F. Leveiller Rh6ne-Poulenc Rorer (RPR), Vitry-Alfortville Research Center, Department of Pharmaceutical Sciences, Preformulation, 13, quai Jules Guesde, BP 14, 94403 Vitry sur Seine Cedex, France Abstract : Drug Substance (DS) Specific Surface Area (SSA), porosity and Particle Size

Distribution (PSD) are important physical characteristics for pharmaceutical applications. For instance the DS surface area can greatly influence the dissolution rate which, in turn, might affect bioavailability. Several analytical methods can be used to charactefise the DS and determine the powder SSA : measurements by gas adsorption (BET method) and gas permeametry (Blaine Fisher method) and calculation from PSD obtained by laser light scattering or from Mercury Intrusion Porosimetry (MIP) curves. In this study we have compared surface areas measured by gas permeametry or gas adsorption with SSA calculated from PSD obtained by laser light scattering or from MIP curves for the case of a low specific surface area micronized DS (SSA in the range of 1 to 3 m2/g). Correlation between specific surface areas measured using a simple and robust technique such as gas permeametry and SSA determined by more sophisticated techniques such as PSD, MIP and BET have been carried out. A good agreement between SBv (surface measured by gas permeametry, Blaine Fisher, SBF) and measured SBETwas obtained. This is due to the fact that the DS studied does not exhibit intraparticular microporosity (both Krypton and air can access all the surface developed by the powder). SBF compared with estimated SHg (estimated from MIP results) and SvsD (estimated from PSD results) show a good lineafity, but SHg and SpsD values are overestimated. This arises due to the simplifying approximations for particles shape included in the theoretical models for PSD and PIM. Although BF provides a direct SSA measurement, the techniques of PSD, MIP and gas adsorption provide complementary information on texture characteristics to better understand and interpret results from process and formulation development studies. However, in some cases, BF can be considered as a complete and adequate quality control method which can easily be set to work within the frame work of production control provided that the method has been validated and applies well to the powder studied.

634 ,Introduction

9

Characterisation of the porous texture and the particle size distribution of powders is of great importance for pharmaceutical applications. There is therefore an increasing need to determine powders properties in view to explain, monitor and control their physical quality. The complexity of the porous texture of materials is such that it generally requires the combined use of several techniques, each of them providing different information [1]. For instance, the specific surface area (SSA) can be determined either by applying a simple technique such as permeabilimetry or by using more sophisticated techniques such as laser light scattering measurement, Mercury Intrusion Porosimetry (MIP) and gas adsorption. Those techniques generally give access to several physical parameters and a wide range of information to yield insights on the phenomena involved in the application of the powder studied. This is illustrated here in the case of a micronised DS for which SSA determination has been found to be relevant for its intended application. All four above mentioned techniques have been applied. A comparison and discussion of the obtained results considering the simplifying assumptions specific to each method have proved to be useful for understanding the micronized DS powder texture and for selecting a relevant quality control method.

Materials

and methods

:

9 Specific surface area (SSA) by gas permeametry

Measurements have been carried out using a Blaine Fisher permeabilimeter (95 Sub-SieveSizer). In this technique, the resistance to fluid flow through a compressed bed of powder is measured and the fineness of the powder is estimated from determination of d, the mean diameter of particles from 0.2 to 50~tm. This mean diameter is then converted in powder's SSA using equation (1), considering the SSA as a sum of hypothetical envelopes around particles. The internal porosity is not taken into account. Mathematical formulas necessary for calibration of the apparatus are derived from the works of Gooden-Smith and Carman [2].

SBu where p is the powder bulk density.

~

6

(1)

635 9Specific surface area (SSA) by gas adsorption

Specific surface areas (expressed in mVg) were measured by Krypton adsorption at 77K (Micromeritics ASAP2400) and calculated using BET equation [3]. Prior to measurements, powder specimens were outgassed under vacuum (5 millitorrs) at room temperature. Krypton was chosen as adsorbate because of the low SSA of some samples (SSA