Studies in Surface Science and Catalysis 128 CHARACTERISATION OF POROUS SOLIDS V
This Page Intentionally Left Blank
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
Amsterdam--- Lausanne m N e w York--- O x f o r d - - Shannon m S i n g a p o r e - - Tokyo
ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands 92000 Elsevier Science B.V. All rights reserved. This work is protected under copyright by Elsevier Science, and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use. Permissions may be sought directly from Elsevier Science Rights & Permissions Department, PO Box 800, Oxford OX5 1DX, UK; phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail:
[email protected]. You may also contact Rights & Permissions directly through Elsevier's home page (http://www.elsevier.nl), selecting first 'Customer Support', then 'General Information', then 'Permissions Query Form'. In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA; phone: (978) 7508400, fax: (978) 7504744, and in the UK through the Copyright L~censing Agency Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London W1P 0LP, UK; phone: (+44) 171 631 5555; fax: (+44) 171 631 5500. Other countries may have a local reprographic rights agency for payments. Derivative Works Tables of contents may be reproduced for internal circulation, but permission of Elsevier Science is required for external resale or distribution of such material. Permission of the Publisher is required for all other derivative works, including compilations and translations. Electronic Storage or Usage Permission of the Publisher is required to store or use electronically any material contained in this work, ~ncluding any chapter or part of a chapter. Except as outlined above, no part of this work may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the Publisher. Address permissions requests to: Elsevier Science Rights & Permissions Department, at the mail, fax and e-mail addresses noted above. Notice No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, ~nstructions or ideas contaaned in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made.
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
This Page Intentionally Left Blank
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
This Page Intentionally Left Blank
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
This Page Intentionally Left Blank
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
<
,'
2.0 H/nm
2.5
3.0
1.0
1.5
2.0 H/nm
2.5
3.0
Figure 4. Components of the isosteric enthalpy as a function of pore widtE The symbols for the high pressure isobars in the top panels are the same as those for the fight hand panel in figure 3. For the low pressure isobars, in the fight hand graph for q,,,, the symbols correspond to those for the left hand (low pressure) isobars in figure 3. can be associated with the character of the potential well over this range of pore widths. At H=O.8mn, there is a deep single potential well at the centre of the slit, between 0.9nm and 1.1nm, this degenerates into two minima separated by a shallow maximum that gradually increases in height. Beyond a pore width of about 1.2nm, the dense adsorbate becomes more strongly localised close to one of the walls at this temperature. From figure 4 it can be seen that there is a very clear contrast in the behaviour of qm over the range of pore widths from 0.9nm to 1.1nm. At low pressures qmdecreases over this range, but increases at higher pressures as the packing goes from predominantly two-dimensional to three-dimensional. Presumably the higher pressures are sufficient to compensate for the extra kinetic energy in the system which is therefore dominated by increasing intermolecular potential energy at higher dimensionality. The combined effect is to produce strong minima and maxima at H=0.9nm and 1. lnm respectively over the higher range of pressures.
2.2. Composite isotherms Composite enthalpy curves and isotherms have been constructed for a number of model micropore distributions, from the equations:
~pu Hi Fi ZH~ F,
(1)
P ( f g=
~p,j qr H, F, ~-,Pq H, F,
(2)
q(fJ)=
16
12
24
10
.
.
.
.
.
2 bar
~_. H/nm ~.o
~.5
45
2~ O"
~6
tO
16
~
~ , ~
(. -----
~
,7 20 .. oo
~10 05
50
lo 100
f/bar
15
0 ~ 150
0
2
4
6
8
p/nm "3
Figure 5. Composite isotherms and enthalpy curves for a set of distributions with skews ranging from strongly negative(I) to strongly positive (5) shown as the upper inset in the left hand graph. The lower inset shows the isotherms over the fugacity range 0-2bar. In the right hand graph, the upper panel shows the isosteric enthalpy, the lower panel shows the qw and qm components. The latter all pass through zero, the maximum difference between these is less than lkJ mo1-1, and is not clearly resolved on this scale. The broken line labelled 2 bar is an approximate indication of the densities at this fugacity.
where/9o and q~ are the database densities and enthalpies tbr a slit of width H, at a ti~acity ot~, and Fi is the distribution. A simple triangular shape was chosen for all the distributions, both symmetrical and skewed distributions were included, and the range of pore widths was varied so as to include or exclude the smallest slit widths and both wide and narrow ranges of pore sizes. A selection from these distributions, and the corresponding isotherms and enthalpy curves, is shown in figures 5 and 6. Figure 5 illustrates the effects of skewing the distributions; five distributions are shown ranging from highly negative (1) through to highly positive (5). The adsorption isotherms are not well resolved over the whole pressure range, but the effects of skewing are apparent when these are shown over a range from 0 to 2 bar. The most notable feature is the curvature introduced by strong negative skewing. It should be noted that all of the excess isotherms for this system pass through maxima at about 40 to 50bar. The enthalpy curves, by contrast, exhibit characteristic shapes. For the most positively skewed distribution there is a maximum; this is a consequence of two effects, a strong initial increase in qm, due to intermolecular interactions in the smallest pores (not clearly discernible on the scale of these figures), and a high initial qw which gradually decreases as the smallest pores become filled. As the skewing becomes more positive, qw falls more rapidly, since there are few small pores with very high adsorption energies, and these are filled at the lowest pressures. As the skewing moves towards the positive side, the maximum becomes suppressed and the initial decrease in qst becomes steeper. This trend is very largely associated with the changes in q~. In the positively skewed distnqgutions, there is only a small fraction of very small (and strongly adsorbing) pores available, these become filled at low density and subsequent
17 12
18 1
10
o
8
r
...'
......>--~..
'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
3. HYSTERESIS IN CANONICAL MONTE SIMULATIONS _ .4r..0.4._ . . . . . . .m~ ....... o ...... - - .e - ~
.o
0.4
o"
. .. d - - o :
-o a.+~-
GRAND CARLO
. . . . . . o
It has been known for m a n y years t h a t in grand canonical Monte p Carlo (GCMC) simulations of s y s t e m s exhibiting vapor-liquid transitions, single phase isotherms can be continued to s u p e r s a t u r a t e d states. Numerous examples of this have also been reported in studies of capillary condensation in single pores (see, for x/x o example, Peterson and Gubbins, 1987 or Walton and Quirke, 1989). Schoen et al. (1989) have argued, in our view Figure 3. Adsorption]desorption isotherms of correctly, t h a t m e t a s t a b l e states in density vs. relative activity for a Lennard-Jones GCMC simulations of fluids in pores 12-6 model of methane in a silica xerogel with occur because of a failure to sample a=1.5 (open circles) and a=l.8 (closed circles) at fluctuations causing the phase change. T*=0.7. In principle the grand ensemble should deliver a s h a r p first order transition for a sufficiently large system, as was first explained in an elegant analysis of a lattice gas model by Lee and Yang (1952). In GCMC simulations near phase transitions between states of very different density, we will observe hysteresis if the algorithm used does not efficiently sample the large density fluctuations necessary to pass from one phase to the other. This is the case with the Metropolis (1953) algorithm, the standard approach to Monte Carlo simulations, which changes the system configuration by moving, adding or deleting one molecule at a time. Indeed, in the statistical physics c o m m u n i t y the development of Monte Carlo algorithms for lattice models which eliminate the hysteresis near phase transitions - essentially by introducing moves which can m a k e very large changes in the d e n s i t y - is an active area of research (Swendsen and Wang, 1987; Wolff, 1989). ....o"
:
9
o
.:
~'
.O
0.2
~'
J
O'
g ..
O 9
ie'~ ~
0
.."
~
D
9
,
,
I
0. l
,
,
,
,
I
0.2
~ ,
,
,
I
0.3
,
~ ,
,
I
0.4
. . . .
I
,
0.5
Schoen et al. (1989) further argue t h a t since hysteresis in the simulations represents in some sense a failure of the Metropolis algorithm, there is unlikely to
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.
This Page Intentionally Left Blank
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~
38 fluid shows only faint change in freezing point against pressure as described by the almost vertical solid-liquid coexistence. Thus the observed depression in freezing below saturated vapor line is thought to be with significant change in a pressure felt by the capillary fluid.
4.3. Mechanism and simple model The capillary effect can be the origin of the abovementioned great change in the pressure: Within nanoscale pores the reduction in pressure may reach up to hundreds of atmospheric pressure in general. Here we try to model this effect with a simple concept of continuum media with isotropic pressure. Again, we understand that this is not scientifically correct in nanoscale pore where direction-dependent pressure should prevail, but our aim here is to establish a simple model for understanding and estimating the freezing in
!
,.., 1.0
I
I
I
(a) Density
~= 0.9 0
> 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 <
~ IE~
-!-2.5 v tL
E
cJ A
|
3 2
i
E 9~1E417
,
llM}9
0
0
5
10
15
20
25 30
35
40
45
50
Po~ ~Idth ~
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 m carbon slits at 77 K [8].
4
8
12
16
20
24
28
32
Pore W i d t h
36
40
(A)
Figure 2." Comparison of PSDs obtained for a Saran char from nitrogen (dashed fine) and argon (sofid fine) porosimetry at 77 K using DFT [16].
43 good agreement with exact simulation results. However, it should be born in mind that DFT or simulation provide an answer only to approximation 2 above. As presently applied, the difficulty of describing the pore topology remains. In this paper we give a very brief account of the methods (Sec. 2). We then show some examples of applications, and compare these more fundamental methods with others in general use. 2. DENSITY FUNCTIONAL T H E O R Y (DFT) Each individual pore has a fixed geometry, and is open and in contact with bulk gas at a fixed temperature. For this system, the grand canonical ensemble provides the appropriate description of the thermodynamics. In this ensemble, the chemical potential p, temperature T, and pore volume V are specified. In the presence of a spatially varying external potential V~, the grand potential functional .(2 of the fluid is [ 11 ] f2Lo(r)] - f L ~ r ) ] - ~ d r p ( r ) [ p - V~(r)] (4) where F is the intrinsic Helmholtz free energy functional, ,o(r) is the local fluid density at position r, and the integration is over the pore volume. F is expanded to first order about a reference system of hard spheres of diameter d, 1
b - ~ r)] - Fhh[,O(r);d] + 2 ff drd~ ,o(r),o(t J )r
- r'[)
(5)
where Fh is the hard sphere Helmholtz free energy functional and ~a, is the attractive part of the fluid-fluid potential. In eq. 5, we have invoked the mean field approximation, wherein pairwise correlations between molecules due to attractive forces are neglected. The attractive part of the fluid-fluid potential is represented by the Weeks-ChandlerAndersen division of the Lennard-Jones potential r ([r - r'[) - r (Ir - r 1), Ir -r'[ > rm (6)
Ir-r'l where rm=2~/6crffis the location of the minimum of the Lennard-Jones potential. The hard sphere term Fh can be written as the sum of two terms, Fh[p(r);d] - kT~drp(r)[ln(A~p(r)) - 1] + kT~ drp(r)f~[~r);d] (7) where A = h/(2nmkT) l/z is the thermal de Broglie wavelength, m is the molecular mass, h and k are the Planck and Boltzmann constants, respectively, and f,x is the excess (total minus ideal gas) Helmholtz free energy per molecule. The latter is calculated from the Camahan-Starling equation of state for hard spheres [12]. The first term on the fight side of eq. (7) is the ideal gas contribution, which is exactly local (i.e. its value at r depends only on p(r)); the second term on the fight is the excess contribution, which is nonlocal. The density ~(r) that appears in the last term of (12) is the smoothed or nonlocal density, and it represents a suitable weighted average of the local density p(r), p ( r ) - ~d~ p(r' )w[Ir- e l ; ~ r ) ] (8) The choice of the weighting function w depends on the version of density functional theory used. For highly inhomogeneous confined fluids, a smoothed or nonlocal density approximation is introduced, in which the weighting function is chosen to give a good description of the hard sphere direct pair correlation function for the uniform fluid over a
44 wide range of densities. Tarazona's model [13] is the one most commonly used for the weighting function. This model has been shown to give very good agreement with simulation results for the density profile and surface tension of LJ fluids near attractive walls. The Tarazona prescription for the weighting functions uses a power series expansion in the smoothed density. Truncating the expansion at second order yields 2
w[lr - r'l: P(r)]- E w ([r - r'l)~=~(r)'
(9)
1=0
Expressions for the weighting coefficients w are given by Tarazona et al. [13]. The equilibrium density profile is determined by minimizing the grand potential functional with respect to the local density, ~p(r)] = 0 at p - Peq (10) 8p(r) A numerical iteration scheme is used to solve this minimization condition for peq(r) for each set of values of (T,/z,H); the hard sphere diameter is determined from the Barker-Henderson prescription [ 14] for each temperature. 3. COMPARISONS OF DFT AND OTHER PORE FILLING MODELS
Several independent studies support the conclusion that DFT is a better model for adsorption in micropores than classical thermodynamics models. Because a detailed knowledge of the morphology of porous adsorbents is usually not available, molecular simulation results for ideal model adsorbents have frequently been used as a standard for evaluating the relative merits of the different pore filling models. One such comparison is shown in Fig. 1 for nitrogen adsorption on model carbon slit pores at 77 K. The modified Kelvin method severely overestimates the micropore filling pressures, whereas the DFT method yields a pore filling correlation that is in very close agreement with the "exact" molecular simulation results. Also shown in Fig. 1 is the Horvath-Kawazoe (HK) pore filling correlation, an analytic adsorption model often used for micropore PSD analysis [15]. The HK method gives a more realistic micropore filling correlation than the Kelvin-based methods; however, the HK model still substantially overestimates micropore filling pressures, as shown by comparison to simulation results. The principal shortcoming of the HK model is that it assumes the adsorbate density is uniform everywhere in the slit pore. In fact, the density profile of a confined fluid is highly structured, and this error leads to an underestimation of the heat of adsorption in the HK model, and consequently an overestimation of the pore filling pressures. An additional test of the robustness of the DFT method is the consistency of PSDs calculated from adsorption experiments using different adsorbates to probe the pore volume. The mean pore diameters of activated carbons obtained from nitrogen and argon porosimetry have been found to agree to within about 10% using DFT as the pore filling model [16]. One such comparison is shown in Fig. 2. Another study [17] reported greater differences in the PSDs computed from DFT models of nitrogen sorption on carbons at 77 K and high-pressure methane sorption at 313 K. The differences were attributed to the quadrupolar interactions of nitrogen with defect sites or heteroatoms on the carbon surface.
4~ In another investigation [ 18], the PSDs obtained using the Dubinin-Stoeckli (DS) [19], HK and DFT methods were compared for a series of activated carbons with different activation times (the longer the time, the greater the microporosity). The HK and DFT methods correctly predict an increase in the micropore PSD as activation time increases, while the DS method does not. The authors ran a second test, in which a mock isotherm was generated via molecular simulation for a graphitic carbon having a Gaussian distribution of pore sizes. The three models were applied to this "experimental" data to see if the original PSD could be recovered (Fig. 3). In most cases, the shape of the Gaussian PSD was not reproduced by the analysis routines. However, DFT performed the best in recovering the PSD maxima for distributions centered in the micropore range. Pore filling model comparisons have also been reported for other porous solids. The inside pore diameters of MCM-41 type adsorbents have been calculated to a high degree of consistency from nitrogen and argon porosimetry (Fig. 4) by using a DFT model of gas adsorption in cylindrical oxide pores to interpret the experimental isotherms [20]. By combining the DFT analysis of the sorption isotherm with X-ray diffraction data on the pore spacing, the pore wall thicknesses of a set of MCM-class adsorbents were determined. These thicknesses were found to be consistent across the set of adsorbents, which lends further strong evidence to the validity of the DFT adsorption model. The Kelvin and modified Kelvin equations, by contrast, overestimate the condensation pressures of nitrogen in cylindrical oxide pores [21 ]. 4. APPLICATIONS OF DFT/MOLECULAR SIMULATION TO PSD ANALYSIS DFT and molecular simulation methods have been applied to the analysis of adsorbents in two main capacities. For nonporous adsorbents, DFT can be used to provide a local isotherm F(P,e) in order to solve eq. (2) for the distribution of site energies on the adsorbent surface [1]. A sample result is shown in Fig. 5 for the site energy distribution of a heterogeneous activated carbon obtained from DFT analysis of the nitrogen sorption isotherm. In applications of DFT to the characterization of porous solids, the surface of the adsorbent is generally assumed to be chemically homogeneous, and the PSD of the adsorbent is then obtained from solution of eq. (1). Results have been reported for MCM-41 pore diameters using nitrogen or argon as the adsorptive at cryogenic temperatures [20-21 ]; and for activated carbon PSDs using nitrogen [6,17], argon [ 16], or helium [22] at 77 K and carbon dioxide at 273 K [23]. Monte Carlo molecular simulation has also been employed to interpret PSDs from supercritical adsorption isotherms of methane and other gases on activated carbons [24-25]. The advantage of using hightemperature (>300 K) isotherms for PSD analysis is that the potentially complicating effects of slow mass transfer and multipole interactions at low temperatures can be avoided. The disadvantage is that the isotherms for mesopores become indistinguishable at supercritical temperatures, whereas at cryogenic temperatures, capillary condensation provides a distinct "fingerprint" of mesopore size.
Figure 3: Cumprism of PSDs o b w mirg the DubinilcSrwckii @IS), H ~ K a w 4 2 0 e @K,,
and &rrsiity *ti& riseoPyPm=-fo interpret an isdAenn generacscificnn, ?nO'kcflh
of m'bagen a&mptim in a m d ? I carbon thrrt has an ihamian dkwibuiion of srir p e widths [la]. ~ a r e ~
sim&lim
meanw w~of8.9A (def l )1169 A (riglaif).
f
w
47 5. CONCLUSIONS It is important to bear in mind that the pore filling models currently in most frequent use (Kelvin, HK, DFT) are all limited by the same assumptions regarding pore geometry, chemical homogeneity, neglect of connectivity, and so forth. At present, DFT is the best available model for the determination of micropore PSDs. Validation against molecular simulation results has established that DFT offers a realistic model of pore filling in chemically homogeneous solids with simple pore geometries. DFT and molecular simulation provide much improved accuracy in predicting the local isotherms in eqs. (1) and (2). They give good results for a wide range of temperatures (including supercritical) and over the full pressure range, in contrast to methods based on the modified Kelvin equation or Horvath-Kawazoe model. However, they involve more computational effort than the older methods. At the present time, DFT is more convenient to use than simulation, because of the computational demands of the latter. However, we expect this situation to change fairly rapidly as computer power increases. Molecular simulation has the advantage that it can be readily applied to more complicated adsorbate molecules, and particularly to more complex pore topologies [26]. This is not the case for DFT. In addition, it may be valuable to apply these methods to other properties besides adsorption isotherms, e.g. structure factor measurements by x-ray or neutron diffraction, and heats of adsorption. Nicholson and Quirke [27] have shown that the use of isosteric heat data provides more reliable PSD determinations. As noted in the introduction, the solution of the Fredholm integral of eqs. (1) and (2) is an ill-posed inverse problem. Consequently, the solution to the PSD can be very sensitive to perturbations in the experimental adsorption data [26]. Some investigators have therefore used regularization to recast the ill-posed adsorption integral of eq. (1) into a well-posed problem. This is done mathematically by introducing additional constraints into the solution technique (e.g. least-squares minimization) to find the PSD. The effect of introducing regularization is to "smooth out" the PSD, as shown in Fig. 6 for a range of smoothing parameter values employed in fitting the PSD of activated carbon to methane adsorption data. An apparent lack of agreement between two reported PSDs for a given material, therefore, may depend as much on whether regularization techniques were used in finding the PSD, as on what pore filling model was used in solving eq. (1). To avoid such confusion, a standard protocol for the use of regularization in PSD analysis should in the near future be developed for the characterization of porous solids. Since the DFT and molecular simulation methods provide an effective solution to approximation 2 of the introduction, the major challenge facing characterization methods is how to develop improved models for the pore topology (approximation 1). Most of the current methods omit effects of heterogeneity other than pore size, as well as connectivity effects. The latter are likely to prove important, since there is evidence that phase transitions such as capillary condensation are strongly affected by networking. A method of simultaneously determining the PSD and network connectivity of a porous solid has recently been suggested, in which adsorption isotherms from a battery of probe gas experiments involving different adsorbates are measured [25]. Each adsorbate probes a different region of pore volume, based on steric exclusion in the micropores, as shown in Fig. 7. By combining the PSD results for the individual probe gases with a percolation model, an estimate of the mean connectivity number of the network can be obtained.
48
00"t t
~ n, o~
fl
bl
i.. ~ ' - ~
It~
Figure 6: PSDs obtained for methane adsorption in square model carbon pores using molecular simulation to interpret an activated carbon isotherm. PSD results are shown for regularization smoothing parameter values of I (solid line), 10 (open circles), 100 (open diamonds), 600 (filled circles), and 800 Oqlled diamonds) [25].
I
I~
15 ~,lum
trs
Figure 7: PSDs obtained using grand canonical Monte Carlo (GCMC) molecular simulation to interpret CH4, CF4 and SF6 adsorption isotherms on activated carbon at 296 K [24].
New approaches based on novel molecular simulation techniques are now emerging which are able to provide much more realistic models of the porous structures. These may be classified into two types: (a) those in which the experimental procedures used to fabricate the material are mimicked in the simulation, and (b) methods based on the use of experimental structural data (small angle scattering data, TEM, etc.) to build model structures that are significantly more sophisticated than simple slit and cylindrical pore models. An example of the first approach is the recent use of quench MD methods to mimic the spinodal decomposition of a liquid mixture of oxides to produce porous silica glasses (controlled pore glass and Vycor) [9,10]. The resulting glasses have a pore topology, pore size distribution, porosity, surface area and adsorption isotherm behavior that closely match those of experimental glasses. An example of approach (b) is the use of off-lattice reconstruction methods [28,29] with TEM data to build more realistic models of porous glasses. In this method a model material is constructed based on the volume autocorrelation function obtained from TEM data. A method that is similar to this in spirit is the use of Reverse Monte Carlo techniques to match the structure of model activated carbons to that obtained from small angle x-ray or neutron data [30]. Method (a) has the advantage that it gives a unique structure, but it requires a different approach for each new class of materials. Method (b) can be applied to a range of materials, but does not yield a unique structure in general. How important this nonuniqueness is for adsorption work remains to be evaluated. It may be possible to alleviate the non-uniqueness problem by using more than one experimental property in the structure determination. At present these methods are in the earliest stage of development, and are highly computer intensive. However, the computer effort needed will decrease rapidly over the next few years as computers become faster. Further
49 development of these methods for a range of types of porous materials could lead to much more sophisticated characterization methods in the next decade. In the case of a particular class of materials, such as porous silica glasses, it would be straightforward to prepare a range of material samples with differing mean pore size and porosity, and to simulate a variety of adsorption and structural experiments on these. The computer could then match the properties of a given experimental material against those of the model materials in the data bank. Provided the models are realistic this should produce an accurate characterization; structure factor, TEM images, mean pore size, surface area, porosity and so on would be available for the model material. The resulting model material could then be used to predict other adsorption properties. Under such a scenario no knowledge of advanced simulation techniques or of statistical mechanics would be needed on the part of the user. Such more realistic models of porous materials can also be used to rigorously test existing characterization methods. The model material is precisely characterized (we know the location of every atom in the material, hence the pore sizes, surface area and so on). By simulating adsorption of simple molecules in the model material and then inverting the isotherm, we can obtain a pore size distribution for any particular theory or method. Such a test for porous glasses is shown in Figure 8, where the exactly known (geometric) PSD is compared to that predicted by the Barrett-Joyner-Halenda (BJH) method, which is based on the modified Kelvin equation. Finally, we note in closing it may be possible to retool some of the simpler adsorption models to improve their predictive capabilities for modeling micropore adsorption. A new method, combining the Kelvin equation with an improved model of the statistical adsorbed film thickness or "t-curve", has recently been proposed [31 ]. This 0.08 . . . . . . . . . . . . . . . . . .
0.06 ~
"
~
o,o,,'
1
O.OB
"A"
'
,
1 \
, 5
0
7
..................
0.06, - ....
0.06
;',
0.o4
~ . ' ~ 3 4
2
....................
0.08
i
,"
.._.__~/
0.00 . . . . . . . . . 0
/~
I'
:"" "
,
BJH
0.02 0.00
lB.
.I . . . . .
'
/
1 ,,
..__j.----/"__"
0
I
2
3
,
: \
4
'
5
6
7
0.08
"C"
0.06
"D"
.D
o,o,
0,00
~,i-.,
0
I
o.o~
,,
" 2 3 4 5 ~ m e ~ r (rim)
6
7
o.oo
:"
'
' ,,,'7-"\
0
I
2 3 4 5 r ~ m m ~ r (rim)
,
6
7
Figure 8: PSDs for model porous silica glasses [10]. A, B, C, D are sample glasses prepared by Quench Molecular Dynamics, and differ in mean pore size and porosity. The solid curves are the exact geometric PSDs for the models; the dashed lines are PSDs predicted by analyzing simulated nitrogen adsorption isotherms for these materials using the BJH method (a form of the modified Kelvin equation). The BJH method gives mean pore sizes that are too small by about 1 nm in each case.
50 computationally efficient method yields pore filling pressures in remarkably close agreement with DFT results, except for very narrow micropores. A problem, however, is that such "fixes" are likely to be strongly dependent on the materials and adsorbates used.
Acknowledgments. We thank the National Science Foundation (grants CTS-9733086 and CTS-9712138) for support of this research and for a NRAC grant (MCA 93S011) which provided supercomputer time. CML thanks the Beckman Coulter Corporation.
REFERENCES 1. J.P. Olivier, in F. Meunier (ed.), Funds. of Adsorp. 6, p. 207-211, Elsevier, Paris, 1998. 2. J.R. Fisher and J.N. Israelachvili, J. Colloid Interfac. Sci., 80 528 (1981). 3. S.M. Thompson, K.E. Gubbins, J.P.R.B. Walton, R.A.R. Chantry, and J.S. Rowlinson, J. Chem. Phys., 81 (1984) 530. 4. B. Peterson, J. Walton and K. Gubbins, J. Chem. Soc. Far. Trans. 2, 82 (1986) 1789. 5. J.P.R.B. Walton and N. Quirke, Molec. Simulation, 2 (1989) 361. 6. C.M. Lastoskie, K.E. Gubbins and N. Quirke, J. Phys. Chem., 97 (1993) 4786. 7. C.M. Lastoskie, K.E. Gubbins and N. Quirke, Langmuir, 9 (1993) 2693. 8. C.M. Lastoskie, N. Quirke and K.E. Gubbins, in W. Rudzinski, W.A. Steele, and G. Zgrablich (eds.), Equilibria and Dynamics of Gas Adsorption on Heterogeneous Surfaces, Studies in Surf. Sci. & Catal., Vol. 104, p. 745, Elsevier, Amsterdam, 1997. 9. L.D. Gelb and K.E. Gubbins, Langmuir, 14 (1998) 2097. 10. L.D. Gelb and K.E. Gubbins, Langmuir, 15 (1999) 305. 11. R. Evans, Adv. Physics, 28 (1979) 143. 12. N.F. Carnahan and K.E. Starling, J. Chem. Phys., 51 (1969) 635. 13. P. Tarazona, Phys. Rev. A, 31 (1985) 2672: P. Tarazona, U. Marini Bettolo Marconi and R. Evans, Mol. Phys., 60 (1987) 573. 14. J.A. Barker and D. Henderson, J. Chem. Phys., 47 ( 1967) 4714. 15. G. Horvath and K. Kawazoe, J. Chem. Eng. Japan, 16 (1983) 474. 16. R. Dombrowski, D. Hyduke and C.M. Lastoskie, submitted to Langmuir (1999). 17. N. Quirke and S.R.R. Tennison, Carbon 34 (1996) 1281. 18. D.L. Valladares, F. Rodriguez-Reinoso and G. Zgrablich, Carbon 36 (1998) 1491. 19. H.F. Stoeckli, J. Coll. Int. Sci., 59 (1977) 184. 20. A.V. Neimark, P.I. Ravikovitch, M. Grun, F. Schuth and K.K. Unger, J. Coll. Int. Sci., 207 (1998) 159. 21. P.I. Ravikovitch, G.L. Hailer and A.V. Neimark, Adv. Coll. Int. Sci., 76 (1998) 203. 22. A.V. Neimark and P.I. Ravikovitch, Langmuir, 13 (1997) 5148. 23. P. Ravikovitch, A. Vishnyakov, R. Russo, A. Neimark, submitted to Langmuir (1999) 24. V.Y. Gusev, J.A. O'Brien and N.A. Seaton, Langmuir, 13 (1997) 2815. 25. M. Lopez-Ramon, J. Jagiello, T. Bandosz and N. Seaton, Langmuir, 13 (1997) 4435. 26. G.M. Davies and N.A. Seaton, Carbon 36 (1998) 1473. 27. D. Nicholson and N. Quirke, in COPS V Proceedings, in press (1999); D. Nicholson, Langmuir, in press (1999). 28. P. Levitz, Adv. Colloid andlnterfac. Sci., 76 (1998) 71. 29. R. Pellenq, P. Levitz, A. Delville and H. van Damme, COPS V Proc., in press (1999). 30. K. Thomson and K.E. Gubbins, paper in preparation (1999). 31. C. Nguyen and D.D. Do, Langmuir, 15 (1999) 3608.
Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 2000 ElsevierScienceB.V. All rightsreserved.
51
Density Functional Theory of Adsorption Hysteresis and N a n o p o r e Characterization Alexander V. Neimark and Peter I. Ravikovitch TR//Princeton, 601 Prospect Av., Princeton, NJ, 08542-0625,
[email protected]
Canonical ensemble density functional theory (CEDFT) has been employed for predicting hysteretic adsorption/desorption isotherms in nanopores of different geometries in the wide range of pore sizes (1 - 12 nm). It is shown that the CEDFT model qualitatively describes equilibrium and spinodal transitions and is in a reasonable quantitative agreement with experiments on well-characterized MCM-41 samples. A DFT-based method for calculating pore size distributions from the adsorption and desorption branches of nitrogen adsorption isotherms has been elaborated and tested against literature data on capillary condensation in MCM-41 samples with pores from 5 to 10 nm.
1. INTRODUCTION The problem of adsorption hysteresis remains enigmatic after more than fifty years of active use of adsorption method for pore size characterization in mesoporous solids [1-3]. Which branch of the hysteresis loop, adsorption or desorption, should be used for calculations? This problem has two aspects. The first is practical pore size distributions calculated from the adsorption and desorption branches are substantially different, and the users of adsorption instruments want to have clear instructions in which situations this or that branch of the isotherm must be employed. The second is fundamental: as for now, no theory exists, which can provide a quantitatively accurate description of capillary condensation hysteresis in nanopores. A better understanding of this phenomenon would shed light on peculiarities of phase transitions in confined fluids. Essential progress has been made recently in the area of molecular level modeling of capillary condensation. The methods of grand canonical Monte Carlo (GCMC) simulations [4], molecular dynamics (MD) [5], and density functional theory (DFT) [6] are capable of generating hysteresis loops for sorption of simple fluids in model pores. In our previous publications (see [7] and references therein), we have shown that the non-local density functional theory (NLDFT) with properly chosen parameters of fluid-fluid and fluid-solid intermolecular interactions quantitatively predicts desorption branches of hysteretic isotherms of nitrogen and argon on reference MCM-41 samples with pore channels narrower than 5 nm. In this paper, we demonstrate that the NLDFT model provides also a good agreement between calculations and experiments for both adsorption and desorption branches of nitrogen
52 isotherms on newly synthesized enlarged MCM-41 materials with pore channels in the range from 5 to 10 nm [8-10]. Based on the recently developed [11] canonical ensemble density functional theory (CEDFT), we concluded that in this range of pore sizes the experimental desorption corresponds to the equilibrium evaporation while the experimental capillary condensation corresponds to the spontaneous (spinodal) condensation. Two kernels of theoretical isotherms in cylindrical channels have been constructed corresponding to the adsorption and desorption branches. For a series of samples [8-10], we show that the pore size distributions calculated from the experimental desorption branches by means of the desorption kernel satisfactory coincide with those calculated from the experimental adsorption branches by means of the adsorption kernel. This provides a convincing argument in favor of using the NLDFT model for pore size characterization of nanoporous materials provided that the adsorption and desorption data are processed consistently. 2. CANONICAL ENSEMBLE DENSITY FUNCTIONAL THEORY OF CONFINED FLUIDS In this paper we employ the canonical ensemble density functional theory (CEDFT) [ 11]. Conventional versions of the DFT imply minimization of the grand thermodynamic potential with respect to the fluid density within fixed solid boundaries at a given temperature T and chemical potential ft. They correspond to the grand canonical (g-V-T) ensemble and are below referred to as GCEDFT. The proposed CEDFT implies minimization of the Helmholtz free energy at a fixed amount of molecules in the pore, N, given temperature T and pore volume V, i.e., in the N-V-T ensemble. Therewith, the chemical potential of the sought equilibrium state is determined in the process of minimization. The resulting adsorption isotherm N(,u, T)traces all equilibrium states including stable and metastable states along the hysteresis loop, which can be obtained with the GCEDFT, and also unstable states inside the hysteresis loop. The obtained isotherms are alike to the van-der-Waals S-shaped isotherms of bulk phase transitions with the backward regions corresponding to the unstable states. These unstable states cannot be realized in a physical or a numerical experiment unless density fluctuations, which drive the system to one of the metastable or stable states, are completely suppressed. The experimental conditions, which may lead to the S-shaped isotherms, were recently discussed by Everett [ 12]. In the CEDFT, the density fluctuations are suppressed by fixing the total amount of fluid molecules in the confinement. As a typical example of CEDFT calculations, we present in Fig. 1 the capillary condensation isotherm of N: in a cylindrical pore mimicking the pore channel in MCM-41 mesoporous molecular sieves. The isotherm is presented in co-ordinates adsorption N versus chemical potential ~t. Calculations were performed at 77 K for the internal diameter of 3.3 nm up to the saturation conditions, point H. We used Tarazona's representation of the Helmholtz free energy [6] with the parameters for fluid-fluid and solid-fluid interaction potentials, which were employed in our previous papers [7]. We distinguish three regions on the isotherm. The adsorption branch OC corresponds to consecutive formation of adsorption layers. Note that the sharp transitions between the consecutive layers are not observed in experiments. They are caused by a well-known shortcoming of the model employed, which ignores intrinsic to real
53 materials geometrical and energetical pore wall heterogeneities. The desorption branch EH corresponds to liquid-like states of condensed fluid. The descending region CE corresponds to unstable states, which cannot be observed in a real experiment. The turnover points, C and E, are the points of spinodal transitions. The fight-most point C of the adsorption branch is the point of spontaneous capillary condensation. At this point, the adsorption layer becomes unstable and the system must jump onto the desorption branch at any experimental conditions. The lett-most point E of the desorption branch is the point of spontaneous evaporation. At this point, the liquid-like state of condensed fluid becomes unstable at any experimental conditions and the system must jump onto the adsorption branch. The points, B and F, of equilibrium transitions,/A, can be defined from the Maxwell's rule of equal areas by integrating along the S-shaped isotherm between the coexisting states: NF(/ze)
f l.tdg - ,u e ( g F - g 8 ) . NB(Ia,)
1
....
0.9
Grand potential
0.8 0.7
t~l::
=f
U
Canonical DFT isotherm -0.5
F
G
-1
H
-
0.6 0.5-J
0
-1.5 ~t:, -2
E
0.4
-2.5 d
0.3
-3
0.2
-3.5
0.1
-4
0 -3
-2.5
-2
-1.5
-1
-0.5
0
~t-m, [k'r'] Figure 1. Nitrogen in a 10 crff (Dmt=~l=3.3 nm) cylindrical pore of MCM-41 at 77.4 K. The chemical potential of equilibrium transition BF, !.tc-~=-1.42 kT, is obtained from the Maxwell's rule and also corresponds to the intersection point of the Grand Potential (solid line). Lines CG and EA, which bound the hysteresis loop, correspond to the spinodal condensation and desorption, respectively.
54 The shape of the isotherm depends on the pore size and temperature. As the temperature increases and/or the pore size decreases, the hysteresis loop becomes narrower and disappears at certain critical conditions. The adsorption and desorption isotherms have been calculated for the N2 sorption at 77K in cylindrical pores of MCM-41 materials in the range 1 - 12 nm. The points of spinodal and equilibrium transitions are plotted in Fig. 2. There are several features worth noticing. As the pore size increases, the line of spinodal desorption saturates at the value corresponding to the spinodal decomposition of the bulk liquid. The line of equilibrium capillary condensation asymptotically approaches the Kelvin equation for the spherical meniscus and the line of spontaneous capillary condensation asymptotically approaches the Kelvin equation for the cylindrical meniscus. This asymptotic behavior is in agreement with the classical scenario of capillary hysteresis [12]: capillary condensation occurs spontaneously after the formation of the cylindrical adsorption film on the pore walls while evaporation occurs after the formation of the equilibrium meniscus at the pore end. Most interestingly, the NLDFT predictions of equilibrium and spontaneous capillary condensation transitions for pores wider than 6 nm are approximated by the semi-empirical equations of the Derjaguin-Broekhoff-de Boer theory [13]. 0.9
oOO~
0.8
9 NLDFT equilibrium transition
0.7 0.6
o NLDFT spinodal condensation
o 0.5
n NLDFT spinodal desorption
0.4 0.3
, ~ ^ A A A A A
A A A~
A AA
0.2
-•
Broekhoff-de Boer (desorption) Broekhoff-de Boer (adsorption)
0.1
10
20
30
40
50
60
70
80
90
100 110 120
Pore size, A
Figure 2. The pore size dependence of the relative pressure of equilibrium condensationevaporation (black squares), spinodal condensation (open squares), and spinodal desorption (open triangles) of nitrogen at 77K in cylindrical pores of MCM-41 materials. The Broekhoffde Boer approximation [ 13] for condensation (solid line) and desorption (crosses) in cylindrical pores is plotted for comparison.
55 3. COMPARISON WITH EXPERIMENTS
Earlier, we have made the following general conclusions regarding the capillary condensation in cylindrical pores [7]. The reversible isotherms in sufficiently narrow pores and the desorption branches of hysteretic isotherms in wider pores correspond to the equilibrium transitions predicted by the NLDFT. The adsorption branches of hysteretic isotherms lie inside the theoretical hysteresis loop. The metastable states on the theoretical desorption branch are not observed. These conclusions were made based on analyses of limited experimental data on reference MCM-41 materials with pores of diameter < 5nm. Sayari et al. [8-10] have recently synthesized enlarged MCM-41 samples with pore diameters from 5 to 10 nm. The N 2 isotherms on these samples are presented in Figs. 3-6 in comparison with the theoretical loops for cylindrical pores of average size, formed by the metastable adsorption branch and the equilibrium desorption branch. The experimental and theoretical hysteresis loops are in a perfect qualitative agreement.
{I
CALCULATIONS OF PORE SIZE DISTRIBUTIONS FROM ADSORPTION AND DESORPTION BRANCHES
We have constructed two kemels of theoretical isotherms in cylindrical channels corresponding to the metastable adsorption and equilibrium desorption branches. These kemels were employed for calculating pore size distributions from experimental isotherms following the deconvolution procedure described elsewhere [7,14]. In Figs.7-8 we present the pore size distributions in the MCM-41 samples [8-10] calculated from the experimental desorption branches by means of the desorption kemel and the pore size distributions calculated from the experimental adsorption branches by means of the adsorption kernel. The experimental isotherms published in [8-10] were used for calculations. The pore size distributions obtained from the desorption and adsorption branches practically coincide, which confirms that the NLDFT quantitatively describes both branches on the adsorptiondesorption isotherm.
5. ESTIMATES OF STRUCURAL PARAMETERS OF MCM-41 TYPE SAMPLES FROM ADSORPTION AND DESORPTION BRANCHES Structural parameters of the MCM-41 materials calculated by means of the NLDFT method from the experimental isotherms published in [8-10] are listed in Table 1. We note a perfect agreement between the results obtained from the desorption and adsorption branches of the isotherms. It is interesting to note, that the pore wall thickness (12-18 A) of wide-pore MCM-41 materials is larger than that usually obtained for conventional MCM-41, and tends to increase with the pore diameter. This is consistent with the results of Stucky et al. [15], who estimated the pore wall thickness of a 60 A hexagonal material to be-17 A.
56
0.045 0.04 0.035 0.03 O
E E 0.025 E O ".= 0.02 o w
o9 0.015
M-4i- (des) --
0.01
~
MCM-41 (ads)
0.005 t
~
NLDFT (des) in a 51.2 A pore NLDFT (ads) in a 51.2 A pore
.,,.
.
0
0.2
.
.
.
.
0.4
.
.
P/Po
.
0.6
.
.
.
.
.
0.8
Figure 3. Comparison of the NLDFT N2 isotherm in a 5.1 nm cylindrical pore at 77 K with the isotherm on a wide-pore MCM-41 sample (a 0 = 6.37 nm, see Table 1) [8, 9].
0.045 0.04 0.035 '~
0.03
0
E E 0.025 =f O "= 0.02 Q. i.. 0
'~ ,,K 0.015 - - ~ MC_,M-41-(ads-)
0.01
--o-- MCM-41 (des) - ~ - NLDFT isotherm (des) in a 55.2 A pore
0.005
, 0
0.2
NLDFT isotherm (ads) in a 55.2 A pore 0.4
P~o
0.6
0.8
1
Figure 4. Comparison of the NLDFT N2 isotherm in a 5.5 nm cylindrical pore at 77 K with the isotherm on a wide-pore MCM-41 sample (a 0 = 6.8 nm, see Table 1) [9].
57
0.045 0.04 0.035 0.03 O
E E ff
0.025
O
0.02
n L O W
"o
0.015 0.01
MCM-41 (des) NLDFT des. isotherm in a 58 A pore
0.005 i
NLDFT ads. isotherm in a 58 A pore
,
0. 0
0.2
0.4
P~o
0.6
0.8
1
Figure 5. Comparison of the NLDFT N2 isotherm in a 5.8 nm cylindrical pore at 77 K with the isotherm on a wide-pore MCM-41 sample (a 0 = 7.61 nm, see Table l) [9].
0.08 0.07
--e--Experimental (ads) --e--- Experimental (des)
0.06
N ~
.
o
0.05
E
0.04
E
.2
~
NLDFT des. isotherm in a 90 A pore .
a.
o .r
0.03 0.02 0.01 0 0
0.2
0.4
0.6
0.8
1
PIP0
Figure 6. Comparison of the NLDFT N2 isotherm in a 9 nm cylindrical pore at 77 K with the isotherm on a wide-pore MCM-41 sample (see Table 1) [ 10].
58
0.14 a0=63.7 A (DES) ...~.. a0=63.7 A (ADS)
0.12
a0=68 A (DES) i ~
0.1
m
...j
..
a0=68 A (ADS) a0=76.1 A (DES)
m 0.08
w
E
."
a0=76.1 A (ADS)
.......
U
o9
0.06 "'A...&
"0
0.04
0.02
g.
.'1
'. "
------
----
30
.
'&
v - - w - -
40
50
60
_
.
70
.
.
.
.
80
Internal pore size, A
Figure 7. The pore size distributions of MCM-41 samples [8-9] shown on Figs. 3-5 calculated from adsorption (dotted lines) and desorption (solid lines) branches of nitrogen isotherms by the NLDFT method.
0.35 .. - 0 - f r o m DESORPTION branch
0.3
- ~ - from ADSORPTION branch 0.25 e~
E
0.2
U
=~ 015 "0
0.1
0.05 0
~
40
'
~
"
.
60
.
,
80
100
120
Internal pore size, A
Figure 8. The pore size distributions of the-9 nm sample [l 0] calculated from adsorption and desorption branches of nitrogen isotherm by the NLDFT method.
59
Table 1 Pore structure parameters of enlarged MCM-41 materials [8-10]
ao,
SBET,
Vp,
code
A
m2/g
cm3/g
5.5
63.7
880
1.0
ads des
6.0
68
880
1.07
6.5
76.1
764
9.0
n/a
1050
Sample
Vporr,
Sporr,
cm3/g
m2/g
A
A
0.97 0.97
790 800
-52 -51
-12 - 13
ads des
1.04 1.04
800 805
-54 -54
-14 -14
0.97
ads des
0.96 0.95
690 690
-58 -58
-18 -18
2.38
ads des
2.2 2.2
1000 1010
-89 -87
n/a
at P/Po=0.9
Branch
Dp DFT
dwalD
5.5, 6.0 and 6.5 are sample codes used in Ref. [9] ao = 2/~3 dl00 is a distance between pores calculated from X-ray diffraction data assuming hexagonal unit cell [8-9]. SBETWas calculated using the molecular cross-sectional area of N2, 0.162 nm2/molecule. Vp is a pore volume determined from N2 isotherms at P/Po=0.6 using the bulk liquid nitrogen density. Vp~ and So~ are the pore volume and the pore surface area, respectively, calculated from the NLDFT method. Dp~ is an average pore diameter estimated from the pore size distributions. dw,~l= a0- Dp~ pore wall thickness assuming cylindrical pores
6. CONCLUSIONS The non-local density functional theory (NLDFT) with properly chosen parameters of fluid-fluid and fluid-solid intermolecular interactions quantitatively predicts both adsorption and desorption branches of capillary condensation isotherms on MCM-41 materials with the pore sizes from 5 to 10 nm. Both experimental branches can be used for calculating the pore size distributions in this pore size range. However for the samples with smaller pores, the desorption branch has an advantage of being theoretically accurate. Thus, we recommend to use the desorption isotherms for estimating the pore size distributions in mesoporous materials of MCM-41 type, provided that the pore networking effects are absent.
60
Acknowledgment This work is supported by the TRI/Princeton exploratory research program and Quantachrome Co. AVN thanks the Alexander von Humboldt Foundation for a travel grant.
REFERENCES 1. D.H. Everett, in The Solid-Gas Interface, E.A. Flood (ed.), Marcel Decker, New York, vol. 2, (1967) p.1055 2. S.J. Gregg and K.S.W. Sing, Adsorption, Surface Area and Porosity, Academic Press, London, 1982. 3. F. Rouquerol, J. Rouquerol, and K.S.W. Sing, Adsorption by Powders and Porous Solids: Principles, Methodology and Applications, Academic Press, San Diego, 1999. 4. M.W. Maddox and K.E. Gubbins, Int. J. of Thermophysics, 15 (1994) 6. 5. A. de Keizer, Th. Michalski, and G.H. Findenegg, Pure & Appl. Chem., 10 (1991) 1495. 6. P. Tarazona, U. Marini Bettolo Marconi, and R. Evans, Mol. Phys. 60 (1987) 573. 7. A.V. Neimark, P.I. Ravikovitch, M. Grtha, F. Schiith, and K.K. Unger, J. Coll. Interface Sci., 207 (1998) 159. 8. A. Sayari, P. Liu, M. Kruk, and M. Jaroniec, Chem. Mater., 9 (1997) 2499. 9. M. Kruk, M.; Jaroniec, A. Sayari, Langmuir, 13 (1997) 6267. 10. A. Sayari, M. Knak, M. Jaroniec, I.L. Moudrakovski, Adv. Mater., 10 (1998) 1376. 11. A.V. Neimark and P.I. Ravikovitch, in Microscopic Simulations of Interfacial Phenomena in Solids and Liquids, P. Bristowe, S. Phillpot, J. Smith, D. Stroud (Eds.), MRS Symposium Proceedings Series, v.492, pp.27-33, 1998. 12. D.H. Everett, Colloids and Surfaces A, 141, (1998) 279. 13. J.C.P. Broekhoffand J.H. de Boer, J. Catal., 9, (1967) 8; 10 (1968) 153; 10 (1968) 368. 14. P.I. Ravikovitch, Ph.D. Thesis. Yale University, 1998. 15. G.D. Stucky, Q. Huo, A. Firouzi, B.F. Chmelka, S. Schacht, I.G. Voigt-Martin, F. Schtith, Stud. Surf. Sci. Catal., 105A, (1997) 3.
Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) 2000 Elsevier Science B.V. All rights reserved.
61
Characterization of Controlled Pore Glasses" Molecular Simulations of Adsorption
Lev D. Gelb and K. E. Gubbins Department of Chemical Engineering, North Carolina State University 113 Riddick Labs, Raleigh, NC 27695-7905 Using a recently developed molecular dynamics procedure, we have prepared a series of models of controlled pore glasses with a range of porosities and pore sizes. Nitrogen adsorption isotherms have been obtained in these models using a parallelized version of the Grand Canonical Monte Carlo simulation technique. These isotherms can be analyzed with standard methods to obtain pore size distributions and surface areas, which can be compared with exact results obtained from the model glasses' atomic structures. In this study, we also measure the partial structure factors for the gas adsorbed in the model glasses at different pressures, and discuss the relationships between features in these data and the pores' geometry.
1.
INTRODUCTION
Although the practice of obtaining pore size distributions (PSDs) of amorphous materials from adsorption and desorption isotherms is quite common and has been in use for many years, the microscopic interpretation of these distributions is often difficult. Nearly all such methods realy on a model-based approach in which the isotherm data is fitted with a distribution of model pores parameterized by very few (usually one, e.g., radius) variables [1 ]. The resulting PSD is dependent both on the isotherm and the model, and only for trivial cases where the material can be so simply described can this curve be interpreted microscopically. That is, if the material itself consists of a collection of unconnected "ideal" cylindrical (or slit-shaped) pores, then a PSD obtained by, say, density functional theory analysis based on cylindrical [2] (or slitshaped [31) pores can be unambiguously interpreted as the original material's distribution of cylinder radius. For any more complex material, in which the pores may be of finite length, of non-uniform diameter, or are not su'aight, the model-based isotherm analysis may still be applied, but the results are no longer simply related to the microscopic structure of the material. These ambiguities are difficult to resolve experimentally, because the microscopic structure of amorphous porous materials is generally not available. Computer simulation is an appealing way to approach this sort of problem, because the results of simulated isotherm analyses can be compared against geometric analyses of the exactly know simulated pore structures. If the computer model of the adsorbent under study is realistic, qualitative (and perhaps quantitiative) results from this approach should be relevant for the
62 corresponding experimental system as well. We have previously used this approach in critical studies of the BET method for surface area estimation [4] and the Barrett-Joyner-Halenda (BJH) method of pore size distributions 15]. We have developed a structurally realistic computer model for controlled pore glasses, and generated several example materials of different pore sizes and porosities. In this paper, we compare information on pore size obtained from geometric analysis of the models, BJH analysis of simulated nitrogen isotherms, and calculatcd adsorbate structltrefactors at both low and high coverages. We lind that for these materials BJH pore size distributions are qualitatively similar to geometric ones, but are quantitatively too sharp and shifted to lower pore sizcs. The adsorbate structure factors show a low-k peak at low coverages which corresponds well with the average pore size from geometric analysis, while at pore filling the structure factors reflect longer-ranged correlations between different parts of the void space.
2.
PREPARATION OF GLASS MODELS
The preparation of controlled pore glasses (CPGs) is based on the near-critical phase separation of a binary liquid mixture, which produces complex networked structures [6]. The original preparations of CPGs were done by Haller [7], who partially phase-separated a mixture of SiO2, Na20 and B203 and etched out the boron-rich phase, leaving a nearly pure silica matrix with a porosity between 50% and 75% and an average pore size as large as 400 nm [8]. The dynamic separation of two immiscible liquid phases is called spinodal decomposition. For liquid mixtures quenched at near-critical mole fractions, this process results in highly connected, interspersed domains of each phase. The growth of the average domain size is given by a simple power law which does not depend on the particulars of the liquid mixture. (For mole fractions far from critical, phase separation proceeds by the condensation of droplets of the minority phase; since these are isolated within the majority phase, this process cannot be used to prepare porous materials.) We prepare models of porous glass by simulating the phase separation of a binary mixture after a quench using molecular dynamics, as a rough approximation of the experimental preparation recipe. The network structures produced by such a quench are insensitive to the specific properties of the liquid mixture, so that the use of a simplified model lluid is still expected to produce materials with the correct topology. This procedure is schematically shown in Figure 1; the simulation details are given in our previous paper [4], except that in this study the simulation cells were all largel, measuring 27 nm on each side and containing 868,000 atoms of the quench mixture. In this study we consider four porous materials. Models (a) and (b) are approximately 50% porous, with mean geometric (see below) pore sizes of 3.23 nm and 4.95 nm, respectively. Models (c) and (d) are approximately 30% porous, with mean geometric pore sizes of 2.76 nm and 4.63 nm, respectively. In order to obtain a pore size distribution and an average (or most probable) pole size directly from the material structure, we proceed by considering the sub-volumes of the system accessible to spheres of different radii 151. Let Vpor~(r) be the volume of the void space "coverable" by spheres of radius r or smaller; a point x is in Vl~,re(r) if and only if we can construct a sphere
63
Fig. 1. Schematic of model generation. Quench molecular dynamics simulations of a binary mixture (top) produce a series of networked structures which are processed into adsorbent models (bottom, shown in cutaway view.) The longer the quench is allowed to proceed, the greater the resulting pore size. The porosity of the model materials is determined by the mole fraction of the quenched mixture. of radius r that overlaps x and doesn't overlap any substrate atoms. This volume is equivalent to that enclosed by the pore's "Connolly surface" 191. Vpore(r) is a monotonically decreasing function of r, and is easily compared with the "cumulative pore volume" curves often calculated in isotherm-based PSD methods I101. The derivative - d V p o r e ( r ) / d r is the fraction of volume coverable by spheres of radius r but not by spheres of radius r + d r , and is an effective delinition of a pore size distribution [ 11 !. The Vpore(r) function can be calculated by a Monte Carlo volume integration. For a material composed of ideal spherical, cylindrical or slit-shaped pores, this analysis yields the exact distribution of pore radii or slit widths. Pore size disu'ibutions obtained in this way for the four materials used in this study are shown in Figure 5. In order to simulate the adsorption of nitrogen in these model pores, we represent the nitrogen molecule with a single Lennard-Jones sphere, with potential parameters GN --0.375 nm and eN/kB -- 95.2 K [ 12]. The parameters for the substratc atoms are set to G - 0.27 nm and E/kB -230 K, which have been used to represent bridging oxygens in silica [ 13]. The Lorenz-Berthelot mixing rules are used to give the inter-species parameters. All potential energy functions in the adsorption simulations were cut and shifted at a radius of 3.5G; no long-range con'ections were used [141. The simulations are performed using a variant of the parallelized Grand Canonical Monte Carlo algorithm suggested by Heffeltingcr and Lewitt [15l, and were generally run on IBM SP2 or Cray T3E supercomputers using 27 processors.
64
10.0
o - - - o (A) E:]---~ (B)
* - - - . (c) (D)
3
12)
..,,_
0
E E I.
5.0
I ! I
0.011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.0 0.2 0.4 0.O
....
018
i
1.0
P/P0 Fig. 2. Adsorption isotherms in all four model systems. F is the Gibbs excess adsorption. The pressures corresponding to the three configurations shown in Figure 3 are marked with arrows. The pressure is plotted relative to the vapor pressure of the model lluid, as determined by independent Gibbs Ensemble Monte Carlo simulations. Chemical potentials were converted to pressures using a virial equation of state.
3.
RESULTS AND ANALYSIS
Adsorption isotherms at 77 K were simulated for each model material. These data are shown in Figure 2. These isotherms all show standard Type IV behavior characteristic of mesoporous materials. They are described well by BET-type models at low pressures, with capillary rises at high pressures and pore filling at pressures near saturation. The (a) and (b) models have considerably higher maximum adsorption than the (c) and (d) models due to their higher porosity. The (a) and (c) models both have capillary upswings at relative pressures around 0.6, while the (b) and (d) models, which have larger pores, show sharper capillary rises between relative pressures of 0.7 and 0.8. Snapshots from GCMC simulations in the (a) model are shown in Figure 3. At low pressures, nearly all the adsorbed gas is found very near to the pore surface, while at higher pressures a thick multilayer state is found, with the local layer thickness varying with the local pore geometry. Narrow sections of the pore network are completely blocked at the highest pressure shown in this figure. For each complete adsorption isotherm obtained, we applied the BJH method [10] to obtain an isotherm-based pore size distribution. The supplementary data (reference isotherm, surface tension, vapor pressure, and molar volume) were obtained tbr the same model fluid in separate
65
Fig. 3. Snapshots of adsorption in the (a) system. These are configurations fi'om equilibrated GCMC simulations at three pressures conesponding to a sub-monolayer coverage, monolayer coverage, and two layers' coverage (neaJ" to pore filling). The light colored particles are the model nitrogen molecules, and the dark material is the adsorbent. simulations [5]. These pore size distributions are shown in Figure 5. The isotherm-derived PSDs are comparable with the geometric data, but are all shifted to slightly lower pore sizes, and are all considerably sharper. Note that the geometric PSDs for the (b) and (d) models are not as smooth as for the smaller-pore (a) and (c) models; this occurs because the (a) and (c) models contain a statistically larger sample of pore network. The isothe~Tn-derived data do not follow this trend; this may be due to the use of a relatively small number of points on each isotherm, or it may be due to a lack of sensitivity of the method. At both low and high adsorption for each system, we calculated the fluid-fluid radial distribution function g(r). From this the fluid-fluid partial structure factor can be obtained through
S ( k ) - l+4~;p
f
r2(g(, " ) - 1)
sinkr kr dr.
(1)
Examples of these curves are shown in Figure 4 for the (a) model porous system at both low and high adsorption, corresponding to roughly one monolayer and pore filling. At both pressures, the g(r) data show both local liquid structure at small r and long-ranged order due to the porous matrix at larger r. In addition, g(r) is dramatically enriched at small r, which is a demonstration of the recently-described "excluded volume effect" [ 16]. The matrix-induced long-ranged order is evident in the structure factor data as a large peak at low k. Our interpretation of this peak, and its dependence on the amount of adsorbed fluid, is that at low adsorption we are seeing correlations between the pore surface and itself (a "surface-surface" function), while at pore filling we axe seeing correlations between the void space and itself, a "void-void" correlation. The peak at low k, especially at pore filling, is reminiscicnt of the well-known "Vycor peak" found in experimental studies of porous glasses, but is found at higher k ( approximately 0.7 + 0.2 nm -l. In experimental systems the Vycor peak occurs at 0.22 nm - l , corresponding to a real-space length of approximately 28 nm, which is much larger than the mean pore diameter of 7 nm[ 17]. In our study, the periodic simulation cell is only 27 nm across, so that any correlations at length scales much larger than 10 nm are likely to be artifacts due to the use of periodic boundary conditions. The fluid-fluid partial structure factor at pore filling is qualitatively very
66
,
~-
. . . . .
low a d s o r p t i o n
1.6
.
.
.
.
.
,
,
~--"
~
!
ption
2.0
rptJon
1
1.4
1.0
v
CO
--~ 1.2
o T-
O
0.0
-1.0 -0.5
1.0
0.0
............................. 0.5 1.0 1.5
Iog~o(k ) / nm -~
0.8
.......
0.0
2.5
5.0
7.5
10.0
12.5
r /nm
Fig. 4. Fluid-fluid radial distribution functions (right) and pmtial structure factors (left) for low and high adsorption in the (a) model porous glass. The low-adsorption data correspond to 2.82 mmol/g adsorbed density (monolayer regime), and the high-adsorption data to 11.51 mmol/g adsorbed density, in the pore-lilling regime. The oscillations at low r in the g(r) data and large k in the S(k) data are due to local liquid stnJcture, while the long-wavelength fluctuations (large r, small k) are caused by the porous material. similar to the solid-solid pmtial structure factor (not shown) which is to be expected since the substrate material and void space are complementary [18]. By measuring these functions in all our adsorption simulations, we have found that each model material has similar behavior. At low pressures (and low adsorption) the paltial structure factor displays a peak at a characteristic k which does not vary with coverage. At high pressures, when the void volume is completely tilled with adsorbed gas. the partial structure factor displays a peak at a different, lower, k. The transition from one state to another is smooth, with the lowpressure peak gradually disappearing and the high-pressure peak gradually growing. The real-space lengths corresponding to these two peaks are plotted in Figure 5 for each system, along with the pole size distributions measured by both geometric analysis and BJH isotherm analysis. It is evident from the plots that the real-space length corresponding to the low-pressure peak in the structure factor is a reasonable estimator of the average pore size, as measured by the geometric analysis explained above. This length tends to be slightly lower (about 0.2 nm) than the maximum in the geometric pore size distribution, and is thus closer to the mean pole size than the most probable one. The other peak in the structure factor, obtained at high pressure, does not seem to correspond to any feature of the pore size distribution, though it may be an equally useful characterization tool. Estimating the accuracy of this technique for predicting
67
1.0
1.0
(a) r
v 0.5 s o9 13_ 0.0
2
~*
analytic B JR
~
'- . . . .
4
~
,
,
6
i
,
8
,
,
I
10
1.0
......
(b)
J~]
0.0
0 2 1.0 r . . . . . . . . . . .
4 6 ~T~-~
8
' J 10
-
(c)
(d)
v 0.5 s o') 13_
,0
~
0.5
. . . .
0
F- ......
! I
0.5
. . . . .
0
i
2
,
4
6
d i a m e t e r (nm)
8
10
0.0
0
2
4
6
.... 8
._J 10
d i a m e t e r (nm)
Fig. 5. Normalized pore size distributions and structure-factor lengths for all four pore models. In each graph, the solid curve is the geometrically-obtained pore size distribution, the dot-dashed curve is obtained from the adsorption isotherm with the BJH method, the solid vertical line corresponds to the structure factor peak at low coverages, and the dashed vertical line corresponds to the structure factor peak at high coverages. mean pore size is difficult in these simulations, because the relatively small cell dimension of 27 nm leads to a precision of only 0.233 nm -l in reciprocal space, so that the position of these peaks is difficult to locate precisely. In addition, noise in the S(k) data at low wavelengths results from the use of a relatively small sample size, so that increasing the system size in these studies would improve both the accuracy and precision of our peak location.
4.
DISCUSSION
This study is part of a continuing effort to investigate the characterization of porous materials by adsorption. Using realistic computer models and Monte Carlo simulations to obtain adsorption isotherms, we can critically evaluate standard characterization techniques by compming isotherm-derived results with more precisely defined geometrical quantities. We have found systematic quantitative discrepancies between BJH-derived pore size distributions and geometrically defined ones, in a series of model porous materials. The isotherm-based PSDs are sharper than the geometric ones, and are shifted by approximately 1 nm to smaller
68 pore sizes. This shift may be due to the use of the Kelvin equation in the BJH method, which is known to lead to systematic underestimations of pore size. If this is the case, then the use of DFT-based methods may improve this situation. The sharpness of the isotherm-derived PSDs is more difficult to explain. It may be that, because the different sections of the pore network aJe not independent, the condensation in one pore section is affected by condensation in neighboring or adjoining sections, which would lead to a sharper capillary rise (and sharper PSD) than would be otherwise expected. Note that desorption isotherms arc also used in isotherm-based analyses, which lead to even sharper PSDs. Because the concept of a pore size distribution of a networked amorphous material is somewhat vague, we are also investigating less ambiguous characterizations. The partial structure factor data presented above contains averaged information about the pore structure; more thorough analysis of the evolution of the adsorbate's structure factor with increasing pressure may yield an alternative form of pore size distribution, or information on the local pore geometry. In this case, the peak location at low pressures seems to be a resonable estimate of the average pore size in these models. We thank the National Science Foundation (grant no. CTS-9896195) for their suppo~ of this work and for the Metacenter grant (no. MCA93S011P) and NRAC allocation (no. MCA93S01 1) which made these calculations possible, and the staffs of the Cornell Theory Center and the San Diego Supercomputer Center for their general assistance.
References [ 1] S.J. Gregg and K. S. W. Sing, Adsorption, Surf.ace Area and Polr)siO', 2 cd. (Academic Press, Inc., London, 1982). [2] P. 1. Ravikovitch, G. L. Hailer, and A. V. Ncimark, in Fundamentals of Adsorption 6, edited by E Meunier (Elsevier, Paris, 1998), pp. 545-550. [3] C. Lastoskic, K. E. Gubbins, and N. Quirke, Langmuir 9, 2693 (1993). [4] L.D. Gelb and K. E. Gubbins, Langrnuir 14, 2097 (1998). [5] L.D. Gelb and K. E. Gubbins, Langmuir 15, 305 (1999). [6] J.W. Cahn, J. Chem. Phys. 42, 93 (1965). [7] W. Hailer, Nature 206, 693 (1965). [81 R. Schnabel and P. Langer, J. Chromatography 544, 137 (1991 ). [9] M.L. Connolly, J. Appl. Cryst. 16, 548 (1983). 110] E. P. Barrett, L. G. Joyner, and P. P. Halcnda, J. Am. Chcm. S~x:. 73, 373 (1951). [ 11 ] P. Pfeifcr et aL, Langmuir 7, 2833 ( 1991 ). [12] M. W. Maddox, J. P. Olivicr, and K. E. Gubbins, Langmuir 13, 1737 (1997). [ 13] A. Brodka and T. W. Zerda, J. Chem. Phys. 104, 6319 (1996).
69 [14] M. E Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon Press, Oxford, 1987). [15] G. S. Heffelfinger and M. E. Lewitt, J. Computat. Chem. 17, 250 (1996). [16] E Bruni, M. Antonietta Ricci, and A. K. Soper, J. Chem. Phys. 109, 1478 (1998). [ 17] E Levitz, G. Ehret, S. K. Sinha, and J. M. Drake, J. Chem. Phys. 95, 6151 ( 1991 ). [18] G. Porod, in Small Angle X-Ray Scattel4ng, edited by O. Glatter and O. Kratky (Acad. l~ess, London, 1982), Chap. 2, pp. 17-50.
This Page Intentionally Left Blank
Studies in Surface Scienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScienceB.V. All rightsreserved.
71
A n e w m e t h o d for the accurate pore size analysis o f M C M - 4 1 and other silica based mesoporous materials Mietek Jaroniec, a Michal Kruk, a James P. Olivier, b and Stefan Koch b a
Department of Chemistry, Kent State University, Kent, Ohio 44242
b Micromeritics Instrument Corp., Inc., Norcross GA 30093
A novel approach is reported for the accurate evaluation of pore size distributions for mesoporous and microporous silicas from nitrogen adsorption data. The model used is a hybrid combination of statistical mechanical calculations and experimental observations for macroporous silicas and for MCM-41 ordered mesoporous silicas, which are regarded as the best model mesoporous solids currently available. Thus, an accurate reference isotherm has been developed from extensive experimental observations and surface heterogeneity analysis by density functional theory; the critical pore filling pressures have been determined as a function of the pore size from adsorption isotherms on MCM-41 materials well characterized by independent X-ray techniques; and finally, the important variation of the pore fluid density with pressure and pore size has been accounted for by density functional theory calculations. The pore size distribution for an unknown sample is extracted from its experimental nitrogen isotherm by inversion of the integral equation of adsorption using the hybrid models as the kemel matrix. The approach reported in the current study opens new opportunities in characterization of mesoporous and microporous-mesoporous materials.
1. INTRODUCTION It is well established that the pore space of a mesoporous solid fills with condensed adsorbate at pressures somewhat below the prevailing saturated vapor pressure of the adsorptive. When combined with a correlating function that relates pore size with a critical condensation pressure, this knowledge can be used to characterize the mesopore size distribution of an adsorbent from its adsorption isotherm. The correlating function most commonly used is the Kelvin equation [1 ]. Refinements make allowance for the reduction of the physical pore size by the thickness of the adsorbed film existing at the critical condensation pressure [1-2]. Still further refinements adjust the film thickness for the curvature of the pore wall [3]. The commonly used practical methods of extracting mesopore size distribution from isotherm data employ Kelvin-based theories [1]. In general, these methods visualize the incremental decomposition of an experimental isotherm, starting at the highest relative pressure achieved. At each step, the quantity of adsorptive involved is divided between pore
72 emptying and film thinning processes, and is exactly accounted for. A necessary assumption is that all pores are filled at the starting pressure. This computational algorithm frequently leads to inconsistencies when carried to small mesopore sizes. If the statistical film thickness curve (t-curve) used is too steep, it will finally predict a larger decrement of adsorptive for a given pressure decrement than is actually observed; since the implied negative pore volume is non-physical, the algorithm must stop. Conversely, if the t-curve used underestimates film thinning, the accumulated error results in the calculation of an overly large volume of (possibly non-existent) small pores. Recently, a method for accurate evaluation of t-curves for silica-based materials has been developed [4], which employs calibration using adsorption data for MCM-41 ordered mesoporous materials [5]. However, even if the t-curve used in calculations is correct, there are other more serious problems that limit the accuracy and reliability of the methods based on the Kelvin equation. These are the inaccuracy of the Kelvin equation itself and uncertainty whether adsorption or desorption data should be used in calculations [1]. Moreover, the approaches based on the Kelvin equation are not valid in the micropore range, since adsorption in micropores is usually much better described as micropore filling than as multilayer adsorption followed by capillary condensation. Only recently, the application of a series of model MCM-41 materials [5] allowed one to convincingly demonstrate that in the case of nitrogen adsorption at 77 K (typically used in the mesopore size analysis), adsorption rather than desorption data should be used in calculations of pore size distributions [4]. Moreover, the Kelvin equation itself requires a certain empirical correction in order to provide results consistent with independent estimation of the pore size [4]. The study [4] provided the means for a reliable determination of mesopore size distributions for silicas, but the approach proposed therein is not valid in the micropore range and does not account for differences in density of adsorbate in pores of different sizes and at different pressures The novel approach for calculation of pore size distributions, which is reported in the current study is based on recent developments in the materials science and in the theory of inhomogeneous fluids. First, an application of experimental adsorption data for wellcharacterized MCM-41 silicas enabled proper calibration of the pore size analysis. Second, an application of a modem theory to describe the behavior of inhomogeneous fluids in confined spaces, that is the non-local density functional theory [6], allowed the numerical calculation of model isotherms for various pore sizes. In addition, a practical numerical deconvolution method that provides a "best fit" solution representing the pore distribution of the sample was implemented [7, 8]. In this paper we describe a deconvolution method for estimating mesopore size distribution that explicitly allows for unfilled large pores, and a method for creating composite, or hybrid, models that incorporate both theoretical calculations and experimental observations. Moreover, we showed the applicability of the new approach in characterization of MCM-41 and related materials.
2. M E T H O D O L O G Y In the following paragraphs we will describe in some detail the mathematical process used to invert the integral equation of adsorption, and the method used to create the model matrix.
73
2.1. The Deconvolution Technique The integral equation of isothermal adsorption for the case of pore size distribution can be written as the convolution:
Q(p) = ~q ( p , H ) f (H)dH
(1)
where Q(p) is the total quantity of adsorbate per gram of adsorbent at pressure p, q(p,H), the kernel function, describes the adsorption isotherm for an ideally homoporous material characterized by pore width H as quantity of adsorbate per square meter of pore surface, and f(H) is the desired pore surface area distribution function with respect to H. Equation 1 represents a Fredholm integral and its inversion is well known to present an illposed problem. Since we are only interested in the numerical values of f(H), we can rewrite equation 1 as a summation:
Q(p) = E q ( p , H i ) f ( H i) i
(2)
where Q(p) is an experimental adsorption isotherm interpolated onto a vector p of pressure points, q(p,Hi) is a matrix of values for quantity adsorbed per square meter, each row calculated for a value of H at pressures p, and f(Hi) is the solution vector whose terms represent the area of surface in the sample characterized by each pore width H i . The solution values desired are those that most nearly, in a least squares sense, solve equation 2. Since the data Q(p) contains some experimental error and the kernel models q(p,H) are not exact, we can expect the results, f(H i ), to be only approximate. Indeed it is a characteristic of deconvolution processes to be unstable with respect to small errors in the data. This problem can be somewhat mitigated by choice of matrix dimensions. If we consider m members of the set of H and a vector p of length n, it is clear that n 8 m must hold. If n = m, the solution vector f(H i ) is most sensitive to imperfections in the data. For n > m, the solution is stabilized because of the additional data constraints. In this work we use an overdetermined matrix for which n > 2 m . There are additionally two other independent constraints on the solution that can be used to improve the stability of the process. One is that each fi be non-negative. The second regularization constraint is to require that for any real sample, the pore size distribution must be smooth. As a measure of smoothness we use the size of the second derivative of f(H):
2 I[d2f(H)dHdH 2
(3)
or in discretized form:
[Df[ 2 = f r D r D f where D is the second derivative matrix:
(4)
74
-1
2
-1
0
0
-1
2
-1
: D
0
0
0
...
0
0
0
0
...
0
".
9
: ,
o
0
.-.
0
0
0
-1
2
-1
0
0
.-.
0
0
0
0
-1
2
-1
(5)
The problem is now reduced to finding the fi such that ]Q - qt] 2 is small (a good fit to the data) and ]Dt] ~ is small (a smooth pore distribution), and f >__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
<
28
I
!
I
1
1
"
I
t
1
1
L
1
L,
1
1
1
2
3
4
5
6
7
"0
0
8
Pore Size (nm)
Figure 2. Equivalent surface potential required reproducing the observed critical pore filling pressures for 13X Faujasite and several MCM-41 materials. Solid points are data. The smooth line is the function used to interpolate to a given pore size class. The model isotherms calculated in this way do not reproduce the low-pressure region of the experimental isotherms because of the pronounced energetic heterogeneity of the MCM41 surface [ 10]. This portion of the data can, however, be well described by density functional calculations using the adsorptive energy distribution extracted by the deconvolution method described elsewhere [8, 11]. Figure 3a shows the model isotherm calculated by density functional theory for a 4.1 nm cylindrical pore together with the isotherm for a flat surface having the adsorptive potential distribution of MCM-41. In Figure 3b we show the normalized experimental isotherm for an MCM-41 material of similar pore size compared to a composite model created from the two curves in Figure 3a. The data can be seen to be closely described by the fiat surface model up to the point of pore filling, and by the uniform surface cylindrical pore model following pore filling. Note that the pore volume per unit area is well reproduced by the theoretical calculation. The matrix models were therefore calculated from a combination of the flat surface and model pore isotherms by the following algorithm: Starting with the lowest pressure point, the amount adsorbed indicated by the flat surface model was compared to that of the pore model; the flat surface isotherm was followed until the amount predicted by the pore model was the greater, then the pore model isotherm was followed for the remainder of the pressure vector.
3. DISCUSSION Others already employed local adsorption isotherms obtained from density functional theory in their calculations of pore size distributions for MCM-41 [16-17]. However, desorption data were used, which imposes two severe limitations on the results of calculations.
77 0.8 ca., b-,
.....
,
.... , ....
,
,/
.......
/
(a) 0.6
er
~D
0.4
~
.,'""
.
.
.
.
o
< 0.2 -
_,,,,~,,,,,"
~
Density Functional Model Flat Surface Isotherm
~
0.0 I 0.0
~
,r
. .
.
.
0.2
l
.
.
0.4
J
0.6
0.8
1.0
Relative Pressure 0.8 E 0.6
0.4 o
<
0.2 g
9
4.1 nm MCM-41 Normalized
t
/
O' 0 . 0
,
0.0
I
I
0.2
0.4
. . . .
t
0.6
....
I
0.8
----J
1.0
Relative Pressure
Figure 3. (a) Isotherm calculated by density functional theory for a 4.1 nm wide cylindrical pore with uniform surface potential (solid points). The solid line is the reconstructed isotherm for a fiat surface having the adsorptive potential distribution of MCM-41. (b) Normalized isotherm for a 4.1 nm MCM-41 (solid points) compared to the composite model for the same pore size. Note that the height of the pore-filling step is accurately accounted for. First, in the case of pores wider than 4 nm, the position of desorption branches of nitrogen isotherms for MCM-41 was found to be dependent not only on the pore size but also on the quality of samples, which was suggested to be caused by presence of constrictions in the porous structure [4]. In contrast, the position of adsorption branches of isotherms for MCM41 was shown to be dependent essentially only on the pore diameter.
78
Figure 4. Pore size distributions for 2.8 nm MCM-41 [12], 4.2 nm MCM-41 [15], 5.5 nm MCM-41 [4], and microporous-mesoporous MCM-41 [18] calculated using the new method for the pore size analysis proposed in the current work. Second, it is difficult to experimentally measure desorption branches of nitrogen isotherms down to the low pressure range and thus it is impractical to collect the data required for determination of pore size distributions in the micropore range. The approach proposed in the current study is free from these limitations and is capable of calculating pore size distributions for both large-pore MCM-41 and microporous-mesoporous MCM-41. As can be expected from data presented in Figure 1, the pore size estimations are especially accurate for typical MCM-41 samples with pore diameters in the range from 2 to 5 nm (see Figure 4) and free or almost free from artificial peaks in the micropore range, which are produced by some other calculation procedures as discussed elsewhere [18]. The primary mesopore volume obtained is in a good agreement with results of the comparative method of adsorption data analysis (for instance, as-plot). Moreover, the new approach provides a good estimate of the specific surface area. The obtained results are in a good agreement with surface areas evaluated for MCM-41 using geometrical consideration [4].
79
10 -6 10-5 10-4 10-3 10-2 10-1 100 l
600'
i
|
5.5 nm
i
t
t
~
.~
10 .6 10-5 10 4 10 -3 10-2 10-1 10 0
-
~r~
~
500
&
400 300
100 O'
o 0.0
0.2
0.4
0.6
0.8
Relative Pressure
1.0
20o
150
"~
100
>"
50
O'
0.0
0.2
0.4
0.6
0.8
l.O
Relative Pressure
Figure 5. Comparison of experimental nitrogen adsorption data for 5.5 nm MCM-41 [4] and microporous-mesoporous MCM-41 [18] with their fits obtained using the deconvolution method with hybrid adsorption isotherms described in the current study. What is even more remarkable, the method proposed in the current study can easily be applied to study microporous-mesoporous materials. Since the method does not produce any significant artificial peaks in the micropore range, the appearance of pronounced peaks in this range is clearly indicative of microporosity. As can be seen in Figure 4, the pore size distribution for an MCM-41 sample with appreciable amount of micropores, as determined using the as-plot method, indeed features a pronounced peak in the micropore range, unlike other nonmicroporous MCM-41 samples considered. The micropore volume determined is in a good agreement with that calculated using the or:plot method. Moreover, when thus determined pore size distribution and the employed composite adsorption isotherms were used to reconstruct the experimental nitrogen adsorption isotherm for the microporousmesoporous MCM-41, an excellent fit was obtained in an entire pressure range used (Figure 5). As expected, remarkably good fits were also obtained for MCM-41 materials that do not have any detectable microporosity (see Figure 5).
4. CONCLUSIONS The current study demonstrated that it is convenient to develop hybrid approaches based on experimental results and statistical mechanical principles to model and predict adsorption in porous media with strongly heterogeneous surfaces. The generated hybrid nitrogen adsorption isotherms are in very good agreement with experimental adsorption data for goodquality MCM-41 samples of different pore sizes. The hybrid isotherms were used as kernel functions in the integral equation of adsorption, thus allowing for calculations of pore size distributions from experimental adsorption data using an appropriate deconvolution procedure. This novel approach for calculation of pore size distributions was found to provide results consistent with other reliable method of characterization ofMCM-41 [4].
80 The new method allows one to evaluate not only pore size distributions, but also specific surface areas, primary mesopore volumes and micropore volumes. Moreover, it is applicable in the micropore range and appears to be essentially free from artefacts produced by many other methods of micropore analysis. Thus, a new approach provides a versatile and convenient tool for characterization of MCM-41, silica-based porous materials and other mesoporous and/or microporous oxides.
ACKNOWLEDGMENTS
The donors of the Petroleum Research Fund administered by the American Chemical Society are gratefully acknowledged for a partial support of this research.
REFERENCES
1. S.J. Gregg and K. S. W. Sing, Adsorption, Surface Area and Porosity, Academic Press, London, 1982. 2. E.P. Barrett, L. G. Joyner and P. P. Halenda, J. Am. Chem. Soc., 73 (1951) 373. 3. J.C.P. Broekhoff and J. H. de Boer, J. Catal., 9 (1967) 15. 4. M. Kruk, M. Jaroniec and A. Sayari, Langmuir, 13 (1997) 6267. 5. 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. 6. R. Evans, in D. Henderson (ed.), Fundamentals of Inhomogeneous Fluids, Marcel Dekker, New York, 1992, p. 85. 7. M. von Szombathely, P. Brauer and M. Jaroniec, J. Comput. Chem., 13 (1992) 17. 8. J.P. Olivier, in J. A. Schwarz and C. I. Contescu (eds.), Surfaces of Nanoparticles and Porous Materials, Marcel Dekker, New York, 1999, p. 295. 9. J.P. Olivier, J. Porous Mater., 2 (1995) 9. 10. M. W. Maddox, J. P. Olivier and K. E. Gubbins, Langmuir, 13 (1997) 1737. 11. J. P. Olivier, in M. D. Levan (ed.), Fundamentals of Adsorption, Kluwer, Boston, 1996, p. 699. 12. M. Knak, M. Jaroniec and A. Sayari, J. Phys. Chem. B, 101 (1997) 583. 13. M. Kruk, M. Jaroniec and A. Sayari, J. Phys. Chem. B, 103 (1999) 4590. 14. A. Sayari, Y. Yang, M. Kruk and M. Jaroniec, J. Phys. Chem. B, 103 (1999) 3651. 15. M. Kruk, M. Jaroniec, J. M. Kim and R. Ryoo, Langrnuir, 15 (1999), in press. 16. P. I. Ravikovitch, S. C. O. Domhnaill, A. V. Neimark, F. Schuth and K. K. Unger, Langmuir, 11 (1995) 4765. 17. P. I. Ravikovitch, D. Wei, W. T. Chueh, G. L. Haller and A. V. Neimark, J. Phys. Chem. B, 101 (1997) 3671. 18. A. Sayari, M. Kruk and M. Jaroniec, Catal. Lett., 49 (1997) 147.
Studies in Surface Scienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000 Elsevier ScienceB.V. All rights reserved.
81
Comparison of the experimental isosteric heat of adsorption of argon on mesoporous silica with density functional theory calculations J. P. Olivier Micromeritics Instrument Corporation, Inc. Norcross GA 30093 USA
Adsorption isotherms of argon on a mesoporous silica, MCM-41, were measured in the temperature range between 77 K and 95 K using a newly designed cryostat. The heats of adsorption were calculated as a function of loading from the slopes of the adsorption isosteres. Theoretical isosteric heats were calculated for-this system using non-local density functional theory, and an adsorptive energy distribution obtained by inversion of the integral equation of adsorption using previously described techniques. The theoretical and experimental results are in good agreement, lending support to the credibility of DFT modeling and the adsorptive energy distributions obtained in this way.
I. INTRODUCTION Modeling physical adsorption in confined spaces by Monte Carlo simulation or non-local density functional theory (DFT) has enjoyed increasing popularity as the basis for methods of characterizing porous solids. These methods proceed by first modeling the adsorption behavior of a gas/solid system for a distributed parameter, which may be pore size or adsorptive potential. These models are then used to determine the parameter distribution of a sample by inversion of the integral equation of adsorption, Eq. (1).
Q(p) = ~ q(p,x)[(x)dx
(1)
where Q(p) is the observed isotherm as a function of pressure, p, q(p,x) is the kernel function describing the modeled isotherm characterized by a single value of parameter x, and f(x) is the frequency distribution of the parameter x. DFT has been particularly useful for obtaining micropore distributions of activated carbons [1, 2], where a simple slit-pore model [3] can reasonably be used. DFT has also been successfully used to model adsorption on unconfined, or free, surfaces of energetically homogeneous adsorbents [4], and to extract the adsorptive energy distribution of heterogeneous surfaces from their adsorption isotherm [5, 6]. Very recently, the inversion technique has been extended to include energetically heterogeneous solids having cylindrical pores in the micropore and mesopore region [7].
82 Because of the importance of these characterization methods, an experimental test of the thermodynamic consistency of the models was felt to be desirable. One such test is to determine how well the models and inversion methods used predict the temperature dependence of the isotherms as represented by the isostefic heat of adsorption. It will be shown that the combined total internal energy of the modeled adsorbate leads directly to the integral heat of adsorption, from which the experimentally observable isosteric heat of adsorption can be calculated and a comparison made. 2. EXPERIMENTAL
2.1 Sample and Equipment The MCM-41 material used in this work was provided through the courtesy of Dr. Jan van Aken, Akzo Nobel Research, Amsterdam. The sample was outgassed at 575K for 4 hours prior to each isotherm determination. The isotherms were measured using Micromeritics' ASAP2010 equipped with 1000, 10 and 1 torr pressure transducers. Standard software was used for performing the measurements. 2.2 Temperature Control. The sample temperature was controlled by a cryostat, shown schematically in Figure 1. Not shown are the wiring for the platinum RTD temperature sensor, the resistance heater contained in the sample cavity block, or the liquid nitrogen level control probe. In this design, the sample cavity accommodates a standard spherical sample tube. The cavity and its close-fitting lid are made of pure copper to minimize temperature gradients. The heat sink is aluminum and the thermal shunts are made of stainless steel. A sensor controls the Figure 1. Schematic dcpiction of thc cryostat, transfer of liquid nitrogen from a large external storage vessel, providing unattended operation for many hours. In the absence of any electrical input, it is clear that the temperature of the sample cavity will decrease until the total heat flux, qa, from the room to the sample cavity is balanced by heat flow, qs, from the cavity to the liquid nitrogen. The vast majority of this latter flux is carried by the thermal shunt and the heat sink. To a good approximation the thermal resistance of the heat sink is negligible compared to the shunt. If we lump the effective thermal conductance of the insulation as K,, and that of the shunt as Ks watts/K, then at equilibrium,
qa = qs
and
Ki(Tr- To)- Ks(Tc- Is), where Tr is room temperature, Tc is the cavity temperature and Ts is the heat sink temperature. Since Ks can be calculated from the dimensions and material of the shunt, Ki can be determined by measurement of the equilibrium value of Tc. Under operating conditions, the shunt must also carry the heat that is input electrically to control the set temperature, hence in general,
83
,~
10
T~ - ( TrK, + T~Ks )/(K, + Ks ) + qe/(K, + Ks )
--. 1.0wallJK It,,= 0.5
where qe is the control input in watts. The operating characteristic is thus linear with power Q.. 6 K,=01 input. Some typical control curves are shown in 2 Figure 2. 0 4 The cryostat is operated under computer = 2 control and easily maintains the cavity temperature within a 0.002K band. Prior to gathering isotherm data, it is Controlled T e m p e r a t u r e (K) necessary to perform determinations using an Figure 2. Cavity temperature versus control empty sample tube over the planned temperature power at several shunt conductivities. range to establish the freespace factor as a function of temperature for the given adsorptive.. These experiments showed that the isotherm baseline was within 0.02 cm 3 STP over the whole pressure range. K,= 0.2
tO
0
..........
80
90
, .........
100
110
, ....
120
,
...........
130
140
,
150
100
170
180
190
200
2.3 I s o t h e r m M e a s u r e m e n t s
Argon isotherms were collected at pressures up to 850 torr at the six temperatures indicated in the Figures. Repeat determinations were performed in several instances. Approximately 0.10g of sample was used, and weighed after degassing. 3. E X P E R I M E N T A L RESULTS The collected data for the adsorption branch of the isotherms are shown in both linear and semi logarithmic format in Figure 3. The desorption branches are shown separately in Figure 4.
700 600
tl.
-"
8013
5O0
~,00
2OO
100
10o t~
d
0
o
2oo
4oo Pressure (ton')
6oo
8oo
~00o
o o ool
o Ol
o1
1
lo
loo
P r e s s u r e (ton')
Figure 3. Argon adsorption isotherms on 4.1nm MCM-4lmesoporous silica at the temperatures shown in the left-hand plot.
84
3.1 Calculated Isosteric Heat
I~ =~
co
%
~o so0
<-o
~0 d 200
87K
j
77K
90K
t
S
92.5K 95K
Ln(p)
The isosteric heat of adsorption is defined by Eq.(2) ~lnp qSt = R(~,-~),na
(2)
hence q~' at various loadings, ha, is obtained from the slopes of the adsorption isosteres. To obtain the isosteres, one must interpolate
Figure 4. Desorptionisothermbrancesat the indicated the pressure at a given quantity adsorbed at temperatures, each temperature. To avoid large interpolation errors, particularly at low pressures, the data were fitted piecewise to well behaved polynomial functions by a least squares method. Typical isosteres are shown in Figure 5. The slope of an isostere was determined by linear regression on the interpolated points. The resulting isosteric heat curves are shown in Figure 6. Because the heat of desorption in the pore filling region is greater than the heat of adsorption in the corresponding region, the observed hysteresis loop becomes smaller as temperature is increased, disappearing at about 97.5K. 4. C A L C U L A T I O N O F HEATS F R O M DENSITY F U N C T I O N A L T H E O R Y
4.1 The Integral Heat of Adsorption Consider a process taking place in an isolated system consisting of a container, in a thermostat bath of infinite capacity, in which na moles of an adsorptive originally at a pressure p l is transferred isothermally from the gas phase to the surface of an adsorbent that was previously in a vacuum. Let the new equilibrium pressure be p2. The initial conditions are n moles of gas having energy Eg per mole and a thermostat of energy E~. The final conditions are
,,-,, 12
-._= .-j -7"
8
0
1/'1"
100
20o
3oo
400
5oo
600
Quantity Adsorbed (cm 3 STP g.1)
Figure 5. Typical isosteres for the isotherms shown in Figure6. Isosteric heat as a function of quantity Fig. 3. The lower curves are for the smallest loadings, adsorbedfor argon on MCM-41.
85 (n-ha) moles of gas having energy Eg per mole, na moles adsorbed having energy Eo per mole
and a thermostat of energy E2. The integral heat of adsorption, q'"', is defined as the heat absorbed by the thermostat in this process. Since the system is isolated, total energy is conserved, hence: E l + rtEg = E2 + (rl - na)Eg + n,~E,~
(3)
By the first law of thermodynamics q,nt = (E2 - E I ) + W
As no work is done, w - O ; therefore q,,t = (E2 - E l ) = n,,(Eg - Ea)
(4)
Assuming the gas phase can be considered ideal naEg = na(-~RT)
The energy of the adsorbate has configurational and kinetic components. The configurational components consist of interactions with the adsorbent surface (wall - fluid interactions) and interactions between adsorbate molecules (fluid - fluid interactions). If we consider the adsorbate as having lost one degree of translational freedom, we can write n aEa = rta(E~ + Effa + R ] )
(5)
The configurational energy terms in Eq 5 are explicitly calculated in density functional theory when evaluating the Grand Potential; so in density functional terms we may write Eq. 4 as q,,,t _ _ ~ dzp(z) V(z) - -i1 [. dzp(z) U(z) + 8 9
(6)
In this equation, z is the normal distance from the adsorbent surface, p is the particle density, U(z) the fluid - fluid potential and V(z) the wall potential, all at position z. Eq. 6 therefore defines the total integral heat of adsorption at any pressure point on a model isotherm calculated by DFT. The differential and isosteric heats of adsorption are defined in terms of the integral heat as qdiff = (Oqmt/Ona)T
and qSt = qdiff + R T
(7)
4.2 Calculating the Heats for a Heterogeneous Surface Eq. 6 allows us to calculate the total integral heat of adsorption on an energetically homogeneous surface using density functional theory or other simulation method. To calculate the heat of adsorption on a real surface we must first determine the distribution of adsorptive
86 energies that describe that surface. This is done through Eq. 1, using the method described previously [5][6]. The isotherm obtained at the normal boiling point of argon, 87 K, was chosen for this analysis, as it represents the midpoint of the investigated temperature range. The energy distribution obtained is shown in Figure 7. In Figure 8 are shown the data used, together with the isotherm reconstructed from the DFT models ..-., 6O according to the distribution of Fig. 7. Since free surface models were used in obtaining ~,o the distribution, only data points at pressures below ~o capillary condensation could be used. ii 20 The total integral heat at pressure p for the heterogeneous surface is given by 0 o
2o
,.o
60
80
,~
,~
q , , , t ( p ) = ZA,q',"'(p)
Potential (10
Figure 7. Adsorptivepotential distribution of argon on MCM-41 at 87K.
(8)
and the moles adsorbed at the same pressure is
re(p)- Y~A,..,(p
(9)
where Ai is the area of the surface characterized by the ith adsorptive potential. The summations are carried out over the observed range of potentials. The differential and isosteric heats of adsorption are then calculated by performing the differentiation indicated in Eq. 7. 5. RESULTS In Figure 9 is shown the isosteric heat of adsorption as calculated by Eqs. 6 and 7 from the DFT models and the experimental results of Fig. 6.
Figure 8. Comparison of the reconstructed isotherm with the experimental data.
Figure 9. Comparisonof the experimental isosteric heat of adsorption with that calculated from the DFT models and the distribution shown in Fig. 7.
87 The scatter seen in the calculated points is a result of the discrete nature of the adsorptive potential distribution. The two results compare very favorably up to the point of capillary condensation at about 300 cm 3 STP g~. 6. CONCLUSIONS The good agreement shown in Fig. 9 is significant in several respects. It helps validate the application of density functional theory to the determination of the energetic heterogeneity of non microporous materials; it supports the use of DFT in the development of characterization methods for porous solids; and it provides a technique for predicting the heat of adsorption with reasonable accuracy from a single isotherm. This latter benefit may find some application in engineering studies. REFERENCES
1. N. A. Seaton, J. P. R. B. Walton, and N. Quirke, Carbon 27:853 (1989). 2. J. P. Olivier, W. B. Conklin, and M. v. Szombathely, in Studies m Surface Science and Catalysis 87, COPS III, (J. Roquerol et al., eds.), Elsevier, Amsterdam, 1994, p. 81. 3. J. P. Olivier, Carbon 36:1469 (1998). 4. J. P. Olivier, J. Porous Materials 2:9 (1995). 5. J. P. Olivier in Proceedings of the Fifth hlternational Conference on Fundamentals of Adsorption (M. D. LeVan, ed.), Kluwer Academic press, Boston, 1996, p.699. 6. J.P. Olivier in Surfaces of Nanoparticles and Porous Materials, (J. A. Schwartz and C. I. Contescu, eds), Marcel Dekker, Inc., New York, 1999, p. 295. 7. M. Jaroniec, M. Kruk, J. P. Olivier and S. Koch, (this conference)
This Page Intentionally Left Blank
Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000 ElsevierScienceB.V. All rightsreserved.
89
A c o m p u t a t i o n a l exploration o f cation locations in high- silica C a - C h a b a z i t e Thomas Grey a Julian Gale a David Nicholson a Emilio Artacho b and Jose Soler b a Department of Chemistry, Imperial College of Science, Technology and Medicine, South Kensington, London. SW7 2AY
b Departamento de Fisica de la Materia Condensada, C-Ill, Universidad Aut6noma, 28049 Madrid, Spain The locations of calcium cations in Ca-chabazite have been explored using three different computational methods. High-silica chabazite was modelled as pure silica-chabazite with aluminium and calcium defects using empirical potential functions within the framework of the Mott-Littleton method. Higher aluminium chabazite (Si/A1 - 5) was explored using periodic models, first with empirical potential functions and then with first principles quantum mechanical calculations. Three sites are found, corresponding to the centre of the double-six ring (D6R) unit, in the cavity above the D6R unit, and in the eight-ring windows. The first two sites correspond closely to those determined from X-ray diffraction. In the periodic calculations the site energies tend to converge as the aluminium content increases especially for the quantum mechanical calculations as a consequence of the delocalisation of the aluminium charge around the framework. The stabilisation due to these effects is found to be more marked for the less stable sites. I. INTRODUCTION The location of extra framework cations is a major problem in characterising zeolites. Simulation is becoming an increasingly powerful tool for the exploration and rationalisation of cation positions, since it not only allows atomic level models to be compared to bulk experimental behaviour, but can also make predictions about the behaviour of systems not readily accessible to experimental probing. In the first part of this work we use the MottLittleton method in conjunction with empirical potential energy functions to predict and explore the locations of calcium cations in chabazite. Subsequently, we have used periodic non-local density functional calculations to validate these results for some cases. Aluminium atom substituents in zeolitic frameworks, because they are formally trivalent rather than tetravalent, give rise to a single negative excess charge on the framework. This negative charge may be countered by a proton on an adjacent oxygen atom or by a metal cation residing in the cavity itself. In hydrated zeolites this cation will be solvated and free in the cavities, on dehydration the cation looses its solvation shell and becomes much more tightly bound to the framework. The siting of the cations in the cavities is associated with (but not completely governed by) the location of the aluminium in the framework, however the most common method of structural investigation in solids, X-ray diffraction, is not able to distinguish between silicon and aluminium. Consequently only information on local order is
90
Figure 1. Eight unit cells of pure silica chabazite illustrating the connectivity of the D6R units. Dark grey is oxygen and light grey is silicon. available from methods such as MAS-NMR. It is generally thought that aluminium distribution in zeolites is fairly random [1] except for the restriction on AI-O-AI triplets imposed by L6wenstein's role. Chabazite has a unit cell containing 36 framework species with high symmetry, R 3 m [2], which reduces the possible number of unique aluminium distributions. The only Secondary Building Unit in chabazite consisting of two 6-rings (6 silicons and 6 oxygens) joined face to face to produce a hexagonal prism, known as a Double 6-ring (D6R) unit. Each D6R unit is then joined to six others via four tings with three above it alternated with three below. Figure 1 shows eight units cells of chabazite. The eight D6R units connect together to enclose an ellipsoidal cavity of about 6.7A by 10A [3]. Eight-ring windows on six sides connect this cavity to adjacent cavities. It has recently become possible to obtain samples of synthetic chabazite showing the full range of possible silicon to aluminium ratios, from pure silica chabazite [4] to so-called AI-Chab, a chabazite with a silicon to aluminiurn ratio of one [5]. 2. METHOD AND BACKGROUND THEORY
The primary objective of this study was to look at the locations of calcium cations in high silica chabazite. In the limiting case, a calcium ion associated with a pair of aluminium atoms in the framework will not be influenced by any other aluminium. In a slightly more realistic case, the influence of the other aluminium atoms can be regarded, to a first approximation, as a uniform isotropic background that will not affect the relative energies of the different calcium sites. A natural approach to this situation, is to model the chabazite initially as being purely siliceous, then introduce just two aluminium atoms and a calcium cation as a defect. 2.1. Defect modelling with the Mott-Littleton method As a defect modelling technique we chose the Mott-Littleton method [6,7,8] as implemented in the modelling package, GULP [9]. This approach models the energetics of a defect in a solid using three concentric spherical regions termed regions 1, 2a and 2b.
91 In region 1, containing the defect and as many neighbours as possible, the species and their relaxation are treated explicitly. This consumes large amounts of computing power and it is not usually possible to obtain satisfactory energy convergence before region 1 becomes too large. Region 1 is therefore embedded in region 2a and region 2b that use more approximate models. Region 2a uses explicit particles like region 1, but the ions only respond to the electrostatic forces arising from the defect, subject to a harmonic restoring force centred on their initial positions. This implicitly assumes that the defect causes only a small change in the energy surface relative to the bulk. For this assumption to be valid, the solid must be relaxed fully prior to introducing the defect. Region 2b, the outermost region, uses a lattice summation technique that implicitly models the ions as responding to the net charge on the defect through polarisation. The potential energy was modelled using formal charges in conjunction with the shell model [ 10] which has been shown to accurately reproduce the structures and relative energies of many zeolite structures [11]. Two-body interactions took the form of a Buckingham potential, coupled with an electrostatic term evaluated with an Ewald sum and the three-body terms for the O-T-O angles were modelled as harmonic. The parameters for the calciumoxygen potential were derived from a fit to the experimental structure and elastic constants of calcium oxide [12]. The shell model [ 13] was applied to the oxygen ions to model their ionic polarizability, and consists of a positively charged point mass surrounded by a negative shell that is connected to it by a harmonic spring. The interaction of the silicon ions with calcium ions was treated as purely electrostatic. A full list of the remaining parameters can be found in Table 1. Prior to introducing the defect, the bulk structure of pure silica chabazite was relaxed to the Table 1 Parameters for the various interatomic species and potentia!s .Charges . . . . CharRe Soecies +2.0 Ca core +4.0 Si core +3.0 A1 core +0.869020 O core -2.869020 O shell Buckingham parameters C/(eV A6) _Species A/eV 0.0 Ca- O shell 1234.96 0.33693 0.0 AI- O shell 1460.3 0.29912 10.66158 0.32052 Si- O shell 1283.907 27.87 0.149 O shell- O shell 22764 Three-Body Harmonic parameters .... Species ko/(eV raft;) 0_o/__~rees -
O shell- Si- O shell O shell- AI- O shell Spring (core-shell) _St~ecies 0 core- 0 shell
2.09724 2.09724
109.47 109.47 /(eVA:) 74.92
v
Cut-0ff/A 10.0 10.0 10.0 12.0 Cut-offs/A 1-2
2-3
1-3
1.800 1.800
1.800 1.800
3.200 3.200
92
1 12
15
1 11
14
Figure 2. The five ahminium configurations that a r e n o t symmetry equivalent, obey LOwenstein's Rule and have both aluminium substitutions in the same D6R unit. A filled circle is aluminium on the upper ring, while an open circle is an aluminium on the lower ring. The silicon sites are numbered clockwise with site 7 directly behind site 1. local energy minimum at constant pressure. Subsequently, the aluminium ions were introduced into the framework as substitutions and the calcium ion was placed into the cavity as an interstitial defect. The restriction was made that the aluminium ions should reside in the same D6R unit. Assuming L6wenstein's rule is obeyed, there are five unique aluminium configurations (see Figure 2). The energies of most of the defects were minimised using the Newton-gaphson method with BFGS [14] updating of the Hessian. However, it was sometimes necessary to use the more demanding Rational Function Optimiser (RFO) [15] which enforces the required number of imaginary eigenvalues of the Hessian, to be zero at the minimum and one when used to locate a transition state as discussed later. Before searching for the calcium cation sites, the convergence of the Mott-Littleton method was checked with respect to region size. Calculations were run for eight different region 1 radii, from 4A to 18A. It was clear that a region 1 radius of at least 10A was required for reasonable convergence. This corresponds to about 300 ions in region 1. Runs were also made for the various aluminium configurations without the calcium ion. The energies obtained in this way were then subtracted from the corresponding defect energies with the calcium, to convert them to binding energies. Initially the calcium ions were placed on the faces of rings as well as at random locations in the cavity. Once many of the distinct minima had been found for specific aluminium configurations, calciums were placed in these positions to verify that no minima had been missed and optimised for all of the aluminium configurations. The calcium ion positions were obtained in Cartesian co-ordinates relative to the centre of region 1, rather than fractional coordinates since ions in a defect model are not replicated periodically. In order to compare with X-ray diffraction data, approximate fractional co-ordinates for the calcium ion were found by assuming that the fractional co-ordinates of the defect centre did not change when the geometry of the defect was relaxed. Positions could then be related to the unit cell of the pure material. Barriers between cation locations were studied using transition state searches. The transition state to pass between two minima is a first-order maximum, with a single imaginary vibrational mode, which may be automatically located with the RFO optimiser. The barrier to migration from one site to another is the energy of the transition state less the energy of the initial state. These transition states were located by first minimising the calcium to a known site and then displacing the cation slightly away from the minimum in the direction of a likely
93 transition state. The structure was optimised toward a first-order maximum. It was necessary to displace the calcium from the minimum in order that there was a component of the gradient in the direction of the path to the maximum. When a transition state was found, the calcium was then displaced again away from the direction of approach and the structure was optimised to locate the second minimum connected by the transition state.
2.2. Periodic lattice calculations The method described above uses empirical potential models to represent the way in which the energy varies with the positions of the species. It is interesting to compare these results with a technique that makes few assumptions about the way in which the species interact. One way to do this is with periodic quantum mechanical calculations. Currently the most accurate technique that is practical for calculations on complex materials is density functional theory, where the exchange-correlation potential is treated in an approximate manner. In this work we use the implementation of density functional theory as embodied in the program SIESTA [ 16]. For brevity, we summarise only the salient features of the method. All atoms were represented non-local pseudopotentials and a double-zeta numerical basis set. For calcium the 3p shell was explicitly included in the valence electronic configuration, through the use of a small core pseudopotential. The calculations were performed using the non-local gradient-corrected functional of Perdew, Burke and Ernzerhof [17] with an energy shift of 0.02 Ry used in the spatial confinement of the orbitals and an underlying grid corresponding to a kinetic energy cut-off of 80 Ry. Due to the size of the unit cell of chabazite it was found to be sufficient to sample the Brillouin zone at the gamma point only. The DFT calculations are more demanding than those using interatomic potentials and have therefore been applied initially to a single unit cell of chabazite. To maintain neutrality, the silicon to aluminium ratio must be greater than 5 (ten Si and 2 AI per unit cell) which is only moderately high. For better comparison with the earlier calculations, using the empirical potential energy functions, we also ran equivalent periodic structures in GULP for two of the aluminium configurations and four of the sites. 3. RESULTS AND DISCUSSION In the earlier X-ray studies of Smith [2] two on natural chabazite, ion exchanged to give a composition of Cal.95A13.9Si8.1024, two sites were found; one at (0.0, 0.0, 0.0) (site I) with a multiplicity of one, and the second at (0.169, 0.169, 0.169) (site II) with a multiplicity of two. However, these sites do not account for all the calcium ions found from chemical analysis so the data were re-examined and some evidence was found for a third site with a multiplicity of twelve at (0.09, 0.18, 0.47). In a later study [ 18] only two sites were found for calcium ions in chabazite, at (0,0,0) and at (0.15996, 0.15996, 0.15996) with two-fold multiplicity. The two generally accepted sites correspond to the centre of the D6R unit, and in the cavity above the centre of the six-ring of the D6R unit. The possible third site, [2], corresponds to the face of the four-tings. 3.1. General findings for high silica chabazite The Mott-Littleton calculations revealed three sites for calcium in the high-silica chabazite, as show in Figure 3:
94
Figure 3. The positions of Site A, Site N and Site B. Located in the centre of the D6R unit in the vicinity of (0.0, 0.0,0.0). 9 S i t e A: A two-fold site located in the cavity, above the centre of the face of the six-rings of the D6R unit in the vicinity of (0.15,0.15,0.15). 9 S i t e B: A three-fold site in the centres of the eight-ring windows in the vicinity of (0.5,0.5,0.0) Site N only occurred for configurations with aluminium ions in both of the 6-rings of the D6R unit. Table 2 gives the positions of all the observed calcium sites, in the absence of translational symmetry. Since we examined five aluminium configurations, our results 9
S i t e N:
Table 2 Site nomenclature and fractional co-ordinates. Site Idealised Mott-Littleton Name fractional coObserved fractional co-ordinates ordinates x/a y/b z/c x/a y/b z/c N 0.0 0.0 0.0 -0.003(3) 0.000(0) -0.007 (5) A . . . . 0.16(1) -0.16(1) -0.155(6) A' 0.172(7) 0.17(1) 0.16(1 ) B1 0.0 - 0 . 5 - 0 . 5 0.196(6) -0.42(2) -0.43(2) B2 -0.5 0.0 -0.5 -0.43(1) 0.108(4) -0.41(1) B3 -0.5 -0.5 0.0 -0.43(3) -0.41(3) 0.094(6) B 1' 0.0 0.5 0.5 -0.110(9) 0.43(1) 0.41(2) B2' 0.5 0.0 0.5 0.41(2) -0.097(4) 0.43(1) B3' 0.5 0.5 0.0 0.382(5) 0.448(3) -0.098(6) Bl@2 0.0 0.5 -0.5 0.003(3) 0.484(4) -0.458(2) Bl@3 0.0 -0.5 0.5 -0.04(6) -0.47(1) 0.47(1) B2@l 0.5 0.0 -0.5 0.471(3) 0.005(1) -0.479(3) B2@3 -0.5 0.0 0.5 -0.48(1) 0.103(8) 0.47(1) B3@l 0.5 -0.5 0.0 0.475(5) -4.77(2) -0.021(1) B3@2 -0.5 0.5 0.0 -0.471(3) 0.48(1) -0.005(5)
Defect centre position x/a 0.0
0.0 0.0 0.1 -0.1 0.1 -0.1
y/b 0.0 " " " " " " " " 0.1 -0.1 0.0 0.0 -0.1 0.1
z/c 0.0
-0.1 0.1 -0.1 0.1 0.0 0.0
95 actually gave rise to five sets of these positions, the positions given in Table 2 being the average positions taken over the difference aluminium configurations. The experimental Xray data are for chabazite samples with Si/Al ratios of about two. This means that we should be somewhat cautious when comparing with our results. However, there is clearly good agreement between site N and the experimental site I, and between site A and the experimental site II. The energies of symmetry equivalent sites were found to differ by less than 1 kJmol 1, suggesting that the accuracy of the energies is of the same order. In addition to the above we also looked at four aluminium substitutions at positions 1,3,10,12 (see Figure 2) with two calcium ions. The most stable pairing was site A with A'. It was found that site N was not an energetic minimum in conjunction with any of the other sites. 3.2. Configurations with both aluminium substitutions on the same ring With two aluminium ions in the same ring the most strongly bound site for these two configurations was site A', which lies above the face of this ring. In fact their relative energies are highly correlated with the distance from the aluminium ions; graphs of energy against distance to aluminium for 1_4 and 1_5 give correlation coefficients to linear fits of 0.89 and 0.91 respectively. For configurations with the aluminium ions on the same ring, site N is not an observed energetic minimum. For 1 4, the B-sites energies were spread over the range 1435 kJmol -~ to 1522kJmol ~. Although the most strongly bound B site is still around 109 kJmol -Z less strongly held than the A' sites, the B site energies bracket the energy of the other A site. Configuration 1 5 is a less symmetric configuration than 1_4 and shows a greater spread of B-site energies but this is mainly due to the more strongly bound site B 1' which lies above the two aluminium atoms. 3.3. Configurations with both aluminium substitutions on the different rings For these configurations site N, in the centre of the D6R unit, is now an observed energetic minimum with a binding energy of 1490 kJmol 1 close to that of site A in section3.2. The two A sites are now approximately equivalent and, with a binding energy of 1570 kJmol ~, are about halfway between the energies of the low and high energy A sites in the section in section 3.2. For all sites except N, there is good correlation between binding energy and distance to the aluminium substitution. Site N lies high above the fit line emphasising the presence of destabilising factors. Although the A sites are still the most strongly bound sites for all configurations, the unusually close proximity of the two aluminium ions in 1_12 gives the nearby B sites a binding energy comparable to that of the A sites. In fact the spread of B site energies for configuration l_12 is the largest seen with both the most and least stable sites. In contrast the highly symmetric configuration l_10 has the lowest spread of B site energies with the aluminium ions far more evenly distributed amongst the sites. A major areas of discrepancy between our study and the X-ray diffraction studies concerns the stability of site N. Most experimental studies have accepted site N (Site I) on the basis of favourable octahedral co-ordination to the oxygens of the D6R unit. Although such octahedral co-ordination is observed here, site N is found to be a comparatively unstable site. Furthermore we only observe site N when the aluminium substitutions occur on different rings. One possible explanation is that site N becomes more stable as the aluminium content of the sample increases. This might occur due to decreased electrostatic repulsion from the Tsites of the D6R unit, coupled with the slight increase in ring size due to the longer AI-O bonds. However, for the single configuration we examined with four aluminium substitutions and two calcium ions we found that site N is not an energetic minimum in the presence of the
96 A sites or site N. If the second calcium was removed then site N becomes more stable than site B 1 (by about 260 kJmol "1) but the A sites were still more stable by around 40 kJmol ~.
3.4. Indirect experimental evidence for the B sites No direct experimental evidence was found for the eight-ring site, site B. This conflicts with our study which predicts that, for high silica Chabazite, many of the B-sites should be more stable than site N. Nevertheless there is some evidence in support of site B being an unoccupied site in Ca-Chabazite. An X-ray diffraction study on Na-Chabazite [19] with a composition Na3.sA13.sSis.2024 found three types of site (the sodium cations caused changes in symmetry that prevent direct comparison), the first two correspond to sites A and N, but the third site was the centre of the eight-ring, in agreement with our site B. Hydrated calcium cations have also been found in an eight-ring window site [20]. Here direct comparison is possible; the fractional co-ordinates relative to the centre of the D6R unit being (0.579(1), 0.579, 0.231 (1)). 3.5. General findings for periodic calculations Configurations I_4 and I_I 0 were examined with sites A, A', N and B 1 and compared to the defect calculations. Both the periodic empirical potential calculations and the periodic DFT calculations gave mainly the same sites as the Mott-Littleton study. With the surprising exception that the DFT calculation found no minimum at site N for 1 4 or I I0. The energies calculated by these three methods represent three different processes The Mott-Littleton calculations find the energy to remove two silicons from pure silica chabazite, insert two aluminiums in their place and insert a calcium ion. The periodic GULP calculations finds the energy change in bringing the ions from infinite separation to build the Ca-chabazite lattice, and the DFT energy is the energy associated with all the nuclei and electrons moving in the field of the pseudopotential. In order to compare the results, the energy of the most stable configuration (I_4 with site A') was taken as a zero point and the other energies were compared to this reference value. Figure 4 shows the energies obtained in this way, with the vertical scale representing how much less stable the site is relative to I_4 with site A' There is a general trend for convergence in the energies of the sites along the series Mott-Littleton to periodic to DFT. This is consistent with prediction. Moving from an isolated defect to a periodic system spreads the number of nearby aluminiums more evenly as interactions can take place with aluminium ions in neighbouring cells. In the DFT calculations the electrons are able to move around the ring which tends to damp the effects of the aluminium, allowing further equalisation of the charge and so further reducing the differences between the sites. One very interesting observation is the marked drop in energy of site N relative to the A sites for the periodic force field calculations This suggests that as the aluminium content increases, the energy of site N might drop faster than that of the A sites. However, for the configuration studied, the B site was dropping faster in energy than the N site and, further, the more sophisticated DFT calculations did not show site N to be a minimum. A more extensive study of a range of periodic aluminium configurations may shed more light on this. 3.6. Energetic barriers to migration in high-silica chabazite The transition state energies for configurations 1_4 and 1_5 (where the aluminiums are on the same ring) were of a similar magnitude and so it is not surprising to find the barrier to migration from site A to site A' are similar: 112 kJmol ~ and 108 kJmol ~ respectively. The
97 barriers to migration in the reverse direction were also of similar magnitude (233 kJmol ~ and 232kJmol ~ for one four and 1_5 respectively), although the increased binding energy of site A' doubled the barrier relative to migration from A to A'. The transition state was situated in each case, about one-third of the way between site A and site A'. It might be expected that site N would lower the energetic barrier to migration, for those configurations where it appears. However, site N proved to be a very shallow minimum and so had little impact on the barrier energies. The barriers to migrate from site A to site N where almost the same as for 1_4 and 1_5 above: 112kJmol ~, 113 kJmol "z and 117 kJmol 1 for 1_10, one-eleven and 1_12 respectively. Migration for from site A' to site N was similar- 112 kJmol l, 115 kJmol 1 and 112 kJmol -I. The energetic barriers to migrate out of site N ranged from just 12.1 kJmo1-1 to 25.0 kJmol ]. The transition state for these cases was generally situated about quarter of the way from site N to the adjacent minimum. The barriers to migration between site A' and Site B 1' seemed to be mainly governed by the binding energies of the initial sites. The actual transition state energies for 1_4 and 1_10 varied by only 25.5kJmol ]. However, the lower binding energy of site B 1 for configuration 1_4 meant that the barrier for migration from site B I' to site A', 91.8 kJmol 4 was significantly lower than for 1_10, 174 kJmol s. A similar but much less marked effect was observed for migration from site A' to site B 1', for 1 4 the barrier was 212 kJmol 1 and for 1 12 it was 253 kJmo1-1. Transition state calculations were also run with the periodic force field model for moving ions out of site N. Interestingly the barrier increases for the periodic model over the defect calculation, this contradicts the failure by the DFT to find a site N which would implies a negligible barrier to migration. 4. CONCLUSIONS The Mott-Littleton method has been employed to model Ca-Chabazite in the limit as the 2.0
i ,ql"
,r-
/
1.5
"---.. / ",,,
i
4--"
iJ
""
o
1.0 a
-,,
o
,, \
4) (=
LU
,,,
\ /
t
9 /\\
/.(,'"
...
..
\/
A
./
*
~
.............................
,
__., ""
:1-
",,.
)
9/ -
"
i
0.0 14a
~
141)1
110a 110m->n 110n 1101ri->e'- 111W
11061
Site and Cordiguralion
Figure 4. Comparison of Mott-Littleton, periodic empirical potential functions and periodic DFT quantum mechanics. The horizontal scale is not significant. Transition state energies are shown as open symbols.
98 silicon to aluminium ratio tends toward infinity. Three sites were found for the calcium ion, corresponding to the centre of the D6R unit, in the cavity above the centre of the 6-rings of the D6R unit and in the eight-rings between the cavities. Of these sites, the first two agree well with experimental X-ray diffraction results. The third is not seen for Ca-chabazite but is seen as a cation site in Na-chabazite. Periodic model calculations generally agree well with the Mott-Littleton study, although these methods reduced the energetic differences between the sites as anticipated. One interesting result from this study is the apparent instability of site N. For high silica chabazite, our study predicts that site B (not observed in experiment) is more stable than the experimentally observed site N. The periodic and DFT studies show a rapid drop in the energy of the N site with increasing aluminium content. However, this observation must be tempered by the even more rapid stabilisation of the B site. For the high-silica chabazite, the barriers to migration were studied and, as expected, diffusion of cations can be ruled out for anhydrous Ca-chabazite at reasonable temperatures. 5. ACKNOWLEDGEMENTS We would like to thank Air Products and Chemicals, Inc for supporting this project. We would also like to thank EPSRC for computing facilities.
REFERENCES 1. D.E. Akporiaye, I.M. Dahl, H.B. Mostad and R. Wendelbo, J. Phys. Chem. 100 (1996) 4148. 2. J.V. Smith, Acta Cryst., 15 (1962) 835. 3. D.W. Breck and E. Robert, Zeolite Molecular Sieves, Kriegar Publishing Company, (1974) 4. M-J Diaz-Cabafias, P.A. Barrett and M.A. Camblor, Chem. Commun., (1998) 1881. 5. K.A. Thrush and S.M. Kuznicki, J. Chem. Soc. Faraday Trans. 87 (1991) 1031. 6. N.F. Mort, and M.J. Littleton, Trans. Faraday Soc. 34 (1938) 485. 7. A.B. Lidiard, J. Chem. Soc. Faraday Trans. 2, 85 (1989) 341. 8. C.R.A. Catlow, J. Chem. Soc. Faraday Trans. 2, 85 (1989) 335. 9. J.D. Gale, J. Chem. Soc. Faraday Trans., 93 (1997) 629. 10. R.A. Jackson and C.R.A. Catlow, Molecular Simulation, 1 (1988) 207. 11. N.J. Henson, A.K. Cheetham and J.D. Gale, Chemistry of Materials, 6 (1994) 1647. 12. T.S. Bush, J.D. Gale, C.R.A. Catlow and P.D. Battle, J. Mater. Chem., 4 (1994) 831. 13. B.G. Dick and A.W. Overhauser, Phys. Rev. 112 (1958) 90. 14. 14 W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes, Cambridge University Press, Cambridge, 2nd edition, (1992) 15. A. Banerjee, N. Adams, J. Simons and R. Shepard, J. Phys. Chem. 89 (1986) 52. 16. D. Sanchez-Portal, P. Ordejon, E. Artacho and J.M. Soler, Int. J. Quantum Chem, 65 (1997) 453. 17. J.P.Perdew, K.Burke and M.Emzerhof, Phys. Rev. Lett., 77 (1996) 3865. 18. W.J. Mortier, J.J. Pluth and J.V. Smith, Mat. Res. Bull., 12 (1977) 97. 19. W.J. Mortier, J.J. Pluth and J.V. Smith, Mat. Res. Bull., 12 (1977) 241. 20. A. Alberti, E. Galli, G. Vezzalini, E. Passaglia and P.F. Zanazzi, Zeolites, 2 (1982) 303.
Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 2000 Elsevier Science B.V. All rights reserved.
99
Density Functional Theory" Diatomic Nitrogen Molecules In Graphite Pores N.N.Neugebauer, M.v.Szombathely Wilhelm-Ostwald-Institute for Physical and Theoretical Chemistry, University of Leipzig, Linnrstr. 2, 04103 Leipzig, Germany
1. Introduction One method for the characterization of porous solids bases on the concept of the adsorption integral equation [ 1, 2]. It requires to access the local isotherms for a wide range of pore widths. Because experiments cannot provide local isotherms of well-defined pores, a big demand results for suitable theoretical descriptions of the physical adsorption. The established DFT-approach [3, 4, 5, 6] concerns inhomogeneous fluids assuming the fluid as spherical panicles which interact via radial symmetric potentials. Caused by the absence of alternatives the spherical DFT approach is applied to describe molecular fluids whose particles have a non-spherical geometry and interact via asymmetric potentials. Thereby the presumption is at the bottom, in accordance to which the anisotropic relations can be replaced by their non-weighted average along the orientations treating these quasi-radial symmetrically. If the homogeneous molecular fluid with isotropically distributed orientations turns to the inhomogeneous fluid with the anisotropic distribution of orientations, then this assumption becomes defective. These imperfections have occasioned to review the spherical DFT approach with respect to a more correct description for fluids which consists of non-spherical particles. The paper applies a statistic thermodynamic approach [7, 8] which uses density functional formulation to describe the adsorption of nitrogen molecules in the spatial inhomogeneous field of an adsorbens. It considers all anisotropic interactions using asymmetric potentials in dependence both on particular distances and on the relative orientations of the interacting panicles. The adsorbens consists of slit-like or cylinder pores whose widths can range from few particle diameters up to macropores. The molecular DFT approach includes anisotropic overlap, dispersion and multipolar interactions via asymmetric potentials which depend on distances and current orientations of the interacting sites. The molecules adjust in a spatially inhomogeneous external field their localization and additionally their orientations. The approach uses orientation distributions to take the latter into account. The paper presents both calculation results for slit-like and cylinder pores and evaluates these using calculation results from the accepted spherical DFT approach. Beside others the paper points out the consequences of the simplified description through the spherical DFT approach for an inhomogeneous fluid which consists of non-spherical molecules.
i00
2. Theory The planar symmetric pore consists of two parallel walls with the distance H between them which infinitely range into the x- and y-direction of the pore-fixed coordinate system. The zaxis stands perpendicularly on the x-y-plane as the normale of both walls. The cylinder pore model places its y-axis as the rotational axis. The z-axis stands perpendicularly on the pore wall as in slit-like pores and runs through the middle of the pore. Hence the x- differs from the g-axis inside the cylinder pore in opposite to the slit-like pore. This fact turns out to be important even for the adsorption of fluids which consists of non-spherical particles. The localization x of an axially symmetric particle can be stated by the localization r of its molecular centre and its relative orientation w, x -- {r,w} ,
w = {0,r
9
(1)
0 labels the angle between the molecular rotational axis and the z-axis of the pore. & describes the rotation around that z-axis of the pore which passes through the molecular centre starting at r = 0 for the molecule on the x-z-plane. The molecular external potential-v M ext,t x) causes the structurization of the adsorbed fluid especially nearby the wall. On condition that the model defines smoothed pore walls as proposed by Steele [9], the external potential depends only on the distance z meaning the z-component of r. That way the potential v~t(z, ~,) describes the interaction between one molecule at { z, w } and the whole wall. In opposite to the spatial constant bulk density/9 6 the density p of the inhomogeneous molecular fluid varies depending on sites and orientations. For that reason p becomes a function of both coordinates, p(r,w) = p(x) designates the mean density of molecules at r with the orientation w. Caused by pore symmetries and smoothed pore walls the dependence on the three components of r reduces to that on only one component which complies with the distance z to the pore wall, p(r, w) -+ p(z, w). The so-called density profile p(z, ~) provides information about the mean density of the fluid particles which appear in the distance z to the wall with the orientation w. A density profile averages the density function along respected planes at each z. Hence p(z,w) describes the inner structurization of the adsorbed fluid macroscopically in contrast to the density function. The obvious thing would be to regard the density profile as product of the so-called particle density profile nM(z ) and the so-called profile of orientation distribution o(z, w). The particle density profile can be accessed integrating the density profile along the molecular orientations,
7"IM(Z) - f '~p(z,~),
p(z,~) - ,,.,(.-)o(z,.,).
(2)
The particle density profile describes the mean density of molecules at the distance z to the pore wall. The profile of orientation distribution describes the distribution of molecular orientations w = {0, r at each z. Any orientation distribution normalizes by f dw o(z,w) = 1. If the orientations of axially symmetric molecules are isotropic distributed, then it follows from o(z,w) = c o n s t the isotropic profile o(z,w) = (4~') -1. In this case all reachable orientations appear with the same probability. The adsorption system consists of a pore, the adsorbed fluid and the bulk fluid. Particles and energies can transfer between the adsorbed and the bulk fluid. The grand canonical ensemble
101 provides a suitable statistic thermodynamic description for this system. The grand partition function E is connected with the grand potential function, f~(T, V, #), where ~ and # denote the volume and the chemical potential. It is possible to relate the grand potential function to the volume expressing it in the case of a homogeneous phase as function of the density, f~(p)'r,p = . T ( p ) y , p -
(3)
N #7-,p .
.T calls the intrinsic free energy, N symbolizes the particle number. In the case of the inhomogeneous fluid the grand potential becomes to a function of the density function, to the functional 12[p]. It can be formulated for the adsorbed molecular fluid which is influenced by the external potential,
fl[p] - y [p] - f d,, p(x) (~ - vy~:(x)).
(4)
The state of thermodynamic equilibrium complies with the minimum in ft. The equilibrium " ~t(r, ~) with respect to the density profile, condition can be expressed at fixed/z - vM
(5)
6~[P] [ - 0 6p(x) p~peq
Furthermore the thermodynamic equilibrium for the considered adsorption system can be identified by the equivalence of both the grand potentials and the chemical potentials in the bulk phase and the adsorbed fluid, f~b = f~ and #b = #. The molecular DFT approach [7, 8] places to our disposal the contributions of the free energy, the solid-fluid-interactions and the chemical potential to the grand potential functional on the basis of suitable model conceptions. The final functional expression f2[p] can be differentiated at fixed wall potential v~t(r, ~) and variables of state {7-, p} in order to yield an analytically given relation which enables the calculation of the equilibrated density profile p~q (z, a:). The free energy :" of the molecular fluid consists of the ideal and non-ideal contributions, y[p] = :-~d[p] + :-W[p]. First the molecular DFT approach replaces the whole intermolecular interaction by the sum of all pair interactions which appear via the pair potential 4~. That procedure fixes the free energy of the system as functional of both the pair potential :b(x~, x~) and the pair density p(2)(X1, X2), 6,T w 54~(xl, X2)
1 2 = ~p( )(Xl, x2).
(6)
This relation provides the starting point for the perturbative approach. Perturbative theories decompose the pair interaction potential of its reference and perturbative parts [ 10],
~(xa, x~) = ~ ( ~ , : , ~ 1 , ~ : ) + ~ ~ p ( ~ , ~ , ~ , , ~ ) .
(7)
The functional integration of (6) along the coupling a from (7) starting at the reference potential with a = 0 up to the real potential with cr = 1 yields [ 10]
1/o' //
7~[p] - ~'rt[p] + ~
d~
dx, dx: p(:)(0~; Xl,X:) ~p (x,, x : ) ,
-- .~"R[P] "t" ,fi.-(l)[p] "F 0((~)
.
(8) (9)
102
Neglecting O(4~,) the molecular DFT approach separates the treatment for the reference system from that for the perturbation. That way it finds the expressions for the interaction contributions .T'R[p] of the reference system and Up[p] of the perturbation to the free energy [7, 8]. The reference system of the molecular DFT approach consists of hard molecules. The molecular approach regards the reference system as an perturbated reference system itself by Wertheims thermodynamic perturbation theory of polymerizations (TPT) [ 11, 12]. The hard nitrogen molecule is composed of two hard nitrogen atoms which can be treat as hard spheres with the diameter rd. g designates the intra-molecular distance between the centres of the bonded spheres. In the case of rigid bonds g changes to the constant bonding length gf. The reference fluid which consists by TPT of non-bonded nitrogen atoms represents the socalled non-associated limit (NAL) of the hard molecular fluid. The nitrogen atoms interact as hard spheres with the diameter rd via the hard sphere pair potential. The density functional theoretical description of the NAL falls back on that which are used by the spherical DFT approach. The latter provides beside other a suitable description for the inhomogeneous hard sphere fluid. The fluid which completely consists of hard diatomics is called the completely associated limit (CAL). The reference system changes from its NAL to its CAL as a result of the perturbation which can be identified as the intra-molecular interactions between the two atoms per molecule. ~9 " R [ P ] -
,TCAL[p]- f'NRAL[p] + ,f'~[p]
,
(10)
where ,T'~ designates the perturbative contribution to the free energy of the molecular reference system. A first contribution to ,T'~t is caused by the bonding between two atoms which constitute one molecule. This direct intra-molecular interaction between the atoms is taken into considerations as a f*-bond. In addition there are intra-molecular interactions of indirect nature between the both atoms of a molecule. These atoms affect each other indirectly by 7z point interactions with all remaining atoms and combinations of atoms. The so-called intra-molecular pair cavity function y*(rM) expresses the ensemble of all indirect interactions which appear between the atoms of a molecule in f-bonds [ 13] and establishes the searched correlation function for all indirect interactions between the atoms inside a molecule. The molecular DFT approach evaluates the cluster expansion to calculate y*(rM) using TPT. This approximation takes into account only presentations with vertices s ('~), n < - 2, for what reason it is called the single chain approximation (TPT1) [12]. [7, 8] The decomposition of the anisotropic perturbative potential 4~P (7) into its isotropic and anisotropic part suits as an excellent method to include this potential into the formalism. By [ 14] the separation of the isotropic part ~, occurs non-weighted averaging Op along the orientations, 4~s(rx2) = (qSp(rl2,Wl,W2))~,~2. Consequently, the molecular DFT approach regards the pair interaction potential as its isotropic part 4~s and its anisotropic part 4~c.The latter ranges positive and negative values for each distance 7- and represents an excess to the isotropic part which depends on the relative orientations, 4~P(r12, ~1, ~2) = ~bs(r12) + 0c(r~2, ~a, ~2). The separation of the attractive pair interaction potential into its isotropic and anisotropic part allows to formulate the corresponding functional expression which describes the perturbative contribution to the free energy, Up [p] = f'~ [p] + 9t-~[p]. A fluid where only long ranging perturbative parts of the pair interaction occur does not
103 require to know all about the pair distribution g(X1, X2)[p ]. The latter can without any effort be replaced by its non-weighted ofientational average. Then it's obvious to approximate this by the radial pair distribution function of the molecular centres which no longer depends on the particle density, g(x,, x2)[p] ~ gs(r)[nM] ~- gs(r).
1//
JZs[p] -- -~
dXl dx2 p(x,) p(x~)g,(r,2)eke(r,2),
(11)
.To[p] - ~
dx, dx2 p(x,) p(x2)g,(r,2)49c (r,2,w,,w2) .
(12)
The isotropic pair potential q~s(r) does not depend on any orientations. Hence it is possible to apply a conventional perturbative decomposition as proposed for instance by Weeks et.al (WCA) [15] or Barker et.al (BH) [16]. Now the isotropic part (1 1) can be integrated without any effort along the orientations wl and w2. That way the considerations arrive at the mean field term which only depends on the particle density profile, .T's[p] --+ ~'s[nM], J2s[TtM]
--
1//
-~
(13)
dr, dr2 riM(Z,)riM(Z2)gs(r12)O,(r,2).
The molecular DFT approach derives an expression 3V~[p] expanding the anisotropic excess parts of the perturbative pair interaction potentials into spherical harmonics. That way the inclusion of the anisotropic dispersion and quadrupolar interactions succeeds [7].
3. Results The adsorption for nitrogen in graphite pores is calculated at standard condensation temperature T = 77.352 K. The calculated isotherms consist of 177 logarithmically distributed pressures p which are taken from the interval 0 < P/Psat < 1. The calculations require the liquid particle density nM,, of the condensed bulk phase at {T, Psat }, the quadrupolar moment #p and the dimensionless anisotropy of the polarizability n to specify the fluid as nitrogen. n -- ( a l l - a L)/(all + 2a.L) [17, 18] in the definition by Spurling and Mason [19]. The optimization procedures provide the quasi-optimal molecular Lennard Jones parameter cr and ~, the hard sphere diameter rd for a nitrogen atom and the atomar energetic Lennard Jones Parameter
([at,
mN
=
TtMllq
= = =
#p n
28.0134 1 0 - 3 0.017372 4.7 10 - 4 0 0.176
/~-3
a r
= -
Cm 2 [20],
rd
=
[21],
~at
=
kg/mol,
3.48844 101.03342 0.74579 178.148
fl,, ks, o', kB.
This paper prefers to apply the perturbative decomposition as proposed by Weeks et.al [ 15]. In contrast to the WDA 3 (T3) by Tarazona [31, that by Curtin et. al. (CA) [41 is known for its consistency with the renormalization condition in the homogeneous limit and does not semiempirically limit the surrounding whose densities come in the integration to determine the weighted density. For that reasons CA is prefered as against T3 for the calculations. If the applied WDA does not matter, then the calculations partially use the WDA 2 (T2) by Tarazona [3]. Furthermore the paper decides to apply the Carnahan Starling equation of state and the diameter of a hard nitrogen atom as the intra-molecular bonding length, ~/ - Yd.
3.1. The adsorbate structurization and isotherms The molecular approach calculates the equilibrated structurization of the adsorbed fluid at each point of state (7,H, p } along the pressure axis as the equilibrium density profile peq(z, w). The fig. 1 shows the calculated structurizations of nitrogen in a slit-like graphite pore with the pore width H = 25 A at pip,,, = 0.0001 and at p / p S a t = 0.99. The left side shows the particle density profiles n ~ ( z )the , right side plots the corresponding profiles of orientation distribution o(z, 8). The figure relates n M on the liquid particle density n,t,,,q.Hence the convergence n ~ ( z ) / n ~ ~-+, , 1 states the convergence of the particle density profile towards the liquid particle density, if the adsorptive completely fills up the pore. In analogy, the factor 47r scales , in the figure through the values for o. That way an isotropic profile, o ( z , 0) = ( - l ~ ) - 'reveals the value 1 along the cos(8)-axis. The top of fig. 2 intermediates an interesting impression about the adsorption arranging the equilibrated particle density profiles on the pressure axis. It uses a slit-like graphite pore with H = 20 A. At low pressures the adsorption starts forming a mono-layer. Increasing pressure fills the mono-layer with particles of the surrounding gaseous bulk phase. If the pressure further increases, then the fluid abruptly fills up the pore. The localization of the molecular centres in the first adsorbed layer increases, what can be constated on the top in fig. 2 through the raising peak in n ~ ( z which ) becomes simultaneously more thin. Inside the already filled pore increasing pressure causes a weak raise of the coverage accompanied by a small raising structurization.
105 It's an obvious thing to relate the amount of adsorbed particles on a volume. The normalization of the orientation distributions enables to access the adsorbed excess volume integrating the particle density profile along the pore volume,
- f
(14)
The bottom of fig. 2 shows the equilibrium isotherm for the adsorption of nitrogen in a slit-like graphite pore with H - 20/~. The shape of the isotherm reproduces the course of the adsorption in agreement with the top of this figure. After the abrupt transition of the adsorbed fluid has been happened the adsorbed excess volume converges towards the liquid particle density riM,;,. 3.2. The results in dependence
on the pore width
In course of both the slit-like and the cylinder pores range infinitely, the coverage offers to be related on the surface of the pore walls. r~ (P)7-'" -
v~%(p)7-,. A
(15)
"
If a plot relates the isotherm as F ~ (p) to the solid surface, then it conventionally uses the unit 1 c c m S T P / r n 2. The latter corresponds to the amount of particles which appear in 1 cm a of the bulk fluid at standard pressure per 1 rn 2 adsorbens surface. The fig. 3 shows calculated isotherms for the adsorption of nitrogen in slit-like graphite pores with H - 5, 10, 15, 22, 50 and 120 A. The left picture plots the isotherms as V~"d,(P) in multiples of nM~q, the fight picture plots the same isotherms as F~ in c c m S T P / m 2. The pressure, where the phase transition happens, shifts in greater pores to higher pressures. In the bulk-limit with H --+ oe that pressure arrives at the saturation pressure of the bulk, pip,at --+ 1. The bulk phase is gaseous within the regarded pressure range. Therefore the adsorbed excess volume trends at increasing pressure against the difference nM,;, -- nMg., ~ nM,;q, "~aads(P)T,H
--+ n M , i q
P/Ps~,t --+ 1.
V
(16)
The left picture in fig. 3 suits for recognizing the trend that the isotherms approach the conver-
1.0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I
4.0
tl
0.7
3.5
" " "
0.6 0.8
~
30
0+
II
li
I
2.5 0.6
~
0., 0.2
o.o
/
-t4
'
/
"" ,'" . . . . . . . . .
-~2
~Z~_~:-~-'~.--
-1o
-g
/ .
-+
-
:4
- -
-~
0+
L '+
I
/ /
2.0
-~,,
o.o
..-"
0.0
o~ o
i
0.2
.
-h
~, _; _2 _, 0 -10
__~.._~-----~
+
,.,
-+
[.I.
- "j " - ".~d.~ . . . .
~,
-~
__
0
In (P/P~t)
....
H = 6Angstr6m, H = 22 Angstr6m,
- ......
H = 10 A n g s t r 6 m , H = 50 Angstr6m,
- --- -
H = 15 A n g s t r 6 m , H = 120 AngstrOm.
Figure 3" Isotherms for nitrogen in slit-like graphite pores at several pore widths: a) as Va~s, b) as F~ 7" = 77.35 K, WDA by Curtin et. al. [4]
106 gence (16) at greater pores from the direction of lower coverages upwards. The right picture relies the coverage on an adsorbens surface. Therefore it takes advantage due the fact that the absolute amounts of particles can be compared which adsorbate in the first adsorbed layer. Hence the external potential component v ~ t ( H - z) of the opposite wall becomes so small that the formation of the first adsorbed layer starts at similar pressures while the pore width increases beginning at the 15 :k-pore. The pressure where the phase transition happens emphasizes as the essential difference between isotherms of differently scaled pores. The fig. 4 supports the interpretations of the isotherms for different pore widths showing the particle density profiles for several pore widths at even three chosen pressures. H = 10 AngstrOm
14
t~(p~,,,d
12
~ ,0
....
.
l
=-1.5
tnfp/p,,d 9,
H = 22 AngstrOm
= -s
= -
I
/
]
tn(t~,~
....
H = 50 AngstrOm
~ = -4
t2
!
~
tn~p/p,,,,)
H = 120
"
tnt~,,,~ : - 1 . ~
to
--
9
....
t,,Ce/t,,.,):-1.~
----
I~(t~'p,,d
AngstrOm
tn t p / p ,,~ ) = -4
= -4
= -0.001
In(p/p,,,)
= - 1.5
In(p/p,,~)
= -0
001
4 2 0
2 i k.~ "':'~'"
0.
t
.
3.
2
4
.
0.
5
2
4
. . . . . . . .
6
/"~
8
00
to
Z/
;
t0
0
~. . . . . . . . ~
AngstrOm
2~
0
l0
20
30
40
50
60
Figure 4: Particle density profiles riM(Z) for nitrogen in slit-like graphite pores at several pore and some selected pressures; T = 77.35 Ix', WDA: Curtin et. al. [4] 3.3. The influence of separate interaction kinds The molecular DFT approach describes the attractive interaction separating the isotropic part as the orientation average from the interaction between pairs of molecules. Regarding the anisotropic part of an attractive pair interaction as an excess to the isotropic part, it contributes the essentially smaller share to the energy of the system in comparison with the isotropic part. [7] shows that the anisotropic parts of the dispersive and quadrupolar interaction only very slightly affect the calculated isotherms. The expression for the indirect intra-molecular interactions approximatively registers the indirect correlations between the atoms of a hard diatomic reference molecule away 3, 4 and more points - the particles of the surrounding reference fluid. The fig. 5 investigates the effect of these interactions on the isotherms at different pore widths. Only if a calculation takes this interactions into account, then the convergence (16) is kept already in the small pore with H -- 11 A.
/ L
f 0.6
H = 11A n g ~
j:
H = 50
H = 25 AngstrOt
AngstrOm
0.4
-12
-10
-8
-6
-4
-2
-12
-10
-8
-6
-4
-2
-12
-10
-8
-6
-4
-2
In (P/Put)
Indirectintra-molecularinteractions:
applied,
---
disabled.
Figure 5: The influence of the indirect intra-molecular interactions on the adsorption of nitrogen in slit-like graphite pores at different widths H" T - 77.35 K, WDA" model 2 by Tarazona [3]
107 3.4. The influence of the pore geometry a)
25
b)
z = 2.11 Angstrbm
z = 2.28 A n g s t ~ m
c)
z = 5.16 Angstrbm
20
3
3
15
a) b)
to
c)
5 0
'
]i ...........
o i 2 34 z I
5 67s
~lo
9
"_ .~,~
costu)
0.2
OX
f~
'
9
0.4
02
cos(O)
"
ox
r
"
" _o~4
-
0.2
0 \
cos:o)
Angstrbm
Figure 6" Nitrogen in a cylindric graphite pore: Particle density profile and three orientation distributions; H - 20 A, T - 77.35 K, p/psat - 0.99, WDA: model 2 by Tarazona [3] The interactions of a nitrogen molecule with the curved wall of the cylinder pore depends additionally on the angle r between the x-z-plane of the pore and the molecular axis. The profiles p(z, w) and o(z, co) do no longer degenerate with respect to rotations around z along r what requires to give o(z, co) as function of both angles, co = { 0, r The fig. 6 contains on the left the equilibrated particle density profile for nitrogen in a cylinder pore with H - 20/~ at p/psat - 0.99. The left picture marks three coordinates z using vertical dotted lines which correspond to the orientation distributions o(0, r a), b) and c). cos(0) - 1 corresponds to the molecular orientation perpendicular to the z-axis of the pore. cos(~5) - 1 means that a molecule has been rotated along 7r/2 out of the z-z-plane around that z-axis of the pore which takes course through the molecular centre. The choice of z - 2.11, 2.28 and 5.16/~ enables to recognize both the change of the orientation distribution along z across the first adsorbed layer in a) and b) and the convergence of the orientation distribution against the isotropic profile, o -- (47r) -1, in direction of the pore centre in c). slit-like pore
cylinder pore
................................ iZM t~t
I• ~'~
_...-'
-
"
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. .#-
.....
9
iI
I I
0.6 0.4
/I 0.0
-12
-10
-8
-6
-4
-12
-2
//"
/
"
-I0
-8
-6
..--i.-I//
-4
-2
In (p/p~,) H
-- I O A n g s t r f m ,
----
H
--
20 AngstrSm,
H
= 50
AngstrSm.
Figure 7: The comparison between the pore geometries slit and cylinder using the isotherms for nitrogen in graphite pores at several pore widths; T - 77.35 K, WDA" model 2 by Tarazona
[3]
108 The fig. 7 compares the calculated isotherms for graphite pores with H = 10, 20 and 50 A which differ in their geometries. The wall curvature of the cylinder pore lowers the pore potential in relation to the slit-like pore of the same width. Consequently the molecular DFT approach calculates that the fluid fills the cylinder pore up at lower pressures as the slit-like pore of the same width. This differences grow in direction of smaller pores. They vanish in the limit H -+ oo of the bulk phase. A nitrogen molecule can locate the centre of an atom first in a distance to the wall which exceeds the radius of a hard nitrogen atom, zmi,~ > rd/2. This range at the z-axis corresponds inside the pore to a volume. This so-called excluded volume has inside a cylinder pore the greater share of the whole pore volume than inside a slit-like pore of the same width. Therefore the isotherms indicate differences between the maximal coverages of both pores at the limit p/p=at -+ 1. If the pore width increases, then that differences vanishes, because the share of the excluded volume decreases.
3.5. The comparison with calculation results of the spherical DFT approach The spherical DFT approach applies radially symmetric potentials to describe the interactions between the particles of the fluid. The calculations using both DFT approaches apply the identical specifications to minimize the affects of secondary meaning reasons. The fig. 8 compares the structurizations of the adsorbed fluid in a slit-like graphite pore with H = 50 A at PiP=at = 0.99 showing the particle density profiles riM(z). The picture a) distinguishes from b) applying different WDA. The molecular DFT approach calculates the formation of the first adsorbed molecular layer in a greater distance to the pore wall and the distinctly smaller dimension of the structurization. Both effects are on the one hand reasoned by the bigger interaction centres of the spherical DFT approach treating these approximatively as radially symmetric particles. That way the external potential of the spherical DFT approach decreases in z-direction at a raising distance to the wall slower as that of the molecular DFT approach. On the other the non-spherical particles of the molecular DFT approach can arrive at the equilibrium state preferring any orientations.
"F" 12
I
~l
'fl
0 -J 0
WDA: CA
b)
WDA: 7"2
tit
II i1/t
/\
5
to
t5
20
25 0
5
10
t5
20
25
Z / AngstrOm spherical D F T approach,
~
molecular D F T approach.
Figure 8" The particle density profiles for nitrogen in a slit-like graphite pore approximating the nitrogen molecules both as radially symmetric particles by the spherical DFT approach and as diatomics by the molecular DFT approach; H = 50 A, T = 77.35 K, p/psat -- 0.99, a) WDA: model 2 by Tarazona [3], b) WDA: Curtin et. al. [4]
109 12 AngstrOm 1.2
.
.
l.o 0.8 ~
0.6
~'~
0.4
20 AngstrOm .
.
- - - - ~ ~
, /Jq
IIMhq
50 AngstrOm
120 AngstrOm
.
_A
..........................
,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
./
0.2
/t
/1" -12
-10
-8
-6
-4
-2
-12
-10
-8
// -6
-4
-2
-12
-10
-8
-6
-4
-2
-12
-10
-8
-6
-4
-2
In (P/P.~l) spherical DFT approach,
molecular D FT approach.
Figure 9" Isotherms for the adsorption of nitrogen in slit-like graphite pores both as radially symmetric particles by the spherical DFT approach and as diatomics by the molecular DFT approach; T = 77.35 K, WDA: Curtin et. al. [4] The fig. 9 compares isotherms for the adsorption of nitrogen in slit-like graphite pores which has been calculated using the spherical and the molecular DFT approach. It exposes some characteristical differences between the isotherms of both DFT approaches. However, the adsorption starts at the same pressures, and both DFT approaches calculate a similar course of the adsorption. The spherical DFT approach receives general acceptance. Hence, the correspondence between the isotherms in essential properties suits for the confirmation of the molecular DFT approach. The isotherms tend to arrive at the convergence (16). As already mentioned the deviations in small pores are reasoned by the excluded volume. Following this considerations, the coverages V ~ ( p ) at the limit p/psat --+ 1 must turn towards nM,~ from below. Though the spherical DFT approach calculates the reconciliation of the isotherms to this convergence (16) in direction of greater pores incorrectly upstairs from the direction of higher coverages. Hence the slit-like pore with H = 12/~ at p/psat --+ 1 shows a unrealistic high averaged particle density of the 1.15 liquid particle densities. On the contrary, the molecular DFT approach calculates that reconciliation at increasing pore width correctly from the direction of lower coverages. The spherical DFT approach accompanies the approximation of real molecules as radially symmetric particles and assumes that the anisotropic relations can be treat as quasi-radially symmetrically replacing it by its non-weighted orientation average. The results show that the legitimacy of this approximation becomes questionable, if the homogeneous molecular fluid changes to the inhomogeneous fluid with anisotropically distributed molecular orientations.
References [1] R.Madey M.Jaroniec. Physical Adsorption on Heterogeneous Solids. Elsevier, Amsterdam, 1988. [2] K.Koch. Verbesserte Methoden zur Charakterisierung von Adsorbenzien auf der Grundlage von Tieftemperaturadsorptionsdaten. PhD thesis, Universit~it Leipzig, Institut f. Phys. u. Theor. Chemie, 1997. [3] P.Tarazona. Phys.Rev.A, 31(4):2672, 1985. [4] W.A.Curtin and N.W.Ashcroft. Phys.Rev.A, 32(5):2909, 1985.
110 [5] T.EMeister and D.M.KroI1. Phys.Rev.A, 31:4055, 1985. [6] R.D.Groot and J.P.van der Eerden. Phys.Rev.A, 36(9):4356, 1987. [7] N.N.Neugebauer. Dichtefunktionaltheoretische Beschreibung der Adsorption: Axialsymmetrische Stickstoffmolekiile in Graphitporen verschiedener Geometrie. PhD thesis, Universit~it Leipzig, Wilhelm-Ostwald-Institut fiir Phys. und Theor. Chemie, 1999. [8] N.N.Neugebauer and M.v.Szombathely. J.Chem.Phys. submitted. [9] W.A.Steele. The Interaction of Gases with Solid Surfaces. Pergamon,Marcel Dekker, Inc., Oxford, 1974. [10] E.Chac6n, P.Tarazona, and G.Navascu6s. Molec.Phys., 51(6):1475, 1984. [ 11] M.S.Wertheim. J. Chem.Phys., 85:2929, 1986. [12] M.S.Wertheim. J.Chem.Phys., 87:7323, 1987. [13] D.Chandler and L.R.Pratt. J.Chem.Phys., 65(8):2925, 1976. [ 14] C.G.Gray and H.E.Gubbins. Theory of molecular fluids, volume 1: Fundamentals. Clarendon Press, Oxford, 1st edition, 1984. [15] D.Chandler, J.D.Weeks, and H.C.Andersen. J.Chem.Phys., 54(12):1930, 1971. [ 16] J.A.Barker and D.Henderson. Molec.Phys., 48(587), 1976. [17] D.E.Stogryn and A.P.Stogryn. Molec.Phys., 11(371), 1966. [18] R.L.Armstrong, S.M.Blumenfeld, and C.G.Gray. Infrared spectra, rotational correlation functions and intermolecular mean squared torques in compressed gaseous methane. Can.J.Phys., 46:1331, 1968. [19] T.H.Spurling and E.A.Mason. J.chem.Phys., 46:322, 1967. [20] W.Steele. Chem.Rev., 93:2355, 1993. [21 ] M.S.Ananth and K.E.Gubbins. Molec.Phys., 28(4): 1005, 1974. With a special acknowledgement for the financial support by the DFG Bonn (DE)
Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) 92000 Elsevier Science B.V. All rights reserved.
Modelling studies of the influence of macroscopic heterogeneities on nitrogen sorption hysteresis
111
structural
Sean P. Rigby Synetix, PO Box 1, Belasis Avenue, Billingham, Cleveland, TS23 1LB, UK
Macroscopic (0.01-1 mm) heterogeneities in the spatial distribution of porosity and pore size in porous materials have been shown to significantly influence nitrogen sorption hysteresis, and therefore the value of pore connectivity obtained from percolation analysis. Methods have then been described which will allow nitrogen sorption to probe the macroscopic structure of porous materials and the results compared with NMR data. 1. INTRODUCTION Methods based on nitrogen sorption [1], mercury porosimetry [2] and electron microscopy [3] have been developed to determine pore connectivity in porous materials. Briefly, the original model for the analysis of nitrogen sorption [ 1] uses a representation of a void structure consisting of a homogeneous three-dimensional random pore network lattice of sidelength L and connectivity Z. NMR imaging studies [4] have shown that porous catalyst support pellets possess heterogeneities in the spatial distribution of porosity and pore size at the macroscopic scale (0.01-1 mm). These heterogeneities have been characterised in terms of a so-called image fractal dimension. This image analysis parameter was found to be constant for pore size images of pellets from the same batch but differ between batches [5]. In this paper it will be shown that macroscopic heterogeneities in the spatial distribution of pore size may influence the percolation transition in the nitrogen desorption experiment and hence influence the value of connectivity obtained using this data and the analysis method due to Seaton [1]. These studies will lead on to methods whereby nitrogen sorption might be used to probe the macroscopic scale. 2. E X P E R I M E N T A L 2D 1H NMR imaging experiments were performed using a Bruker DMX 200 NMR spectrometer with a static field strength of 4.7 T yielding a proton resonance frequency of 199.859 MHz. Spin density and spin-lattice relaxation time (7"i) images, which probe porosity and pore size respectively, were obtained using a spin-echo pulse sequence employing 90 ~ selective and 180 ~ non-selective pulses. The imaging sequence was pre-conditioned using a saturation recovery pulse sequence and an echo time of 2.6 ms was used. All images were of dimension 128 x 128 pixels with an in-plane resolution of 40 ~m. The samples studied in this work were two alumina tablets, E1 and E3, an alumina extrudate E2, an alumina sphere G3 and two sol-gel silicas G1 and S 1. All the samples have earlier [6] been shown to have unimodal pore-size distributions from mercury porosimetry, except G3 which was bimodal and included for comparison.
112
3. THEORY 3.1. Simulations of sorption experiments on model representations of catalyst support pellet macroscopic structure derived from NMR images The value of the NMR spin-lattice relaxation time in each of the pixels of an image may be converted to a pore size by the adoption of a relaxation model. For a liquid imbibed in a pore space the relaxation rate is enhanced. This is believed to be due to interactions between a thin layer of liquid and the solid matrix at the solid/liquid interface increasing the relaxation rate. There is then also diffusional exchange between this surface-affected layer and the rest (bulk) of the liquid in the rest of the pore. In the case here where the pore sizes are several orders of magnitude smaller than the rms displacement of the probe water molecules employed, the "two-fraction fast-exchange" model of Brownstein and Tarr [7] will be used, where the overall measured value of Tz is given by: 1 (1 LS) 1 XS 1 T--l = - -V ~ + ~ T1---s'
(1)
and 9~ is the thickness of the surface-affected layer, T~s is the relaxation time in the surface layer, TIB is the relaxation time in the bulk fluid and S V is the pore surface area to volume ratio ( =2/r for cylinders). The values of ~, and T~ are taken as 0.3 nm and 3 s [8], respectively. The value of T~s for a particular sample may be determined from variable saturation experiments and is described in more detail elsewhere [8]. It is therefore possible to convert a value of T 1 for a pixel into a cylindrical pore diameter. The signal intensity in an NMR spin density image is linearly related to the local average voidage fraction in the volume represented by the pixel. If the total pore volume is known and it is assumed that the model constructed from the image is representative of the whole sample then local specific pore volumes may be allocated to each pixel depending on the local voidage fraction. The macroscopic model consists of a 2D square lattice cut from the image. Each lattice site (pixel) is considered to be a domain where the pore volume and local average pore size are allocated according to the respective data from NMR spin density and T~ images. The standard nitrogen sorption experiment may be simulated for the model grid. This involves progressively increasing the pressure of nitrogen 'applied' to the model and reconstructing the isotherm. During the adsorption process, the increase in the amount of nitrogen adsorbed at each pressure increment arises from contributions both from increases in the t-layer thickness in pores where capillary condensation is yet to occur, given by the expression of Harkins and Jura [9], and from capillary condensation in those pores in which the core (i.e., volume outside t-layer) radius then satisfies the Kelvin condition. For the purposes of the simulations on the macroscopic model the relevant pore diameter used in the Kelvin equation is the locally averaged pore size for each domain obtained from the pixels of the TI map. If a unimodal pore network of arbitrary size is considered then, if the spatial distribution of pore sizes is non-random, the desorption percolation transition would be apparently smeared out (in addition to any finite size effect). It is possible that particular pores occupied by liquid-like phase might gain access to the vapour phase before would be expected to be the case for a purely random system because the actual layout of the pores might provide a convenient access route that would not have existed at that bond occupation level in a random system. The simulations of the nitrogen sorption
113 experiment on the models derived from NMR images represent a way which might be employed to remove this effect. Using the terminology of Seaton [ 1], F is defined as the number fraction of pores in the percolation cluster and f is defined as the number of pores below their condensation pressure (and thereby potential members of any percolation cluster provided they have access to the vapour phase). The ratio of F f at any given pressure may be determined from the experimental sorption data. For a system in which pore sizes are heterogeneously distributed the value of F may be increased or decreased (depending on spatial arrangement) compared with a homogeneous random structure. A correction factor is necessary to account for this effect in order to fit the F(]) curve to obtain a better value of the estimate for an average pore connectivity. The experimental nitrogen sorption results represent the total behaviour of the system. The macroscopic model derived from the pellet MRI images represents the macroscopic behaviour of the system. The underlying mesoscopic pore network lattice may have many topological forms, each with a different bond percolation threshold. Due to the nature of the nitrogen sorption experiment the fraction of open bonds is a function of the applied relative pressure and thus, via the Kelvin equation, "pore size". Hence the percolation transition would occur at a different "pore size" for a given pore size probability density function depending on how those pores were arranged and connected up in the network. This means that the "pore size" for the percolation transition in the macroscopic model, which is 2D site percolation, does not necessarily correspond to the "pore size" at the percolation transition of the underlying mesoscopic network, which is 3D bond percolation. However, in order to relate the macroscopic model to reality it is clear that if the macroscopic model represents the large-scale structure of the real material then the percolation transition for the macroscopic model must coincide with that of the real material. However this coincidence will not occur in "pore size" terms (except in the particular special case when the whole pore structure is just like that of the macroscopic model) but in terms of the more fundamental percolation parameters. At the most fundamental level the percolation threshold for a model, be it as a representation of the whole pore space or merely the macroscopic scale, must equate to the percolation threshold for the real material. For the general case for non-infinite lattices, the percolation threshold has been [10] fundamentally defined as: 02F
a2
=0.
(2)
In the following discussion the subscript o refers to the experimentally observed percolation threshold, whilst the subscript a refers to the percolation threshold for the model derived from NMR images representing only the macroscopic scale. It is proposed that to relate the macroscopic model to reality then the following relation is taken to hold:
c3f~o) c
\ bf2~
c
=0,
(3)
where the subscript c refers to the critical value of the parameter in brackets at the percolation threshold. Using the theory described by Seaton [ 1] it is possible to relate the percolation parameters f and F to measurable quantities for real materials. Starting from
114 the position defined in equation (3) for both the model and the real material it is possible to establish a series of given parameters: - - ~ J c - 0 --->
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~ <<x m~
-
and
t, x
y
(2) m~ << y we c a n replace (2) with its Taylor d e v e l o p m e n t :
l t~ 2 2x
lti~)
(3)
z-- Y
(4)
We i n t r o d u c e
.,,t~ l z
-
= . . . .
X
,,,
2 x
t'(63t't~ 6m~
= ~
+-
,,2 I
(5)
6-x5-
I
--+
(6)
x
In a d i a g r a m w h e r e z is plotted v e r s u s x e a c h of the m e a s u r e d p o i n t s (rex, tl) a n d (m2, t ~ ) w o u l d be r e p r e s e n t e d by a line, a c c o r d i n g to eq. (6}. The i n t e r s e c t i o n gives u s the v a l u e s of x a n d z we are looking for. The i n t e r s e c t i n g point is c h a r a c t e r i s e d by" t2
(2) 6
3 12
-
12
--+
1112
X
,
H11
X 2 ~lll 2
~
~
3
A 3 -
6-
nl I
m 2
We define:
/
ll -
II
t2
X
X"
nl I
t2
ti~
1"/72
/771
(7)
3 --+
,, i_0
ill 2
l~
112
/712
m 1
A2 = -
:
(8)
Ill I
li 3
A, =
1.
-
[1
1712
//11
/
(lO)
F r o m ( 9 ) w e get for t 2 = n t~"
A~
11 Fll I
-
-
1"112
= 11
1121111 A 2 = I)2
El111112
A]
] n m] - m 2
A3
(11)
111., ~ In 11112 -
1131111
-
A,
I
AoM
-
-
A~
(,,'-,,).,.-a,,M
(.2_,,).,. +A.M
I n s e r t i n g of eq. (15) into (I0) yields:
(12)
Ill 1ill 2
t13 Bll -- l'lt 2
A.
Ell.,
A3 = li ~
A 2 t] n2m] - m 2 A2 n2m~ - m 2 We define" m 2 = n i n e - A M
A~ ,, (,,'-,,)m, +AoM
(9)
(13)
(14) (15)
153
5_, , ) . , . A. . M I} ,,).,.
_ 3 1 ( n 2 - 1 1 ) m , + A , , M { l _ I 1 8A.,MI(n ! -27(n 3 n)nh-A.M 3 [-~n2_, A first o r d e r a p p r o x i m a t i o n l e a d s to: 1 _ x
1
2
or
-- -x" ,, ( / , -
or
r - x-
2 I,
(16}
n ( n - 1)m,
A,,M
(17)
l) .1. l.
I t2 ( t 2 - t l ) m 1 2 t2m ] -t]m 2
Eq. (6) r e a d s in a p p r o x i m a t i o n I n s e r t i n g (18) + (19) in (4) gives"
(18)
(19)
nl l
Ii
m -y=zx=
'e
(20)
2 t 1 q:m, - t,m 2 )
Eqs. (18) a n d (20) m a k e it p o s s i b l e to c a l c u l a t e the a d s o r p t i o n d a t a r a n d with a simple c a l c u l a t i n g e q u i p m e n t from only two m e a s u r e m e n t s . 2
For t 2 / t ~ = n = 2 eq. (20) r e s u l t s in dfintti's e q u a t i o n
m -y-
m~
(21)
2 nl 1 -- !112
3.
CALCULATION OF E R R O R
In o r d e r to o b t a i n a n i m p r e s s i o n of the e r r o r s involved in a p p l i c a t i o n of the t w o - p o i n t e x t r a p o l a t i o n m e t h o d we u s e in a n e x a m p l e m ( ~ ) - 1 and r = 100. So eq. ( 1 ) r e a d s : tl /
nh - 1 - e l,~ (22) We r e a d the i n d i c a t e d m a s s rn~ at a first m e a s u r i n g point a n d we a s s u m e t h a t t h i s i n d i c a t i o n is correct" t~ 1 t~2 mg~ =m~ (23) 100 2 10000 We s u p p o s e the r e a d i n g of the s e c o n d p o i n t i n c l u d e s a n e r r o r Am,,,, c a u s e d by the b a l a n c e : 12 l t ~" FAn,. (24) lO0 2 10000 This l e a d s to a n e r r o r in the e x t r a p o l a t e d v a l u e c a l c u l a t e d by m e a n s of eq. (20), w h e r e b y we m a k e a first o r d e r a p p r o x i m a t i o n in the n u m e r a t o r a n d a s e c o n d o r d e r a p p r o x i m a t i o n in the d e n o m i n a t o r : trig2
= 1112
+ l~lll w
=
154 ll'-
t2 (t2 - t~ ) m2~ n~
t: (t: -t, )loooo
m
2t, (,2mg,-,,mg2)
2,,
t lI ......
loo
m
l,
-
tl2
2.1oooo
_
t 1 t, tl t2 -+_
2.10000
-tiAra "'
/
J (25)
10000 - 1+
9A m
12 (t2 _ t, )
"
The e r r o r of the b a l a n c e Am,,, affects a n e r r o r of the e x t r a p o l a t e d result: Am
4.
"
=
t2
-Am~
(26)
DISCUSSION
Already with JS_ntti's 3PM a t i m e s a v i n g of the stepwise m e a s u r e m e n t of n i t r o g e n i s o t h e r m s u p to 70 p e r c e n t w a s possible; 2PM is even faster. For both m e t h o d s we show t h a t the gain of the s h o r t e n i n g of the m e a s u r e m e n t time is a c c o m p a n i e d by a d r a w b a c k , i.e. the 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 , w h i c h is s h o w n to be inversely p r o p o r t i o n a l to the s q u a r e of the m e a s u r e m e n t time. In case the m o l e c u l a r a d s o r p t i o n m e c h a n i s m is not a given factor before the s t a r t of the m e a s u r e m e n t , the application of the time saving m e a s u r e m e n t will involve e x t r a u n c e r t a i n t i e s . The g r e a t s t r e n g t h of 3PM is the fact t h a t he only n e e d s t h r e e m e a s u r e m e n t s to c a l c u l a t e the e q u i l i b r i u m value of a d s o r p t i o n rm. In the p r e s e n t p a p e r we show t h a t only two m e a s u r e d p o i n t s suffice. It h a s to be m e n t i o n e d t h o u g h t h a t with 2PM we a s s u m e t h a t the b e g i n n i n g of the a d s o r p t i o n at t = 0 is b e y o n d d o u b t . With 3PM on the c o n t r a r y there is no need to k n o w the b e g i n n i n g of the a d s o r p t i o n curve. D i s a d v a n t a g e of both 2PM a n d 3PM is t h a t one h a s to be c e r t a i n t h a t the a d s o r p t i o n m e c h a n i s m is d e s c r i b e d by eq. (1). REFERENCES
1. O. dgmtti, O. Ounttila, E. Yrjgmheikki: On c u r t a i l i n g the m i c r o - w e i g h i n g time by a n e x t r a p o l a t i o n m e t h o d . In" T. Gast, E. R o b e n s (eds.)" Progress in V a c u u m M i c r o b a l a n c e T e c h n i q u e s , Vol. 1. Heyden, London 1972, p. 345353. 2. E. Robens, C.H. M a s s e n , J.A. Poulis: On c u r t a i l i n g the time 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 by extrapolation. IX. P O R O T E C - W o r k s h o p fiber die C h a r a k t e r i s i e r u n g von feinteiligen u n d p o r 6 s e n F e s t k 6 r p e r n , 11.-12. 11. 1998, Bad Soden.
Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 9 2000 Elsevier Science B.V. All rights reserved.
155
R a t i o n a l d e s i g n , t a i l o r e d s y n t h e s i s a n d c h a r a c t e r i s a t i o n of o r d e r e d m e s o p o r o u s silicas in t h e m i c r o n a n d s u b m i c r o n size r a n g e M. Grtin, G. Btichel, D. Kumar, K. Schumacher, B. Bidlingmaier and K.K. Unger* Institut ftir Anorganische Chemie und Analytische Chemie, Johannes GutenbergUniversit~it, Duesbergweg 10-14, D-55099 Mainz, Germany This paper describes a novel process for the preparation of spherical mesoporous silica spheres in the submicrometer and micrometer size range. Tetra-n-alkoxysilanes are hydrolysed and condensed in the presence of nalkylamine as nonionic template and ammonia as catalyst. The porosity and the morphology parameters can be independently adjusted in wide ranges. These materials are promising adsorbents in separations techniques and valuable catalyst supports. 1. I N T R O D U C T I O N Silicas belong to the classical adsorbents which are grouped into aerogels and silica xerogels according to their dispersity (1). These technical products are termed as generic adsorbents which possess a wide applicability in industry and a low specificity in adsorption processes. On the other hand porous silicas used as packings in analytical chromatographic separation techniques (2) -in particular those applied in affinity chromatography (3,4)- are considered as physically and chemically tailored adsorbents. They show a high specificity towards distinct target compounds with a limited applicability. In between those two groups designed adsorbents are required. Design in this context means that their pore structural properties, surface chemistry and particle morphology can be highly flexible and adjusted to the adsoptive separation of target compounds based on rational concepts through modelling and databases (5). With respect to application, specificity, performance, productivity and development cost they are intermediates between generic and tailored adsorbents. Designer adsorbents should fulfil the following requirements :
* corresponding author
156 9 A d j u s t m e n t and control of the primary and secondary pore s t r u c t u r a l p a r a m e t e r s either by in-situ synthesis or by p o s t t r e a t m e n t 9 Fine-tuning of the surface chemistry by chemical reaction and by coating processes, respectively 9 Control of particle morphology, particle size and particle size distribution in a wide range of pore sizes 9 Reproducible and rugged m a n u f a c t u r i n g process with upscaling possibilities This paper describes an a t t e m p t to produce designed mesoporous silica adsorbents for adsorptive separation processes of value added chemical products from nanoscale to pilotscale.
2.
EXPERIMENTAL
2.1. C h e m i c a l s Tetraethoxysilane (TES 28 SQ) and aqueous ammonia (reagent grade, 32 wt%) were a gift from Merck KGaA, Darmstadt, Germany. 2-propanol (99+ %), ndodecylamine (98 %) and n-hexadecylamine (90 %) were purchased from Aldrich, Steinheim, Germany. 2.2. S y n t h e s i s The appropriate n-alkylamine was dissolved in a mixture of isopropanol and w a t e r at room t e m p e r a t u r e . Afterwards an appropriate a m o u n t of a m m o n i a was added. Then tetraethoxysilane was added under stirring and the reaction mixture was left overnight. The product was isolated by filtration on a sintered glass filter. A representative batch is given below : 5.1 g 450 ml 500 ml 6 ml 29 ml
n-hexadecylamine (90%) water, deionised 2-propanol aqueous a m m o n i a (32 wt%) tetraethoxysilane
(0.021 mol ) (25.2 mol) (6.53 mol) (0.1 mol) (0.13 tool)
2.3. R e m o v a l of t e m p l a t e 2.3.1. Solvent extraction 1.0 g of as-synthesized material was combined with 50 ml of 2-propanol and refluxed for 12 h. Afterwards the product was isolated by filtration and subsequent w a s h i n g with 50 ml of 2-propanol on a sintered glass filter. The product was dried at 363 K for 24 h. 2.3.2. Calcination The as-made material was placed on a porcelain crucible and submitted to calcination in air at 823 K for 5 hours (heating rate : 1 K/min).
157
2.4. 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 The original materials were subjected to a hydrothermal t r e a t m e n t to enlarge the average pore diameter. Details will be published in a forthcoming separate paper (6). 2.5. C h a r a c t e r i s a t i o n Nitrogen sorption m e a s u r e m e n t s were performed either on a Micromeritics ASAP 2010 (Micromeritics I n s t r u m e n t Corporation, Norcross, GA, USA) or on a Quantachrome Autosorb 6B (Quantachrome Corporation, Boynton Beach, FL, USA). All samples were degassed at 423 K before m e a s u r e m e n t for at least 12 hours at 10 -~ Pa. X-ray diffraction (XRD) patterns were recorded on a Seifert TT 3000 diffractometer (Seifert & Co, Ahrensburg, Deutschland) using Cu-K~ radiation of 0.1540598 nm wavelength. Diffraction data were recorded between 0.4 ~ and 14 ~ 2 | at an interval of 0.02 2 0 . A scanning speed of 1 ~ 2 0 per minute was used. Scanning electron micrographs were recorded using a Zeiss DSM 962 (Zeiss, Oberkochen, Germany). The samples were deposited on a sample holder with an adhesive carbon foil and sputtered with gold. 3.
SYNTHESIS CONCEPTS
Figure 1. Synthesis concepts for the preparation of mesoporous silica spheres. The synthesis of ordered mesoporous silicas of the MCM-41 type serves as profound starting basis for the tailoring of pore structural parameters. The classical synthesis of MCM-41 is performed with a silica source and an ionic
158
template eg. n-alkyltrimethylammonium bromide (7). The formation of a defined mesostructured phase takes place via an organic-inorganic assembly. The removal of the template by calcination yields a material with an unidimensional hexagonal array of pores in the low mesopore size range. By varying the n-alkyl chain length between C12 and C20 the average pore diameter can be adjusted in the range between 1.5 and 3.5 nm. In the course of expanding the synthetic concepts different types of templates were applied such as polar non-ionic, gemini types, oligomeric and polymeric. In this way the average pore diameter could be increased up to 50 nm (8). It would be highly advantageous to implement conditions where spherical porous particles are formed with variable bead size. One successful attempt was published by Stucky (9). However, the bead size was relatively large ranging from 0.2 to 2 mm. Our concept is based on the use of long chain n-alkylamines as templates which were first applied by thee group of Pinnavaia in neutral conditions (10-13). The advantage of their type of template as compared to ionic ones is that the template can be removed by extraction from the mesopores because it is not strongly bound in the organic-inorganic assembly. In 1968 St6ber reported on the synthesis of non-porous beads in the submicron size range using tetraethoxysilane (TEOS), ethanol as solvent and ammonia as morphological catalyst (14). We have combined the two concepts by carrying out the hydrolysis and condensation of TEOS in a 2-propanol/water mixture with long-chain n-alkylamines as templates and ammonia as catalyst at pH 10 to 11. In this way porous silica spheres in the submicron to micron size range were obtained. One key feature of the novel synthesis was to use a co-solvent eg. 2propanol in the starting reaction mixture to achieve a homogeneous solution. The reaction could be performed at room temperature without using an autoclave. The beads are formed within a period of minutes. After washing and calcination beads with the following properties were obtained. Table 1 Properties of the silica beads after synthesis Porosity
Morphology
spec. surface area
400-1,000 m2/g
appearance
spherical, not agglomerated
spec. pore volume
0.2-1.0 cm3/g
particle size
0.1-2.3 ~rn
average pore diameter
2.5-3.5 nm
Figure 2 shows a typical X-ray diffractogram of a calcined silica which was prepared with n-hexadecylamine as template.
159
d
v
CD
r
CD
.c_
0 .....
'2 . . . . .
4 .....
(~ . . . . .
8 .....
1'0" " " " 1~2" . . . .
4
2 theta
Figure 2. X-ray powder diffractogram of mesoporous silica, particle size 91.8 l~m, t e m p l a t e 9n-hexadecylamine, the Bragg peak corresponds to a d-spacing of 4.10 nm.
The X-ray diffractogram exhibits one sharp Bragg-peak in the low-angle range region which is caused by the regular a r r a n g e m e n t of the pore walls. Obviously this m a t e r i a l is not as well ordered as eg. MCM-41, which usually shows three or more Bragg peaks. Typical nitrogen sorption isotherms of a silica sample p r e p a r e d from n-hexadecylamine are shown in figure 3. 5OO
E
o
-6 o ..Q o
o
E o >
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<7.5nm and Vm; p t " bulk density calculated from textural properties and skeletal density; SBET" specific surface area obtained by BET method; Pt " pressure of change of mechanism during mercury porosimetry (change from collapse to intrusion); dp " particle diameter measured by TEM; So 9specific geometrical surface area.
182 One of the most interesting textural properties of the dried gels is their bulk density (Pb.~). A second independent estimation of the bulk density (pt) can be made by : 1
Pt =
1 (2) Vv+-P, where p s is the skeletal density and Vv is the specific total pore volume obtained by addition of the specific pore volume obtained by mercury porosimetry (~~g), the cumulative volume (V~um
100 ~ ........................................................
t A
t~
E
t,,)
lO 11
E o >
E
0.1
O.Ol 4 0.1
1
10
pore diameter (nm)
Figure 3. Pore size distributions of X3 (11), A I (0) and $2 (Q).
100
1000
183 X3 and A1 have micropores of the same size but A1 is much less microporous than X3. The supercritical drying induces a partial or even a total disappearance of the microporosity [ 13]. The distributions of X3 and A1 are the same in the range of the large mesopores and the small macropores. A1 has larger pores than X3 which is normal because of the partial shrinkage during the drying in ambient conditions. Aerogels shrink a little during the drying in supercritical conditions but to a far smaller extent than xerogels. Monodisperse silica sphere slab $2 has much smaller pores than X3 and A1 because of the compact arrangement of the spheres. $2 and X3 have similar amounts of" microporosity but different sizes of the micropores. The silica particle size dp (table 2) decreases from 23 to 13.8 nm for the xerogels and from 12.5 to 7.7 nm for the aerogels when the ratio EDAS/TEOS increases from 0.025 to 0.1 The specific surface area SBET decreases when the particle diameter increases and for a given particle size, the specific surface area of the aerogels is smaller than that of the xerogels because of the reduction of microporosity due to the supercritical drying. The differences between the particle sizes of the xerogels and aerogels is due to two factors :the difference of dilution and the partial disappearance of the microporosity in the aerogels. The particle size was corrected for both differences of dilution and microporosity to homogenise the samples. Samples X5 and A5 have the same dilution (R=10) and the same EDAS/TEOS ratio (0.1). Because of the nucleation process by EDAS [2], the same number of nuclei was created and the number and size of the particles is the same in both samples before drying. Thus the matter volume of one particle in both X5 and A5 is the same atter drying (matter volume of one particle = n dp3 / 6 e where e is the void fraction of one particle). By dividing the particle diameter dp by e 1/3, the difference of microporosity between xerogels and aerogels has been taken into accoum. To refer all the samples to the same dilution (R=10), the effect of the dilution for samples A1 and A2 (R=20) has been assumed identical to the one existing between sample A3 (R=20) and A5 (R=10), A3 and A5 having the same EDAS/TEOS ratio. Thus the corrected silica particle size dp/e 1'3 decreases from 39 to 21 nm for the xerogels and from 38 to 18 nm for the aerogels when the ratio EDAS/TEOS increases from 0.025 to 0.1. A So specific geometrical external surface area (table 2) was calculated from the diameter of particles measured by TEM (dp) assuming spherical non aggregated particles : 6
& -
(3)
P~ -d o The values of $6 computed from the particle diameters are much smaller than the specific surface area determined from N2 adsorption-desorption isotherms (SBET) for the xerogels and slabs. This may arise either from an underestimation of the 5"o surface area, due to the assumption of perfect sphericity of particles (this effect cannot fill up the big difference existing between $6 and SBEX), or from internal microporosity of the panicles. This last assumption appears to us the most realistic. The special case of the aerogels (SG larger than SBETor $6 a bit smaller than SBET) can be due to the small microporosity of the aerogels. Here the effect of the assumption of non aggregated particles for the calculation of So can be felt. It can lead to an overestimate of the external surface $6 compared to Sr3EXbecause in the N2 adsorption isotherms, the contact surfaces between particles is not accessible for nitrogen.
184 4. DISCUSSION From its definition (relation (1)), k should be related to the structure and the geometry of the filaments through d. Therefore the diameter of the silica particles dp of the xerogels and aerogels determined by TEM and from N2 adsorption data [2] was plotted against the k constant (figure 4). The correlation curves are nearly horizontal and the correlation coefficient are not good. The comparison should be made between k and the size of the aggregates da (figure 4) because the aggregates can be considered as the real building blocks of the threedimensional network and the buckling occurs at the agglomerate and aggregate level. The aggregate size was also determined by two means 9TEM and N2 adsorption data as described previously [2]. The correlation is good. The slabs of non aggregated monodisperse silica particles of the same size range than the xerogels and aerogels (S 1-$3) are only intruded by mercury during mercury porosimetry. So a necessary condition for the presence of a crushing mechanism is the aggregation of the particles to form a three-dimensional network.
1
60 ~,50 E c."lDm 4 0 5.
-o30
o
A
20 10-
50
100
k (nmIVlPa~~
150
200
Figure 4. Particle diameter dp determined by TEM (~) and N2 adsorption data (m) and aggregate diameter da determined by TEM (A) and N2 adsorption data (0) versus k. Xerogels are represented by full symbols and aerogels by open symbols.
185 Table 3 Geometric diameter evaluation of xerogels and aerogels by TEM and nitrogen adsorption Sample dp (nm) do (nm) d~ (nm) da (nm) TEM N2 TEM N2 + 6% + 7% X1 23.0+1.7 28 66+15 70 X2 18.3_+0.8 22 56_+10 62 X3 15.9_+0.9 18 37+4 42 X4 _a 16 -~ 36 X5 13.8_+1.4 15 -" 44 X6 12.0_+0.7 10 _a 22 X7 9.7_+0.6 8 -a 14 A1 12.5_+1.1 24 44-+7 57 A2 8.7_+0.5 15 31_+6 36 A3 7.7+1.0 10 25_+5 30 A4 _a 9 -~ 18 A5 11.3+1.4 13 32-+4 35 a not measured dp " particle diameter from TEM and N2 adsorption data and da ' aggregate diameter from TEM and N2 adsorption data.
Xerogel X7 has silica particles of a diameter of nearly 10 nm but its aggregates are very small (- 15 nm). X7 undergoes only crushing during mercury porosimetry. Aerogel A2 and A3 are constituted by smaller particles than X7 (8.7 and 7.7 nm respectively) but large aggregates (31 and 25 nm respectively). Those aerogels undergo successively crushing and intrusion during mercury porosimetry experiments. This strengthens the conviction that it is the size of the aggregates that is the important morphological property controlling the resistance towards compression during mercury porosimetry experiments.
5. CONCLUSIONS The results with the slabs of monodisperse non aggregated silica spheres (of the same size range than the xerogels and aerogels) which undergo only intrusion during mercury porosimetry implies that the particles need to be aggregated so that the compaction mechanism takes place. The presence of a mixed behaviour (crushing followed by intrusion) during mercury porosimetry experiments, the value of the pressure of change of mechanism Pt and thus the value of the constant k of the buckling equation are related to the size of the aggregates. The fact that samples with small particles (do < 9 nm) but large aggregates (da > 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 <58-106 24 62 MCM-41c Ar <58-106 28 74 MCM-41 c Ar <58-106 36 87 MCM-41c Ar <58-106 42 100 MCM-41 ~ C2H4 <116-184 24 <116a MCM-41 ~ C2H4 < 116-184 28 130 M CM-4 lc C2H4 <116-184 36 148 MCM-41 c C2H4 < 116-184 42 163 MCM-41 ~ C5Hlo 243-313 39 253-273 MCM-41 ~ C~Hlo 273-323 29 B MCM-41 ~ CC14 273-323 34 303-323 MCM-41 C02 < 156-215 24 156 MCM-41 ~ C02 < 156-215 28 173 MCM-41 c C02 < 156-215 36 195 MCM-41 c C02 < 156-215 42 215 MCM-41c H2 20-77 31.5 b MCM-41 N2 <57-77 28 57 MCM-41 c N2 <57-77 36 68 MCM-41 ~ N2 <57-77 42 76 MCM-41 c 02 <64-102 24 64 MCM-41 ~ 02 <64-102 28 76 MCM-41c 02 <64-102 36 91 MCM-41 ~ 02 <64-102 42 102 MCM-41 ~
Hyst. Obs.? d Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes
a: predicted, b: could not be determined, c: synthesis procedure of ref (2), d: Was there any hysteresis observed for minimum of one sample? CN carbon nanotubes, Ph-MCM-41 Phenyl modified MCM-41, Pol-MCM-41 polymer bonded MCM-41. Syl-MCM-41: silylated MCM-41.
190 and mk-bottle effect [1]; the thermodynamic and mechamcal mstability of the adsorbate meniscus using tensile stress hypothesis [4,6,7]; the intrinsic pore size distribution [8]; heterogeneity of the adsorbate surface [9]; the microscopic statistical mechanical approach [10]; and the empirical approach [5]. Initial attempts using the microscopic statistical mechanical approach have not yielded satisfactory quantitative matches with experiment [5,6] and subsequently only a few researchers [4,5,6,8,9] found success in explaimng the absence of hysteresis in MCM-41, though the latter models are yet to be tested for various adsorbates. Based on the assumption of surface heterogeneity in MCM-41, it has been shown [9] that the adsorption isotherm of mtrogen at 77.4 K in MCM-41 is reversible for the pore size in the range of 2.8-3.2 nm. More recently, use of the Saam-Cole theory [11] in conjunction with the concept of an intrinsic pore size distribution has led to the conclusion [8] that the adsorption isotherm of nitrogen at 77.4 K on MCM-41 is reversible for pores below 3.6-3.8 nm. Also, based on the thermodynamic and mechanical stability of the memscus usmg the well-known tensile stress hypothesis, it has recently been shown [4,6,12] that DcH is around 3.4 nm for N2 adsorption at 77.4 K, close to the experimental value of about 3.84.3 nm [4]. The present work deals with analysis of the adsorption isotherm and the hysteresis observed in case of pure MCM-41 of various pore sizes, and mixtures prepared in our laboratory. Models reported in the literature, as well as one proposed by the authors explaining the criticality of hysteresis and of capillary condensation, are applied to interpret experimental data for various adsorbates. 2. T H E O R E T I C A L BACKGROUND 2.1 The S a a m - C o l e a p p r o a c h This approach has been originally proposed as an alternative to the Kelvin theory and can be used for estimating the critical thickness during adsorption or desorption [11]. In a cylindrical pore of radius R, if the change m chemical potential of an adsorbate molecule in the symmetrical state (cylindrical meniscus, during adsorption) and asymmetrical state (hemispherical meniscus, during desorption) are defined by A~s and Ap~ then at equilibrium, the thickness of the adsorbed film can be obtained by usmg the stability criterion 0A~/& = 0 and 5A~a/St = 0. When A~s and A~a are expressed appropriately [8], these stability criteria provide an analytical expression between the critical thickness difference (At = t~-t~) and the radius of the pore, R, given by
(1)
It has been proposed [8] that the adsorption isotherms in MCM-41 may be reversible if the uncertainty in mtrinsic pore size (as a result of uncertainties in
191
the position of the adsorbate molecule on the surface of the solid) exceeds the At value (which determines the symmetry-asymmetry transformation).
2.2 Modification of the Saam-Cole approach The Saam-Cole approach has several approximations, among which are the neglect of the solid-adsorbate interaction and curvature effects on the adsorbate chemical potential, and curvature effects on surface tension in symmetrical and asymmetrical states, while modeling the multilayer region. Here, a more accurate version of the above approach has been introduced and tested for explaining the reversibility of adsorption m MCM-41. For fluid molecules mside a cylindrical pore of radius R, the mcremental potential function has been expressed as [4,6,7] where ~vs(r, R) represents the net interaction potential between an adsorbate molecule at r and the entire solid surrounding the pore, while ~FF(r,R) represents the corresponding potential if the bulk fluid was instead present in place of the surrounding solid. Both these potentials incorporate the interfacial density profile. Using an analysis similar to that described in section 2.1, the equations for estimating the critical thickness are given by
r
aO(R-t,R)
at Or Ot
y v ~ , ( R - t+ A / 2 ) _ 0 ( t ) (R-t-2~2) 3 ~
y v:[(R-t) 2 - A 2/2) =0(t~) (R-t-A/2)Z(R-t-2) 2
(2)
s
(3)
Therefore, for a given mtrinsic pore size distribution (following the approach of Inoue et al. [8]), At (= ts- ta), and the hysteresis critical pore size (DcH=2R) can be evaluated by simultaneously solving Eqs. (2) and (3).
2.3 T h e r m o d y n a m i c and m e c h a n i c a l stability of the interface. While studying adsorption in mesopores using the molecular continuum model we have found [4,6,7] that there exist two critical diameters based on thermodynamic analysis of the adsorption, and two more when the mechanical stability of the meniscus is considered. These criticalities refer to the critical pore diameter below which there either exists a different mechanism of adsorption, or the adsorption is reversible. Here we provide a brief outline of these criticalities. The chemical potential of the fluid adsorbed in a cylindrical pore of radius R can be expressed as [6,7] g~(r,R)- gj(r,R)+ ~(R-r,R)- constant(R). After considering the interracial free energy changes, the equation for the thermodynamic stability of the equilibrium cylindrical mterface was obtamed, which on further differentiation leads to the condition
192
02~ ~2
2y~v;(R-t+A) -
(4)
(R_t_2/2)4
which must be satisfied by the critical pore size below which surface layering followed by capillary condensation cannot occur. The condition for capillary coexistence at the hemispherical meniscus can be expressed as
R)+
Iv dV-
~'o
2y~v;(R-t) 2
[(R-t)(R-t- 2)+ Actz- / 4](R-t- 2)
= o
(5)
Thus Eq. (4) and (5) provide two criticalities based on a purely thermodynamic analysis of the adsorption in the cylmdrical pore. During adsorption or desorption, although the thermodynamic stability criteria are satisfied, the condition for mechanical stability of the meniscus has to be satisfied. The mechanical stability criteria for the cylindrical memscus (during adsorption) and hemispherical meniscus (durmg desorption) are given by [4,6,7,12] y~
(6)
(R-t-A/2) 2y~ (R-t-2)
(7)
respectively. When the equality in the stability criterion given by Eq. (6), or Eq. (7), is solved with Eq. (4), or Eq. (5), the estimates of the critical diameters can be obtained. Clearly Dcp, which is obtained via the mechanical stability of the cylindrical meniscus, bounded by the equality in Eq. (6), represents the critical pore diameter below which surface layering can not occur. In pores below this size, adsorption must proceed by volume filling. On the other hand, the equality in Eq. (7) bounds the mechanical stability of the hemispherical meniscus during evaporation, and provides the critical pore diameter, DCH, below which this meniscus is absent. In such pores, the condensation is reversible and hysteresis does not occur. While both these critical sizes are evident m MCM-41, which has a narrow size distribution, m conventional mesoporous media which have a wide pore size distribution only the critical size for absence of condensation Dee will be observable, and can be obtained from the lower closure of the experimental hysteresis loop.
193 3. E X P E R I M E N T A L S E C T I O N Siliceous MCM-41 samples of six different pore sizes were prepared following the procedure reported in the literature [2,4,6] using alkyl trimethyl ammomum halide surfactant templates CnH2n+I(CH3)3NX (termed as C8, C 10, C 12, C 14, C 16 and C18, indicating the number of carbon atoms in alkyl chain length of the surfactant, X being the halide group). Three additional samples were prepared by mechanical mixing of the different pore size samples: CM1 (approximately 50% C10 + 50% C14), CM2 (50% C12 + 50% C16) and CM3 (50% C12 + 50% C18). Characterization of the pure samples of MCM-41 was performed with X-ray diffraction, scanning as well as transmission electron microscopy, mercury porosimetry, small angle neutron and X-ray scattering, and gas adsorption, with details given elsewhere [4,6,12,13,14,15]. Adsorption isotherms of argon, oxygen, nitrogen and carbon dioxide were measured on a volumetric ASAP 2010 apparatus. 4. R E S U L T S A N D D I S C U S S I O N 4.1 A d s o r p t i o n on MCM-41 M i x t u r e s Nitrogen adsorption isotherms on pure MCM-41 samples at 77.4 K indicated that the hysteresis critical diameter lies somewhere between 3.8 nm (a)
ff~; 8o0
~o ~ ~~
c
i(a)
/
20.
I
~
i
1
i .
~
z~mo
15
_ I~
10
oo
02
04
06
08
O0
o
relabve pressure ( P ~ O
.
02
.
.
04
.
o5!
/
1
06
08
10
!
1 O0
relabve pressure ( P / P : )
25 ~
/
9
/
I
(d)
if" 6oo
,
o5
: 20
40
60
80
O0 25
2OO
/
~
""'
z:
004
oo
04
06
08
relabve pressure (P/P~
0
i
15
20
25
30
35
diameter (A)
F i g u r e 1. Adsorption isotherm of nitrogen at 77.4 K on (a) CM1, (b) CM2, (c) CM3 and (d) pore size distribution of CM2 by BJH method, e: adsorption, O: desorption.
40
60
80 S
05 .
4O
/
;
1 10
Ii 20
i
15
~.~ ~ ~ 1
ool lO
40 i
20
, I
05 t
0 02
000
02
~ 2Z
I~ 10 I
100
o
15
20
(d)
20!i;
o O6
/
,
1
i(c)
7O0
"6 >
1 ,oi
2/<)" 2 / '
i
i
20
'
---j l
o
z~
25 I (b)
c
6O
pore diameter
80 [A]
J oo
.......
20
1. . . . . . . . . . . . . . .
40
60
80
pore diameter [A]
F i g u r e 2. Relationship between At (=ts-ta) and pore diameter for (a) N2 (77.4 K), (b) 02 (77.4 K) and (c) Ar (77.4 K) and (d) Ar (87.5 K) adsorption on MCM-41 (lines: 1: method of Inoue et al. [8]; 2: Eqs. (2), (3); 3: method of Broekhoff and de Boer [16])
9
194
and 4.3 nm. Therefore, for the adsorption of mtrogen in mechanically mixed samples, it is expected that filling and emptying of the individual pores will occur reversibly in confirmed by our experimental findings as shown in Figure 1. The results indicate that the hysteresis region is unique and unchanged in mixtures. CM1 and CM2. It is expected that the adsorption isotherm of CM3 shows two condensation jumps, one of reversible and irreversible each. These results are Application of various theories for estimation of PSD indicated that peak position in the PSD curve for a mixture of two MCM-41 samples of different pore diameter (refer Table 3) is very close to that obtained for the pure samples. 4.2 The c r i t i c a l d i a m e t e r s DHC and DcP. By combining the Saam-Cole theory with the concept of mtrinsic pore size distribution, it has recently been shown that DHc for nitrogen adsorption at 77.4K on MCM-41 is about 3.6-3.8 nm [8]. This is very close to the experimental value, Section 2.2, was also found to give maccurate results for different adsorbates as well as for adsorption at different temperatures, as can be seen from Figures 2 and 3. The results of the modified Saam-Cole approach, when combined with Broekhoff and de Boer's theory [16], (shown in Figure 2a), are found to be close to the experimental results.which lies between 3.8 and 4.3 nm. However, it was found that when this approach is applied to adsorption of other gases on MCM41, it gives mconsistent results, as shown in Figure 2. As shown in Figures 3 and 4, it was also found to produce mconsistent results when applied to adsorption of 0.6
Symbol adsorbate .
A~
O
0.5
9
[] ,5 0.4
V
0.3
5 |
0.2
o
) , ........ ~,
,,,~/
o,
~
SF,
9
Xe Ar
.... . /
//5
[]
~ -~/,/ fi
t/
//',
I V 1~r, I ~,A //-
//Z
/
\/ ~r
,
8
.../-
31 /
~ ,z/ .
conventional / , ~ I /// porous / //" / Y/" rnaterialsJ /~"
7/~7
I , 1.6
. =/" /,A
co, j / 7 ~
,"
~,',6
~9 / /
~///
c#, !
A
I-.-
=s
N2
1.8
K,r,~,,~4
//
~ I
/!
~'
,:
<
95 K 10OK
1.4-'
105 K
--,,
~/
1
"~85K 80 K
/
1.2
77.4 K
0.1
0.0
0.00
0.05
0.10
0.15
cgD
F i g u r e 3. Variation of TCH or Top with pore diameter D. Predictions1: [8], Eq. (1); 2: Eqs. (2),(3); 3: [10]; 4: [5]; 5-8: current model (Section 2.3).
0.20
1.0' 20
30
40
pore diameter [A]
F i g u r e 4. Relationship between At and D for nitrogen adsorption on MCM-41 at different temperatures using model described in section 2.2.
195
Table 3 Estimates of pore diameter (nm) of mixture of MCM-41 samples by various models (values corresponding to two peaks are given). Sam. CM1 CM2 CM3
BJH 1.37 1.65 1.72
Ads 2.04 2.42 2.96
BJH Des 1.49 2.11 1.76 2.52 1.96 3.04
HK 20.3 24.6 25.6
SF 29.6 35.7 43.4
23.3 28.2 29.3
BD 33.8 40.9 50.4
21.1 24.6 24.6
28.0 32.0 37.5
DFT 23.4 29.5 25.2 34.3 27.3 37.0
nitrogen at different temperatures. The modified version of this model, which has been discussed in
4.3 T e m p e r a t u r e d e p e n d e n c e of DcH and DcP As the two critical diameters for adsorption of gases m mesoporous solids, DCH and Dcp, increase with increasmg temperature [5]. We have tested various theories against this experimental finding, and compared the results with the experimental DCH data on MCM-41 shown in Figure 3. An empirical relation [5] gives results quite close to the experimental DcH data as shown by curve 4 in Figure 3. It is often assumed that for any adsorbate Dcp and DcH are the same, and approximately 2.0 nm, which is also the arbitrary lower mesopore limit according to IUPAC classification [1]. However, it is found here that this limit is actually close to the critical diameter for meniscus stability durmg evaporation. The predictions of the microscopic statistical mechanical approach [10] which assumed Dep and Dell to be the same, appear to be consistent with the experimental values for Dc~, as shown by curve 3 in Figure 3. As already discussed, the assumption that DcP and DcH a r e equal is inconsistent with the recent experimental results. The predictions of the approach of Inoue et al. [Eqs. (1)-(3)] indicates that DCH decreases with increasing temperature, as shown by curve 1 in Figure 3. This is inconsistent with the experimental results, which indicate that DCH increases with temperature. It was found that the modification of the approach of Inoue et al. [Eqs. (2) and (3)] also gives this inconsistent trend, as evident by curve 2 in Figure 3. The plot of (t~-ta) [obtained from this approach] versus pore diameter for different temperatures is shown in Figure 4. It can be seen that for a given pore diameter, the value of (t~-ta) increases with mcreasing temperature, yielding a decrease in hysteresis critical diameter with mcreasing temperature. This is inconsistent with the experimental results. The predictions of the approach proposed by the authors (discussed in section 2.3) based on the thermodynamic and mechanical stability of the meniscus for different adsorptives are as shown by curves 5-8 in Figure 3. The results for Dc~, obtained by using the molecular parameters of nitrogen, argon and oxygen, shown by curve 5, 6 and 7 respectively m Figure 3, are seen to be well within the range of the experimental data for adsorption of various gases on MCM-41.
196
5. CONCLUSIONS The reversibility of adsorption isotherms of mtrogen on the MCM-41 mixtures is dependent on the behavior of the pure samples, demonstrating the umqueness of the hysteresis region. As expected, the pore size distribution of the mixtures had two peaks, each corresponding to the pore size of the individual components in the mixture. Of the approaches for predicting the critical pore sizes DcH and Dcp, the approach proposed by the authors based on thermodynamic and mechanical stability of the adsorbate in the cylindrical pores was the closest to the experimental data for adsorption of gases on MCM-41. The Saam-Cole approach, in conjunction with the recently proposed concept of intrinsic pore size distribution, gives inconsistent results with regard to the effect of temperature on the critical pore size. The results also indicated that the true value of DcH for nitrogen adsorption at 77.4 K may lie between 3.8 nm to 4.3 nm, consistent with the previous results. It is seen that the mimmum pore sizes for capillary hysteresis and condensation predicted by our theory are close to those estimated from the empirical correlation of data. The pore diameters obtained by various models for uniform pore size MCM-41 samples are close to the estimates based on adsorption on their mechanical mixtures. REFERENCES
,
.
4. o
6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
S. J. Gregg, K. S. W. Sing, Adsorption Surface Area and Porosity, Academic Press, New York, 1982. J. S. Beck,, J. C. Vartuli,; W. J. Roth, M. E. Leonowicz, C. T. Kresge, K. D. Schmitt,, C. T-W. Chu, D. H. Olsen, E. W. Sheppard, S. B. McCullen, J. B. Higgins and J. L. Schlenker, J. Am. Chem. Soc. 114 (1992) 10835. A. Sayari, Chemistry of Materials, 8 (1996) 1840. C. G. Sonwane, S. K. Bhatia and N. Calos, Ind. Eng. Chem. Res., 37 (1998) 2271. K. Morishige and M. Shikimi, J. Chem. Phys., 108 (1998) 7821. C. G. Sonwane and S. K. Bhatia, Chem. Eng. Sci., 53 (1998) 3143. S. K. Bhatia and C. G. Sonwane, Langmuir 37 (1998) 2271. S. Inoue, Y. Hanzawa, K. Kaneko, Langmuir 14 (1998) 3079. M. W. Maddox, J. P. Olivier, K. E. Gubbms, Langmuir, 13 (1997) 1737. R. Evans, R, U. Marini Bettolo Marconi, P. Tarazona, J. Chem. Soc., Faraday Trans. 82 (1986) 1763. M. W. Cole, W. F. Saam, Phys. Rev. Lett. 32 (1974) 985. C. G. Sonwane and S. K. Bhatia, submitted to Langmuir (1998). C. G. Sonwane and S. K. Bhatia, Langmuir, in press, (1998). C. G. Sonwane, S. K. Bhatia, and N. Calos, submitted to Langmuir (1998). C. Nguyen, C. G. Sonwane, S. K. Bhatia, D. D. Do, Langmuir, 14 (1998) 4950. J. C. P. Broekhoff, J. H. de Boer, J. Catalysis, 9 (1967) 8.
Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScienceB.V.All rightsreserved.
197
C o m p r e h e n s i v e S t r u c t u r a l C h a r a c t e r i z a t i o n Of MCM-41: F r o m M e s o p o r e s To P a r t i c l e s C. G. Sonwane, A. D. McLennan and S. K. Bhatia* Department of Chemical Engineering, The University of Queensland, St. Lucia, Brisbane, QLD 4072, Australia
In the present work the meso- and macro-structural characteristics of the mesoporous adsorbent MCM-41 have been estimated with the help of various techniques. The structure is found to comprise four different length scales: that of the mesopores, the crystallites, the grains and of the particles. It was found that the surface area estimated by the use of small angle scattering techniques is higher, while t h a t estimated by mercury porosimetry is much lower, than that obtained from gas adsorption methods. Based on the macropore characterization by mercury porosimetry, and the considerable macropore area determined, it is seen that the actual mesopore area of MCM-41 may be significantly lower than the BET area. TEM studies indicated that MCM-41 does not have an ideal mesopore structure; however, it may still be treated as a model mesoporous material for gas adsorption studies because of the large radius of curvature of the channels.
1. I N T R O D U C T I O N The discovery of the family of model mesoporous adsorbents ~ MCM-41 has resulted in intensive research in their synthesis and applications, as well as in the refinement of existing adsorption models. ~-s These materials are gainmg importance as a result of the reported presence of an ideal pore structure, the ease of tuning the pore diameter between 1.5 and 10 nm, and very high surface areas of the order of 1000 m2/g. Although macrostructure characterization is important for the interpretation of adsorption dynamics and catalysis effectiveness, it has received very limited attention for MCM-41, though some electron microscopic observations of uncalcmed material have been reported. 9 This is possibly because of the other novel features associated with these materials, which have attracted the bulk of the attention. The total surface area estimated from gas adsorption is reported to * To whom correspondence should be addressed. Email: [email protected]. Fax: +61 7 3365 4199. Telephone: +61 7 3365 4263.
198
be very high, but the results are neither verified with any other techniques nor has the actual contribution of the mesopore area been established. Among the objectives of the current work is the establishment of an overall structure of MCM-41 over the various length scales, starting from mesopores up to the particles. Also, the surface area of MCM-41 has been estimated here by several techniques. To the best of our knowledge such a comprehensive structural characterization has hitherto not been published.
2. E X P E R I M E N T A L
MCM-41 materials of various pore sizes were prepared by hydrothermal synthesis usmg alkyltrimethylammonium halides as templates (with alkyl chain length of n = 8, 10, 12, 14, 16, 18) following the established procedure. ~.~~In a typical synthesis, sodium silicate, water and an appropriate quantity of surfactant template were mixed with stirring. The resulting mixture was allowed to stir for 30 rain at room temperature. The gel was then heated in a sealed stainless-steel reactor at 373 K for 7 days. The product was heated, washed, filtered and dried in ambient conditions for 2 days. It was then calcined at 823 K (with an imtial heating rate of 5 K/min) for 20 h m the presence of air. The calcined MCM-41 samples were characterized by scanmng and transmission electron microscopy (SEM and TEM, respectively), X-ray diffraction (XRD), mercury porosimetry, small angle X-ray and neutron scattering (SAXS and SANS, respectively), gas adsorption, laser particle size analysis, optical microscopy and helium pycnometry. The uncalcmed samples were not characterized by any of these techniques. The adsorption isotherms on calcmed MCM-41 samples were measured on a Micromeritics ASAP 2010 analyzer using standard volumetric techniques. Although we utilize only the nitrogen data here, isotherms of oxygen, argon and carbon dioxide are provided elsewhere. ~~ Before the analysis, the samples were degassed at 250~ for a m m i m u m of 12 h at about 6 • 10 .6 Tort. The measured mesopore volume and XRD d spacmg allowed us to calculate the mesopore diameter of each MCM-41 sample from geometrical considerations. ~~ Mercury porosimetry was carried out on a Micromeritics Autopore II 9220 porosimeter over the pressure range 0-412 MPa. SANS patterns were obtained using the LOQ facility of ISIS, at the Rutherford Appleton laboratory in Oxfordshire, U. K. Liquid-hydrogen-moderated neutrons in the w a v e l e n ~ h range 2-10/~ were used to investigate structures in the size range 20-1000 A from data collected over 0.005 < s < 0.22 ~-1. The optical microscopy was carried out on a Leitz Metallux 3 (Cambridge Instruments Quantimet 570 Image Analyzer) microscope. SAXS data was collected from samples packed in Lindemann glass capillaries, usmg a custom-built Kratky camera with a position-sensitive detector, operating with Quartz monochromated Cu Ka radiation. The data sets were backgroundsubtracted and de-smeared using Glatter's ~:~.~4procedure.
199 3. R E S U L T S
AND DISCUSSION
3.1 S u r f a c e
Areas Estimated
By Various
Techniques
The MCM-41 s a m p l e s s y n t h e s i z e d in our laboratory were initially characterized by X-ray diffraction a n d nitrogen gas adsorption. Typical characterization plots for the C14 sample are shown in Figures 1 and 2. Well-defined p e a k s were obtained by XRD for all samples studied, a n d indicates a typical honeycomb a r r a n g e m e n t of pores. T r a n s m i s s i o n electron m i c r o g r a p h s of the samples 1~ also indicated a typical honeycomb p a t t e r n of the mesopores. E s t i m a t e s of XRD d spacing (100) a n d pore size for the various samples are given in Table 1. It can be seen t h a t d spacing and pore size increase with alkyl chain length, consistent with previous studies. 1.4 T a b l e 1. E s t i m a t e s of d-spacmg, pore size, crystallite size, grain size and particle
size for various MCM-41 samples. ~ Crystallite Grain Particle Sample d-spacing Mesopore diameter diameter diameter (nm) diameter (#m) (#m) (pm) (nm) 0.02 0.94 6.52 C8 2.89 2.30 C10 2.92 2.73 0.05 0.84 6.28 C12 3.12 2.96 0.05 0.78 5.85 0.06 0.55 5.76 C14 3.47 3.38 0.05 0.33 6.23 C16 3.79 3.78 C18 4.33 4.36 0.04 0.49 6.18 # The mesopore size was estimated by using gas adsorption and XRD d-spacing, the crystallite size was estimated from line broadening of X-ray diffraction, the gram size was estimated by mercury porosimetry and the particle size was estimated from the optical microscopy, as discussed in the text.
30 ,r 100 O
E
CC.'- L,. -C, -C ..C-. ~ > C i . ~
~
'
E
o~
C
25 ~
O ""J
.~ 20 ~
t-
/
,4 I... v
,
/ /
ttJ t-O
m 15-~
I ~
@q
,
z o
i
t--
o
E
~
<
1
~4
L_ 0
2
3
4
5
(
20 (degrees) Figure 1. X-ray powder diffraction pattern of C 14-MCM-41
~-~
2 5
i
l
0.0
0.2
0.4
0.6
Relative pressure,
0.8
1.0
P/P0
Figure 2. N2 adsorption isotherm at 77.4 K of C 14-MCM-41
200 T a b l e 2. Surface area (m2/g) estimated by various techniques. Adsorption (BET) N2
Ar
Ar
O2
CO2
(77 K) (77 K) (87K) (77 K) (195 K)
Hg Porosimetry
SAXS SANS CWT VWT
C8 C10 C12 C14
937 1318 1280 1162
1100 973 1027 1015
873 965 963 954
1063 1150 1163 888
946 868 1123 1018
19 143 194 299
939 1665 1835 2579
1333 2616 -
645 648 656 606
661 1024 1016 933
C16
1240
895
1125
909
1013
365
2599
2588
615
986
C18
1123
920
942
1043
1338
295
2745
3941
607
902
The estimates of surface area of MCM-41 by various techniques are given in Table 2. The surface area from gas adsorption was obtained from the BET equation which, while questionable for microporous materials, should be suitable for the predominantly mesoporous MCM-41. Although the surface areas for all the samples using different adsorptives are in the range of 900-1300 m2/g, there are no trends observed. The BET surface area represents the total surface area r a t h e r t h a n the mesopore area. Recent studies 4 have indicated that the BET method overestimates the surface area of MCM-41. This was attributed to the possibility of considerable overlap of monolayer and multflayer adsorption in the recommended range of pressures for BET analysis. Estimates of the surface area Sm were obtained using 4 the following equation, with surface area and pore radius calculated from geometrical considerations, and on the assumption t h a t MCM-41 is made of infinitely long cylindrical pores arranged on a two-dimensional hexagonal lattice (similar to t h a t considered 1~ for estimating pore diameter),
Sm
2Vp
4rd~
R
p~ [.,f3(ZR + W) z - 2zR 2].,
(1)
in which vp is the specific pore volume, p., is the skeletal density and W is the wall thickness. The value of W was taken as 1 nm for the constant wall thickness (CWT) approach, while for variable wall thickness (VWT) approach 11 it was estimated using
~/32dx~ - 1.2125dxR.DI W - ----~
PsVp 1+ PsVp
(2)
where dXRD is the d spacing obtained from the X-ray diffraction pattern. Equation 2 has been obtained from the expressions of pore diameter and the XRD d spacing using the structural assumption indicated above validated by
201 microscopic observations. ~5 This approach is preferable to the alternative based on conventional adsorption models (Dubmm-Astakov, Saito-Foley, and BJH), in view of their observed 1~ inaccuracies in describing adsorption in MCM-41. As evident in Table 2, the surface areas obtained by CWT are lower than those estimated by the BET technique, while those from VWT with wall thickness estimated from the primary mesopore volume are closer. Surface areas of MCM-41 have also been estimated by SAXS and SANS, usmg the Debye equation16 for the surface area of a random space-filling tessellation
4xl04r162
Area
-
(3)
but these are much higher than those from gas adsorption methods (see Table 2). In Eq. 3 ~b, and ~ represent the solid and pore volume fraction, respectively, while a and d~p represent the correlation length and apparent density, respectively. Estimates of the surface area of C8 from the Debye equation are close to those from gas adsorption, indicating its surface randomness, consistent with our previous findings by HRTEM. ~~ This is not the case for the C10-C18 samples, for which the earlier suggestions ~7 of a geometrically heterogeneous bilayered surface have been modified 18 to indicate a smooth surface. This is consistent with our own fractal characterization 19 using molecular tiling. Consequently, further studies overcoming the structural limitations of the Debye equation are necessary to obtain an unequivocal model of the microstructure for the C10-C 18 samples using SAS data. The surface area of MCM-41 obtained by mercury porosimetry, calculated usmg the Rootare-Prenzlow equation, 2o is lower than that found by the adsorption method, as shown in Table 2. In general for MCM-41, the surface areas obtained were in the following order: mercury porosimetry < gas adsorption < SAXS < SANS. The mesopore diameters of the MCM-41 studied in the current work are in the range of 2 . 3 - 4.4 nm, and the lowest diameter of the cylindrical pores in which mercury can penetrate (at the highest pressure studied in this work) is about 3.2 nm. Therefore, if the walls of the pores are rigid, for the samples C14C 18 the surface area reported by mercury porosimetry is too low.
3.2 Mesopores Details of the calculation procedure for estimating the mesopore size of MCM-41 by geometrical considerations using the mesopore volume and the XRD d spacing have been recently reported by various researchers. ~~ Estimates obtained usmg the nitrogen adsorption isotherm at 77.4 K indicate a consistent increasing trend in pore size with increasing alkyl chain length, as shown m Figure 3 and Table 1. These results are consistent with the literature ~,1~ and were also found to be consistent with theoretical predictions. ~o The wall thickness estimated from these results is in the range 0.6-1.1 nm for the C8-C18 samples. This is consistent with the recently reported wall thickness 11,21 based on geometrical considerations. Figures 4a and b show that the pores of MCM-41, which are
202 9
.
:
..
................
. . . . . ..
i9 " ..
" " ~ " ~ ~ 4. 'i ~ 5.
:
:
~: ::
:. "i ~ ":~..
9
:i
~.::
:
9 "::
:
':
.. 9
:~:
.~" ~.~:~:~:~: : ~ : ~
.
~
:
~
i :
_
9~."
._ 20 n,'n
9
i~
.,::
:
~.
:'.
~
:.:,~.,:::""..i. . ,.4 ;.:. :..~.:.~.:... .'":]'":" :" ..... :,: ::~ .....
"~T~
; ?~",:.i 9 : ~::~:
.""
"
,q:}."~ ...' ~ ' h ; ~?.:,:~ :
.~".'~, . , . : . .
~}u~""~~'~:."~~!~ ~ti:::;: ~9 ,. . . . . ~,t~ .~ ...... :~,~ ~.', }~ t.~:::.,:.~. ":~. ' : :::.. ,~. ~,}0~.} .... ~,,,If,L, ~,:.~; ,: ~:~,...:!.,.~.~! '.-.~.~:'.~
~
~~---~-:~~. ~ ~ ~ - - : ~ ......... ,,'
Figure 3. Comparison of pore, crv'stallite, gram, and particle diameter for various MCM41 samples.
:,,,~ ...
~..
~=:==;~'! "
~.~
~;.
:.~..'.
:~.~.'." '~ :~ " ~{'~'" 9 . .?~ ~.. .... "~" ~ ] :. ~,.:~::
9 " " .. .. . . . .
....
9 ," g
9
.
.
.
i "~:i: ~:'~/~ ,':" ;:~! ~.'' ,~.:~ }~....~ ....
9~ t
~.~..' . . . . . . 9,'~::I:
...:~i.-
Figure 4. Transmission electron micrographs of (a) mesopores and (b) crystallites in MCM41.
generally thought to be straight channels, are actually curved with small constrictions along the length of the pore, confirming the recent findings. 22 The radius of c u r v a t u r e can be seen to be much higher t h a n the diameter of the pore, as well as the length scale of molecular interactions. Although it is difficult to estimate the constrictions quantitatively at such magnifications, the TEM pictures clearly indicate their presence in all the mesopores. Since it is known t h a t the fluid-solid and fluid-fluid interaction forces are not significant beyond a few molecular diameters, the c u r v a t u r e of the pore channels m a y not have any significant effect on adsorption. While we have not a t t e m p t e d to quantify the curvature, it should be possible to do so based on statistical image analysis of digitized TEM micrographs. Thus, even though MCM-41 does not have an ideal mesopore structure, it m a y be t r e a t e d as a model adsorbent. It m a y be noted t h a t these observations are based on our findings from the C16 sample. Similar studies with the others are yet to be conducted, but the resulted are not expected to be different. 3.3
Crystallites
MCM-41 is considered as crystalline on a macroscopic level because of the regular a r r a n g e m e n t of the mesopores in a honeycomb fashion; therefore, it is possible to estimate crystallite size perpendicular to the basal plane with the help of the Xray diffraction p a t t e r n u s m g the Scherrer equation, 23 which has been widely used 2426 to estimate the crystallite diameter for various materials. However, this technique m u s t be used with caution, smce faults or other defects can also result in line broadening. The calculated crystallite sizes are shown in Table 1 and
203
Figure 3. These values are close to those from TEM, ~ which show crystallite sizes in the order of 65 nm. E s t i m a t e d crystallite sizes of various MCM-41 materials reported in the literature are shown m Figure 5, along with the results of the present work. The crystallite sizes lie largely in the range 0.01-0.06 ~tm. It can be seen from Figure 5 t h a t an mcrease in the (CnH2n+I)N+(CH3)3X - surfactant chain length results in an increase in d spacing; this either gives an increase in crystallite size, l~,e7 or results in no distinguishable t r e n d m the case of the p r e s e n t work. I n c r e a s m g the chain length of n e u t r a l amine surfactants zs gives HMS materials of almost constant crystallite size, while no t r e n d was seen in the crystallite size of MCM41. 2s Increasing the h e a d group size of the (C16H33)N+(CH3)2(CnH~.n+l)X" surfactant 29 showed an mitial decrease, and then a final mcrease, in crystallite size with increasing n (and d spacing). A decrease in crystallite size with greater d spacings are noticed for MCM-41 materials p r e p a r e d with increasing template concentration in the synthesis gel. 3~ Conversely, MCM-41 p r e p a r e d at higher t e m p e r a t u r e s and for longer reaction time displays increasing crystallite size with d spacing, al Increasing the amount of mesitylene added to the reaction mixture results in higher d spacing~2 with a slight mcrease in crystallite size, but incorporating v a n a d i u m mto the MCM-41 framework 33 decreases the d spacmg while increasing crystallite size. From the above discussion it is clear t h a t the dependence of MCM-41 crystallite size on d spacing is inconsistent. The average ordering of mesopores is only a few orders of m a g n i t u d e higher t h a n the mesopore diameters, indicating the imperfection of the MCM-41 materials. I Mesopores
o.lo
,
'.
11 ~---v.~-- 27 9 27 9 28 ::; 28i i
~" 0.08 =L
v
.N 0.06
--~--29 *, 30 - - ~ - 31 ~ 31' ---~- 32 + 33
-~ 0.04
o 0.02
[]
o.oo
20
30
40 50 d spacing (A)
60
Pres. work
!
70
Figure 5. Estimates of crystallite size for various MCM-41 type materials.
Figure 6. Meso- and macrostructure of MC~ 41.
204
3.4 Macropores, grains and particles The macropore size distributions of C8-C18 obtained from mercury porosimetry data had two peaks; however, the peak observed at very high pressures of mercury is not considered because of the possible collapse of the structure at high pressures. The macropore diameter decreases in going from C8 to C16, with exception of C12 whose pore diameter is higher than that of C8. The pore diameter of C 18 is also found to be higher than that all other samples except C 12. Mercury porosimetry data can also be used to estimate grain size/particle size, assuming the shape of the particles to be spherical, usmg 1.5Rp(1 - cM) g
(4)
where rg is the grain radius, cm is the macropore porosity (estimated from the macropore volume obtained by mercury porosimetry), and RP is the average macropore radius (taken from the peak of the pore size distribution curvelS). The diameters of the grains obtained by this method are given in Table 1 and Figure 3. These estimates of grain size are roughly 10 times greater than those obtained for crystallites. Micrographs ~5from SEM of C 18 indicate that the average particle size is about 8 gm, close to the findings by laser particle size analysis. 15 These results are also consistent with our estimates of particle diameter by highresolution optical microscopy, given in Figure 3 and Table 1. The above analysis gives a clear picture of the meso- and macrostructure of MCM-41 materials synthesized in our laboratory. It is evident that these MCM41 samples after calcination consist of particles, which are made up of grains. These grains again consist of crystallites which could be hexagonal prism shaped, consisting of mesopores running parallel to the axis of the prism, depicted in Figure 6. Estimates of meso- and macro-porosity ~5 indicated that both porosities decrease with increase in mesopore size.
4. C O N C L U S I O N S On the basis of the results of various characterization techniques, it was found that MCM-41 consists of 4 levels of structure: mesopores, crystallites, grains and particles. All these levels have been successfully characterized. Estimates of surface area by SAXS and SANS are higher, while those from mercury porosimetry are much lower, than those estimates by BET methods; the estimates obtained from geometrical consideration usmg variable wall thickness are close to the BET results. It was confirmed that mesopores in MCM-41 are curved rather than straight channels and, even though they do not have an ideal mesopore structure, they can be considered as model mesoporous materials for gas adsorption studies.
205
Acknowledgement This r e s e a r c h h a s been s u p p o r t e d by a g r a n t from the A u s t r a l i a n R e s e a r c h Council. The a u t h o r s are grateful to Dr N. Calos, Mr Ben Schulz a n d Dr N. K i n a e v for t h e i r help in microscopy.
REFERENCES 1. Beck. J. S.; Vartuli, J. C.; Roth. W. J.: Leonowicz. M. E.: Kresge. C. T.: Schmitt. K. D.: Chu, C. T-W.; Olsen. D. H.: Sheppard. E. W.: McCullen. S. B.: Higgins. J. B.: Schlenker. J. L. J. Am. Chem. Soc. 1992. 114, 10835. 2. Ravikovitch, P. I.; O'Domhnaill, S. C.: Neimark, A. V.: Schuth. F.; Unger, K. K. Langmuir 1995, 11, 4765. 3. Maddox, M. W.; Olivier, J. P.; Gubbins, K. E.; Langmuir 1997, 13, 1737. 4. Kruk, M.; Jaroniec, M.: Sayari. A. Langmuir 1997. 13. 6267. 5. Bhatia, S. K.: Sonwane, C. G. Langmuir 1998.37. 2271. 6. Inoue, S.: Hanzawa, Y.: Kaneko, K. Langmuir 1998. 14. 3079. 7. Morishige, K.; Shikimi, M. J. Chem. Phys.. 1998. 108. 7821. 8. Sonwane C. G.; Bhatia, S. K. Chem. Eng. Sci. 1998.53. 3143. 9. Khushalani, D.; Kuperman, A.; Ozin, G. A.; Tanaka. K.: Garces, J.: Olken. J. J.; Coombs. N. Adv. Mater. 1995, 7, 842. 10. Sonwane. C. G.; Bhatia, S. K.; Calos. N. Ind. Eng. Chem. Res. 1998.37. 2271. 11. Kruk. M.: Jaroniec. M.; Sayari. A. J. Phys. Chem. B. 1997. 101. 583. 12. Dabadie, T.; Ayral, A.: Guizard. C.: Cot. L.: Lacan. P. J. Mater. Chem. 1996, 6. 1789. 13. Glatter, O. In Small Angle X-ray scattering; Glatter. O.. Kratky. O. (Eds); Academic Press: London, 1990; p. 165. 14. Wachtel, E. Personnel communication, Department of Chemical Physics, Weizmann Institute of Science, Israel, 1997. 15. Sonwane C. G.; Bhatia, S. K. Langmuir, in press. 16. Debye, P.; Anderson, H. R.; Brumburger. H. J. J. Appl. Phys. 1957. 28. 679. 17. Edler, K. J.; Reynolds, P. A.; White. J. W.: Cookson. D. J. Chem. Soc. Faraday Trans. 1997, 93, 199. 18. Edler, K. J.; Reynolds, P. A.; White, J. W. J. Phys. Chem. B 1998. 102. 3676. 19. Sonwane, C. G.; Bhatia, S. K. Langmuir. submitted 1998. 20. Rootare H. M.; Prenzlow, C. F. J. Phys. Chem. 1967, 71. 2733. 21. Kruk, M.; Jaroniec, M.: Ryoo, R.; Kim. J. M. Microporous Materials. 1997. 12. 93. 22. Chenite, A.; Page. Y. L.: Sayari. A.: 1995. 7. 1015. 23. Klug, H. P.: Alexander. L. E. X-Ray Diffraction Procedures for" Polycrystalline and Amorphous Materials. Wiley: New York. 1974. 24. Rao, V. U. S. Energy and Fuels 1994. 8. 44. 25. Masson, O.; Rieux, V.; Guinebretiere, R.; Dauger, A. Nanostructured Materials. 1996, 7, 725. 26. Ishimori, T.; Yamashita, M.; Senna. M. Part. Part. Syst. Charact. 1994, 11, 398. 27. Ravikovitch, P. I.; Wei, D.; Chueh, W. T.: Hailer. G. L.: Neimark. A.V.J.J. Phys. Chem. 1997, 101, 3671. 28. Tanev, P. T.; Pinnavaia, T. J. J. Chem. Mater. 1996, 8. 2068. 29. Huo, Q.; Margolese, D. I.; Stucky, G. D. Chem. Mater. 1996.8. 1147. 30. Corma, A.; Kan, Q.; Navarro, P. J.; Rey, F. Chem. Mater. 1997.9. 2123. 31. Cheng, C. F.; Zhou, W.; Klinowski, J. Chem. Phys. Lett. 1996. 263. 247. 32. Zhang, W.; Pauly, T. R.; Pinnavaia, T. J. Chem. Mater. 1997.9. 2491. 33. Luca, V.; MacLachlan. D. J.; Morgan. K. Chem. Mater. 1997.9. 2720.
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.
207
C h a r a c t e r i z a t i o n of m e s o p o r o u s MCM-41 a d s o r b e n t s by v a r i o u s techniques J. Goworek, W. Stefaniak and A. Bor6wka
Maria Curie-Sldodowska University, Faculty of Chemistry, Department of Adsorption and Planar Chromatography, 20-031 Lublin, Poland Two mesoporous silica molecular sieves synthesized by using n-octadecylammonium bromide and n-dodecylammonium bromide as a templates were characterized for their pore size distribution by temperature programmed desorption method and low temperature nitrogen adsorption method. The pore size distributions and total pore volumes determined by the two methods agree quite well and are within experimental error.
1. INTRODUCTION The discovery of the crystalline mesoporous molecular sieves of MCM-41 type has stimulated considerable interest in their structure, further investigations on the synthesis, adsorption properties and possible applications [1-7]. These materials are characterized by relatively high surface area, high pore volume and controlled pore size with narrow pore size distribution. As a result they have potential uses as catalysts for chemical reactions. MCM-41 silicas have long, hollow channels arranged in a hexagonal structure. Uniform sized channels may exhibit various diameters depending on the used organic template and the conditions of synthesis. Various types of surfactant molecules are used as templates during this synthesis. In the present paper a comparison of the results concerning the porosity of two types of MCM-41 silicates derived from nitrogen adsorption and temperature desorption (TPD) is presented. These two techniques give similar values of the parameters characterizing the porosity for rigid materials [8-11]. Testing efficiency of the TPD method for model materials with controlled pore size is of great interest if we take into account the simplicity and velocity of thermogravimetric technique.
208 2. E X P E R I M E N T A L
Two mesoporous silica sieves SiC12T and SiC18T were synthesized by previously described method [12], using ammonia as catalyst, n-Octadecylammonium bromide and n-dodecylammonium bromide were used as template reagents. After synthesis the solid and solution phases were separated using a centrifuge. The solid phase was repeatedly washed with deionized water to remove the other components from its surface and dried at 100~ Next both samples were calcined at 300~ to remove organic template. However, during calcination part of template molecules forms various organic components which may be easy removed by using benzene and methanol. Part of alkylammonium surfactants due to pyrolisis forms carbon deposits on silica surface. Partial burn-off of the carbon deposits was performed by further calcination at 500~ in oxygen atmosphere for 5 h. In Table 1 are collected the contaminations of carbon before and after high temperature calcination. The elementary analysis was performed using CHN Analyser (PerkinElmer). The presented results illustrate the decrease of carbon content during burn-off process. Both mesoporous silica were characterized by powder XRD using X-ray diffractometer DRON 3 (USSR) with step scanning 0.02 ~ Adsorption/desorption isotherms of nitrogen were measured using an automatic sorption analyzer Micromeritics ASAP 2010. The TPD measurements were carried out using Derivatograph C (MOM Hungary) and quasi-isothermal program of heating process. The dry silica samples were mixed with excess of benzene or water to form pastes. Then wet samples were placed in a platinum crucible of conical type [13], which facilitates to keep self-generated, saturated vapors atmosphere of wetting liquids over the sample. Thermogravimetric experiment involves the measurements of weight loss of liquid (benzene or water) against temperature. The main feature of applied heating mode is a maintenance of the constancy of temperature inside crucible when loss of sample weight is high and exceeds 0.5 mg.min -~. This situation occurs when intensive evaporation of liquid from a group of pores of similar dimensions takes place. 3. RESULTS AND DISCUSSION Figure 1 shows X-ray diffractograms for investigated samples. A sharp and well defined XRD peaks indicate the existence of ordered pore structure in the samples. The Bragg peak for SiC18T sample is shifted slightly in the direction of smaller values of 2 0 .
209 4000 b~
~
a
(/)
3000-
9
d spacing: 3.37 nm ,, 4.49 nm
~~ A
*t,,
c~.
E
.__ v
Or) Z UJ I-Z --
2000
-
1 0 0 0
-
0
Zl
0
2
4
6
8
10
2O
Fig. 1. X-ray diffraction patterns of mesoporous silicas after heating at 500~ a - SiC12T; b - SiC18T. The nitrogen adsorption/desorption isotherms of the samples SiC12T and SiC18T are shown in Figs. 2 and 3. Nitrogen adsorption isotherms for silica heated at 500~ i.e. after burn-off processing are higher in comparison to those calcined at 300~ However, their shape is identical. Observed effect may suggests that part of pores blocked by carbon deposits becomes available for nitrogen molecules after processing in higher temperature. It is worth to note that contamination of carbon in both silica samples sharply decreases after calcinacion at 500~ (see Table 1). 600
(D
E
ej 15 .Loo {D
500
IOIC] I n l
Q 0 E]~
qnO qi~ 0 q i o ~ Q n ~
~oQQOmo uo q~o
400 300
OlD I 0 i0
[] o~
2
n o
200
(D
E 0
>
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)
/
,
\
(c) I
'
I
'
I
'
!
'
!
120 100 80 60 40
'
I
20
'
I
0
'
I
'
I
'
I
'
I
-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
'
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.
'~
--E
.~ ~o!
20
a)
~ 15
7 __0 10
1
d)
z
- lO I
F--
k-n
z~ 0 0
\
5
z o o 100
200
300
400
REDUCTION TEMPERATURE
E ......
35 30
~ 25 z 0
20
~ 13_
15
D z 0 o
10
~
500
~
z .9.o
~
,
200
L__
~
15
Z _0
10
o0 300
400
i,
500
j 100
10
.-E
10
-~ o E
8
z O
6
n
4
~
2
I.-
5
0 o
200
300
400
REDUCTION TEMPERATURE / ~
/
'
200
i !
\ 300
400
500
REDUCTION TEMPERATURE / ~
c)
100
-I,
\
,
--...
o
50O
e)
E
z
I-12_
co z 0 0
400
"E" 20
5
20
300
REDUCTION TEMPERATURE / ~
REDUCTION TEMPERATURE / ~
E
\,
200
100
I-
100
o
~
b)
J
'\
'
500
I
~
o
'
'
'
7
200
300
400
500
f)
i
-_ 1oo
REDUCTION T E M P E R A T U R E / ~
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~
<
: SF 9 ~
0.0 0.0
i
,
I
l
I
@
i
I
l
l
l
2.0
1
,
l
i
l
4.0
1
6.0
l
l
l
l
8.0
Pore Width (nm) Figure 2. Dependencies of the adsorption potential on the pore width calculated according to the equations (3) (SF curve), (4) (curve KJSe) and (5) (curve KJSc). The KJSc curve was calculated via equation (5) using the Harkins-Jura-type expression for the statistical film thickness t, which gives a good representation of the experimental t-curve only in the range of relative pressures from 0.1 to 0.95. Therefore, this curve deviates from points at high values of A, which correspond to low values of p/po. Data for the ZLZ curve are from Zhu et al. [29]. multiplication of the adsorption potential distribution, X(A), by the derivative of the adsorption potential with respect to the pore width, dA/dw, gives the HK pore size distribution. The derivative dA/dw is essential in converting a model-independent APD to a model-dependent PSD. Basing on the HK approach [1] Saito and Foley (SF) [7] proposed an analytical equation to express the dependence between the pore width w and the adsorption potential A for the cylindrical pores: A : - 1 2 x 1 0 2 5 n'N(N,, A, + N A AA)d-~x Z {(k + 1)-' (1- d / w ) zk [(21/31)a, (d/w) '~
--~k(d/W)4]}
(3)
k=l
where N is the Avogadro's number, Na is the number of adsorbate molecules per unit area, NA is the number of atoms per unit area of the adsorbent, d is the sum of diameters of the adsorbent atom and adsorbate molecule, and ~k, [3k, Aa, and AA are constants defined in [6]. More details about equation (3) and parameters used can be also found in [2,6,8-10,24]. Shown in Figure 2 is the A(x)-curve calculated according to the SF equation for cylindrical pores [7] using parameters listed in [24]. This figure contains also the dependence between A and w reported in [26], which was established experimentally by using a series of highquality MCM-41 materials. This relation expressed in terms of A assumes the following form:
229
w(nm)=4 •
10 6 y V / A
+ 2t(A) + 0.6
(4)
where y = 8.88x 10 -3 N/m is the surface tension of liquid nitrogen at 77K, V = 34.68x 10 .6 m3/mol is the molar volume of liquid nitrogen and t(A) is the statistical film thickness (tcurve) of nitrogen on the silica surface expressed as a function of the adsorption potential A. The t(A)- dependence was obtained in [26] on the basis of nitrogen adsorption isotherms for a series of good-quality MCM-41 samples and a reference macroporous silica. Kruk et al. [26] showed that in the range of relative pressures from 0.1 to 0.95 the experimental dependence t(A) can be accurately represented by the Harkins-Jura expression. Substituting this expression into equation (4) gives the following formula for the pore width w:
w (nm)= 4 x 10 6 )" V / A "t- 1.0196(0.0307
+ 0.4343 A / RT) -~
+ 0.6
(5)
In addition to the A(w)-curve generated by the SF equation (3) for cylindrical pores as well as those expressed by equations (4) and (5) we also plotted A(w) recently reported in [29]. As can be seen in Figure 2, all A(w)-curves are decreasing functions which approach each other in the range of larger pores. As can be seen from Figure 2 the SF curve lies below that established experimentally on the basis of good-quality MCM-41 materials [26]. The curve reported recently by Zhu et al. [29] lies between them. A substantial difference between the A(w)-curves is clearly visible in the transition range from micropores to mesopores. Although in the range of larger pores this difference is less visible because the A(w)-curves are slowly decreasing functions, it still has a profound effect on the pore width evaluation.
o ..~
8.0
,E 6.0 --
..~ ,l,,,,a
4.0 -
=9
2.0
O
a,
,4"./5.5
/,:
9}
3.8
/
;i !/r
4.6
N---/ i" "% --~,',,"~..7-'>"--~--/"
0
ra~
<
: 6.5nm
2.8
0.0 0.0
0.3
0.6
0.9
1.2
1.5
Adsorption Potential (kJ/mol) Figure 3. Adsorption potential distributions for the MCM-41 samples studied obtained by a simple differentiation of nitrogen adsorption isotherms. The A(w)-curves shown in Figure 2 were used to calculate the dA/dw derivative, which is necessary for conversion of APD to PSD via equation (2). Adsorption potential distributions for the MCM-41 samples studied are shown in Figure 3. As can be seen in this figure there is a correlation between the position of the distribution maximum and the pore width.
230 In contrast to APDs for carbonaceous materials, which often exhibit a visible peak in the range of higher adsorption potentials that reflects the monolayer formation [20,30,31], the X(A) functions for silicas are featureless in this range due to a strong energetic heterogeneity of their surface. APDs shown in Figure 3 were employed to calculate PSDs according to equation (2) using dA/dw obtained by differentiation of the A(w)-curves presented in Figure 2. Thus, for each MCM-41 sample four PSDs were evaluated. The first one, denoted as KJS* was obtained by a rigorous method reported in [26]. The remaining three curves were calculated according to the HK method using the dA/dw-derivative from the SF equation for cylindrical pores as well as those reported by Kruk et al. [26] and Zhu et al. [29]. A comparison of these PSDs is shown in Figures 4 and 5 for the 3.1 and 6.5 nm MCM-41 samples. It can be seen that the maximum of PSD obtained by the HK method with the experimentally established relation (4) agrees well with that predicted by Kruk et al. [26]. However, the maxima of the remaining two PSDs are shined in the direction of lower pore widths. The relative error for the pore widths calculated by using the SF A(w)-relationship may reach 40% in the transition range from micropores to mesopores, and it decreases gradually with increasing pore width. This error leads to the underestimation of the pore width about 1.4 nm, which is clearly demonstrated in Table 2 showing a comparison of the pore widths calculated by different version of the HK method. In addition, the relationships between the pore widths calculated from adsorption data using different methods of the pore size analysis and those evaluated independently from the XRD data are presented in Figure 6. These relationships are linear and almost parallel in the pore range studied. The data reported by Kruk et al. [26] coincide with the HK predictions when the experimentally established relationship (4) is used. The relation between A and w predicted by the SF equation for cylindrical pores as well as that reported by Zhu et al. [29] lead to the underestimated pore widths.
2.0
e~
1.5
/
o
.4,..a
1.0-
/
SF
/ ZLZ 9
/
KJS"
/KJS
.4.,.a raO
0.5 N
!
oe~ o ca.,
0.0
-
1.0
.... l
,
< l
I
1 ""/r~',
2.0
" i
-~-
9 -,-
.........
9 9 ~-'"--;
3.0
-'
4.0
Pore Width (nm) Figure 4. Comparison of PSDs for the 3.1 nm MCM-41 calculated by the HK method with the SF (eq. 3), KJS (eq. 4) and ZLZ (ref. [29]) A(w)-relations. The KJS* pore size distribution was obtained by the method reported in [26].
231
E
0.8 -
-R-
KJS*
0.6 _
0
=
,.Q
s
0.4 -
F
ZLZ
/
5.0
6.0
KJS\
r~
?5
o.2
N C~ O
0.0 2.0
3.0
4.0
7.0
8.0
9.0
Pore Width (nm) Figure 5. Comparison of the pore size distributions for the 6.5 nm MCM-41 calculated using the HK method with the SF (equation 3), KJS (equation 4) and ZLZ (ref. [29]) A(w)dependencies. The KJS* pore size distribution was obtained by the method reported in [26]. "~"
7.0
k
6~ ~=
~
"
5.0
9 - SF
4.0
-
3.0
20 O
1.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Pore Width from X R D (nm) Figure 6. Dependencies between the pore widths at the maxima of suitable PSDs obtained from nitrogen adsorption data and the pore width evaluated from the XRD spacing via equation (1). All closed points correspond to the maxima of PSDs obtained by the HK method with the SF (equation 3), KJS (equation 4) and ZLZ (ref. [29]) A(w) curves. The open circles correspond to PSDs evaluated by the KJS method, which incorporates the MCM41 calibrated t(A) and A(w)-relations into the BJH algorithm [26].
232
Table 2 Mesopore widths at the maxima of PSDs obtained by the HK method using different relations between A and w. Sample Wros (nm) wHi< (nm) WZLZ(rim) WFs (nm) 2.0 2.30 1.10 1.37 1.32 2.8 2.76 2.00 2.17 1.61 3.1 3.01 2.30 2.43 1.82 3.8 3.77 3.23 3.21 2.48 4.6 4.38 4.01 3.81 3.03 5.5 5.62 5.60 5.03 4.19 6.5 6.48 6.80 5.87 5.06 and wFS - primary mesopore widths at the maxima of PSD obtained by the HK method with the KJS (equation 4), ZLZ [29], and SF (equation 3) A(w)-relationships. WHK denotes the pore width at the maximum of PSD obtained by HK method using the original HK equation for slit-like pores with parameters for nitrogen on the carbon surface at 77 K.
WKJS , WZLZ
1.5
/
E O
F.
1.0
--
/
3.1
0.5-
N
o~
O
0.0
'
J
I
1.0
i
i
i
,
I
2.0
,
i
i
l
I ~ ~
3.8 nm
?!
t
i
3.0
~'-'~'J~''-'~
4.0
5.0
Pore Width (nm) Figure 7. Comparison of PSDs obtained by the HK method with the A(w) relationships given by equations (4) (circles) and (5) (lines). While in equation (4) the experimental t-curve was used, equation (5) was obtained by using the Harkins-Jura fit for the t-curve, which is much less accurate for relative pressures smaller than 0.1. Although the maximum of PSD can be reproduced by the HK method assuming that an accurate A(w) relation is used, this method fails to predict the PSD shape in the microporemesopore transition range. As can be seen in Figures 4 and 5, all PSDs obtained by the HK method exhibit tail over the range of small pores and even a small peak in the micropore range. These additional features on PSD may be incorrectly interpreted as indicators of microporosity. This unrealistic behavior of PSD in the range of small pores arises from the
233 fact that the HK method, which bases on the condensation approximation, ignores the thickness of the surface film in the pore size analysis. While the surface film correction is less important in the range of larger mesopores, it is essential in analysis of the microporemesopore transition range. On the other side, implementation of this correction in the HK method is almost impossible. Therefore, the assessment of microporosity in mesoporous solids by the HK method is very risky because the presence of aforementioned tail and/or small peak, which can arise from the deficiency of this method and/or from the existing microporosity. It should be noted that the position of the resulting PSD depends strongly on the A(w)-relation (see Figures 4 and 5). Also, its shape depends on the A(w)-relation and particularly on the accuracy of the t-curve used for its derivation. This effect is clearly visible in Figure 7, which contains PSDs obtained by HK method with the experimentally established A(w) relation given by equation 4 [26]. These PSDs (circles in Figure 7) still exhibit a peak in the micropore range but it is much smaller than that visible on PSDs calculated for a less accurate t-curve. Although the latter was obtained by approximation of the experimental t-curve (circles in Figure 2) by the Harkins-Jura equation (solid line in Figure 2), its accuracy is much smaller in the range of relative pressures below 0.1 [26]. This relatively small deviation between the experimental and fitted t-curves leads to much larger difference on the PSD curves in the micropore range. Finally, let us comment on the use of the HK equation for slit-like pores for the pore size analysis of MCM-41 materials, which possess hexagonally ordered cylindrical mesopores. Galameau et al. [24] indicated that the HK equation derived for slit-like geometry with parameters for the nitrogen/carbon and argon/oxide adsorption systems gives pore widths, which are much closer to those determined by equation (1). In order to check this observation we evaluated the pore widths for the MCM-41 samples studied using the HK method with the A(w) relation for slit-like geometry and the parameters for the nitrogen/carbon system at 77K [6]. Although, these values are closer to the true pore widths than those obtained by means of the SF equation (3), they are still underestimated in the range of smaller pores and slightly overestimated in the range of larger pores (see Table 2). On the other side, as it was pointed out in [24], it is impossible to justify the use of the HK equations for slit-like pores for characterization of siliceous materials such as MCM-41 materials, which exhibit well-defined arrangements of cylindrical or close to cylindrical mesopores. 4. CONCLUSIONS It is shown that the position of PSDs calculated by the HK method depend strongly on the A(w)-relationship used. For instance, the pore widths at the maxima of PSDs obtained by the HK method with the Saito-Foley expression for cylindrical pores are underestimated about 1.4 nm. However, the HK method with the relationship between A and w established on the basis of good-quality MCM-41 materials [26] provides an accurate estimation of the pore widths of mesoporous silicas. While the position of PSD may be improved by a proper selection of the A(w)-relation, its unphysical features remain. The height of main peak is significantly reduced in order to compensate the appearance of an artificial small peak and tail in the micropore-mesopore transition range. These artifacts arise from the condensation approximation used in the HK method, which does not provide a good representation for the volume filling of micropores.
234 ACKNOWLEDGMENTS
The donors of the Petroleum Research Fund administered by the American Chemical Society are gratefully acknowledged for support of this research.
REFERENCES
1. 2. 3. 4.
G. Horvath and K. Kawazoe, J. Chem. Eng. Jpn., 16 (1983) 470. G. Horvath, Colloids & Surfaces, 141 (1998) 295. M. Jaroniec, K.P. Gadkaree and J. Chorea, Colloids & Surfaces, 118 (1996) 203. M. Jaroniec, in "Access in Nanoporous Materials", T.J. Pinnavaia and M. Thorpe (eds), Plenum Press, New York, 1996, pp. 255-272. 5. R.K. Mariwala and H.C. Foley, Ind. Eng. Chem. Res., 33 (1994) 2314. 6. J. Choma and M. Jaroniec, Adsorption Sci. & Technol., 15 (1997) 571. 7. A. Saito and H.C. Foley, AIChE, 37 (1991) 429. 8. L.S. Cheng and R.T. Yang, Chem. Eng. Sci., 16 (1994) 2599. 9. L.S. Cheng and R.T. Yang, Adsorption, 1 (1995) 187. 10. A. Saito and H.C. Foley, Microporous Mater., 3 (1995) 531. 11. A. Gil and M. Montes, Langrnuir, 10 (1994) 291. 12. J. S. Beck, J. C. Vartuli, W. J. Roth, M. E. Leonowicz, C. T. Kresge, K. D. Schrnitt, C. TW. Chu, D. H. Olson, E. W. Sheppard, S. B. McCullen, J. B. Higgins and J. L. Schlenker, J. Am. Chem. Sot., 114 (1992) 10834. 13. J. C. Vartuli, K. D. Schrnitt, C. T. Kresge, W. J. Roth, M. E. Leonowicz, S. B. McCullen, S.D. Hellring, J.S. Beck, J. L. Schlenker, C., D.H. Olson and E. W. Sheppard, Chem. Mater., 6 (1994) 2317. 14. P.T. Tanev, M. Chibwe and T.J. Pinnavaia, Nature, 368 (1994) 321. 15. P.T. Tanev and T.J. Pinnavaia, Science, 267 (1995) 865. 16. E. Prouzet and T.J. Pinnavaia, Angew. Chem. Int. Ed., 36 (1997) 516. 17. G.S. Attard, J.C. Glyde and C.G. G61tner, Nature, 378 (1995) 366. 18. A. Corma, V. Fomes, M.T. Navarro and J. Perez-Pariente, J. Catal., 148 (1994) 569. 19. M. Kruk, M. Jaroniec and J. Choma, Adsorption, 3 (1997) 209. 20. M. Kruk, M. Jaroniec and J. Chorea, Carbon, 36 (1998) 1447. 21. D.L. Valladares and G. Zgrablich, Adsorption Sci. & Technol., 15 (1997) 15. 22. D.L. Valladares, F. Rodriguez-Reinoso and G. Zgrablich, Carbon, 36 (1998) 1491. 23. R.D. Kaminsky, E. Maglara and W.C. Conner, Langmuir, 10 (1994) 1556. 24. A. Galameau, D. Desplantier, R. Dutartre and F. DiRenzo, Microporous Mater., 27 (1999) 297. 25. A. Sayari, P. Liu, M. Kruk and M. Jaroniec, Chem. Mater., 9 (1997) 2499. 26. M. Kruk, M. Jaroniec and A. Sayari, Langrnuir, 13 (1997) 6267. 27. M. Kruk, M. Jaroniec and A. Sayari, J. Phys. Chem., B 101 (1997) 583. 28. E.P. Barrett, L.G. Joyner and P.P. Halenda, J. Am. Chem. Soc., 73 (1951) 373. 29. H.Y. Zhu, G.Q. Lu and X.S. Zhao, J. Phys. Chem. B, 102 (1998) 7371. 30. M. Kruk, Z. Li, M. Jaroniec and W.R. Betz, Langrnuir, 15 (1999) 1435. 31. M. Kruk, M. Jaroniec and K.P. Gadkaree, Langmuir, 15 (1999) 1442.
Studies in Surface Science and Catalysis 128 K.K. Unger et al. (F_Aitors) 92000 Elsevier Science B.V. All rights reserved.
235
Dynamic and structural properties of confined phases (hydrogen, methane and water) in MCM-41 samples (19A, 25A and 40A). o
J.P. Coulomb a, N. Floquet a, Y. Grillet b, P.L. Llewellyn b, R. Kahn ~and G. Andr~ c aC.R.M.CZ-C.N.R.S., Campus de Luminy, Case 913, 13288 Marseille Cedex9- France. bC.T.M.- C.N.R.S., 26 rue du 141 ~ R.I.A., 13003 Marseille - France. CLaboratoire L~on Brillouin, C E A - Saclay, 91191 Gif-sur-Yvette C e d e x France.
The structural a n d / o r dynamic properties of confined phases (mainly hydrogen, methane and water) in MCM-41 samples (19/k, 25/k and 40/k) have been investigated by neutron diffraction (ND) and incoherent quasi-elastic neutron scattering (IQENS) respectively. A special interest concerns the temperature dependence of the structural range order Lr and of the translational mobility Dt which characterizes the molecular sorbate species. Abrupt variations of such structural (L~oher.) and dynamic (Dt) properties versus temperature are clear signatures of capillary phase transitions. A good illustration is the solidification at T = 62 K of the confined methane phase in MCM-41 (0 = 40/k). We have also investigated the structural and dynamic properties of the physisorbed film on the inner pore surface for the hydrogen / MCM-41 (0 - 24 - 25/k) system. A clear evidence of a solid physisorbed film in coexistence with a capillary liquid phase has been observed at T = 14.6 K.
1. I N T R O D U C T I O N MCM-41 material synthesized in 1992 by the Mobil Oil Company [1, 2] is up to now the first model mesoporous material as a consequence of its well defined porosity, composed of an hexagonal structure of cylindrical mesopores (whose diameter can be monitored in the range 20 - 100 A). MCM-41 samples are very suited to analyze the capillary condensation phenomenon. In particular the phase diagram of the confined capillary phase can be determined. Such a "capillary phase diagram" is characterized by the capillary critical temperature Tr and the capillary triple point temperature Tet. Recent studies of the thermodynamic properties of confined phases (Ar, N2, O2, C2H4 and CO2) in MCM-41 have pointed out that their critical temperatures Tee are strongly displaced to-
236
w a r d s the low t e m p e r a t u r e s in comparison with their bulk critical t e m p e r a t u r e s T3c [3, 4]. The t e m p e r a t u r e displacement (T3c - T~c) increases on decreasing the MCM-41 mesopore diameter. More recently, structural analysis of capillary phases (Kr and H20) in MCM-41 (0 = 700 40 .~) has clearly shown t h a t their Kryptor~ A 600 freezing t e m p e r a t u r e s also are strongly Methane 9 =. 9 9149 "= 9 9 9 1 4 9 * displaced to the low t e m p e r a t u r e range a. 500 I.in comparison to their bulk triple point u) 400 t e m p e r a t u r e s T 3 t [ 5 - 7 ] . Depending on E o 300 the t e m p e r a t u r e range, the capillary 9 Nitrogen phase is a capillary hypercritical fluid (21'= 200 (T > Tee), a capillary liquid (Tct < T < 100 T = 77.4 K Tee) or a capillary solid (T < Tct). Nitrogen, m e t h a n e and krypton confined 0.0 0.2 0.4 0.6 0.8 1.0 phases in MCM-41 (0 - 40 A) at T = PIP 77.4 K are good illustration of such Figure 1 9Sorption isotherms of N2, three types of capillary phases. Their Kr and CH4 on MCM-41 (0 - 40 A) at sorption isotherms, which are shown on T = 77.4 K. Figure 1, belong to the type IV (only the adsorption branches have been represented). They present similar characteristics : physisorption of a film in the low relative pressure regime (P/Po < 0.1) and formation of the capillary phase in the m e d i u m relative pressure regime (0.3 < P/P0 -< 0.45, P0 is the s a t u r a t e d vapor pressure). Despite such a p p a r e n t similarities, the capillary phase states are quite different. From the microcalorimetric and neutron diffraction analysis of the three sorbates examined in MCM-41 (0 - 40 .~), we can determine the nature of the capillary phases with confidence. Only krypton gives rise to a strong
x'x~[ ++§
"o
+
~,:~;~~ ,
,
,
I
,
,
,
I
,
,
.
I
,
=
,
I
,
,
,
o
24
1.5 104
T =77.4 K ~
--o
Kr 16
~L,,- N2
,. . , - -
,. I/
:~ 1.0 104
d
~ 0
,
0
,
,
I
20
,
,
,
I
40
.
,
,
I
60
,
,
,
I
,
,
,
80
100
Loading ( % )
Figure 2 9Microcalorimetric measurm e n t s of N2, Kr and CH4 confined phases in MCM-41 (0 - 40 A) at T -77.4 K.
5.010 3
1.2
1.6
2.0
o(K')
2.4
2.8
Figure 3 9N e u t r o n diffractograms of N2, Kr and CD4 confined phases in MCM-41 (0 - 40 A) at T - 78 K.
237
exothermic signal during the formation of the capillary phase (Figure 2). Moreover such a sorbate is characterized by a medium range order (Lcoher. = 30 /~), whereas m e t h a n e and nitrogen capillary phases present only a short range order (Lcoher.-< 17/~, Figure 3). At the present time, krypton is the only example of capillary solidification at a temperature where the sorption isotherm can be m e a s u r e d [6]. Concerning nitrogen confined phase in MCM-41 (0 = 40 A), K. Morishige et al. [4] have determined the capillary critical t e m p e r a t u r e (Tcc = 73 K). Above such a t e m p e r a t u r e Tcc < 77.4K the confined N2 phase is an hypercritical fluid (state which prevents any observation of the hysteresis loop in the sorption isotherm). Quite recently, we have observed the solidification at T = 62 K of the m e t h a n e phase confined in MCM-41 (0 - 40/~), the results are described in the present paper. Due to the fact that a well developed hysteresis loop characterizes the sorption isotherm of such a system we can deduce that m e t h a n e capillary phase is a normal capillary liquid at T = 78 K (the critical t e m p e r a t u r e Tcc >> 78 K). A s u m m a r y of the structural properties of the three considered sorbates is shown on Figure 4. It is interesting to note t h a t only the N2 capillary phase does not present any solidification. Schematic representation of the capillary phases in MCM-41 (O = 40 A) depending on the t e m p e r a t u r e range is represented on Figure 5. 5O
Z ~ 40
n
Krypto
t
24
r-
22 ,,~ 30
A 20
20
u
o %ooo~
6oooo
o o
T> T~
~, ~
=~10 0
--;J~- 5o%- ~ 5-5-~ b-( o %- oo 6"ooo ~oOOOo~OOO
18 = 0
f N" ogen
2o
~L~,I,,.,I.,,,I.,,,I
30
40
/~
,,,1
~
,,I,
,~,
,I,,,
7ol 8 o I 9 o
Tct(CD4)Tcc(N2)Tct(Kr )
v
~16
Tot< T < T~
lOO
T ( K )
Figure 4 : Coherence length Lcoher. versus t e m p e r a t u r e for confined N2, Kr and CD4 phases in MCM-41 (0 = 40 A).
T
Figure 5 9Schematic representation of the three capillary phase states of confined phases in MCM-41 (0 = -40 A).
238
2. R E S U L T S A N D D I S C U S S I O N One characteristic of the MCM-41 material is the amorphous character of its walls. As a consequence the inner mesopore surface should be quite energetically inhomogeneous. Probably the structure of the physisorbed film, which grows up at the beginning of the pore filling, presents a lot of defects. In a large t e m p e r a t u r e range this film is probably a solid film, as evidenced by our present results concerning the h y d r o g e n / M C M - 4 1 (0 - 25 ,~) system described below. Such a physisorbed solid film seems to coexist with the different states of the capillary phase (hypercritical fluid, liquid and solid). We have to keep in mind t h a t during the capillary solidification or crystallization, there is no phase correlation between the different diffracted signals coming from each mesopores. This feature m a y explain why the coherence length Lcohe~ is r a t h e r small even for the capillary solid phase. Detailed analysis of the early solidification stage (the nucleation) seems to be a difficult problem to solve. Solidification of confined w a t e r in MCM-41 begins to be investigated in details [3, 7, 8]. W a t e r sorbate presents 35 0.6 several interesting characteristics. It 30 L / o.s does not wet the inner surface of silicic coh 0.4 MCM-41 mesopores, the w a t e r sorption 25 % isotherms belong to type V [9 - 11]. The ~20 0.3 o influence of the physisorbed film is 15 0.2 ~ greatly reduced. In addition H20 is very suited to a direct m e a s u r e m e n t of 0.1 the molecular translational mobility Dt 5 0 by incoherent quasi - elastic n e u t r o n 220 240 260 200 280 300 T(K) scattering (IQNS). One of the main difference between the solid phase and Figure 6 9Molecular mobility Dt and the liquid phase is the molecular mobilcoherence length Lcoher versus tern- ity values Dt, which are different by perature of confined w a t e r in several order of m a g n i t u d e in the two MCM-41 (O = 40 A) confined phases. We have m e a s u r e d Dt of w a t e r in MCM-41 (0 = 40 A) in a large t e m p e r a t u r e range 213 - 283 K (for a loading = 90 %). The results are represented on Figure 6. The translational mobility Dt of confined w a t e r molecules vanishes between 228K and 238K (10 -s cm2s~< Dt-- 0.4 10 .6 cm2s-~). T e m p e r a t u r e r a n g e where is located the a b r u p t variation of the coherence length L~oher. (T = 234 K) is interpreted as the solidification phase transition signature [5, 7]. Our Dt (T) d e t e r m i n a t i o n is a direct confirmation of such a conjecture. Solidification of confined w a t e r in MCM-41 samples of smaller diameter have also observed. Such phase transitions appear to be continuous [5, 8] or more a b r u p t [7] concerning for instance the H20 / M C M - 4 1 (O = 25 ,~) system. Some specific influence of the MCM-41 (O = 25/~) samples used by the different groups can not be o
|
~
|
|
|
|
,
|
|
i
,
239
excluded. We plan to investigate soon such a system by IQNS. N e u t r o n diffraction studies of m e t h a n e and benzene confined phases in MCM41 (O = 40 A) samples versus t e m p e r a t u r e have indicated t h a t the solidification of the two sorbed species at T = 62 K and T = 170 K respectively. The structural properties of the CD4 confined phase are s u m m a r i z e d on Figure 7 and Figure 8 5000,
.
25
O=40A
4000
L
coher.
= 16.7A
T = 77.3 K
m~,,3000
o = 2s
C
+
o 2oo0 o
L
= 22.6 AJ~i~ coher. ~ ; ~ I!~
-J
T = 39.1 K
15
'~
1000 1
1.5
2
2.5
Q ( A "1)
3
Figure 7 9N e u t r o n diffractograms of confined CD4 phase in MCM-41 (0 = 40 A) m e a s u r e d at two t e m p e r a t u r e s T = 77.3 K and 39.1 K
10
.... 30
i .... 40
i .... 50
i .... 60
i .... 70 T(K)
80
Figure 8 : Coherence length LcoherVerSUS t e m p e r a t u r e of CD4 confined phase in MCM-41 (0 = 25 .~ and 40/~).
(those concerning C6D6 will be published elsewhere). The coherence length L~ohe~ which characterizes the molecular organization of confined m e t h a n e in MCM-41 (0 - 40 A) undergoes an abrupt variation around T - 62 K. We i n t e r p r e t such a sudden increases of Lcoher when decreasing t e m p e r a t u r e as the signature of a capillary phase solidification. We have to recall t h a t no phase transition has been observed for confined m e t h a n e phase in MCM-41 (0 = 25 A) [12]. In t h a t l a t t e r case, Lcoher. is constant versus the t e m p e r a t u r e . The capillary phase transi100o tion appears to be continuous for CD4 confined phase when the MCM-41 pore HD ( T = 14.6 K ) A diameter is reduced down to 25 A. Reo~ 800 + call t h a t concerning the hydrogen / Q. + 9 + I-u) 600 MCM-41 (0 = 25 A) system, also no \ + o,) E phase transition has been observed INO D ( T = 16.4 K ) ~-- 400 2 [12]. The sorption isotherm of the hyI, M d r o g e n / M C M - 4 1 (0 - 25 A) system be200~ longs to the type IV, but its particularity is t h a t the first stage of the mesopore filling (i.e. the physisorbed film 0 0.2 0.4 0.6 0.8 1 1.2 P/P growth) is more developed t h a n the seco Figure 9 9 Calibration sorption iso- ond one (i.e. capillary condensation). In t h e r m of HD confined phase in MCM- other words, the film thickness is larger t h a n for the other sorbed species 41 (O = 24 A) at T -- 14.6 K
240 [13]. Such a system is well suited to analyze the properties of the physisorbed film on the inner surface of the MCM-41 mesopores. We have measured the molecular mobility Dt of confined hydrogen in MCM-41 (0 = 24/~) by IQNS both versus the t e m p e r a t u r e and the sorbate loading. The calibration isotherm measured at T = 14.6 K during the IQNS experiment is represented on Figure 9. The sorption isotherm of the D2/MCM-41 (0 = 25 A) system measured at T = 16.4 K is also shown for comparison [12]. At T = 14.6 K, for a hydrogen loading equal to 33 % (during the physisorbed film growth) the incoherent neutron scattering signal is a pure elastic peak. We do not observe any peak broadening (in the whole wave vector Q range 0.35 < Q < 1.38 ,~-1). Recall that Dt is proportional to the IQNS peak broadening (the diffusional model used in the analysis of the experimental results have been already published [14]). The measured IQNS peaks are shown on Figure 10. When we increase the hydrogen loading, an IQNS peak Adsorbed solid film :3
Loading =
33 %
t
ei
U) Z LU IZ
~
l~O
= 0.94 A "1
Z i!1 P Z ,,,.,
O = 0.72 A "1
Q = 0.53 A "1 -0.2
0
0.2
AE(meV)
Figure 10 9IQNS spectra measured for a HD confined phase in MCM-41 (0 = 24 A) at T = 14.6 K for a hydrogen loading = 33 %.
-0.2
0
0.2
AE(meV)
Figure 11 : IQNS spectra measured for a HD confined phase in the same MCM-41 sample: T= 14.6 K, hydrogen loading = 85 %
broadening AE appears. AE increases up to a loading equal to around 95 %. On Figure 11, we have represented the IQNS spectra measured at T = 14.6 K for a hydrogen loading equal to 85 %. The observed IQNS peak broadening means t h a t the hydrogen capillary phase is a fluid phase at T = 14.6 K (recall t h a t the triple point t e m p e r a t u r e W3t of the bulk HD hydrogen isotope is T3t - 16.6 K), whereas the HD physisorbed film, which coexists with the capillary phase, is a solid film. Recall t h a t the film thickness is probably equal to two layers [12]. We have m e a s u r e d the molecular mobility Dt in the HD capillary fluid phase versus t e m p e r a t u r e for the hydrogen loading 85 %. The results are presented on Figure 12 and Figure 13. An IQNS peak broadening AE is observed down to T = 9.5 K, the HD molecular mobility Dt vanishes in the temperature range 7.0 - 9.5 K. Recall t h a t the coherence length Lcoher. which characterizes the molecular hydrogen organization in the confined D2 phase in MCM-41 (0 = 25 A) does not present any change in the same t e m p e r a t u r e range (Figure 12) [12]. The apparent solidi-
241
35 , !,tr
O = 0.94 A ~
,1~ T = 7.0 K '~'
~
it
tI"
_oBBBB~~
T=11.9K'
~
~,Y" T
,
,
i
,
,
,
i
,
,
,
i
30
D-L 2
~ 0.6
i
r
.
,
I
,
.
,
I
,
,
~
2.5
/
2 A
._=
/
O
1.5 o
"
0.8 1 1.2 h E(meV)
Figure 12 9IQNS spectra measured for HD confined phase in MCM-41 (24/k) at different temperature 9 T = 14.6, 11.9, 9.5, 7.0 and 4.7 K.
&
3
u
, , , I , , , I , , , I , , , I ~ , , I , , ,
0.4
,
.J9 15
146K
~
,
coher.
-/
10
, . , I , , , I
,
HD- D
~. 25 ,,<: ~' 20
T=9.5 K ~~
,
0.5
/
/ 4
,~,~
I
6
,~=~---I-r""~l
8
, , ,
10
,
,
I
12
,
,
,
I
14
,
,
,
o 16 18 T(K) I
,
,
,
Figure 13 : Mobility Dt and coherence length Lcoher. versus temperature for hydrogen HD and D2 confined phases.
fication of the HD capillary phase in the temperature range 7.0 - 9.5 K has no influence on the molecular organization. Such a behavior is different t h a n those previously observed for the H20 / MCM-41 (0 = 40 A) system. A strong influence of the thick physisorbed film observed for the hydrogen sorbate may explain such a behavior difference.
3. C O N C L U S I O N Confined phases in MCM-41 samples behave as bulk (3D) condensed m a t t e r when the mesopore diameter 0 _ 40 A, 60 three capillary phase types are obMCM-41 Benzene o~ 5o served (capillary solid phase, capillary O=40~ liquid phase and capillary hypercritical o 40 ~ K ethane fluid phase). Nevertheless, the confinerypton i_~ 30 ment induces a strong displacement toWater wards the low temperature side of the ~'~ 20 ater critical temperature Tr162and of the trii-'~ 10 ple point temperature Tct. We have summarized on Figure 14 all the re0 5 10 15 20 sults that we have obtained in our Q /Q p mol. studies concerning the solidification Figure 14 :Solidification point tem- t e m p e r a t u r e Tct of different confined perature (Tct) of confined phases in species in MCM-41 (0 = 40 A). We obMCM-41 : d i s p l a c e m e n t (W3t-Wc)tfr3t serve that the biggest the molecular versus diameter ratio between MCM- sorbate, the largest the temperature 41 pore (Op) and confined molecules displacement AT (for the benzene confined phase Tct ~ 170 K, T3t = 279 K, a (0~o].) A
,ic
i
~
,,,,.,
0
,
,
,
,
I
,
,
!
i
i
i
,
,
,
i
i
|
,
,
242 very large temperature displacement is observed). In addition we have also represented the results concerning confined water in three different MCM-41 samples (0 -- 19 A, 0 = 25 .~ and 0 = 40 A). We observed that as it is expected, the temperature displacement AT increases when decreasing the MCM-41 mesopore diameter. Acknowledgments
:
The authors would like to thank kindly Prof. K.K. Unger (Maintz - Germany) and Dr. J. Patarin and Prof. H. Kessler (Mulhouse - France) for MCM-41 sample supply.
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. C.T.Kresge, M.E. Leonowicz, W.J. Roth, J.C. Vartuli and J.S. Beck, Nature Vol. 359 (1992) 710. K. Morishige, H. Fujii, M. Uga and D. Kinukawa, Langmuir 13 (1997) 3494. 4. K. Morishige and M. Shikimi, J. Chem. Phys. 108 (1998) 7821. 5. K. Morishige and K. Nobuoka, J. Chem. Phys. 107 (1997) 6965. 6. J.P. Coulomb, Y. Grillet, P. Llewellyn, C. Martin and G. Andre, Proceedings of the 6 th Int. Conf. of Fundamental of Adsorption, Ed. F. Meunier, Elsevier (1998) 147. N. Floquet, J.P. Coulomb, C. Martin, Y. Grillet, P. Llewellyn and G. Andre, Proceedings of the 1 2 th Int. Zeolite Conference, Ed. M.J. Treacy et al., Material Research Society (1999) 659. K. Morishige and K. Kawano, J. Chem. Phys. 110 (1999) 4867. 9. P.J. Branton, P.G. Hall, M. Treguer and K.S.W. Sing, J. Chem. Soc. Faraday Trans, 91 (1995) 2041. 10. P. Llewellyn, F. Sch~ith, Y. Grillet, F. Rouquerol, J. Rouquerol and K.K. Unger, Langmuir 11 (1995) 574. 11. S. Inagaki and Y. Fukushima, Microporous and Mesoporous Mater. 21 (1998) 667. 12. J.P. Coulomb, C. Martin, Y. Grillet, P. Llewellyn and G. Andre, Studies in Surface Science and Catalysis, Vol. 105 (1996) 1827. 13. N. Floquet, J.P. Coulomb, S. Giorgo, Y. Grillet and P. Llewellyn, Studies in Surface Science and Catalysis, Vol. 117 (1998) 583. 14.C. Martin, J.P. Coulomb, Y. Grillet and R. Kahn, Proceedings of the 4 th IUPAC Symposium on Characterisation of Porous Solids, Ed. B. Mc Enaney et al., The Royal Society of Chemistry (1997) 359. .
.
.
.
Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 92000 Elsevier Science B.V. All rights reserved.
Estimating
243
P o r e Size D i s t r i b u t i o n f r o m
the Differential Curves of Comparison P l o t s
H. Y. Zhu and G. Q. Lu"
Department of Chemical Engineering, The University of Queensland, St. Lucia, QM 4072, A ustrafia Comparison plots, t- or o~-plot were constructed from the data of nitrogen adsorption on porous solids and on a nonporous reference. The variations in adsorption amount V with respect to t or ors, represented by the tangent of the plots, dV/dt (or dV/dots), are indicatives of the pore filling and thickening of the adsorbed layer. The shape of the differential plots, dV/dt (or dV/dots), versus t (or Ors) thus provide reliable information of the pore size distribution (PSD) of the adsorbents. Sharp peaks were observed on the differential plots for the samples of a uniform pore structure, such as alumina pillared clay and MCM-41 samples, because the filling of the uniform pores occurs in a very, narrow range of relative pressure, and thus a very, narrow range of t or ot~. For the samples of irregular pores, a broad peak on the differential curve is observed, reflecting a wide PSD. Besides, the position of the peak on t axis is intrinsically correlated to the pore size. An empirical expression for such a relation is suggested to be D = 6.347t, using experimental data of MCM-41 samples of various pore sizes. With this simple relation we can convert the differential curve to a PSD curve for microporous and mesoporous solids. This approach involves no mechanism of adsorption, concerning only the phenomenal process of adsorption by porous solids. It avoids theoretical assumption (and thus the accompanying limitations), and complicated calculations. For the purpose of deriving PSD information from adsorption isotherm it is reliable and ready to be applied over a wide range of pore sizes. INTRODUCTION The comparison plots, t-plot ~ and its modified version, ot~-plot 2 are convenient means for comparing the shape of the isotherm under test with a reference isotherm of a nonporous solid. If the porous solid concerned and the nonporous solid are similar in surface nature, the deviation from the reference isotherm is attributed to the different surface geometry from a fiat plane, i.e. pores, existing in the sample. The adsorption on the nonporous solid at various relative pressures (P/Po) can be converted to the statistical thickness of the adsorbed film on the nonporous solid, t. Plotting the amount adsorbed by a sample against t, results in the so called t-plot. For nonporous samples, the plot is a straight line passing through the origin. Deviations from such a straight line are attributed to existence of pores in the porous solid. Detailed discussion on this topic can be found in the literature. 3 In an ot,,-plot proposed by Sing, 2 the ors value at a certain relative pressure is the ratio of adsorption on the nonporous Corresponding author [Phone: 61 7 33653735 Fax: 61 7 33654199 Email: maxlu~q:cheque.uq.edu.au ]
244 reference at that P/Po to that at a P P0 of 0.4. It is not difficult to find that the value of t or o~s obtained from one reference at a P Po is different by a constant 3 Thus, the features of ot~-plot are similar to those of t-plot. Study on the deviations from the straight line of a nonporous reference can provide useful information of the pore structure. The comparison plot methods have been widely used to determine the micropore volume of porous solids. 3 The micropore volume obtained from the comparison plot methods is reasonable not only for a broad spectrum of solids, such as carbons, porous silicas, metal oxides and zeolites, but also for various adsorbates. It naturally leads to efforts on deriving more detailed information on porosity of a solid from these plots. Brunauer and his co-workers 4 proposed a micropore analysis method, termed as the MP-method, to calculate the micropore size distribution using t-plot. Recently we made an effort on modifying this method 5.6 We found that the pore diameter of a novel family of mesoporous materials, MCM-41 samples that consist mostly of a long-range ordered hexagonal arrays of uniform mesopores (cylindrical tubes) could be estimated with a satisfied accuracy from the comparison plot. 5 The value of the pore size thus obtained is in good agreement with the pore dimension obtained from powder X-ray diffraction measurements, which provides an independent estimation of the pore size in these samples. This suggests that these plots are capable of providing detailed information of the pore structure over micro- and meso-pore ranges. This can be an advantage of the approach based on the comparison plots, because conventional methods have serious difficulties to cover such a wide pore size range. In previous studies, we have demonstrated that the differential curve of the t-plot can reflect qualitatively the pore size distribution of mesoporous solids. 56 In this study the investigation on the relation between the differential curve and the pore size distribution of porous solids is extended over the range of micropores and mesopores. Meanwhile, we examine whether the relation is quantitatively reliable with respect of pore size and pore volume. 2. E X P E R I M E N T A L 2.1 Samples Microporous solid selected in this study is alumina pillared montmorillonmte (AIPILM) which exhibits well-defined slit-shaped micropores. Four mesoporous sohds are examined. Two silica MCM-41 samples prepared with quaternary ammonium surfactants: dodecyltrimethylammonium bromide (the main carbon chain of the ammonium has 12 carbon atoms, C12) and cetyltrimethylammonium bromide. They are labeled as MCM-41 (C12) and MCM-41 (C 16), respectively. The other two are commercial porous silicas (Kieselgel 60 and silica gel 40 A from Aldrich).
2.2. Nitrogen adsorption Nitrogen adsorption-desorption isotherms were measured at 77.3 K using a commercial volumetric adsorption system Autosorb-1 or NOVA-1200 (both from Quantachrome Corp.). The samples were outgassed at 10 -4 Torr and 573 K for 3 h prior to the analysis. X-ray powder diffraction ( X R ) patterns were obtained on PW 1840 diffractometer (Phillips), with Co Kc~ radiation, 40 KV, 25 mA. 3. RESULTS
3.1. XRD measurements For AI-PILM, the basal spacing of the sample was evaluated from the dool diffraction peak and the interlayer free spacing between the clay sheets, which is regarded as ~ndicatlve
245 of the width of pores formed by intercalation, were derived. For MCM-41 samples, a sharp &00 peak as well as the secondary reflections at larger angles are observed. The mesopores in the samples are uniform and cylindrical in shape, and hexagonally arranged. The pore dimension can be derived from the position of the [ 100] peak: d.~a = a~ - wall thickness (ao = 2d~oo/~/3), assuming that the wall thickness for silicate is 10 Angstrom. 3 The pore size thus derived are listed in Table 1. Table Pore sizes derived from XRD measurements (A) .. Samples pore width pore diameter A1-PILM 7.6 MCM-41 (C12) 27.5 MCM-4 I(,C 16) 34.2
3.2. N2 adsorption isotherms The nitrogen adsorption isotherm at 77 K on AI-PILM is shown in Fig. 1. Most of the adsorption occurs in the low P'Po region because the presence of large number of micropores in the pillared clay. Fig 2 shows the isotherms of the mesoporous samples. Steep increases in adsorption are observed at a relative pressure around 0.2 for MCM-41 (C12), at above 0.3 for MCM-41 (C16), and above 0.7 for Kieselgel 60. For silica gel 40 A adsorption increases significantly at relative pressures above 0.4, but it is not as steep as the other three. These pronounced increases are attributed to capillary condensation in mesopores, and thus, are indicatives of the presence of mesopores in large quantities. If the sizes of these mesopores are larger, such an increase will occur at higher P P0. Therefore, the mesopore sizes of these samples are in the order of MCM-41(C12)<MCM-41(C16)<silica gel 40 A< Kieselgel 60.
150
i :. i
120:
o
Adsorption - Desorption /
/ ~ ,
..... ........ -+e -2~ * ~~.~.~=450 -~ 600.
~-
e
.4
/
E
MCM-41(C 12) MCM-41(C 16) silica gel 40 A Kleselgel 60 ~ g ~ f
~i 2
/~" i
~o
~
~ 300 -
g
.,-~
o
<
rael
< 150
30
! Q
0' 0.0
0.2
0.4
0.6
0.8
1.0
Relative pressure, P Po
Fig 1 N2 isotherm of alumina pillared clay.
o 0.0
0.2 0.4 0.6 0.8 RelatB.'e pressure. P P{,
Fig 2 N: isotherm of mesoporous solids.
1.0
246 3. t-plots
For A1-PILM adsorption is observed predominantly in the region of t below 2 A (Fig 3). It is followed by an inflection at slightly above 2 A, indicating that fine micropores in this solid have been filled. Beyond the inflexion point, adsorption varies almost linearly with t. If the surface area available for adsorption remains unchanged, then the tangent of the tplot is constant. This suggests that the fine micropores are predominate pore group and other pores existing in this sample are not important.
120
J J 90
-
60
-
O
[... ~q
&
o
O
!
<
! 0
600
o
!
1 E
9
500 o 400 "
r.~
o 300
.,,,~
0
.,z < 200
0
3
100 0 6
9
9
12
15
18
Figure 3. t-plot of A1-PILM.
ca., [--
'
6
t, in Angstrom
E
I
r
9
0
MCM-41(C 12) MCM-41(C 16) Silica gel 40A Kieselgel 60
!
. ,O ..,
12
15
18
t. in Angstrom
Fig 4 shows the t-plots of the four mesoporous silica samples. These plots consist of three linear stages. According to Branton et al 7: the initial stage represents multilayer adsorption on the pore wall; the following steep one, capillary condensation in mesopores: and the last one, adsorption on the external surface. It is noted that the second stage for the two commercial silicas covers a broader t range (over 3 A), compared to the range for the two MCM-41 samples (less than 0.5 A). The capillary condensation over a wide t values implies a broad pore size distribution in the samples.
Figure 4. t-plot of the four mesoporous solids.
4. Differential curves The tangent of the t-plots, dV/dt, is plotted against t for four samples in Figures 5. These differential plots illustrate the variations of I" with t. On first inspection, we see that the relationship between the size of the main pore group in the sample and the position of the peak on t-axis: as the pore size increases, the peak which corresponds to the filling of this pore group shifts to the larger t direction. For AI-PILM, which is known as a microporous solid, the peak of the differential curve occurs at a t value of 1.32 N, while for silica K-60 which has a mean pore diameter of 60 A, the curve peaks at t = 10.4 A. Between these two, we observe the peaks for two MCM-41 samples and silica gel 40~ occur in the same order of
247
their mean pore diameter: MCM-41 (C12) < MCM-41 (CI 6) < silica 40A. The mean pore diameter of silica 40A is < about 40 A, according to the e~,-, calculation using the BJH E method. 8 It is very interesting [--that the peaks on these curves can be related to the ,,,,,2 "~ pore structures of the samples. There should be an intrinsic relation between the pore size and the position of the peak on the t axis. We now try to derive an empirical expression for this relation from known experimental data of A1PILM and MCM-41 samples of various pore sizes. These samples have a well-defined pore structure and a narrow PSD. The pore sizes of the samples "improved MP method". 5 In Fig 6, the are plotted against the corresponding
~.... c ....
300
240 "
AI-PILM MCM-41(C12) MCM-41(CI6) Silica-40 Klesegel 60
.....
180"
120
i=: ~ ' ~ '
60 -
0 0
3
6
9 t,
12
15
18
A
Figure 5. Differential curves of the samples, derived from the t-plots
can be obtained from XRD measurements or the pore sizes of several MCM-41 samples thus obtained peak positions on the differential curves (the solid circles). A straight line (the solid line) of D = 6.347t 80 best fits these data points. E 0 The data in Table 1 and pore diameter of / = 60 jr / a0 commercial silicas obtained / by BJH method are also given in Fig 6 (the open .,..a squares) for comparison. It E 40 shows that pore dimensions ,-q determined by XRD {D 1 technique or the BJH o 20 ~ method are in good agreements with th~s simple empirical relation over wide range. We may apply this 0 " ..... simple empirical relation to 0 2 4 6 8 10 convert the t axis of the P e a k p o s i t i o n on t a x i s differential curve to pore s~ze, giving a clear F i g u r e 6. T h e r e l a t i o n b e t w e e n t h e p o r e s i z e indication of the pore size of MCM-41 sam pies and their peak position of the sample under on t h e d i f f e r e n t i a l c u r v e s . consideration.
248
0.8
On the other hand, the peak shape may reflect the distribution of pore volume over pore size of the samples. For MCM-41 samples, sharp peaks are observed. This means that filling of all mesopores occurs at almost the same relative pressure. In contrast, for the commercial mesoporous silica, of which a disordered pore structure is known, a broad peak on the differential curve is observed, reflecting a wide pore size distribution. In Fig 7, the area under the differential curve in Fig 5 is plotted against the volume of the major pore group in the samples. This pore volume was calculated by extrapolating the linear portion of high t to the adsorption axis, similarly to the approach of calculating
,J/
E06
i
9
,
r
~D
=~ 0.4 i -~ ~D
o 0.2'
/
0.0 0
~ 5
l0
15
20
Area under differential curves Figure 7. R e l a t i o n b e t w e e n the area u n d e r the differential c u r v e s and the pore v o l u m e o f the s a m p l e s . micropore volume using t or ~s-plot. A good linear relationship between the two is observed, suggesting that the peak area is an indicative of the pore volume. The area under the curve equals to the amount adsorbed by the solid. It is noted that there could be a substantial adsorption in the pores already, prior to the pore filling. The pore volume reflected by the area under the peak itself should be smaller than the real volume of the pores. The area under the differential curve up to the point where the pore filling has completed is more closely related to the real pore volume. If we convert the term of dV/dt to dV/dD,
----o---- A I - P I L M MCM-41(C12) MCM-41(C16) Silica 40A -K i e s e g e l 60
0.8
O. 6 E
~
" 0.4
i
O. 2
0 0 0
1
2
3
4
5
6
7
8
9
Pore size, nm F i g u r e 8. P S D s of the s a m p l e s d e r i v e d from the d i f f e r e n t i a l c u r v e s
10
249 and t to D using the equation of t and D, obtained from the straight line in Fig 6, the differential plots in Fig 5 become the curves illustrating the pore size distribution of the sample (Fig 8). Discussion Most of the methods developed for calculating pore size distribution is based on certain a theory or theoretical equation, such as the well-known Kelvin equation, 3 DR equation 9 or HK method. 10 However, the assumptions of a theory or equation invariably impose limitations on their applications. For instance, application of the Kelvin equation to ultramicropores is unreasonable, and so does the application of the DR equation or the HK method to mesopores. In contrast, the proposed approach is completely empirical. We can derive the PSD of micro-and meso-porous solids without any limitation from a particular theory or a theoretical equation. Being applicable over a wide pore size range is also an outstanding advantage, in particular, for dealing with a solid containing both micropores and mesopores in considerable quantities. Generally, conventional methods have difficulty in dealing with a wide pore size range and, thus, can not provide a comprehensive information of PSD for such a solid. In principle, the PSD given by the differential curve may not be precise, as we stated in the previous article. 11 Approximations come from the estimation of pore size and pore volume in the approach. Theoretical analysis indicates that the relation between the pore sizes and the position of the peak on t axis is not strictly linear as shown in Fig 6. It should be slightly concave downward, but the deviation from the linear relation in a range below 4.5 nm is negligible. For large pore size (>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
~
<
~
,
(
/
.
~
j
J ,','l~
//
-
both v)lot and v~h2ot bands and a-species has ,..
,..
a heterogeneity. Then, the observed spectra in the 2320-2220 cm -~ range were deconvoluted
[
,
|
9
9
2300
using the observed band profile at P/Po = 0.05 for v2ot band, three Lorentzian curves for
v2f13, v h~P',--, 2 and
Lorentzian
v)2[3~ bands,
curve for v3 + v4 band
one of
physisorbed acetonitrile, and a horizontal
9
|
-
9
2280
9
|
'
'
2260
'
i
9
-
2240
9
2220
Wave number / cm l Fig.3.
Resolved
infrared
absorption
spectra
of
adsorbed acetonitrile in the C ~ N stretching v 2 region at (a) PIP, = (I.15. (b) 0.37 (after capillary condensation). Circles denote observed data. The v ) ~ and vztC[3 bands are shown around 2250 cm ~.
256 base line. The least-squares fitting was carried out under the following assumptions to reduce adjustable parameters. That is, only the intensity and peak frequency of the VzOt band which are measured at P/Po - 0.05 are variable, the intensity ratios of the v2f13, v,h~13,, and v2h:13 bands are 1:0.332:0.083, and the bandwidth of Vzh~13 is equal to that of v2h213. The examples of the resolved spectra are shown in Fig. 3. The calculated composite curves shown by a solid line reproduce well the observed spectra. The band shape of the v2 band at P/P,, = 0.15 is nearly similar to that at P/Po = 0.05 (Fig. 3a), as expected. We must be, however, cautious about the discussion on the change of the v213 band in the low P/P,, region, because the v213 band below P/Po = 0.24 should have inevitable uncertainties.
The absorbance of the v2f13 and v2et bands obtained was plotted against P/Po in Fig. 4. The results in the previous paper were also shown by dashed line for comparison. The Vf(>-
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
(
"'\~, <)
, 2.5
0
. . . .
O. I . . . .
i 0.2 . . . .
P/P.
| 0.3 . . . .
0.4
Fig.5. Changes in half-band width of the v.,t~ bands with adsorption. The plots with dashed line show the previous results. And a dashed horizontal line denotes the half-band width of the x,: band of liquid acetonitrile at 298 K.
257 bonded surface hydroxyl increases gradually above P/Po = 0.15.
3.4. Motional states of adsorbed acetonitrile. The relationship between the half-band width (half width at half-maximum heights) of the v:fl3 band and P/Po is plotted in Fig. 5. The half-band width values in the preceding article [9] were larger than those obtained in this study. The present half-band width of the v:tl3 band decreases steeply at P/Po = 0.30. This sudden decrease is in a beautiful agreement with the shape of adsorption isotherm. Therefore, we can say that this fitting procedure is more reliable. Hence the relaxation process of an acetonitrile molecule transforms on capillary condensation. If the infrared band profile of single vibrational transition is given by Lorentzian and the band profile corresponds to the reorientational and vibrational time-correlation functions of exponential form, the relaxation time is expressed by, x = (2=cAr,_,)-'
(1)
"~-' = "t~' + "R',
(2)
where Av,/: is half-band width (cm-l), x, is reorientational relaxation time, and 1:, is vibrational relaxation
time.
Therefore,
we
can
obtain
the
more
exact
information
about
the
reorientational-vibrational relaxation of an acetonitrile molecule from the half-band width of the Vee]3 band from the above analysis. The x values for the v,fl3 bands calculated by eqn. (1) are summarized in Table 1. It is expected that an acetonitrile molecule physisorbed just below the steep rising of adsorption isotherm, that is, prior to the capillary condensation, undergo fewer collisions with its surroundings than a molecule in the liquid state. However, the x values of physisorbed acetonitrile in the range of P/P, = 0.15-0.27 are smaller than those of bulk liquid. The result suggests that the reorientational motion of an acetonitrile molecule in this state is comparatively fast because of the small intermolecular torque, although the infrared band involves the contributions of the reorientational and vibrational relaxation (eqn. Table 1 Relaxation time of an acctonitrilc molecule state
tcmp (K)
"I:(ps)
adsorbed state over the range P/Po = 0.15-0.27
303
1.5
adsorbed state over thc range P/Po = 0.32-0.37
303
1.7-1.8
liquid
298
1.7
258
(2)). In this case, we guess that, it is unlikely that the vibrational relaxation of physisorbed acetonitrile concerned is faster than that of liquid molecule. A b o v e P/Po = 0.30, the half-band widths of the v2f13 band tend to be narrower than that of bulk liquid (Fig.5). That is, 1: values are slightly longer than that of the bulk liquid at the same temperature. Accordingly, it is concluded that motion of acetonitrile molecules condensed in m e s o p o r e s is a little more perturbed than that of bulk liquid.
References [1] P.J. Branton, K. Kancko, N. Sctoyama. K. S. W. Sing, S. Inagaki, Y. Fukusima, Langmuir 12 (1996) 599. [2] P. L. Llcwcllyn, Y. Grillet, E SchiJth, H. Rcichcrt, K. K. Ungcr, Microporous Mater. 3 (1944) 345. [3] S. Inagaki, Y. Fukushima, K. Kuroda, J. Chem. Sot., Chem. Commun. (1993) 680. [4] P.J. Branton, K. Kaneko, N. Sctoyama, K. S. W. Sing. S. Inagaki, Y. Fukusima, Langmuir 12 (1996) 599. [5] R. G. Gordon, J. Chem. Phys. 43 (1965) 1307. [6] H. Shimizu, J. Chem. Phys. 43 (1965) 2453. [7] W. G. Rothschild, Dynamics of Molecular Liquids. Wiley, New York (1984). [8] A.I. Burshtcin, S.I. Tcmkin. Spectroscopy of Molecular Rotation ill Gases and Liquids, Cambridge University Press (1994). [9] H. Tanaka, T. Iiyama, N. Uckawa. T. Suzuki. A. Matsumoto. M. Griin, K.K. Ungcr, K. Kancko, Chem. Phys. Lett. 293 (1998) 541.
[10] S. Hashimoto, T. Ohba, S. Ikawa. Chem. Phys. 138 (1989) 63. [ 11] M. Grfin, K.K. Ungcr, A. Matsumoto, K. Tsutsumi. Microporous Mesoporous Mater. (1998) [12] T. liyama, K. Kancko, J. Phys. Chem. (in preparation). [13] Y. G. Vladimir, E Xiaobing, B. Zimci. L. H. Gary, A. O. James, ,I. Phys. Chem. 100 (1996) 1985. [ 14] K. F. Purcell, R. S. Drago, J. Am. Chem. Sot.. 88 (1965) 919. [15] C. L. Angcll, M. V. Howcll,,l. Phys. Chem. 73 (1969) 2551. [16] I. Suzuki, J. Nakagawa, T. Fuzikawa, Spectrochim. Acta. 33A (1977) 689.
Studies in Surface Scienceand Catalysis 128 K.K. Ungeret al. (FAitors) 92000ElsevierScienceB.V. All rightsreserved.
259
SYSTEMATIC SORPTION STUDIES ON SURFACE AND PORE SIZE CHARACTERISTICS OF DIFFERENT MCM-48 SILICA MATERIALS M. Thommes a, R. K6hn b and M. Fr6ba b* a
Quantachrome GmbH, Rudolf Diesel StraBe 12, D-85235 Odelzhausen, Germany Institute of Inorganic and Applied Chemistry, University of Hamburg, Martin-Luther-King-Platz 6, D-20146 Hamburg, Germany Email: [email protected] Fax: **49-40-42838-6348
We present results of a systematic study of the sorption- and phase behavior of argon, krypton and nitrogen at 77 K and 87 K on different pristine mesoporous MCM-48 silica phases of mean pore diameters 2-3 nm and on a MCM-48 silica/iron(III) oxide host-guest compound. Argon and krypton sorption isotherms on all MCM-48 silica materials revealed phase transitions accompanied by sorption hysteresis of type H1 well below the bulk triple point temperature. Details of the sorption hysteresis depend on temperature and pore size, e.g. with increasing temperature and decreasing pore size a shrinkage of the hysteresis loops is observed. MCM-48 silica consists of two interwoven, but unconnected three dimensional pore systems. Because of this special structure the cubic MCM-48 silica phase is considered as a matrix to immobilize catalytic active species onto or within the silica walls. The analysis of nitrogen and argon sorption isotherms at 77 K and 87 K indicates that the impregnation of a pristine MCM-48 silica phase with iron(III) oxide has led indeed to a coating of the inner surface of the silica walls. 1. I N T R O D U C T I O N In 1992, researchers of the Mobil Oil Company introduced a new concept in the synthesis of mesoporous materials. They used supramolecular arrays of surfactant molecules as templating agents in order to obtain mesostructured silicates or alumosilicates which retain after calcination an ordered arrangement of pores with diameters between 2 and 10 nm and a narrow pore size distribution comparable to that of zeolites. These materials called M41S phases give access to the regime of the mesopores which is very interesting for different kinds of new size selective applications, e.g., molecular sieves, catalysis and nanocomposites [1 ].
260 The structure directing agents used for the synthesis of the M41S phases are lyotropic phases of amphiphilic surfactant molecules. One can distinguish between three different phases that will be formed at certain concentration/temperature conditions [2]: (i) MCM-41 phase, hexagonal arrangement of one-dimensional pores; (ii) MCM-48 phase, cubic symmetry, two interwoven, but unconnected three-dimensional pore systems; (iii) MCM-50 phase, lamellar. Variations in the pore size distribution are possible by using surfactant molecules with different alkyl chain lengths or by so called expander molecules like mesitylen accumulated in the hydrophobic core of the micelles [3]. In contrast to MCM-41, the synthesis of MCM-48 is more difficult, which is the reason, why most of the interest in mesoporous molecular sieves has been concentrated almost exclusively on MCM-41 in the past and very little information was available on MCM-41. Because of the special pore structure the cubic MCM-48 silica phase is considered as a matrix to immobilize catalytic active species onto or within the silica walls or as a host to accomodate certain guest compounds. So far attempts to introduce for example iron or iron oxide species into the mesoporous silica structure were limited to the hexagonal MCM-41 phase [4,5]. Especially the magnetic, electronic, and catalytic properties of such systems seem to be interesting We have focused our work especially on the cubic MCM-48 silica phase because the channels within the three dimensional pore structure of MCM-48 silicas contain intersections which allow a higher accessibility to catalytic sites. In addition to the importance of the M41S materials for size- and shape-selective applications, these materials have been also regarded as a suitable mesoporous model adsorbent for testing theoretical predictions of pore condensation. Pore condensation represents a first order phase transition from a gas-like state to a liquid-like state of a pore fluid in presence of a bulk fluid reservoir, which occurs at a pressure p less than the saturation pressure p0 at gas-liquid coexistence of the bulk fluid [6,7]. In this sense pore condensation can be regarded as a shifted gas-liquid bulk phase transition due to confinement of a fluid to a pore. Recent work has shown that in fact the complete phase diagram of the confined fluid is shifted to lower temperature and higher mean density as compared with the bulk coexistence curve [e.g., 8,9]. A characteristic feature associated with pore condensation is the occurrence of sorption hysteresis, i.e pore evaporation occurs usually at a lower p/p0 compared to the condensation process. The details of this hysteresis loop depend on the thermodynamic state of the pore fluid and on the texture of adsorbents, i.e. the presence of a pore network. An empirical classification of common types of sorption hysteresis, which reflects a widely accepted correlation between the shape of the hysteresis loop and the geometry and texture of the mesoporous adsorbent was published by IUPAC [10]. However, detailed effects of these various factors on the hysteresis loop are not fully understood. In the literature mainly two models are discussed, which both contribute to the understanding of sorption hysteresis [8]: (i) single pore model: hysteresis is considered as an intrinsic property of the phase transition in a single pore, reflecting the existence of metastable gas-states. (ii) nen~,ork model. hysteresis is explained as a consequence of the interconnectivity of a real porous network with a wide distribution of pore sizes. Pore condensation and sorption hysteresis are of great importance for the characterization of porous media by the analysis of appropriate sorption isotherms (e.g., nitrogen, argon and
261 krypton sorption at 77 and 87 K). So far most systematic sorption studies have concentrated on MCM-41 and sorption hysteresis of type H1 (IUPAC classification) was observed for several fluids [e.g., 11,12]. The occurence of sorption hysteresis in MCM-41-silicates, which consists of a one-dimensional channel system indicates that sorption hysteresis is here an intrinsic property of the pore fluid. In order to assess the influence of a well defined three dimensional pore network structure on pore condensation and hysteresis we performed systematic sorption studies of pure fluids on MCM-48 silicas. Here we present the first systematic study on the pore size- and temperature dependence of the sorption- and phase behavior of argon, krypton and nitrogen in the well defined, threedimensional pore network of pristine mesoporous MCM-48 silica and MCM-48 silicaJiron(III) oxide host-guest compounds. 2. E X P E R I M E N T A L
2.1. Synthesis of mesoporous MCM-48 silica The MCM-48 silicas were synthesized by stirring 1.0 mol TEOS and 0,5 mol KOH in 62 mol H20 for 10 min. After adding of 0.65 mol CI6TAB (A,B), respectively 0.7 mol C14TAB (C) and 10 min of vigorous stirring the white and creamy solution was filled into a teflon-lined steel autoclave and statically heated at 388 K for 48 h. The resultant white precipitate was filtered and washed several times with warm deionized water. Drying gave a white powder which was calcined at 823 K in flowing air for 6 h to the products A, B and C.
2.2. Synthesis of MCM-48 silica/iron(III) oxide host-guest compounds The impregnation procedure was carried out by stirring the product B in a 1.6 m aqueous solution of iron(III) nitrate for 10 rain. The dispersion was seperated by centrifugation. The residue was dried in vakuum and calcined at 673 K in a N2 flow for 6 h to receive the product
B-Fe203. 2.3. Sorption experiments The MCM-48 silica materials were prepared as described above. Controlled-pore glass (CPG 120) was supplied by BAM. Nitrogen (purity 99.999 vol%), argon (purity 99.999 vol%) and krypton (purity 99.996 vol%) was supplied by Messer Griesheim GmbH. The detailed adsorption- and desorption isotherms were measured using a volumetric technique (QUANTACHROME AUTOSORB I). Before each measurement the sample was outgassed at 393.15 K for 12 h under vacuum.
262
3. R E S U L T S A N D D I S C U S S I O N 3.1. Characterization of pristine MCM-48 silica and MCM-48 silica/iron(Ill) oxide hostguest compound by sorption of N2 (77 K) and Ar (87 K)
N 2 ] 77K
600 500 e~o e,-,
E
400
'9,
--
300
~D
E
= o >
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<20<30 ~ (not shown in figure 1). The 110 and 200 reflections respectively located at 20 = 3.62 ~ and 20 -- 4.34 ~ appear only after 8 crystallization days (diffractogram a of Fig. 1D). Moreover these peaks are not well defined, indicating the poor arrangement of channels in the materials. Very long crystallization time is necessary (at least 11 days) to obtain well-ordered hexagonal MCM-41. As the crystallization temperature is raised, the 110 and 200 reflections are detected earlier and earlier as shown in Table 1. The intensity of these two reflections increases with crystallization time and temperature. We can also notice a significant decrease of the quantity of amorphous phase and an increase of the crystallinity and of the value of the dl00 parameter. However, long crystallization time at high temperature (> 8 days at 120~ or > 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<20<30 ~, not shown here) are present in the mixture.
Table 1 Position of 110 and 200 reflections Crystallization temperature (~
Crystallization Time (days)
Position of 110 reflection (20 in o)
Position of 200 reflections (20 in o)
80 lO0 120 140
8 4 1 1
3.62 3.73 3.56 3.38
4.34 4.25 4.06 3.87
272
,1=A1
B
~
C
"x
II
c
._=.
I
J'
=
41.9
I
1
9
9
!
2
i
9
3
i
9
4
i
9
1
5
.a, 1
9
2
2e(o)
4 6~
"
~
~
_
i
42.
.~--
9
i
9
4
~'~
;'~ 20( ~)
_
L_
D
z~e
E
43.6
...
=
Jt i I I
p5
~7,s
,
;
.
5 :-~
1
~
5
20( ~)
_
2st
i
3
2
3
4
5
6
1
10
.;
15
20
,
25
30
2e(~
!
2
i
3
9
!
4
9
!
5
9
6
20( ~) 20( ~ )
Figure 1. Variation of the XRD pattern with crystallization time, A I ; B 94; C 96; D 8 and E 11 (days) and temperature, a 80~ b 100~ c 120~ d 140~ F is the expanded XRD pattern of sample synthesized at 120~ for 11 days. The XRD results show that under studied conditions, the formation of well-ordered hexagonal MCM-41 is favored with increasing crystallization temperature and time. The value of the dl00 parameter is found to increase also with crystallization time and temperature.
273 It is observed that 80~ is a too low temperature to obtain materials with good quality. Crystallization times more than 11 days is necessary to synthesize compounds with wellordered hexagonal array. At 100~ the materials are well formed atter 4 days whereas only 1 day is needed at 120~ and 140~ But for these last two temperatures, longer crystallization times (> 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
"
I
6
"
I
8
"
I
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
This Page Intentionally Left Blank
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
-50
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.
I 15
'
I
10
'
I
"
5
I
0
'
I
-5
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
,
i
,
I
'
i
'
I
'
i
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
"2"-
r., N
275
.,,.,,
%-V-MCM-41 .4 0.5%-V-MCM-41 ~.
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
i
: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.
This Page Intentionally Left Blank
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<0.14
0.9
D=28.6 A
.
0.8
D=21.4 A
0.7
O
~0.10
I9=17.8 A D=13.7 A
._~ 0.6 -8 0.5
D=7.5 A
0.08
..= e-,
D=12A
~ 0.4
- - D=I2,~ ............ D=30 A .......... D=40 A --*-D=60 A --D=80 A
0.12
L.
0.3
0.06
/
/,..5:'"
"
O
,
e-,
0.0
" I"
"
,
,
o 0.00
E
9
-8
-4
-3
-2
"7
~: 0.25 9
Total
.
0.20
.'
l)
z<
0.15
-~ L
9
o 0.10
..'" .
L
."
"I
,,"
~0.15
'
Figure 8. Simulated exohedral adsorption o f nitrogen at 77 K in isolated SWCNTs.
Figure 7. Simulated endohedral adsorption o f nitrogen at 77 K in isolated SWCNTs.
f.,
-1
iogl0 P/P0
logl0 P/P0
O
""
;f; ,"
0.02
0.1
~.~.~
,.~""
.......... D = I 2 0 A . ~ ' ; "
.oL . 0.04
0.2
/[. "~
......... D = I 0 0 A
L_
"
i
..,.; r
r.~
Exo
.E
Endo ~.. 0.05
~.O.lO
...'""
"~
-~Z
'
..Q I,.,, O
O
~0.05
'" "J
o 0.00
E
,,
"
O
-6
0.00 -4
log l0 (P/P0) Figure 9. Simulated endohedral, exohedral and total adsorption o f nitrogen at 77 K in an isolated SWCNT of diameter 30 A.
'
-;
'
-'1
'
()
log lo (P/Po)
Figure 10. Simulated exohedral adsorption of nitrogen at 77 K in an open and closed SWCNT of diameter 30 A.
Another point is that due to the interaction between nitrogen molecules adsorbed inside and outside the tubes, both endohedral and exohedral adsorption will be enhanced, see Figure 10 for example which shows exohedral adsorption in an open and closed tube, D = 30 A. Simulated isotherms o f nitrogen at 77 K for closed square SWCNT arrays are shown in Figure 11. At small tube separations, the amount adsorbed increases with increasing tube diameter. However, at larger tube separations, the amount adsorbed decreases with increasing tube diameter. The isotherms are mainly type I or type IV, depending on tube diameters and separations. If the tubes are open, the amount o f nitrogen adsorbed will increase markedly as
320 shown in Figure 12, especially at small tube separations where endohedral adsorption is more important. However, at larger tube separations where exohedral adsorption plays a more important role, the increase in the amount adsorbed by open tubes is not so significant. 60G D 60G D (A)(A) 50 ...-'10 30 (A) (A) - 50 ob ....,10 6 "6 , .-10 6 "6 40 E ...... E 40 4.....,'10 15 E "'" E " 10 15 .-'.4 . 4 30 / / , . ' .. " o 30 /" ,.";?~"10 30 ~'~ 30 ,, . /
...
,,
r
.-
..' z / "
/,fi"
o 20
.,"
t~
= 10
o
o
~_...---:"
f
.".'"-' ,;" , , " ;:,)"" ....... 4 30 .4'..' .-..... 4 15 .-.......... :,,.' 4 6 .. ._._..a,,.... j
_k
O
./..
.
.'
9
e' ,: .."
"~ 20 c~
1
'
"
-! _.~'-,'!-.4_: . . . . . . . . . -4 15
E
o 10
,,"
,--'..7
.:z:i
9
c~
o
6
-k
log 10 (P/p0)
; log 10(P/Po)
Figure 11. Simulated adsorption of nitrogen at 77 K in square arrays of closed SWCNTs of different configurations.
Figure 12. Simulated adsorption of nitrogen at 77 K in square arrays of open SWCNTs of different configurations.
5.2. E x p e r i m e n t a l results o f nitrogen adsorption at 77K
Experimental nitrogen adsorption isotherms at 77 K obtained on the different nanotube samples are shown in Figure 13. We have seen no differences between the SWCNT coming from the webs or the collaret in terms of nitrogen adsorption. According to the IUPAC classification, the isotherms are of mixed type I (at low relative pressures)/II (at medium relative pressure), indicating the presence of a certain amount of microporosity as well as the development of mesoporosity, especially for the SWCNT sample. No hysteresis loop closure can be clearly observed; this indicates that some nitrogen is retained within the nanotube structures. In Table 2 are listed the specific surface areas as well as the micropore volumes according to the Dubinin-Asthakov method [39] of the different nanotubes samples. The MWCNT and BCNT samples exhibit very low surface areas, while the surface area of the SWCNT is consistent with the external surface area calculated for bundles of SWCNT (Table 1). Beside some studies [17, 20] that show the potential of carbon nanotubes to be good adsorbents, nitrogen adsorption experiments on nanotubes presented here and published so far [27, 28] show very low surface areas from 10 to 300 m 2 g~ even on opened tubes [28]. These values are far less than the surface areas of typical activated carbon used for gas storage which approach 1500 m 2 gl. Table 2 Data calculated from experimental nitrogen adsorption isotherms at 77 K MWCNT BCNT SWCNT
BET surface a r e a / m 2 [(1 15 10 302
DA micropore volume / 0.006 0.004 0.142
cm 3
g-l
321
,..-,
SWCNT
14o
E E ,.o o
!
12
w
108 9 i
4
..,....
~
9 9
ii
wll
r
MWCNT---~
o
0.'0
'
I
0.2
'
i
0.4
9
0.'6
'
018
'
BCNT 1.0 I
'
relative pressure, p / P0 Figure 13. Experimental nitrogen isotherms at 77 K for MWCNT, BCNT and S WCNT. 6. C O N C L U D I N G
REMARKS
There is some qualitative agreement between experimental measurements and simulations of nitrogen adsorption at 77 K in nanotube samples. Simulations suggest that interstitial adsorption may be important in nanotube arrays. However, amounts adsorbed experimentally do not reach levels expected from simulations. This may be due to insufficient purification of the nanotube samples, though the square array model of nanotube assemblies also might also need modification. Currently, work is proceeding in both these areas Bath, and in extending these ideas to consider the potential of nanotubes as gas storage media. ACKNOWLEDGEMENTS The authors would like to thank the University of Bath and the European Union (TMR contract ERBFMBICT972773) for financial support. The authors also thank colleagues at the University of Sussex, UK and the CSIC, Spain for their collaboration in providing the nanotube samples. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8.
S. Iijima, Nature, 354 (1991) 56. T.W. Ebbesen and P. M. Ajayan, Nature, 358 (1992), 220. T.W. Ebbesen, Ann. Rev. Mater. Sci., 24 (1994) 235. C. Journet, W. K. Maser, P. Bernier, A. Loiseau, M. Lamy de la Chapelle, S. Lefrant, P. Delniard, R. Lee and J. E. Fisher, Nature, 388 (1997) 756. A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C. Xu, Y. H. Lee, S. G. Kim, A. G. Rinzler, D. T. Colbert, G. E. Scuseria, D. Tomanek, J. E. Fisher and R. E. Smalley, Science, 273 (1996) 483. D.L. Carroll, P. Redlich, X. Blas6, J. C. Charlier, S. Curran, P. M. Ajayan, S. Roth, M. Ruhle, Phys. Rev. Lett., 81 (1998) 2332. M. Jos6-Yacam~.n, M. Miki-Yoshida, L. Rend6n, J.G. Santiensteban, Appl. Phys. Lett., 62 (1993) 202. A. Hamwi, H. Alvergnat, S. Bonnamy and F. Beguin, Carbon, 35 (1997) 723.
322 9. M.S.P. Shaffer, X. Fan and A. H. Windle, Carbon, 36 (1998) 1603. 10. P. M. Ajayan, T. W. Ebbesen, T. Ichihashi, S. Iijima, K. Tanigaki and H. Hiura, Nature. 362 (1993) 522. 11. T. W. Ebbesen, P. M. Ajayan, H. Hiuara and K. Tanigaki, Nature, 367 (1994) 519. 12. S. C. Tsang, P. J. F. Harris and M. L. H Green, Nature, 362 (1993) 520. 13. S. C. Tsang, Y. K. Chen, P. J. F. Harris and M. L. H. Green, Nature, 372 (1994) 159. 14. E. Dujardin, T. W. Ebbesen, A. Krishnan and M. M. J. Treacy, Adv. Mater., 10 (1998) 611. 15. P. M. Ajayan and S. Iijima, Nature, 361 (1993) 333. 16. M. Terrones, N. Grobert, J. P. Zhang, H. Terrones, J. Olivares, W. K. Hsu, J. P. Hare, A. K. Cheetham, H. W. Kroto, D. R. M. Walton, Chem. Phys. Lett. 285 (1998) 299. 17. A. C. Dillon, K. M. Jones, T. A. Bekkedahl, C. H. Kiang, D. S. Bethune and M. J. Heben, Nature, 386 (1997) 377. 18. C. Nfitzenadel, A. Zi~ttel, D. Chartouni and L. Schlapbach, Electrochem. Solid-State Lett., 2 (1999) 30. 19. K. Wang and J. K Johnson, J. Chem. Phys, 110 (1999) 577. 20. G. Stan and M. W. Cole, J. Low Temp. Phys., 110 (1998) 539. 21. F. Darkrim and D. Levesque, J. Chem. Phys., 109 (1998) 4981. 22. Y. F. Yin, T. J. Mays and B. McEnaney, Fundamentals of Adsorption 6, Ed. F. Meunier (1998) 261. 23. Y. F. Yin and T. J. Mays, Carbon '98, Strasbourg, France, (1998) 831. 24. G. E. Gadd, M. Blackford, S. Morrica, N. Webb, P. J. Evans, A. M. Smith, S. Leung, A. Day and Q. Hua, Science, 277 (1997) 933. 25. C. C. Ahn, Y. Ye, B. V. Ratnakumar, C. Witham, R. C. Bowman Jr. and B Fultz, Appl. Phys. Lett., 73 (1998) 3378. 26. A. Chambers, C. Park, R. T. K. Baker and N. M. Rodriguez, J. Phys. Chem. B. 102 (1998) 4253. 27. E. B. Mackie, R. A. Wolfson, L. M. Arnold, K. Lafdi and A. D. Mignone, Langmuir, 13 (1997) 7197. 28. H. Gaucher, Y. Grillet, F. Beguin, S. Bonnamy and R. J. M. Pellenq, Fundamentals of Adsorption 6, Ed F. Meunier (1998) 243. 29. S. Inoue, N. Ichikuni, T. Suzuki, T. Uematsu and K. Kaneko, J. Phys. Chem. B, 102 (1998) 4689. 30. W. A. Steele, The Interaction of Gases with Solid Surfaces; Pergamon Press: Oxford, 1974. 31. J. Breton and J. Gonzalez-Platas, Chem. Phys., 101 (1994) 3334. 32. D. H. Everett and J. C. Powl, J.C.S. Faraday Trans I, 72 (1976) 619. 33. Y. F.Yin, T. J. Mays and B. McEnaney, Carbon '97. Penn State, USA, (1997) 66. 34. M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1987. 35. D.J. Adams, Mol. Phys., 29 (1975) 307. 36. D.J. Adams, Mol. Phys., 32 (1976) 647. 37. D.Y. Peng and D.B. Robinson, Ind. Eng. Chem. Fundamental, 15 (1976) 59. 38. A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit. J. Robert, C. X~ Y. H. Lee, S. G. Kim, A. G. Rinzler, D. T. Colbert, G. E. Scuseria, D. Tom~nek, J. E. Fisher and R. E. Smalley, Science, 273 (1996) 483. 39. S. J. Gregg and K. S. W. Sing, Adsorption, Surface Area and Porosity, 2nd Ed., London, Academic press, 1982.
Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 9 2000 Elsevier Science B.V. All rights reserved.
323
Application o f the ~ M e t h o d for A n a l y s i n g Benzene, D i c h l o r o m e t h a n e and M e t h a n o l Isotherms D e t e r m i n e d on Molecular Sieve and Superactivated Carbons P.J.M. Carrott, M.M.L. Ribeiro Carrott and I.P.P. Cansado Departamento de Quimica, Universidade de I~vora, Col6gio Luis Ant6nio Vemey, 7000-671 Evora, Portugal
Reference data for the adsorption of benzene, dichloromethane and methanol have been used to construct (x~ plots for the adsorption of these vapours on Carbosieve, Takeda molecular sieve carbons, Maxsorb superactivated carbons and a charcoal cloth. It is shown that the ct~ method can give satisfactory results when applied to organic adsorptives provided that good quality adsorption data at higher pressures is available. It is also shown how analysis of the as plots can lead to useful information about the pore structure of the different types of carbon, and some of the difficulties associated with the use of nitrogen adsorption at 77K for the characterisation of microporous carbons are discussed.
1. INTRODUCTION
The txs method was initially proposed in 1969 [ 1] and was subsequently used extensively to analyse adsorption isotherms, principally of nitrogen at 77K, determined on a very wide variety of different types of solid [2,3]. The method essentially involves a graphical comparison between the shape of an isotherm obtained on the adsorbent with that obtained on a non-porous standard of known surface area. It follows that the availability of a standard isotherm is of primordial importance and the fact that it was only at the end of the 80's that the method began to be widely used to analyse adsorption isotherms determined on activated carbons was principally due to the lack of suitable standard data. The problem was initially resolved by making use of a non-porous precipitated silica coated with carbon by means of CVD of furfuraldehyde [4]. Later on, the standard data obtained with this adsorbent were thoroughly tested, and confirmed, by various research groups using a variety of carbons prepared in conditions which lead to the formation of non or weakly graphitized and completely non-porous materials [5-8]. In the original paper one of the major advantages put forward in favour of the ocs method over the contempary t method was that it allows a similar type of analysis of adsorption isotherms of other adsorptives, besides nitrogen, to be made. This is of particular importance in the case of activated carbons where it is customary to make use of a range of probe molecules of different size, shape, polarizability and polarity in order to carry out a more complete characterization. A number of authors have since demonstrated the general feasability of doing this and reference data for the adsorption of neopentane and butane, for
324 example, have been proposed [9,10]. It should be pointed out, however, that there has not been a sufficiently widespread use of the published data, nor any interlaboratory comparisons, which would allow us to establish how much confidence can be placed in the results obtained when the data are applied to the widest possible range of real carbon adsorbent materials. We are currently in the process of publishing reference data for various adsorptive molecules of different size and polarity which we hope other research groups will be able to evaluate. In this paper, we will present a sunanaary of some of the results obtained with benzene, dichloromethane and methanol, and show how application of the reference data can be used to obtain useful information about the pore structure of molecular sieve carbons and superactivated carbons.
2. EXPERIMENTAL
Organic vapour adsorption isotherms were determined gravimetrically at 298K using a CI Electronics vacuum microbalance with pressure measurement by means of Edwards Barocell capacitance manometers. The sample temperature was controlled by means of a continuous flow of a water/antifreeze mixture with the temperature being measured at a point close to the sample. Vapour pressures at the temperature of measurement were calculated from the data given in ref. 11. Nitrogen adsorption isotherms at 77K were determined using a CE Insmmaents Sorptomatic 1990. Before determination of the isotherms each sample was outgassed at 673K. More complete details will be given elsewhere [12]. The reference data used had previously been defined on the basis of work carried out using various non-porous carbon blacks including SterlingFT, Elftexl20 and N330 and N375 blacks produced by Carbogal. The microporous carbons studied here include carbon molecular sieves supplied by Supelco (Carbosieve), Takeda (MSC-3A, MSC-4A and X2MH 6/8 designated T3A, T4A and TX2 in this paper) and Kansai Coke (Maxsorb MSC-25 and MSC30, designated M25 and M30 in this paper). In addition, a sample of Takeda MSC-5A (designated T5A in this paper) was kindly supplied by Prof. K. Kaneko of Chiba University in Japan. All of the Takeda sma~les were granulated, the Maxsorbs were powdered and Carbosieve was in the usual bead form used for chromatography. One sample of activated charcoal cloth, VK50, was also studied.
3. RESULTS AND DISCUSSION
The isotherms and corresponding as plots are given in Figs. 1 and 2. It can be seen from Fig. 1, in particular, how the distortion of the isotherm shape, due to the enhancement of the heat of adsorption which occurs in narrow micropores, becomes increasingly less significant as the size of the adsorbing molecule decreases, and the ratio pore size/molecular diameter increases, along the series benzene-dichloromethane-methanol. It can also be seen that the degree of distortion of the isotherm shape is significantly greater with the Takeda samples suggesting that they all have smaller pore sizes than Carbosieve, VK50 and the Maxsorb carbons. At higher values of relative pressure all of the as plots are approximately linear with the apparent range of linearity being greater in the case of benzene than in the case of the other
325 Table 1 External surface areas in mEgl estimated from as plots of different adsorptives.
M25 M30 Carbosieve VK50 T3A T4A T5A TX2
nitrogen
methanol
dichloromethane
benzene
36 40 40 30 0 7 1 15
90 90 42 36 11 10 12 22
103 91 30 14 13 25
32 29 26 30 3 8 7 12
Table 2 Micropore volumes in cm 3g'l estimated from txs plots of different adsorptives.
M25 M30 Carbosieve VK50 T3A T4A T5A TX2
nitrogen
methano 1
dichloromethane
benzene
0.96 1.09 0.43 0.67 0 0.15 0.16 0.24
0.84 0.98 0.32 0.51 0.16 0.18 0.19 0.20
0.86 0.98 0.02 0.16 0.19 0.20
0.87 1.01 0.32 0.42 0 0.14 0.12 0.19
two adsorptives. From the slope and intercept of the plots the values of external surface area and micropore volume given in Tables 1 and 2, respectively, were calculated. For comparison, the values obtained from the corresponding nitrogen isotherms are also given in the tables. It can be seen from Table 1 that in most cases reasonable qualitative agreement, within _10m2g 4, between the different estimates of external area is found. The principal exceptions occur when the apparent range of linearity of the Orsplots is less extensive and when the range of pore sizes is greater. Thus, methanol and dichloromethane give, in all cases, values of external surface area greater than those given by benzene and nitrogen and this difference becomes very high with the Maxsorb carbons. We can conclude from these results that although the ~ts method can be used to analyse adsorption isotherms of organic vapours, it is essential to identify correctly the beginning of the linear range of the plot. This will vary, depending on the type of carbon and also on the specific adsorptive molecule used. In all cases, however, sufficient and reliable high pressure data is necessary. From a practical standpoint the measurement of highly accurate adsorptions at higher pressures poses some dificulties. In the gravimetric method only small quantities of sample can normally be used and hence the amount of external surface actually present in the
326 apparatus will typically be only about 5m2. If we wish to determine points spaced by Ap the required precision in mass determination is given by Am = (Ap x M x A x w) / (cz~calibration factor)
(1)
where M is the molecular weight of the adsorptive, A the external surface area of the adsorbent and w the mass of adsorbent used. For example, in the case of benzene, dichloromethane and methanol adsorption on a carbon with external surface area of 40m2g~ and using 0.1g of sample, this gives Am-13Ftg, -15Ftg and ~8Ftg, respectively, for points spaced by Ap~.01p ~ These amounts are close to the practical limits of standard commercial microbalances when included as part of home made adsorption lines and careful experimental procedures are therefore necessary if reliable results are to be obtained. Turning now to the micropore volumes, it is useful to consider the different samples sequentially. Takeda T3A The results obtained with T3A illustrate one of the two major difficulties associated with the use of nitrogen at 77K for characterising microporous carbons. It is well known that T3A does not adsorb nitrogen at 77K. On the other hand, the results in Fig.2 show that the larger methanol molecule is readily adsorbed and even the dichloromethane molecule adsorbs if left to equilibrate for a sufficiently long time (the step in the isotherm corresponds to a considerably longer equilibration time than was allowed for the other points). This difference in behaviour at room temperature and at 77I( is probably partially due to a much slower rate of diffusion at 77K. It seems likely, however, that the almost complete exclusion of nitrogen at 77K is also associated with shrinkage and vitrification of the carbon which would result in pore entrances being not only smaller but also much more rigid. Maxsorb M25 and M30 The results obtained with the Maxsorb carbons illustrate the second major difficulty associated with the use of nitrogen. It can be seen from Table 2 that the Maxsorb carbons do not exhibit a molecular sieve effect with the organic adsorptives. On the other hand, nitrogen gives a pore volume which is about 10~ higher. This type of behaviour has previously been found with other carbon adsorbents and, in view of the results just discussed for Takeda T3A, can not be explained by assuming that the carbons contain some small pores accessible to nitrogen but not to the organic adsorptives. We must conclude therefore that the packing of nitrogen molecules in carbon micropores is more dense than that in the bulk liquid. Takeda T4A With this sample the highest micropore volume is given by methanol. Furthermore, the methanol isotherm is reversible indicating not only that all accessible pores are larger than the methanol molecule but also that they can all be entered via pore entrances which are larger than the methanol molecule. Increasing the molecular size to that of dichloromethane and then to that of benzene results in a decrease in micropore volume and the appearance of low pressure hysteresis on the isotherms, particularly that of benzene. These results suggest that about 10% of the pores or pore entrances of T4A are smaller than dichloromethane (which is completely excluded from these pores), a further 10% are smaller than benzene (which is
327 completely excluded, and the adsorption of dichloromethane in these pores is activated), and a high proportion of the remainder are of size close to the minimum dimension of a benzene molecule (~0.41nm). Benzene molecules can enter all of these pores but, as the pore size and the molecular size are similar, pore filling is an activated process, and a significant amount of irreversibility appears on the isotherm. It should also be noted that the nitrogen micropore volume is about 10% higher than the benzene micropore volume, that is, a similar difference to that found with the Maxsorb carbons and therefore probably due to the uncertainty over the density of the nitrogerL Takeda T5A With this sample both methanol and dichloromethane give reversible isotherms and the same micropore volume. A much smaller micropore volume is given by benzene indicating that almost 40% of the pores or pore entrances are of size between that of dichloromethane and benzene. On the other hand, only a relatively small amount of low pressure hysteresis is present on the benzene isotherm indicating that the remaining pores and pore entrances are significantly larger than the benzene molecule. A more complete characterisation of this sample would require the use of a larger probe molecule, such as neopentane. The difference between the nitrogen and benzene micropore volumes is about 20%, that is, much greater than found with the Maxsorb carbons. However, it is not possible to say whether this indicates a true molecular sieving of nitrogen in a proportion of very narrow micropores or whether the density of nitrogen in TSA is even higher than that in the wider micropores of the Maxsorbs.
Takeda TX2 With this sample all three organic adsorptives give almost the same micropore volume and low pressure hysteresis is either absent or, in the case of benzene, very small. These results indicate that all of the pores and pore emrances are larger than the benzene molecule. It is interesting to note that, according to the manufacturers, this sample is also a 5A molecular sieve (which could be verified using, for example, neopentane). In terms of pore size distribution and total pore volume, therefore, it represents a significant technological advance over the T5A sample. With this sample also, the difference between the nitrogen and benzene micropore volumes is significantly greater than found with the Maxsorb carbons being, in fact, very similar to the difference found with T5A. VKS0 and Carbosieve VK50 shows a pronounced molecular sieving of benzene whereas Carbosieve gives the same micropore volumes for both benzene and methanol. However, previous work has shown that a significant amount of the pore volume of both adsorbents is also accessible to the much larger neopentane molecule and that a significant proportion of the pores and pore entrances must therefore be larger than 0.62nm (the size ofa neopentane molecule) [13,14]. Unlike TSA and TX2, therefore, VKS0 and Carbosieve are not 5A molecular sieves. Both of these samples, especially VKS0, give much greater differences between the nitrogen and benzene micropore volumes than was found with the Maxsorbs.
328
0.6p* 0.4p*/ 0.Sp* 0.9p* 0.94p* 0.96p* 12.t BEN7]~'~NE
e ~ ~
9
,0. ~ a ~ _ . . _ _ ~_
8.
M30
1
~
10.
ooo~176
_
~
,
2
I
!
!
-
~
I
M301
~
,
VK50
!
3
4
!]
8- ~
O
I 6-~
E 6-
VK50
0
i
4 i 2fl~"l~'~-E~dl~l~D~&''O-OO'--Oq ~oOO-O--O-OOO-O-O-O-O-O ' Carbosieve 2 0.2
0.4
p/p*
0.6
DICHLOROMETHANE
0.8
1.0
1
2
~s
5
0.94p~ 0.4p*0.6p*0.Sp*0.9p* ~ 0.96p*
M30
16
.
i
14
14
!
M251
12
12
"d 10
. r 10
16
";'C~I) E
E
8
E
6
~| 6
4
4
2
2
8
0~6 " 0~8 " 1.0
" 0~2 " 0~4
0.5
p/p*
I
ND0 ,o~_OGO--O - o o ii~ O0
2.5
I
I
I
I
I
I
20.
oo o
i
i
~
15, i 9 10,
2.0
25-
11
20,
1.5
0.94po 0.4p" 0.6p* 0.Sp~ 0.9p* ~1 0.96p*
25,J METHANOL
":~
1.0
,_-------0--0 ~ 0 _0.0-0--0-0-0 000-0
0.2
0.4
p/p*
0.6
E 15E
-0
VK50
m 10
Carbosievr
0.8
1.0
1
2
3
4
ff's
Figure 1. Adsorption isotherms and corresponding ~ plots for benzene, dichloromethane and methanol adsorption on Maxsorb M25 and M30, VK50 and Carbosieve.
329
2.5
0.61}~ 0.4p'/ 0.Sp" 0.gp* 0.94p*0.96p*
I BENZENE
<15 o ~
-o
-O
9- - _ o
~~_--o-_q~---i~,=,~
1"5~ C ~ _ ~ . ~ ~ O ( ~ - - ~
'~1~
9+ 9
"~ 1.5-
T J ~ 5A "
E ~1.00.5
11.5
0.2
0A
0.6
T3A
T3A
, - , , , - , _ o _ _.o _ _ o,~ , Q - - ~9- T - - o - o , .
.
0.8
1.0
2
/
DICIILOROMETHANE _ ~ ~ O
;
" ;
s
as 0.94p0 0.4pQ0.6p* 0.Sp*0.9p~ ~ 0.96p0
p/p"
~ ~w
I
w
w
~
1
I
3.0 2.5
a
~o,,~2.0 / n 0
2.0 .w/ :'
1= 1.5~ /
E 1.5: 1.0 0.5
~0-0-0--0-0-0/ .
,
!
9
o~
,
03
o;
0~J
o~O--O
i
T3A ,
!
o,
9
0.5
1.0
1.0 a
1.5
2.0
2.5
' 0.94pO o.4p" O.6p- O.Sp- 0.9p" ; 0.96p"
p/p
O
METHANOL
TX2
I
]
i
I
i
I
,
,
i
i
11
4 E3
E 1 9
)|i
~=
i
9
1 0.2
0.4
p/p"
0.6
0.8
1.0
1
O.s
2
3
4
Fig.2 - Adsorption isotherms and corresponding ~s plots for ben~ne, dichloromethane and methanol adsorption on Takeda T3A, T4A, T5A and TX2.
330 4. CONCLUSIONS The results presented show that the o~s method can be applied to adsorption isotherms of organic vapours. However, it is important to obtain reliable measurements at higher pressures, in the region -4).6-0.95p~ and, as the necessary precision is close to the limits of our current adsorption equipment, this implies that in future work of this nature the experimental procedures used need to be carefully considered. Analysis of the Cts plots can be used to obtain useful information concerning the pore (or pore entrance) size and distribution of commercial molecular sieve and superactivated carbons. A more complete characterisation of some of the samples would require the use of larger molecules than those used here. Reference data for the adsorption of neopemane has already been published [9] and this would appear to be the best choice for extending the range of molecular size in future work. The results also highlight two difficulties associated with the use of nitrogen for the characterisation of microporous cabrons. These are the uncertainty over the density of nitrogen adsorbed in micropores and the shrinkage and vitrification of the carbon at the very low temperature of 77K.
AKNOWLEDGEMENTS
The authors are grateful to Prof. K. Kaneko of Chiba University (Japan), Dr. W.R. Betz of Supeleo (US), Takeda Co. (Japan), Kansai Coke Co. (Japan) and Carbogal (Portugal) for the provision of samples and to the Funda~o para a Ci~ncia e a Tecnologia (Portugal), the Fundo Europeu para o Desenvolvimento Regional (FEDER) and program PRAXIS XXI (project no. PRAXIS/3/3.1/MMA/1781/95) for financial support.
REFERENCES ~
2. .
.
5. .
.
8. 9. 10. 11.
K.S.W. Sing, Chem.Ind., (1968) 1520. S.J. Gregg and K.S.W. Sing, Adsorption Surface Area and Porosity, 2nd edition, Academic Press, London, 1982. F. Rouquerol, J. Rouquerol and K.S.W. Sing, Adsorption by Powders and Porous Solids, Academic Press, London, 1999. P.J.M. Carrott, R.A. Roberts and K.S.W. Sing, Carbon, 25 (1987) 769. F. Rodriguez-Reinoso, J.M. Martin-Martinez, C. Prado-Burguete and B. McEnaney, J.Phys. Chem., 91 (1987) 515. A.M. Voloshehuk, M.M. Dubinin, T.A. Moskovskaya, G.R. Ivakhnyuk and N.F. Fedorov NF. Izv.Akad.Nauk.SSSR, Ser.Khim., (1988) 277 (in Russian). P.J.M. Carrott and K.S.W. Sing, Pure Appl.Chem. 61 (1989) 1835. M. Knflc, M. Jaroniec and ICP. Gadkaree, J.Colloid Interface Sci., 192 (1997) 250. P.J.M. Carrott, R.A. Roberts and K.S.W. Sing, Langmuir, 4 (1988) 740. M.J. Sell6s-P&ez and J.M. Martin-Martinez, Carbon, 30 (1992) 41. R.C. Reid, J.M. Prausnitz and B.E. Poling, The Properties of Gases and Liquids, 4th edition. New York: McGraw Hill 1987.
331 12. 13. 14.
P.J.M. Carrott, M.M.L. Ribeiro Carrott, I.P.P. Cansado and J.M.V. Nabais, Carbon, in the press. P.J.M. Carrott and J.J. Freemma, Carbon, 29 (1991) 499. P.J.M. Carrott R.A. Roberts and K.S.W. Sing,. In K.K. Unger, J. Rouquerol, K.S.W. Sing and H. Kral (editors), Characterization of Porous Solids, Elsevier, Amsterdam, 1988, pp.89-100.
This Page Intentionally Left Blank
Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) o 2000 Elsevier Science B.V. All rights reserved.
333
Characterization of porous carbonaceous sorbents using high pressure-high temperature adsorption data G. De Weireld, M. Frere and R. Jadot Factul6 Polytechnique de Mons, Thermodynamics Department, 31 bd Dolez, 7000 Mons, Belgium, E-mail: [email protected] This paper aims at presenting the results of the potential theory applied to high pressure and high temperature adsorption data for both sub and supercritical fluids. We used two different procedures for the calculation of the reference characteristic curve. The first one is based on the works by Ozawa, Agarwal and Dubinin. The second one is based on the works by Dhima and Neimark. The second method leads to satisfactory results as it is possible to obtain a unique characteristic curve but it requires the revision of the classical laws relating the characteristic curve to the structural properties of the adsorbent. Using this procedure, it has been possible to point out the influence of the buoyancy effect on the adsorbed phase for the high pressure data and to propose a method to correct it. 1. I N T R O D U C T I O N The determination of the structural properties of porous adsorbents is of prime importance in the field of gas and liquid adsorption technology. Indeed, the pore shape, the pore dimensions and the chemical structure of its walls are the main characteristics to be considered when studying the potentiality of a given adsorbent to fit a given application. As far as the microporosity of heterogeneous solids is concerned, one must note that the different methods now available are not satisfactory. These methods are based on the theoretical treatment of experimental adsorption data. Such data generally consist of a nitrogen adsorption isotherm at 77 K. The methods differ in the theoretical treatment which is used. A majority of them are based on the Generalised Adsorption Isotherm (GM) also called the Integral Adsorption Equation (IAE). The more recent approaches use the Monte Carlo simulations or the density functional theory to calculate the local adsorption isotherm. The analytical form of the pore size distribution function (PSD) is not a priori assumed. It is determined using the regularization method [ 1,2,3]. Older methods use the Dubinin-Radushkevich or the Dubinin-Astakhov models as kernel with a gaussian or a gamma-type function for the pore size distribution. In some cases, the generalised adsorption equation can be solved analytically and the parameters of the PSD appear directly in the isotherm equation [4,5,6]. Other methods which do not rely on the GAI concept are sometimes used: the MP and the Horvath-Kawazoe methods are the most well known [7,8].
334 Few studies have been devoted to the comparison of all these methods [9,10] so that it is quite difficult to dispose of satisfying conclusions on their efficiency. On the theoretical point of view, the methods based on the GAI concept and on molecular simulation calculations should be the most efficient ones. However a recent study has shown that the Stoeckli method (based on the DubininAstakhov theory ) [6] gave results similar to those obtained from the molecular simulation methods [9]. On the other hand, the H-K and the MP methods are known to be rather inconsistent. In the near future, the development of the molecular simulation methods and the availability of results of comparison studies for a wide range of microporous sorbents should make the situation clearer. However, these methods are always based on the same kind of experimental data: a N2 adsorption isotherm at 77 K. These experimental conditions are very often far from those prevailing in the industrial applications. The use of a single adsorption isotherm within standard conditions could be considered as an advantage as it simplifies the experimental part of the characterization procedure. On the other hand, the possibility of using adsorption data in a wider temperature and pressure domain of conditions and for a large range of adsorbates should be helpful to prove or to invalidate the efficiency of the theoretical treatments. Besides, it would allow to adapt the complete characterization procedures and thus the choice of the experimental conditions in order to fit the final application in which the porous medium will be involved. This work can be considered as the first step of a more general study devoted to such a topic. We used high pressure (up to 10.000 kPa) and high temperature (303,323,343,363 and 383 K) adsorption isotherms for five different adsorbates (At, N2, CH4, C3H8, n-C4Hlo). Some of them are supercritical in the whole range of T and P conditions (N2, At, CH4). n-C4H~o is subcritical; C3H8 is subcritical except for the highest temperature isotherm. We completed these data by a classical 77 K nitrogen adsorption isotherm. As to the theoretical treatments, methods derived from the potential theory have been used. These methods are the easiest way to perform porosity analysis from experimental data related to different adsorbates. The final purposes of this study are: to point out the most efficient theoretical treatment (among those based the potential theory) which would lead to a unique characteristic curve; to discuss about the possibility of obtaining structural information about the adsorbent form such a characteristic curve; - to show the buoyancy effect on the adsorbed phase and to propose a correction procedure based on the theoretical treatment. -
-
2. E X P E R I M E N T A L SECTION The high pressure-high temperature adsorption isotherms have been measured using a RUBOTHERM magnetic suspension balance. The adsorption isotherms and the detail of the experimental procedure are presented elsewhere [11,12]. Considering the measurement accuracy of each sensor (mass, temperature and pressure), the relative errors on the adsorbed mass and on the pressure are estimated respectively to 0.3 and 0.5 %; the temperature is measured with an accuracy of 0.1 K. The main cause of experimental error is not the lack of accuracy of the sensors but rather the buoyancy effect on the adsorbent sample on the one hand and on the adsorbed phase on the other hand. The first contibution is taken into account by
335 determining the volume of the adsorbent sample prior to all measurement. This determination is carried out using the He method: the force exerted on the evacuated sample is measured at different pressures: this force is supposed to be equal to the buoyancy effect on the sample matrix. It is quite difficult to give a magnitude of the buoyancy effect on the adsorbent and to discuss its relative importance in comparison to the adsorbed mass: this importance depends on the adsorbate- adsorbent system and on the temperature and pressure conditions. This effect appears clearly when the non-corrected adsorbed mass decreases as pressure increases. Considering CH4 at 303 K, the maximum of the non-corrected adsorbed mass is reached at 1500 kPa. At such a pressure, the discrepancy between the corrected and the non-corrected adsorbed mass is already 30%. The buoyancy effect on the adsorbed phase is much more difficult to calculate as it requires the knowledge of its volume. It is not taken into account in the rough experimental data so that they should be presented as excess data. The estimation of the buoyancy effect on the adsorbed phase is one of the aims of this paper; its importance is discussed in section 4. The 77 K N2 adsorption isotherm has been measured by an OMNISORP-100 sorption analyser The adsorbent we considered is an activated carbon F30-470 type provided by CHEMVIRON CARBON (total micropore volume : 0.394 10.3 m 3 kg 1 , total pore volume 0.497 103 m 3 kg 1, mesopore and macropore surface area : 56 l0 s m 2 kg 1 ; determined by the tplot method). 3. T H E O R E T I C A L SECTION The potential theory is based on the concept of the characteristic curve [13,14]. It is defined as the function of the adsorbed volume V (m 3 kg ~) versus the adsorption potential e (J mol-~). V and e are calculated with the following equations: (1)
V - m(T,P)v (T,P) f
f
\\
e - R T In f~ IT, P~[T)) f(T, P) in which: -
-
-
-
(2)
m(P,T) (kg kg ~) is the adsorbed mass va (m 3 kg l ) is the molar volume of the adsorbate in the adsorbed phase for a given temperature T(K) and a given pressure P(kPa) R is the ideal gas constant = 8.314 (J mol l K l) Ps(T) (kPa) is the saturation pressure at temperature T f (T, P) is the gas fugacity of the adsorbate at temperature T and pressure P f~ (T, Ps(T)) is the fugacity of the adsorbate at temperature T and pressure Ps(T)
m (T,P), T and P are experimental data .va, f and ~ can be calculated from T and P. For a given adsorbate-adsorbent system, the characteristic curve should be unique whatever the temperature and pressure conditions of the experimental data. When considering different adsorbates on the same adsorbent, the ratio of the adsorption potentials for a given value of the adsorbed volume V should be constant whatever the value of V:
336
I
t ads21 --13 ~ ~ adsl )
(3)
in which
E;adsl and ~ads2 are the adsorption potentials corresponding to a given value of V respectively for adsorbate 1 and adsorbate 2 /3 is thus constant and called the affinity factor of adsorbate 2 (adsorbate 1 being considered as a the reference) The potential theory has been widely used in the last decades. Such a success is mainly due to the predictive character of this method. Once va, f, fs and 13 are known, it is possible to calculate any isotherm if the reference characteristic curve of the adsorbent is known. A lot of research teams have tried to improve the initial theory by proposing different correlations for the determination of va [ 15,16,17]. The calculation of Ps and thus fs for supercritical fluids is another problem which has been much debated [18,19,20]. Besides, it is possible to relate the reference characteristic curve to the porous structure of the adsorbent so that the theoretical treatments are very ofen used as characterization methods. The way the mathematical expression of the reference characteristic curve can be related to the micropore size distribution function of the adsorbent has also been widely discussed in the literature [4,5,6]. In this paper we consider two different methods for the calculation of v, and f~: The first one has been developed by Ozawa et al. [15] and Dubinin [18]. The molar volume of the adsorbate in the adsorbed phase is calculated by v a - v b exp(f2(T- Tb ))
(4)
in which: Vb (m s mol 1) is the molar volume of the liquid adsorbate at the normal boiling point Tb
-
(K) - f2 (K l ) is the thermal expansion coefficient f~ = 0.0025 K -i (Ozawa et al.[ 15])
(T~ - T b ) (Dubinin [18]) in which - b (m s mo1-1) is the van der Waals co-volume Tc (K) is the critical temperature -
(5)
337 These expressions have been used both for sub or supercritical conditions, f and f~ are calculated using the R-K-S equation of state for subcritical conditions. For supercritical fluids we considered:
(6)
in which: - Pc (kPa) is the critical pressure In the second method developed by Dhima and Neimark [19, 20, 21], the molar volume of the adsorbate in the adsorbed phase is calculated by: v -
Z~RT
(7)
P.
in which: - Pa (kPa) is the internal pressure of the adsorbed phase - Z, is the compressibility factor of the adsorbate in the adsorbed phase. It is a function of temperature T and internal pressure P~ P~ is calculated by:
I
p _ q~, - R T 1.3RL
)2
p~
(8)
in which: qst (J mol ~) is the isosteric heat of adsorption at low coverage Za is calculated using the chain of rotators equation of state [22]. fs and f are calculated using the same equation of state respectively at Pa and P. The same procedure is used in sub or supercritical conditions. As to the 13 parameters, they are available in the literature or may be calculated from the polarisabilities and for the quadrupole moments [23 ]. The reference characteristic curves have been used to calculate the structural properties of the adsorbent. First of all, we applied a classical Dubinin-Radushkevich treatment (In V versus
In V - In VDR
~2 ref E~ef
(9)
338 in which: V D R (m 3 kg 1) is the D-R micropore volume e~cf(J mol 1) is the adsorption potential of the reference adsorbate - Eref (J mol 1) is the characteristic energy of the reference adsorbate. It is related to the average pore diameter H by equation 10: -
H-
79200
E ref (10)
in which: -
H ([~) is the average pore diameter We also applied the same treatment with a gaussian PSD.
4. RESULTS AND C O M M E N T S The adsorption isotherms have been treated using the first method. Using equations l, 2 and 3 to calculate V and er~f(the reference adsorbate is N2) and equations 4, 5, 6 and the R-K-S eos for the calculation of va, f and f~, we obtained the reference characteristic curve. It is presented in figure 1. The analysis of figure 1 leads to the following conclusions: Using experimental data in such a wide range of experimental conditions allows to obtain a characteristic curve in the whole domain of er~f. Such a domain is larger than the one obtained with only one standard isotherm (77 K Nz isotherm). - The curve seems to be unique and to have a gaussian-like behaviour. The only discrepancies are due to: - the very low pressure data (high ere0 of the 77 K N2 adsorption isotherm (nonequilibrium data, inefficiency of the treatment in the very low pressure domain) the high pressure data (low e~of) of the subcritical fluids (capillary condensation in the mesopores) the high pressure data (low e~0 of the supercritical fluids (predominance of the buoyancy effect on the adsorbed phase). In fact studying each adsorbate separately shows that the temperature effect is not well described by this method. As an illustration, figure 2 presents the DR plot of the nitrogen data. -
-
-
The average deviation on V between the 77 K data and the supercritical ones is 50%. Using the DR treatment to calculate the micropore volume and the average pore diameter (equations 9 and 10) should not lead to satisfactory results. Such results are presented in table 1. The structural properties have been calculated for each adsorbate separately. We eliminated the non-valid data that is to say the very low pressure data of the 77 K N2 adsorption isotherm, the high pressure data for supercritical fluids and the capillary condensation data.
339
07 i 0.6 -,
E
o
0.4--
E -
O >
<
0.5-
0.3--
- - - - N2(77 K)
0,
N2
o
0 . 2 - -1
9 Ar
0.1
,
CH4
,
C3H8
_.,
0
.
.
.
.
.
5000
.
10000
n-C4H10
I
15000
20000
Adsorption potential g,~,-(J tool -~) Figure 1
Reference characteristic cuwe (method 1)
O.OOE+O0
5.00E+08
7
-8 -9 >
-10 -11 -12 --
r 4,
-13 -14 -15 -16 Eref
2
(j2 mol -2 )
1.00E+09
Figure 2
DR-plot of the N2 data (method I)
340 Table 1
Structural properties of activated carbon F30-470 obtained
by a DR plot of the reference characteristic curves (method 1)
voR
(m3kg l)
"
(h)
IVca,-Vexpl IVa,-Voxpl V
exp
V
exp
Limited data 10.1%
13.2%
all T
Ar
0.139 10 "3
6.86
N2
0.390 10"3
10.65
77K
0.169 10 "3
8.03
T>Tc
CI-I4
0.220 10-3
10.33
5.3%
6.5%
all T
C3H8
0.415 10 "3
17.80
3.9 %
6.5%
all T
n-C4Hlo
0.432 10 "3
17.02
1.6 %
6.4%
all T
Table 1 shows that the micropore volume of the adsorbent depends on the adsorbate although the magnitude is physically acceptable: the supercritical fluids provide low VDR values whereas the subcritical fluids provide commonly accepted values of the micropore volume. This is due to the fact that the supercritical fluids provide high erof values so that the extrapolation to the y-axis intercept is not accurate. This lack of accuracy is strengthened by the dispersion of the experimental data due to the inefficiency of the procedure to represent the temperature effect. As a consequence, the H values (related to Ercf that is to say to the slope of the DR plot) fluctuate a lot from one adsorbate to another. The average deviations calculated on the limited experimental data which have been used to determine VDR and H are rather good except for N2 (not mentioned in table 1 because the sub and supercritical data have been treated separately) for which the problem of the temperature effect appears in a more stringent way. A complete treatment (determination of the parameters of the gaussian PSD) did not lead to any improvement neither in the characteristics nor in the deviations. We did the same work using the second method (equations 1, 2, 3, 7, 8 and the C-O-R eos). The reference characteristic curve is presented in figure 3.
341
0.45 0.4
-
0.35 0.30
,--, 0 . 2 5 -
>
~)
0.2- - - N 2 (77 K)
0.15cA
o N2 9 Ar
0.1-
<
CH4 9 C3H8 , 9 n-C4H10
0.05 0 10000
I
I
15000
20000
25000
30000
35000
Adsorption potential eref (J moll) Figure 3
Reference characteristic curve (method 2)
One observed the same behaviour of the non-valid data as in figure 1. The most striking fact is the translation of the butane curve. We have been able to show that this effect was due to the value of the low coverage isosteric we took for butane. Given the shape of the isotherm (high initial slope), it is difficult to obtain accurate values of the isosteric heat in the low coverage area using our high pressure apparatus. As a consequence, we took the isosteric heat for butane equal to two times its isosteric heat on graphitized carbon black. Previous works have shown that such a procedure led to an overestimation of the isosteric heat which may range from 20 to 60 % given the adsorbent and the adsorbate. Using an isosteric heat equal to 80 % of the previous one, the butane characteristic curve would be superposed to the others. Accurate values of qst of adsorbates exhibiting a high initial isotherm slope are easily obtained using an appropriate experimental device (using a chromatography method for example). On the other hand the temperature effect is well represented. Indeed, figure 4 shows that it is possible to represent the supercritical N2 data and the 77 K N2 data using a unique DR plot (in the validity domain of the procedure and for non erroneous experimental data).
342 0.00E+00
5.00E +08
1.00E+09
I
t
-6
1.50E+09
Figure 4
-7-
DR-plot of the N2 data (method 2)
-8-9
>
-10 -11 -12
-
-13 -14 -
"4
-15 -16
2
Eref
Table 2
(j2 mol-2)
Structural properties of activated carbon F30-470 obtained by a DR plot of the reference characteristic curves (method 2)
VDR
H
( m3 kg 1)
(/~)
]Vcal_ VexpI V
exp
]Vcal _ Vcxp] V
cxp
Limited data Ar N2 CH4
C3H8 n-C4H10
0.403 10 -3
5.16
7.4 %
11.4 %
0.666 10 -3
5.82
4.2 %
24 %
0.901 10.3
6.52
4.1%
31%
0.970 10 -3
7.06
2.8 %
6.1%
1.050 10-3
6.28
1.2 %
3.3 %
Table 2 presents the structural characteristics of the adsorbent obtained from a DR plot treatment of the characteristic curves of each adsorbate. The fact that the temperature effect is well described leads to more stable values of the DR plot slope and to lower values of the average deviation. As a consequence, the H values does not fluctuate in the same way as in table 1. However, the obtained values are too low. Besides, such stable H values do not prevent the fluctuations of VDR. Such fluctuations can be attributed to the fact that the characteristic curves are located in a arcf area which seems to be translated of 10000 J mol 1 from the y-axis whereas the first method provides nearly-zero arcf values This is not surprising
343
as f~ and va are calculated in a quite different way. As a consequence, the way we calculate VDR and H is questionable. It explains why we obtain rather high values of the micropore volume and too low values for the average pore diameter. The equations relating the characteristic curve to the structural properties of the adsorbent should be adapted to this treatment. Table 2 shows that the average deviation is much higher when calculated on all the experimental data than when calculated on the limited data. It was not the case in table 1. Besides, this effect is well marked for the supercritical fluids whereas for the subcritical fluids there is no significant change. In fact the DR plot obtained from the characteristic curves calculated by the second method fit the limited experimental data in such a way that the discrepancies which appear when considering all the data are mainly due to the buoyancy effect on the adsorbed phase. As a consequence the characteristic curve obtained by this procedure can be used to perform the buoyancy effect correction on the experimental data. Such a correction is zero for subcritical adsorbates for which the gas density is low compared to the adsorbed phase density. For supercritical fluids, such a correction may reach 30% of the non corrected adsorbed mass. Figure 5 shows the calculated (from the DR parameters) and the experimental reference characteristic curves. At low eref (high pressure), due to the buoyancy effect on the adsorbed phase, the experimental data are lower than the calculated ones. Figure 6 shows the corrected and non corrected isotherms for At. 0.18 9e ~ t a l
0.16 -
car~enstic
CUla,'eS
9calculed~ t e n s t i c
,E 0.14-
curves
0.12"9 ;>
0.10.08-
o 0.06<~9
0.04-
~ll|wl@ m
0.02 -
I 0 Figure 5
-I
Ih
1(X)(X) 2(X)(X) 30030 Adsoxption potential er~f(J n'D1-1)
9 4(X)00
Calculated and experimental reference characteristic curves for Ar
344 Figure 6
0.2 0.18
m 9
0.16 "7
9 9 9
0.14 012
ff
_
9 I
Ol
_ 9
I
_-- 9
9 9 9
9 _ t / m . - mm9 m, .,,-, __,mm~_ m 9 1 4 9 ~mSmr149 ~milIm"
_9 I
9 9 CL.qi m
Corrected and non-corrected adsorption Ar isotherms
i I
wV
5. C O N C L U S I O N S
Among the methods available for the calculation of the reference < 0.06 characteristic curve from 0.04 + ,amm" . . . . . . . experimental isotherms, we 0.02 +Wl : m $ non-corrected adsorption Ar isotherms 1 chose two procedures. The 9corrected adsorption Ar isotherms mfirst one based on the Or- =' t t i works by Ozawa, Dubinin 0 20 40 60 80 100 and Agarwal, is a classical Pressure* 10 .2 (kPa) one easy to use. The second one based on the works by Dhima, Dubinin and Neimark is based on a more coherent analysis of the initial potential theory. Using high temperature, high pressure data for sub and supercritical fluids, we have shown that it was possible to obtain a characteristic curve covering a wide ~rof area which largely overlaps the ~rof domain of the classical N2 data at 77 K. The first method gives a poor representation of the temperature effect with, as consequence, the impossibility to use a unique characteristic curve for the characterization procedure. This curve is not even unique for a given adsorbate. The second method is more efficient but problems occur when passing from one adsorbate to another if the low coverage isosteric heat of adsorption is not accurately determined. If this problem can be overcome, it is possible to obtain a unique characteristic curve. Unfortunately the classical laws relating the characteristic curve to the structural properties of the adsorbent are no longer valid. Anyway, the second method has been successfully used for the evaluation of the buoyancy effect on the adsorbed phase which was still an unsolved problem of the high pressure measurements. In this work, we did not identify any improvement of the average deviation when passing from a simple DR plot treatment to a gauss 9 PSD analysis. Anyway, this conclusion cannot be considered as general as it depends on the adosbent.
O:l~l
t~ 0.08
g Im]r'm_ • 9 9 1 4 9 1 4 9 1 4 9 IV 9 $ 9 mW_m 'v mm 9 mmmlmmmm miIf 9
i
9 I*
9
m
ml
9
.
345 REFERENCES
1. T.J. Mays, Proceedings of the 5th international conference on Fundamentals of Adsorption, M.D. Le Van (Ed.), Kluwer- Dordrecht (1996) 603 2. N.A. Seaton, J.P.R.B. Walton and N. Quirke, Carbon, 27 (1989) 853. 3. C. Lastoskie, K-E. Gubbins and N. Quirke, J. phys. Chem., 97 (1993) 4786. 4. M.M. Dubinin and H.F. Stoeckli, J. Coll. Int. Sci., 75 (1980) 34. 5. M.M. Dubinin, Carbon, 23 (1985) 373. 6. H.F. Stoeckli, Carbon ,27 (1989) 962. 7. J.H. de Boer, B.G Linsen, Th. Vanderplas and G.J. Zandervan, J. Catal., 4 (1965) 469. 8. Q. Horvath and K. Kawazoe, J. Chem. Eng. Jap. 16 (1983) 470. 9. P.J.M. Carott, M.M.L. Ribeiro Carott and T.J.Mays, Proceedings of the 6th international conference on Fudamentals of adsorption, F. Meunier (Ed.), Elsecier- Paris (1998) 677. 10. M. Kruk, M. Jaroniec and J. Choma, Adsorption, 3 (1997) 209. 11. G. De Weireld, M. Fr6re and R. Jadot, Meas. Sci. Technol., 10 (1999) 117. 12. M. Frere, G. De Weireld, R. Jadot, Proceedings of the 6th international conference on Fundamentals of Adsorption, F. Meunier (Ed.), Elsevier - Paris (1998) 279. 13. M. Polanyi, Transaction Faraday Society, 28 (1932) 316. 14. M.M. Dubinin and LV. Radushkevich, Docklady Akademici Nauk.S.S.S.R., LV (4) (1947) 327. 15. S. Ozawa, S. Kusumi and Y. Ogino, J. Coll. Int. Sci., 56 (1976) 83. 16. W. H. Cook and D. Basmadjian, Can. J. Chem. Eng., 42 (1964) 146. 17. R.K. Agarwal and J.A. Schwarz, Carbon, 26 (1988) 873. 18. MM. Dubinin, Chem. Rev. ,60 (1960) 235. 19.M.M. Dubinin, A V. Neimark and V.V. Serpinsky, Carbon, 31 (1993) 1015 20. A. Dhima and S. Jullian, Proceedings of the 1996 AICHE annual meeting. 21. A.V. Neimark, J. Coll. Int. Sci., 165 (1994) 91 22. B.J. Alder, D.A. Young and M.A. Mark, J. Chem. Phys., 56 (1972) 3013. 23. R.K. Agarwal and J.A. Schwarz, J. Coll. Int. Sci., 130 (1989) 137.
This Page Intentionally Left Blank
Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000 ElsevierScienceB.V.All rightsreserved.
347
Influence o f the porous structure of activated carbon on adsorption from binary liquid mixtures A. Dery|o-Marczewskaa, J. Goworek a and A. ~;wia~tkowskib aFaculty of Chemistry, M. Curie-Sk|odowska University, 20-031 Lublin, Poland E-mail: [email protected], pl blnstitute of Chemistry, Military Technical Academy, 00-908 Warsaw, Poland Three carbon samples showing differences in pore structure are chosen to study the effect of porous texture on adsorption from liquid solutions. The benzene adsorption/desorption isotherms are applied to determine the properties of geometrical surface structure of investigated carbons. The liquid adsorption data are analyzed in terms of the theory of adsorption on heterogeneous solids. The relation between parameters of porous structure of the activated carbon samples and parameters of adsorption from the liquid phase is discussed. 1. I N T R O D U C T I O N Character of porous structure and chemical nature of surface active groups determine the process of adsorption from gas and liquid phases to a large extent. Generally, for adsorption from liquid mixtures the greater effect of chemical character of a solid surface was found. Recently, the influence of geometrical structure of activated carbons [ 1,2] and silica gels [3,4] on adsorption from binary liquid mixtures has been studied. Significant effect of pore sizes on the formation of surface phase was confirmed. However, the investigated activated carbons were obtained from various raw materials. This led to the differences in carbon matrix structure (sizes of graphite-like crystallites and amount of amorphous carbon). Moreover, one can observe the differences of chemical composition of these samples as a result of divergent material structure and content of mineral impurities. In the present paper the activated carbon samples of various porous structure obtained from the same raw material are used. The character of porous structure of investigated carbons is determined on the basis of adsorption/desorption isotherms of benzene vapor [5]. The volumes of micro-, supermicro- and mesopores, the surface areas of micro- and mesopores, the adsorption energies and the pore dimensions are calculated by applying the DubininRadushkevich equations [6,7]. The influence of pore structure on adsorption from liquid phase is studied for four chosen adsorption systems: benzene + n-heptane and benzene + 2propanol- two carbon samples showing differentiated porosity. The energetic heterogeneity of liquid adsorption systems is taken into account by using the theory of physical adsorption on heterogeneous solids. The parameters characterizing liquid and gas adsorption are discussed in order to find a correlation between the pore dimensions and the composition of a liquid surface phase.
348 2. E X P E R I M E N T A L 2.1. Materials The commercial granulated activated carbon of type A was produced from hard coal in activation process with steam by the Wood Dry Distillation Plant (Hajnowka, Poland). After grinding and sieving it was separated by elutriation method into several fractions of different burn-off [5]. Three samples characterized by strongly differentiated burn-off and activation degree were chosen for experiments. 2.2. Experimental methods 2.2.1. Measurements of benzene adsorption/desorption isotherms The adsorption/desorption isotherms of benzene vapors were measured at 293K by gravimetric method using the McBain-Bakr balance. 2.2.2. Adsorption from binary liquid mixtures The specific surface excess isotherms for binary liquid mixtures: benzene + n-heptane and benzene + 2-propanol were measured by static immersion method [8]. The concentrations of equilibrium solutions were determined using HP 5890 gas chromatograph from HewlettPackard. The initial mixtures over the whole concentration range served for detector calibration. The surface excess of a given component was calculated from the relation: .:
_
_ .i)/..
where x, and x, are the mole fractions of component "i in the initial and equilibrium solutions, respectively, n ~ is the initial number of moles in contact with adsorbent of mass m. O
!
~
3. R E S U L T S A N D D I S C U S S I O N 3.1. Calculation Methods 3.1.1. Carbon characteristics The benzene adsorption/desorption data were used to analyze the porous structure of activated carbons. The BET specific surface area, SBEr, was estimated from the linear BET plot. The adsorption process in microporous materials is well described by the pore filling model. Taking into account the heterogeneity of micropore structure, a special form of Dubinin-Radushkevich equation, the two-term DR isotherm was applied [6,7] allowing for determination of micropore volumes and adsorption energies:
II
W - W01exp - ~
In
II
+ W02 exp - ~
In
(2)
In the above, W is the amount adsorbed per unit mass of the adsorbent, Wol and Woe are the limiting volumes of adsorption in micro- and supermicropores, fl is the similarity coefficient, Eol and Eo2 are the characteristic adsorption energies in micro- and supermicropores, respectively, p is the gas pressure, ps is the saturation pressure, T is the temperature and R is the ideal gas constant.
349 The linear dimensions (slit-pore half widths) of micro- and supermicropores were determined from their relation to the characteristic adsorption energies Eo, (i--1,2), assuming the slit-pore model [9]
Xo,-,r
(3)
where the proportionality factor ~c, is 11.87 and 12.80 kJ nm/mole, respectively for microand supermicropores [ 10]. The geometric surface of micropores was calculated by applying the relationship proposed by Dubinin [9]:
s= - 1000. w0 / Xo
(4)
The surface of mesopores was calculated from the relationship [6]
S= e .: !
cr
f RTln - ~ a p
(5)
Qo
where ty is the surface tension of adsorbed liquid, ao is the amount of adsorbate at the initial point of hysteresis loop and a= is the limiting value of adsorption. The mesopore volume was estimated from the difference of the total and micropore volumes. 3.1.2. Adsorption from binary solutions Regarding a strong non-homogeneity of the experimental adsorption systems the isotherm data for liquid mixtures were analyzed in terms of the theory of adsorption on energetically heterogeneous solids. The global isotherm equation may be written in the following form [111:
x~ - I xl~,'(x[2, e'2 )Z(=,2 )dr
(6)
A
where x~ is the mole fraction of the component "1" over the whole surface phase, x~j is the mole fraction of the component "1 on a given type of surface sites, x(2 - x( /x2, Z(~12) is the distribution function of differences of adsorption energies g~-c2, and A is the integration region. Assuming the ideality of surface and bulk phases, one can express the local isotherm as the Everett equation [12]. In such a case, the global isotherm equation (6) generates a group of isotherms, which can be presented in the form of generalized Langmuir (GL) equation [13]:
(7)
350 In the above, the heterogeneity parameters m and m* characterize the shape (width and asymmetry) of adsorption energy distribution function, and the equilibrium constant, K~:, describes the position of distribution function on energy axis. For the special values of heterogeneity parameters m - m ~ e (0,1) the isotherm (7) reduces to the known Langmuir-Freundlich (LF) equation:
X 1
(8)
--
The experimental adsorption isotherms were analyzed by using the following linear form ofLF eq. (8)s
In XI2
-- /'Pl
In K
12 %-/~1
In x(2
(9)
The mole fraction x~ was evaluated from the experimentally measured excess adsorption isotherms according to the following equation:
r~ - , ( /n ~ + x{
(10)
where n s is the total number of moles adsorbed in the surface phase, i.e. the adsorption capacity. The value of adsorption capacity was estimated from the data of benzene adsorption. 3.2. Discussion In order to study the differences in pore structures of the analyzed carbons AC-2, AC-3 and AC-4, the adsorption/desorption isotherms of benzene vapor were measured. In Figure 1 these isotherms are shown and compared with the benzene isotherm on ash; with regard to a very small adsorption on ash its share may be neglected. The presented isotherms are of type IV according to IUPAC classification. The sharp increase of adsorption is observed for the relative pressures lower than 0.175; it proves the existence of micropore structure. Moreover, visible hysteresis loops for all carbons means that they possess a distinct content of mesopores. Generally, one can find that the isotherm shapes are similar for all carbon samples, however, the lower adsorption values are observed for the carbon AC-2 and the highest for AC-4. Benzene isotherms were applied to estimate the BET surface area, $8E7; and the values of parameters characterizing micropore structure: the geometric surface of micropores, Sg, the limiting volumes of adsorption in micro- and supermicropores, Wol and Wo2, the characteristic adsorption energies in micro- and supermicropores, Eoj and Eo2, the slit-pore half widths of micro- and supermicropores, Xol and Xo2, and mesopore structure: mesopore surface, Sine, mesopore volume, l~",,,e.These values are presented in Tables 1 and 2. Comparing the values of structure parameters one can state that the carbon AC-4 is characterized by the highest value of SBET (925 m2/g), however, its pore structure has relatively small amount of micropores (57% of small micropores in the total amount of micropores) and greater amounts of supermicropores and mesopores. The opposite tendency is observed for the carbon AC-2 - the lowest BET surface area (745 mE/g) and relatively high content of small micropores (83%).
351 Table 1 Structural parameters of studied carbons
Carbon SBET
Sme
Vme
Sg
Wol
Eol
W02
E02
~ Wo
AC-2
745
82
0.196
510
0.256
21.12
0.052
13.78
0.308
AC-3
805
98
0.221
524
0.230
21.27
0.114
12.49
0.344
AC-4
925
120
0.280
537
0.223
20.37
0.171
11.15
0.394
sample [m2/g] [m2/g] [cm3/g] [m2/g] [cm3/g] [kJ/mol] [cm3/g]
[kJ/mol] [cm3/g]
Moreover, the linear dimensions of supermicropores increase from the carbon AC-2 to AC-4. Thus, generally in the structure of carbon AC-2 the pores of small sizes prevail. These differences in carbon porosity should influence the process of adsorption from gas and liquid phases. Earlier investigations presented in the papers [4,14] suggest a higher selectivity of adsorption in respect to preferentially adsorbed component for adsorbents containing narrower mesopores. Similar effect should be expected for microporous materials. In order to study the influence of porosity type on adsorption from liquids the measurements of specific surface excess isotherms were performed for binary liquid mixtures: benzene + n-heptane / carbon AC-2 and AC-4 benzene + 2-propanol / carbon AC-2 and AC-4. In Figures 2 and 3 the experimental excess isotherms are shown for four studied adsorption systems in the coordinates n~'/n' - x~ - x ( . Benzene is preferentially adsorbed as well from n-heptane as from 2-propanol. For both mixtures adsorption is higher for the carbon AC-2. u
- e9- AC-2 AC-3 -e.- AC-4
E E 4
~.,~, .,o")r !
~~-~
,,~~~'~'~ -~ ~
Table 2 Structural parameters of studied carbons Carbon XOI X02 (mol/Z Wo ) sample [nm] [nm] [%]
r
I
O F----
~1
0
0.2
-
,
0.4
-
piPs
i
0.6
0.8
1
Figure 1. Benzene vapor adsorption/ desorption isotherms on the carbons AC-2, AC-3, AC-4 and ash at 293K.
AC-2
0.562
0.929
83
AC-3
0.561
1.025
67
AC-4
0.583
1.148
57
352 0,2
0,4 41,
II
IIT , -
-x, 0,1 ~x
_.
0,3
-.7
9AC-4 9
,I
0,2 0,1
-. AC:4 I * AC-2
,
J
-0,1 0
0,2
0,4
0,6
Xll
0,8
-0,1
1
Figure 2. Excess adsorption isotherms for benzene (1) + n-heptane (2) on the carbons AC-2 and AC-4 at 293K.
0
0,2
0,4
0,6 xj ~ 0,8
1
Figure 3. Excess adsorption isotherms for benzene (1) + 2-propanol (2) on the carbons AC-2 and AC-4 at 293K.
In Figures 4 and 5 the individual adsorption isotherms x; - f(x() are presented. For both mixtures the mole fractions of benzene in surface phase are higher for the carbon AC-2. It means that the adsorption phase is richer in preferentially adsorbed component, i.e. benzene. Thus, the selectivity of adsorption is higher in the case of carbon with narrower micropore system.
0,8
0,8
-
0,6
0,6
,t.-
~x
0,4 9
0,2
AC'41
0,4
1
f
0,2 .
9
'
0,5
x,j1
1
Figure 4. Individual adsorption isotherms for benzene (1) + n-heptane (2) on the carbons AC-2 and AC-4 at 293K.
",?-
i
0
0,5
xl 1
Figure 5. Individual adsorption isotherms for benzene (1) + 2-propanol (2) on the carbons AC-2 and AC-4 at 293K.
353
l:
"x c
. ,.--
,c_, AC-2
~x
./
-2 -4
-2
I
le AC-4!
r'--
Inx112
2
4
Figure 6. Linear LF adsorption isotherms for benzene (1) + n-heptane (2) on the carbons AC-2 and AC-4 at 293K.
I
.I
-2 0
l
-4
-2
0
inxS22
4
Figure 7. Linear LF adsorption isotherms for benzene (1) + 2-propanol (2) on the carbons AC-2 and AC-4 at 293K.
The experimental systems were also analyzed by applying the linear form of LF isotherm, eq. (9). In Figures 6 and 7 these linear dependencies are drawn for all adsorption systems. Quite a good correlation was observed between the experimental points and theoretical lines. It means that this isotherm describes well the studied systems. In Table 3 the values of parameters of LF isotherm characterizing these systems are compared. All adsorption systems show moderate heterogeneity effects. The values of equilibrium constants are higher in the case of liquid mixtures adsorbed on the carbon AC-2. It confirms the earlier conclusion about the increase of adsorption selectivity for adsorbents showing narrower pores and is in good accordance with the observations made for mesoporous materials [3,4]. Table 3 Parameters characterizing adsorption from binary liquid mixtures Adsorption system n s [mmol/g] m
In K12
Benzene (1) + n-Heptane (2)/AC-2
5.48
0.84
0.70
Benzene (1) + n-Heptane (2)/AC-4
7.22
0.86
0.50
Benzene (1) + 2-Propanol (2)/AC-2
5.48
0.67
1.31
Benzene (1) + 2-Propanol (2)/AC-4
7.22
0.72
1.06
354 CONCLUSIONS Earlier studies on the effect of porous structure on adsorption suggested a higher selectivity of adsorption from solutions with respect to the preferentially adsorbed component for solids containing narrower mesopores. The results presented in the paper confirm this effect for microporous activated carbons. Relatively higher values of adsorption equilibrium constants for the carbon AC-2 in comparison to the carbon AC-4 are in good accordance with the sequence of individual adsorption isotherms. The surface mole fractions of benzene are higher for the carbon AC-2 over the whole concentration range. This carbon sample contains relatively high number of micropores with their higher share in the total pore volume.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Swi~tkowski and J. Goworek, Carbon, 25 (1987) 333. Buczek, A. Swiatkowski and J. Goworek, Carbon, 33 (1995) 129. J. Goworek, A. Nieradka and A. D~browski, Fluid Phase Equil., 136 (1997) 333. J. Goworek, A. Deryto-Marczewska and A. Borowka, Langmuir, in press. S. Zi~tek, M. Mioduska, T. Zmijewski and A. ~;wi~tkowski, Mat. Chem. Phys., 48 (1997) 1. M.M. Dubinin, Carbon, 23 (1985) 373. M.M. Dubinin, Carbon, 27 (1989)457. J. Goworek and A. Nieradka, Colloids Surf, 97 (1995) 27. M.M. Dubinin, Carbon, 18 (1980) 355. M. M. Dubinin, Carbon, 19 (1981) 321. M. Jaroniec and R. Madey, Physical Adsorption on Heterogeneous Surfaces, Academic Press, London, 1988. D. H. Everett, J. Chem. Soc., Faraday Trans. I, 61 (1965) 2478. M. Jaroniec and A. W. Marczewski, Monatsh. Chem., 115 (1984) 997. M. Borowko and W. Rzysko, Ber. Bunsenges Phys. Chem., 101 (1997) 1050.
Studies in Surface Science and Catalysis 128 K.K. Unger et al. (Editors) 9 2000 Elsevier Science B.V. All rights reserved.
355
A d s o r p t i o n M e c h a n i s m of W a t e r on C a r b o n M i c r o p o r e
w i t h in Situ Small Angle X- r ay S c a t t e r i n g 'I'
l i y a m a A . ' M . I ~ i k o ~, '1' S ~ z ~ k i '~ a ~ ( l K. Kax~ok() A
AMaterial Science, Graduate School of Science and 7'ethnology. ('h,iba Uni,,er.si/y. ,]apan n Department of Chemistry, I"acully of Science and 7'ethnology, 7 ' o k y o l)enki University, Japan A bs( ra('t
The in situ small-angle X-ray scatlering (SAXS) pr()files ()f water adsorbed ()n pilch-|)ased a('livaletl carbon fibers (ACF) of the pore width w---- ().g and 1.1n)n were )neasure(l at 303K and different relative pre&sures. The SAXS spectrum of A(:F of w ~= l.ln~n in (he direction of des()rpti()n (lid not overlap that in lhe a(lsorpti()n direction, showing the hysteresis behavior. The Ornslein-Zernike (()Z) theory was apl)ii('(t to analyze Ill('. SAXS data in order to investigate tile strut! ure of waler )n()le('ular as,4e)nl)ly in lhe carl)on )ni('r()t)()re using Ill(' (lensily fluctuation of the syste~n. These data lead that water )n()l(.wules l)rodu('e Ill(" large ('luslors in lhe )nit'rot)!)re, and these, clusters have different slrllt't ilres on the courses of a(ts()rpt ion and (](~())'pl ion. On t he other hand, Ihe SAXS profiles of A(;F of u, --= 0.8nm at different relative pressurm has n() hysteresis ('()in(-iding t hat the water a(t.,~)rpt i(m !sot berth has no hysteresis. These resul! s explicit ly suggest that the st ru('t ures of the war er )n()le('ular a,~se)nl)lies on adsorption and desorption are different from ea('h ol her in ('ase ()f (he presen<'o <)f adsorpli()n hysleresis.
1
tile a(Is(wbed rn()lecules (),ll()tlw aclive sties act as n,I-
Introduction
T h e behaviors of water molecules confined in a ('())lfined space have a t t r a c t e d much at tenti()n fi'()m biology, geoh)gy ,'rod chemistry.
T h e surface tensi()n ()f
w a t e r d e p e n d s strongly on the c u r v a l u r e of the g a > liquid interface, leading to tile depression ()f tile f)'(.~,zing point of water in a confined space, which has been
believed to be associated with biological and geol()gical processes [I, 2]. T h e macr()scopic properl ies of water co)!fined in the confined space are n()t sufliciently ~)ld e r s ( o o d fi'om (.he molecular level vet. A l t h o u g h the a d s o r p l i o n of w a t e r by microp()r()us carbon
h~s been studied for mmLv years [3-5], (1)e
a d s o r p t i o n mecha)~ism is not clearly elucidatc~1.
The
w a t e r - c a r b o n m i c r o p o r e systmn has a col~)radict ory haLure, because t h e c a r b o n surface is hydrophobic. \Vat er molecules are slightly ads()rbed at low relative pressure, indicating the hytlrophobicity ()f carb()n surface. A p r e d o m i n a n t w a t e r ads())'ption begins at t l~e mid,lie range of relative pres.sure.
T h i s steep adsorpti(m up-
take |la_s been believed to be associated with the cluster formation t h r o u g h D u b b i n i n - S e r p i n s k y lnechanisnl. Recently, I i y a m a et al.
gave an obvi()us evidence f()r
the formation of organized molecl~lar asse)nbly of wal er with in situ X-ray diffraction [6 I. McC'allun, et al.
It}
investigated the mechaa~ism of w a t e r adsorption on act i v a t e d carbon usi~lg the molecular sim~flati()n, sh()wing *Present Address: ])epart.ment of Chemis) ry, Faculty of Science. Shinshu University, 3-1-1 Asahi, Mat sumo( o, Nagano ',~f)()8621, .lapan, e-mail:l iiyama~'gil)ac.shh~shu-u.a(,.jp , l"ax:g 1-26337-2559
clei f~w [he f(),'nlali(m ()[' larger w a l e r ('i,islers in [he p()ro.
T h e aclsorpt i()n is(,thenn ()f lnicr()p()r(,lls c a r b o n s ,)f (lie It(!re wi(lth w :
ca.
O.7nm has an apparent a(l-
s()rpt ion hysleresis i~l t h e higll rela! ire pressure raj~ge. T h e exlent ()f hvsleresis (tel)raids (m tile p, we widlh ()f ('arl)()ll lllicr(q)()re. lmn ()t" u" <. ca.
'l'he snlall carb(m )llicr()p()re sys-
().Tll))i Ilas n()ads(wpli(m hysleresis.
"l'h(' llw('llat)is)n ()f atls())'p! i~))l hvslt:r(,-s'is ()n lit(: waler('arl>()n n)ic)'t)p()re sys! t')ll is n()t sl)flici('nl ly l)nders)()()d, It)(). We ne<,(l It) sI It(Ix' ()f water adsorpt it))! wil h a pl)ysical )nel ho(l ()l l)('r t ban t he )noasureme))( ()f ( he ads()rp(i())l is()I herin. Activale(l ('arl)()n filters (A('I:) can ()ff(,r hydr()ph,)bic )llicr()p()res wllicll are ma(le of graphi( ic unit s( ruct llres [8 I()[. A ( ' l : s have the great )nicr()p()re voll)nm and c()))si(le)'ablv !)nil(!)'Ill slit-shapc~l naicr()p()r(~, co)npare(l wil h c()nv('nl i()))al acl iva(ed carb()ns [I I. 12]. 'l'l,e A('I" is availal)le in (l,e p()re wi(]th ral)ge of 0.7 (() l.,l)))n.
'l'heref()rp, lit(, graph!lie )nicr()p,)res of A C F
('all be rt,gar(led as g()()(l hydr()pl)()bic nat)!)spaces. In lh(' pr(,ce(li)Ig palter tl)(~t, autl)()rs sl)()wed the efft,<'( ive)wss ()f lit(: X-ray diffract i()n (XI{I)) methr
f()r
detor)nining tile il)t(,r)n()leclllar strl)cll)t'e ()f water ill graph!tic )llicr()p()res (l~)e It) the good t r a n s p a r e n c y ()f carb()n agains!
X-ray [(;1.
An electron radial distri-
bu)i()n fi)ncti()n (EI{I)I:) analysis [13] f()r XI{I) d a t a sll()we(l t l)e pr(,s(,))ce ()f a w(,ll-()rderc~l strict'It)re ()f walt,) in I l,(' graph!! it' )ni('r()p()r('s al 3031(; 1I)(, a(Is()rbc~l water llas a )n())t' ()rder('d slr,)cl~)te t h a n liquid. |>~1
356
less than ice and the structure of water molecules in
SAXS st)twtrum wit h an X-ray tube operate(t at. 35kV
the 0.Shin-pore is more ordered compared with that
and 15mA.
of 1.1nm-pore case at 303K [14].
Also it, was shown
The X-ray scattering d a t a were corre('ttul for m, X-
that the ordered structure of water in 0.8nm pores at
ray absr
303I( is ahnost similar to that at, 143K. The authors
reeled X-ray scattering intensity l ( s ) of the sample at
showed also the effectiveness of in situ XRD method
s is simply given by
In the SAXS measurement, tile ctw-
for determination of the intermolecular structure of
/0
/(,)-- )o(p) Io~,(.~)
CC14, Ctl3OtI, and C2It.~OH in the graphitic nlicro-
(1)
pore [15-18]. The information on intermolecular structures of ad-
where Iob., (s) is t he observed X-ray sea! tering in! ensity
sorbed molecules in micropores can be obtaiuml by in
at s, I , ( P ) is tile translnitting X-ray intensity with t.lle
situ XRD measurement, ms mentioned above, t towever,
waler a(Is()rl)e(i sample (it depend on tile water vapor
still we have no information on the shape and size of
pressure. 1)). and I0 is the X-ray intmlsity withou! the
adsorbed molecular ~semblies. The in situ small mlgle
sample at s - 0. 13(~lh I a ( P ) and I0 were measured
X-ray scattering (SAXS) can provide the.se informa-
at 35k\" and 15mA. reln<)ving the
tion. It is well known that activated carbon strongly
and using all alunlinum plate 2ram in t lli<'kness ,as the
scatters X-ray at small angles due to the por()sity ()f
X-ray attenuat()r. \Ve ('()lislru('t(~t all ill situ SAXS sample chain-
carbon sample itself [9, 19]. The scattering pn)file (~t" A C F at. smaller angles changed dramatically wit h wa-
her [1G]. l)()lvethyleneterephthalat~film ("[{ullfiler""
ter humidity and the scattering entity wat er-ads()rbe(!
T()ray ('()., lad.) were used for the windows ()f in situ
A C F in air were discussed [19,201. We need to measure
lneasuring ('halnber and sample h()lder.
The sample
a more exact SAXS d a t a on water-adsorbed A ( ' F in o f
chamber is connected to tile gas adsorption systena.
der to discuss the adsorption mechanism of water. \Ve
The adsr
constructed a new in situ SAXS apparatus. The sam-
measllre(t silnult aneously by t he volu~ne-lnet ric met h()d
ple cheanber for the X-ray measurement w,as connected
under tim same c(m(litions as lhe SAXS measurelnent.
i(m is()! herlll of waier on the samples can be
The procedure of SAXS measurement at different
to the vacuum-adsorption system for controlling the The axlsorbed am(rant can be
fracti(,rlal fillirJg 0 of water at 303I( is as f~)llows. The
measured by a volume-metric method sinufltaneouslv
grollnd A ( ' F was packe(t ill a slit-shaped SAXS cell and
on the SAXS measurement using this apparatlm.
preheated at 383K an(I l m P a for 2h. Then SAXS r
adsorption conditions.
We
tried to elucidate the adsorption mechanism of water
A('F" in xa('~(, at 303[( was measured. \Valet vapor was
on activated carbon by in situ SAXS measurement I21].
adsorbed on ACt: at 303K, an(t then the SAXS profile
2
ce(lure was repeated until P,/I~ - 0.8, and then the
of the water ads()rbed-ACF was measured.
Experimental Two kinds of pitch-based activated carbon fibers
(PIT-g mid PIT-20) were used. The micropore stru('tures were determined
by the
high resolution
N9
adsorption isotherms at 77I(. "File water adsorption isotherms were gravimetrically determined at 303K after preheating at. 383K and l m P a for 2h.
This pro-
SAXS t)rofiles of tile sample on desorplion was measure(t.
3
R e s u l t and D i s c u s s i o n
7. 9 1
Pore structures and water adsorption
We mea-
N2 adsorpl i~)n is()t herms at 77I( were (,f Type I. The
sured SAXS spectra by use of a two-axial three--slit
specific sllrfa<'e area aa, lhe external surfa<'e area oc,,ext,
system (Mac Science Model No.3310) with a ('uKor ra-
and tile lnicrop()re vohinm ll,"0
diation with a nickel filter to reduce a ('uK/~3 radiation.
tracting pore effect lnethod using the high res(-)llflion
The scattered X-rays were detected by a linear-type
or., plots [12] f()r the N2 adsorption isotherm are shown
position-sensitive proportional counter ( P S P C ) wit h a
in Table I. The external surface area a~,ext is negligi-
window 50ram long and 10ram wide. A scattering pa-
bly small compared wit h a , . The average pore widths
rameter s (s = 47r sin 0/,\; 20 and ,\ are the scattering
u: fl'om both of a~ and I1."0 are also) sh~)wn in Table I.
angle and the wave length of X-ray, respeclively) rang-
The mi('r()p()re widths (,f PIT-5 and PIT-20 were 0.8
ing from 0.035 to 1.2A -1 was covered.
All measltre-,
and l . l n m , resl:)ectively.
[[ere tile mi('rr
volulne
nmnts were carried out in the transmission gc~maetry
was ~,bt ain(ul by use ()f lhe l)lllk liquid density of N:~ at
tbr tile sample.
77K.
It took 60 - 90rain to measure ea('h
357
"7
8OO
=;
600
~ [
i
400
-
._.
(A)~
~
L.
~ 2oo
~I
0.2
0.4 Relative
0.6 pressure,
P/Po
0.8
0
00.s
0,
0 ~.s
0..~
s ( = 4nsin0/~.)
Figure 1: Water adsorption isotherms of ACFs at 303K. F-I, ~ " PIT-20, O , ~ " PIT-5. The solid and dotted curves denote ad8orption and desorption, respectively.
i
d
0.zs
0 s
0
s.s
/ ,~ ~
i
(B) i
The water adsorption isotherms at. 303I'( are shown in Figure 1, that were of Type V. The saturate(t ,'uncmnts of water adsorption of PIT-5 and PIT-20 were 29() and
9"
r
"r"
790rag/g, respectively. The densities of water a(lsr
,_J
on PIT-5 and PIT-20 are 0.86 and 0.81g/cm 3, respec-
[
tively, on the assumption that water completely filled o
for W0. The adsorbed water density smMler than t)~llk
worthy that the adsorption hysteresis depends on the pore width.
In case of narrow pore system (PIT-5;
w = 0.8nm), the desorption-branch aJmost overlaps the adsorption one, which has a steep rising part near
P/Po = 0.4. On the contrary, the wide pore system (PIT-20; w = 1. lnm) h ~ a remarkable adsorption hy~ teresis.
The inflection points of adsorption and (ie>
orption branches on PIT-20 are 0.73 mid 0.56 of t~,/t)o, respectively.
3.2
Changes of S A X S profile with water adsorption
Figure 2(A) shows the SAXS profiles of wateradsorbed PIT-5 (w - 0 . 8 r i m ) as a function of 0. The SAXS profiles for all relative pressures had no peak and
0 l
0 l.s
0 .~
s (=4nsin0/?~)
liquid density should be caused by an ordered sparse structure even at room temperature [14]. It is n o t ~
0.0.s
0 .~s
/ ~
0.s
0 .~_s
I
Figure 2: The small angle X-ray scattering profiles of wat er-adsorbe(t ACFs as a function of t lie fract i(ma] filJillg ~ of water. (A): PIT-5 (u,-:: 0.grim), (B): PIT-20 (u, = l.lntn). O: 0 -- 0((;arbon only), I--]: 0 = 0.5, /__x: 0 -~- 0.8. The solid and dotted curves denote adsorption and desorption, respect ively. increases and then d ~ r e a s e s with (~ at. the smMl-s region o f s ~-: 0.2. T h e s c a t t e r i n g i n t e n s i t y vs. ,,~ r e l a t i o n for the higher 0 regicm is not line,'u'. In the hysterr sis region (c~)rres'poliding to O :- 0.5 in Figure 2(t~)), the SAXS c,lrves on adsr
and desorpt i<m do ilr
overlap, indical ing that t lie water moleclllar assemblies have different struct u r ~ cm adsr
3.3
and desorption.
Or~zstcin-Zernikc analysis of S A X S behaviors
We at)plie(! the Ornstein-Zernike (OZ) plot to tile
the scattering intensities d ~ r e a s e with the increase of
SAXS data. According to the OZ ther
s over the whole s region. The solid lines denote the
ple~'% the scattering intensity near s - 0 is given by [22]
adsorption process aJ~d the slope of the linear relation becomes smaller with the increase of 0. The scatter-
I(s)--|
I(0) { ~2.~2
for the sam-
(2)
ings on desorption are overlapped to those of adsorp-
where 6, is the ()Z correlation length and ](0) is tl,e
tion process, corresponding to absence of ads~,rption
zoro-angle scattering intensity. The s(~-called Ornstein-
hysteresis. Figure 2(B) shows SAXS profiles of water-ads~wbed
Zenlike plot ~)f 1/1(0) 7ps. s 2 for scattering d a t a of water adsorbed PIT-2{) sh~)wn as Figure 3. The. plots (~f the
PIT-20 (w = 1.1nm) as a flmct.ion of 4). The scatter-
water adsorbed A ( ' F are linem" over the wh~le 0 region.
ing intensity decreases gq'adually with 0 in the wi(t~, s
The two physical qumitities, ~ and I(0), are deterniined
region of s > 0.2. However, scattering intensity once
from t lie slope mid intercept of the plot. The zero-angle
358
2..;
-
II -
....
I
II
9 1,5
.,~ '~,~~!- ..............-m.............. m
....
II
0
0.02
0.0,1
0.06
s2/A
0.08
0
O. 1
0.2
0~ 0.~, Fractional filling, r
-~
Figure 3: T h e Ornstein-Zernike plot for S A X S frown water-adsorbed P I T - 2 0 (w = 1.1n~n). "l'he horizonlal axis is
0~
Figure l" "l'he zero-angle X-ray ~'attering in!ensilies l(s - 0) ~)f water adsorb~l A(?I:s against the fiacti~mal tilling O r walor at 303K. ["] , m : PI'l'-20
s~ and the vertical axis is the reciprocal of scatlering intensity. O; 0 - 0(Carbon only), 17; 0 = 0.3, ~ : o ----0.7, O ; 0 = 0.8. The solid and dolled curves denote adsorpt ion and dmorption, respectively.
(w 1.1n~n), O , ~ : I'IT-h (w 0.gn~). The solid an(I de)tied curves denote ad.'~)rt)lion and d ~ ) r p t i o n , respect ively.
scattering intensity, 1(0), is directly associated wi! h lhe
3.4
density fluctuation, ( ( A N ) 2 ) / N , of the s y s t e ~ ,
l')w a
single c o m p o n e n t system, it is given by
~(0) _- z ~. ((A;v)~) N
\Ve have tw~ t ) ~ i b l e
zne('llanisms fi~r a~ls~wptir
water ln~iec,lles in t l,e hy(Irr
(:~) '
iN:
Stru.ctTzral adsorption mechanism
is a clusl~w fiwlllati~m ~nr a(llaver ~li~del.
and ail(~tller is a llni['cwln
ll~wever, tile interact!era of a waler
with tile grapllitic p(~re-wall is l ~
wl~ere N is the m~mber of molecules mid Z is tim num-
Zll~,lr
ber of electrons in a molecule in the corresponding vr
in(lute l lie fcwllmti~m r
ume V.
t l~e zn~sl t)r~bable ~ w h a n i s ~
T h e water-adsorbed AQ'F has three ccmq)r
iinifr
nent.s, cm'bon, adsorbed water and vapor. The elect r~m
~f water m~dec~lr
density of bulk liquid water and graphite cryslal are
t)rcq)~,sr
0.55 and 1.33mol/cm 3, respectively,
0 f~r t l~e el)ewe tw~ ~nr
t tence t l~e den-
r
~zlicr~,pcwes. One
slnall to
ar
[lence,
is the cl~sler fiw~nati~m
in t l~e 10'dr~q)l~r
~icrcq)~wes as
earlier. T h e relaticmsl~ips between I(()) and be c ~ q ) l e t e l y dif-
ferent frr
p r e d o m i n a n t in t.he whole density fluctuation r lhree
unifiw,~ acllaver m~ctel, l l,e eleclr()ll el(rosily (liifermme
components-system.
\Ve can describe the cl~ange of
each r
shoulr
sity fluctuat.ion with wafer adsorption sh(~uld be the
bet wee~ p~wr
(shcwr l"ig,~re 5). I,, case ,~flhe and p~we spaces becr
t l~e prr
adsorpt.ion using the I (0).
cloister fiw~nalicm gives rise 1r the density fluctuation
Fig~re 4 shows the I(0) ~s. 0 relalionships fiw water-
of waler a(isr
small wit h
electron densit.y fluctuation of the system with water
icm. ()n tl~e r162 rary, t l~e
i~ p~wes, lea(ling I~ an i~crease r Acc~rdingly, the increase r
adsorbc
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
4. R e s u l t s Fig. 1 depicts the SEM image of tile fractured surfa{'e of a carl)oil film. Tile ot)ser\'ed smooth surface and the fracture shows glassy cllaracter. No pores could be observed in the displayed resolution.
364
Eigure 1. SEM image of a fractured carbon film (upper part" smooth surface, middle: fracture, bottom- support).
The mass specific scattering cross sections of the carbon film and the precursor vs. the scattering vector are given in fig. 2. Inhomogenities in the mesoscopic range dominate the scattering of the precursor. After pyrolysis the carbon film shows a pronounced micropore shoulder for scattering vectors q > 1. Tile macroscopic density p of the carbon film was (12384-170) k g / m 3 and the skeletal density ps necessary for the evaluation was assumed to be 2000 k g / m 3 as for graphite. Inserted in fig. 2 is a fit (solid curve) using the assumption of spherically shaped micropores with a log-normal size distribution" 1
1
~xp
(lrz2(R/R0)) -
.
(s)
This is a commonly used model function for size distributions. The adjustable parameters of the fit function given by eq. 5 are R0, the radius in the maximum of the pore size distribution, the relative width a and ~.i_~l]2 J\p/ln. According to eq. 7 the mean pore volume Vp, and the mean pore radius ]~p of a single pore were determined from the fitted
365 100
I
_!
_-%
I
I
I
carbon film precursor film fit
--II
, II
I .8
.•
,=,
I '
I
I ]
'
I '
I
! '
I I
'
!_-
6
.4
|
a_
g
_, oO
O0
=qi.i = o
~ ,
q. 'E
.2
-
.1
i
I
2
'
8
R [,~]
10-
.o'.
!
I
1
10
q [nm-ll Figure 2. Mass specific cross section vs. scattering vector of the carbon film and the precursor. The insert shows the fitted pore size distribution assuming spherical pores.
distribution. The porosity (1 -qS) is calculated from eq. 4 by using I/;, and the value at the plateau of the scattering curve as the cross section for q --+ 0. In addition, for small scattering vectors qR < 2 the Guinier approximation S(qR < 2) ~ exp(-q2/~*2/.5) [7] was fitted, assuming homogeneous spheres with radius R*. This was done in order to check whether this simple approximation is useful for an estimate of the mean micropore radii without assuming a pore size distribution. With the third fit parameter 5q2 ;Vv/rn ' and eq. 2 the mean specific number density A~/rn of micropores with radius R v is known as well as from Np/~-
( 1 - O)/(V~p).
Thus, the total specific micropore volume and V / m - ( 1 - O)/p and S / m - S p ( 1 - O)/('v-Tp ), in tab. 1. After applying the pressure gradient ~ p to the film, was determined from the measured linear
(9) surface carl be (tetermined according to respectively. The results are summarized sample, tile permeability Ps of the carbon (stationary) pressure change [dl)/dt]s in a
366
Table 1
Parameters derived from the size distrib~tior~ fit (Re: Radi~s of lh~ ma.rimum i~, th~ lognormal distribution: or: width of the' dist~'ibutio~: _k~lz.\'~/m: co~trasl• de~tsitg: Rp: mean radius of a si,~glc por~: S/,,~: total sp~ciJic .su,:fac~- a,'~a: l l,/r~: total ~p~cifi'c micropore volume; R*: pore radius from Guiltier appro.rimalio~). t~o
(7
['-tlTt] 0.53 +0.05
0.12 +0.06
Rp
Arl21\Tz~/rn [C'712g-IHIH, -6 ]
Jill-Ill
2.72 +0.38
0.53 -t-0.05
1 --
0
0.38 4-0.01
~ l, ll- l 1 [('l,13(J -1 ]
,~'111--1
R"
[C,,12(] -1 ]
['llll]
0.31 4-0.01
420 4--10
0.56 4-0.0"2
calibrated volume I / o n the low press~re side of tl~e sa~nple, via the equation
':"["1
P" = A ix-p -d-i
( o)
where A and d are the surface perpendic~lar to tl~e gas ttow (tirectioI~ ai~d I t~e tt~ick~ess of the sample, respectively. The results for t~elium a~(t i~itrogeI~ are given i~ l al). 2. Within the error limits, the l~elium permeabilit\" of tl~e cai'})oI| film is i~(tet)eI~(le~l of
Table 2
Permeability P~ of the carbon film d~.l~,'mi~d from ~q. 10. 5..50
(1.'2 -}- 0.6)- l0 -12
~ '2.10 -1'='
the mean p r e s s u r e p .... across t}lesan~t)le. SiIl~'eIlitr*)~Cll lcaka~('l}lroll~}l l}l(' saTl~l)lcall~t leakage of the sample c}lamber were iIl t}l~' salllr or~t~'r of n~agIlil ll~t~', lie ac~llral~' IlilrO~C'II t)ermeability could be determiIle,l. Iloxve\('r. lllis allows 1o ,teri\e axl llt)I)er lilnit fl)r flit" Ilitrogen permeability. [lpon recording the pressure after applying a t)ressllre I)lalse across the sample, the so called "'lag time" rt can be extracted [10]. TlleI'et)\'. vl corresI~OIltls to tile iI~Iercet)t of l]le extrapolated stationary 1)ress~re c}~aI~ge [dp/dl].~ wit}~ tl~e t i m c a x i s [11]. TI is relale(t Io the transient permeability Pt via ~-~ - d~/(6P~). :ks a result of tl~e small samt)le tl~ick~ess the lag time was very short a~(t co~ld ~ol l)e deter~niI~ed wil}~ s~fficie~t acc~racy. Fig. 3 shows the apparent curI'e~t vs. voltage fi'on~ cyclic volta~nInetI'y for a~ ~ t r e a t e ( 1 carbon film (ref) and the same filin a~odicallv oxidized for 300 .~ at "2.-1 i vs. :\g/:\g('l (ox). By cycling the untreated film eleclrode a \'er\" tlal a~(t (tistorted v o l t a n ~ n o g r a m is observed. This indicates that .S'Oi~--io~s tl~at arc a~tsort)ed at I)ositive t)ole~tials c a i ~ o t penetrate the small pores. Tl~e l~igt~eI" cui're~l al i~egalive t)ole~tials is c o ~ e ( ' t e d witl~
367
'
I
'
I
'
I
'
I
'
0.2
~' u
E
0.0
.4-...,
r-
,I.=..
-0.2
o
-0.4
/
J I
-0.2
............ C-film (ref) C-film (ox) ,
0.0
I
0.2
,
I
0.4
0.6
0.8
voltage vs. Ag/AgCI [V]
Figure 3. Cyclic voltammogramms in 1 M H2S04 at 2 rnV/s sweep rate, and potential vs. Ag/AgCl-electrode for the untreated carbon film (ref) aIld the same film anodically oxidized for 300 s at 2.4 V vs. Ag/AgC1 (ox).
chemisorbed oxygen [13]. Surface oxides also act as as repulsing force for 5'042-. After electrochemical oxidation the current has increased drastically. Several redox peaks are observed around 0 V and 0.4 V vs. reference, and at the inversion points of the voltammogram. They can be attributed to electroactive surface groups as quinone/hydroquinonespecies that contribute to the total capacitance in addition to the double layer capacitance. This so called "pseudo capacitance" is mostly reversible in contrast to the irreversible faraday contribution at the inversion points at -0.2 V and 0.8 V. respectively. The frequency dependence of the capacitance derived from tile relation C - 1/IwZ" I, where Z" is the imaginary impedance, is given in fig. 4. The capacitance per unit external area of the untreated film is found to be 16 txF/crn 2 at 1 Ha. This is in the range of the capacitance measured for unporous carbon surfaces [14]. Below 1000 Hz only a slight frequency dependence of the capacitance is observed. In contrast, the low frequency capacitance of the oxidized film is more than two orders of magnitude higher. It decreases rapidly towards higher frequencies. For 1000 Hz and above both curves proceed similar. The capacitance of the untreated film can be regarded as exclusively due to double la.yer charging of the external film surface.
368 w
i
,
,,ww,
I
.
*
linJll
I
,
v
,
l,ww,
I
9
,
w
,ivvw
*
i
llJ*ll
I
w
v
~
*
v , , , , ,
I
v
I
w
wlww,
~
n
*
~**l.I
I
f
f
,
10
U_
E
1
o c
0.1
o cl..
0.01
o 1E-3 0.1
C-film (0x) *
1
I
i
I
*llll
10
i
9 ~ . l . l l
1 O0
1000
.........! I
I
10000
frequency [Hz]
Figure 4. Frequency dependence of the capacity obtained from impedance spectroscopy for the untreated carbon film (ref) and the same film anodically oxidized for 300 s at 2.4 V vs. a g / a g C 1 (ox).
After the oxidation a considerable part of the inner micropore surface contributes to the double layer. In order to estimate the "created" inner surface area the capacitance of micropore per unit surface has to be known. According to Prgbstle et al. [5] this capacitance is 6 # F / c m 2. By disregarding pseudo capacitance, a specific inner micropore surface accessible for SO~--ions can be estimated now from the measured specific capacitance. The maximum specific capacitance of 12.5 FIg yield from impedance spectroscopy at 0.1 Hz gives an inner surface of 208 m2/g . 5. D i s c u s s i o n The theoretical porosity ( 1 - p/ps) corresponds to the porosity derived from eq. 4. Within the error level, the fitted parameter ~rl2Np/m from tab. 1 is in agreement with the theoretical value of 3.17 cm29-]nrn -6 determined by using eq. 2 and eq. 9. By fitting a constant to the homogeneous part (plateau) of the scattering curve and using Vp from eq. 7, Ar/2Np - 3.12 cm29-1nm -s is obtained, in accordance with the theoretical value. The radius derived by the Guinier approximation (assuming homogenous spherical pores)
369 is, in spite of the rough model assumption, in good accordance with the mean radius of the distribution function. As a result, the Guinier approximation represents a quick method to get an estimate of the mean micropore radius for this material. It should be noted, that the applied spherical model is just an approximation and does not necessarily represent the real structure of the micropores. However, the structural "resolving power" of this method is improved by assuming a pore size distribution. The additional structural parameters obtained are the distribution width and the number density of pores, which allows a calculation of pore volume and surface area, even for ultra,-microporous materials, where no Porod decay do/dft(ql~ >_ 4.5) <x q-4 [6] is observed within the measured scattering vector range (here: q,~,~.R ~ 4). The permeability gives informations about the openings available for gas transport. An independence of the helium permeability on the mean pressure leads to the conclusion that there is no viscous flow through macro openings. Otherwise P, would be proportional to the ratio of the mean pressure p,~ and the viscosity q (Ps ~ l),~/q) [9]. Generally, the magnitude of the openings can be deduced from the Knudsen number, K - ,X/d, the ratio of the mean free path k of a molecule (ku~ -- 184 nm (STP)) and the distance between the pore walls d. For K >> 1, only molecular diffusion through mesoscopic openings and/or activated micropore diffusion occurs. In the case of molecular diffusion
P~ oc, v @ / m must be valid. Since the derived permeabilities differ by about a factor of 103, micropore diffusion must dominate the gas transport through the carbon film. A plausible explanation is: If the relevant size of the interconnected pores or fissures is only a little larger than the diffusing molecules, the transport process is due to micropore diffusion [12]. This behaviour was observed by other groups in molecular sieves and activated carbons. In the case of the thin carbon film, no molecular diffusion or macroscopic flow is superposed as in most other carbons. Thus. the observed transport inechanism proceeds exclusively across micropores. Since helium atoms possess a critical diameter of 2 .~t they could pass through openings which are excluded for tile nitrogen molecules with a critical diameter of 3 ./1. The critical diameter gives the smallest opening which can be penetrated by the molecule. In case of micropore diffusion the interaction with the surface potential plays an important role, so that the same formalism as for surface diffusion or transport in an adsorbed phase [9] can be applied. Hence, a further insight into the transport mechanism can be given by studying the nature of surface diffusion. One significant effect is the temperature dependence of the permeability. In this case the Arrhenius relation must hold: P
(T) - Po
(11)
A proof of this exponential temperature dependence would be a further test if micropore diffusion takes place in the carbon film. From the electrochemical point of view. the ol)served inicropores are only accessible for the electrolyte cations upon anodic oxidation. The anodic oxidition causes either an opening or a widening of previously inaccessible pores. As a result of the additional surface the double layer capacitance increases. In addition, electroactive surface groups are developed containing a pseudo capacitive contribution. In order to learn more about the oxidation process, SAXS measurements on the oxidized sample have to be carried out.
370 6. C o n c l u s i o n
Small angle X-Ray scattering, steady state permeability ailalysis, cyclic x'oltammetry and impedance spectroscopy are excellent tools for ttle characterization of ttlin microporous carbon films and similar materials. These methods are complemerltary and cover a wide range of structural information. Tile results of tills work are important for ai)plication of ultra-thin microporous carbon films iil the field of supercapacitors and filter systems. REFERENCES .
2. .
4. .
6. 7. 8. 9. 10. 11. 12. 13. 14.
R. W. Pekala, C. T. Alviso, ~later. Res. Soc. Syrup. Proc. 270 (1992)3. G. M. Jenkins, K. Kawamura. Polymeric carbons - carbon fibre, glass and char, first ed. Cambridge University Press Cambridge ['I{ (1976). V. Bock, A. Emmerling, R. Saliger, J. Fricke, J. Por..~lat. 4 (1997) 287-2.94 . R. Petrieevid, G. Reichenauer, \'. Bock, A. Emmerling, .l. Fricke. J.Non-cryst.Solids 225 (1998) 41-45. H. PrSbstle, R. Saliger. J.Fricke. these pI'oceedillgs. H. G. Haubold et al., Rex,'. Sci. Instrum. 60 (1989) 1943. A. Guinier, G. Fournet (19.55), Small-Angle Scattering of X-rays, New York: \Viley. A. s J. Fricke, J. Non-Crysl. Solids 145 (1992) 113. G. Reichenauer, J. Fricke, Mater. Res. Soc. Syrup. Proc. 464 (1997) 345. W. R. Vieht, Diffusion In and Through PolyIners (Hanser Publishers, 1979), p.20. G. Reichenauer, C. Stumpf, J. Fricke, J. Non Cryst. Solids. 186 (1995) aa4. R. M. Barrer, Zeolites and Clay Minerals as ~lolecular sievies. Academic Press, London (197s). J. Koresh, A. Softer, J. Electrochem. Soc 124 (1977) 1379-1385. H. Shi, glectrochemica Acta. \7ol. 41 No. 10 (1996) l{~aa-16ag.
Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) o 2000 ElsevierScienceB.V. All rightsreserved.
371
Electrochemical Investigation of Carbon Aerogels and their Activated Derivatives H. Pr6bstle, R. Saliger and a. Fricke Physikalisches Institut der Universit~it Wiirzburg. Am Hubland, D-97074 W~irzburg, Germany Carbon aerogels are highly porous materials prepared via pyrolysis of resorcinol-formaldehyde aerogels. Depending on the mixing ratio of the ingredients entering the sol-gelprocess the porosity and pore size distribution of the carbon network can be varied. The major part of the pores is accessible to ionic conductors. For that reason the application of carbon aerogels as electrodes for supercapacitors is promising. In the present paper aerogel electrodes are modified via thermal and electrochemical activation procedures, e.g. oxidation in CO2-atmosphere and anodic oxidation in sulfuric acid. respectively. The electrochemical double layer of activated and non-activated aerogels is investigated using cyclic voltammetry and impedance spectroscopy. In combination with BET-measurements these methods provide a detailed insight in the surface structure and charging process of carbon aerogels. First results indicate a dependence of the surface capacitance of untreated carbon aerogels on their microstructure. Micro- and mesopores exhibit different storage capacitances (6.6 and 19.4 # F / c m 2 in 1 M sulfuric acid, respectively). An optimized thermal activation procedure of low density aerogels at 950~ in controlled CO2- atmosphere leads to an increase of the specific surface area and capacitance. On the other hand, the increase of the capacitive current after anodic oxidation in sulfuric acid is caused by electroactive surface groups, while the BET-surface area remains almost constant.
1. I n t r o d u c t i o n Carbon aerogels are nanostructured sponge like materials derived via a sol-gel process. The first step in their formation is the coi~densation of resorcinol with formaldehyde in aqueous media, catalyzed by sodium carbonate. The resulting structure is a crosslinked aromatic polymer, which is pyrolized in an inert atinosphere to form carbon aerogels [1]. During the last years progress has been made introducing carbon aerogels into electrochemical charge storage devices, namely supercapacitors [2]. An appreciable advantage of carbon aerogels in comparison with commonly used powder electrodes is their monolithic structure. It enables the fabrication of binderless electrodes which provide a low cell resistance. The structure of the electrochemical double layer in carbon based electrodes is closely related to the physical and chemical properties of the adjacent bulk material. Micropores
372 for example exhibit a lower capacitance than mesopores [3]. While the former consist mainly of graphitic basal planes, the surface of mesopores bears edge planes saturated with surface functional groups which enhance the capacitive current. There are several methods to improve the capacitive behaviour of carbon based electrodes. Gas-phase oxidation increases the surface area of the samples [4]. A method which adds surface functional groups to the carbon surface is the anodic oxidation in dilute acids. Among various functional groups formed by the latter method there are quinone-like species which exhibit reversible redox properties and therefore contribute to the total capacitance of the samples [5]. The charge storage mechanism in the latter case is of faradaic origin and therefore totally different from the pure electrostatic charge separation, which is dominant in thermally activated carbons. Nevertheless the capacitance per unit area, which can be reached by surface functional groups is up to 100 times larger than the electrostatic double layer capacitance [6].
2. Experimental and data analysis RF aerogels have been prepared according to the following procedure: Resorcinol (R) was dissolved in formaldehyde (F) in a molar ratio of 1:2. Subsequently sodium carbonate (C) dissolved in water was added as catalyst to control the size of the primary particles and the density of the RF-gels [7]. The polymerisation of the sol was performed in three temperature steps (30~ 50~ and 90~ with a duration of one day for each step. The RF-gels were dried subcritically with respect to acetone and cut into slices. Afterwards the cylindrical RF-slices were pyrolyzed in argon atmosphere at 800~ or 1050~ respectively. The thickness of the resulting carbon slices was about 1 ram, the cross-section-area 1- 1.3 cm 2. Before electrochemical measurements, the carbon aerogels were immersed in 1 M sulfuric acid for one day. Thermal activation of the samples was performed as described in [8]. The aerogels were pyrolyzed at 1050 ~ and subsequently activated under controlled CO2-flux at 950 ~ for two hours. The electrochemical activation was carried out in successive reduction and oxidation in 1 M sulfuric acid. The corresponding potentials were +2.40 V (oxidation) and -0.35 V (reduction) vs. reference (Ag/AgC1). After each step 10 cyclic voltammograms were recorded followed by an impedance measurement. Both methods were initiated by an open circuit measurement for 1200 s. The density and surface area was determined after exchanging the electrolyte against destilled water and drying the samples at 90~ for three days. The surface area of the non-activated and activated samples were derived via N2-adsorption at 77K using a Micromeritics ASAP 2000 apparatus. In order to remove physisorbed water the samples were evacuated at 300~ before starting the adsorption measurement. The corresponding meso- and micropore surface areas were received via t-plot evaluation [9]. In order to investigate the charging characteristics impedance spectroscopy and cyclic voltammetry was applied. The measurements were performed in a glass cell using a three electrode arrangement with an Ag/AgC1 reference electrode, whereby 1 M sulfuric acid served as electrolyte. The investigated carbon aerogel was sandwiched between a platinum plate and a platinum grid stretched over a teflon fi'ame. The same setup with an
373
: --~.-
-electrolyte-
3.0 2.5 2.0 A
E t---
o g4
1.5
T" .... -carbon-matrix-
x--O
1.o
0
0.5 0.0
-0.5
a 0.5
'
1.'0
b '
1.'5
c '
210
9
9
2.5
'
3.'0
'
315
'
410
9
I
4.5
'
5.'0
Z' ( O h m )
Figure 1. Impedance spectra (real vs. imaginary part) of an carbon aerogel and the corresponding equivalent circuit. The RC-circuit parallel to the double layer capacitance (circuit with dotted lines) corresponds to pseudocapacitances due to reversible redoxgroups on the carbon surface [10]. The position x = 0 denotes the pore entrance of the cylindrical pore adjacent to the reference electrode. The corresponding frequencies are between 20 kHz and 8.25 mHz (region a to c).
arbitrarily chosen carbon aerogel served as counter electrode. A Solartron 1287 potentiostar controled the voltage on the test electrode. The impedance data were evaluated by a Solartron FRA 1250 impedance analyzer. A typical impedance spectrum of a porous carbon electrode and a corresponding equivalent circuit model which describes the forni of the impedance plot is shown in fig.1. The ladder network regards the porous electrode consisting of uniform cylindrical pores with a blocking surface and takes the existence of redox-groups into account [10]. According to this model, the high and middle frequency region (region a and b) describes the penetration of the AC-signal into the pores, including the effect of a contact capacitance of the sample holder [11]. At low frequencies (region c) the signal attains the total surface of the sample. The differential capacitance Caiff was derived in this capacitive frequency region at 8.25 mHz according to C d i f f -"
~-}7
"
(1)
It is worth noting that this-capacitve response appears also in models, which regard the more realistic situation of nonuniform pore size distributions [12,1:3]. The frequency range applied in the impedance spectroscopical investigation was between 20 kHz and 8.25 mHz with an amplitude of 30 mV at open circuit. The cyclic voltammetry technique makes use of a triangular voltage ramp applied to the
374 test electrode. The corresponding current response for an ideal, frequency independent capacitance C ensues from the relation Q = CU, and its derivative
(2)
0-c(7.
According to eq. 2 a constant current appears in the cyclic voltammogram (CV) when Q is plotted versus U. In real systems such as porous carbon electrodes, both load resistances due to the spatial distributed capacitance in the pores (circuit model in fig.l) and surface functional groups cause a deviation from the rectangular CV-shape. While the first induces a finite time constant in the charging process, the latter are identified by current peaks in the CV [14,6]. The voltage range used for cyclic voltammetry was-0.2 to 0.8 Volt vs. Ag/AgC1 at a scanrate of 5 mV/s, respectively. 3. R e s u l t s 3.1. N o n - a c t i v a t e d aerogels In table 1 the densities and surface capacitances of various carbon aerogels are shown. The data reveal that the surface capacitance varies from one species to another. According to S h i e t al. the micro- and mesopore surface areas were separated and the total capacitance C~'ta~ of the samples was split up in contibutions from both pore species [3]. The correlation can be expressed as Cdt~l
-
C~I es~
x
5'm~o + 0 3 icr~
x
Smic~o,
(3)
introducing C~'es~ C~'icr~ as the capacitance of the respective pores weighed with their corresponding surface parts S'meso and ,--q'micro .which were derived from the t-plot. A plot of C~t~tal/Smeso vs. Smicro/Smeso in fig. 2 gives a straight line with a y-intercept representing C~'~~s~ and a slope corresponding to C~ icr~ respectively. The micropore capacitance of 6,6 #F/cm 2, which results from the linear fit of the data, is in the range of the double layer capacitance of basal plane oriented graphites and confirms the graphitic structure of aerogel micropores [5]. On the other hand the higher mesopore capacitance can be attributed to the edge plane character of this surface species containing a rough surface with functional groups [5]. Despite the good correlation of adsorption and electrochemical measurements with the above transformation it should be mentioned that the evaluation via t-plot analysis Table 1 Density and surface capacitance of different carbon aerogels pyrolized at 1050~ The surface capacitance was derived dividing the capacitance calcuted from the impedance data at 8.25 mHz by the BET surface area. 5-105}, error must be assumed for the evaluated data. sample number A B C D E density (g cm -3) 0.77 0.70 0.95 0.69 0.46 surface capacitance (pFcm -2) 1 4 . 4 1 1 . 4 1 1 . 1 10.7 7.7
375
meso
0.8
Cz,
= ( 19.4 _+ 1.2 ) laF/cm
micro
2 2
0.7 E
0.6 0.5
0
0.4
0.3 0.2 0.1
,
0
l
1
,
-I
,
2
I
3
,
I
4
i
J
5
'
l
6
i
l
7
i
i
8
9
l
9
9
I
10
S ~c / S r~.o
('~t~ /~-'mesovs. Smicro/Smeso of differently structured carbon aerogels and the Figure 2. t~,dl derived double layer capacitances according to eq. 3.
bears the possibility of overestimating the mesopore surface in samples containing small pores [9]. Nevertheless the total surface area of the samples which has been derived via BET-transformation at small relative pressures to calculate the surface capacitance can be regarded as quite accurate for microporous carbons [15]. To sum up the results the deviation of the surface capacitance is a meaningful supplementation in characterizing the microstructure of porous conducting materials. Beyond that by dividing the total capacitance by the surface capacitance the determination of the surface area of samples with known pore size distribution is possible. This enables especially the characterization of ultra thin carbon films which can not be analyzed by adsorption measurements because of their low mass. Since any change in the chemical composition of both surface and skeleton changes the capacitive behaviour but not necessarily the BET surface area the surface capacitance is an important parameter to control activation procedures on carbon electrodes (see chapter 3.2). 3.2. A c t i v a t e d aerogels In fig. 3 the applied voltage steps used for electrochemical activation for two different carbon aerogels are plotted. The capacitances of the samples derived via impedance spectroscopy at 8.25 mHz according to eq. 1 after each step are also shown. The physical and
376
--A--.
F*
-- ,--- G * --o--voltage
2.5
steps
Q..--..~
11
2.0 p"
> V
1
I
S"
ca
9
/
I
/
f S'
I
f
I v r
10
f f
I
f
/
1 I
1.5
/
f
I
I
ui > 9 0.5 t
1
>
O
0.0
s
/
[]
I
r
,,&
8
O ~"
7
o
6
v
-n
I
s
/
s
t
s
,,n
-0.5 ,
0
.
l
600
.
,
1200
.
,
1800
.
,
2400
.
,
3000
.
l
"
3
3600
time(s)
Figure 3. Voltage steps (left coordinate) used for the activation and their corresponding capacitance values (right coordinate) vs. activation time. The data at t - 0s refer to the untreated samples. The corresponding physical data are shown in tab. 1.
electrochemical data of the samples are summarized in tab. 2. The anodic oxidation clearly increases the capacitance of the samples (fig. 3). In addition especially a reduction step increases the capacitance of the oxidized samples. Both the removal of oxides which have been formed on the surface and of the gaseous oxidation products account for this behaviour [16,5]. Accordingly the increase in capacitance after the first reduction step at t = 600 s indicates the existence of oxide groups already on the untreated surface. Earlier investigations on the anodic oxidation of activated carbons in dilute acids revealed that 20% of the applied current is consumed by the build up of various surface oxides whereas the remaining current is used to remove surface molecules and to form CO2 [17]. However the current data from the aerogel activation are hardly useful in determining the amount of removed carbon and attached oxides because the current transformation at the platinum sample holder can not be disregarded. The increase in both surface capacitance and density of the activated samples account for added functional groups on the surface, as indicated for the samples F" and G" in
377 comparison with their untreated species in tab. 2. Although the carbon surface is certainly roughened after oxidation the BET surface area remains almost unchanged, since the value is related to the total mass of the activated samples including the added oxide groups. More detailed information on the structural changes after the activation reveal the cyclic voltammograms of the samples (fig. 4). While the CV of the untreated sample F0 exhibits a clear capacitiv behaviour, as indicated by the constant current region, the charging/discharging curves of the activated sample F" are modified by two redox peaks. By applying a lower scan rate (0.2 mV/s) the CV reveals two symmetrical redox peaks. Their center is located around 600 mV vs. NHE. The surface species can therefore be identified as quinone/hydrochinone-like groups [5]. In addition the charging curves of the oxidized samples exhibit higher time constants, demonstrated by the spreaded form of the CV (fig. 4). An explanation is given in terms of additional load resistances which appear in the equivalent circuit of a pseudocapacitive interface (fig. 1). Other factors explaining the increased time constant are a higher electrode resistance due to the oxidation of the carbon skeleton and the hindered accessibility of the pores caused by added surface species. The first effect is strongly pronounced in the case of the high density aerogel G" as can be deduced from the flattened form of CV. The fine structure of the latter with an averaged skeleton dimension in the range of 10 nm is obviously more susceptile to the oxidation process than the coarse structure of sample F0 with dimensions up to 70 nm. The corresponding structural data have been derived via small angle scattering as described in [18]. According to tab. 2 the surface capacitance after CO2-activation of the low density sample (F**) is reduced from 14,1 to 7,2 #F/cm 2. The value is close to the micropore capacitance derived in the previous chapter and demonstrates the microporous character of the sample, as expected for high surface area carbons [5]. The redox peaks at 0.9 V and 0.2 - 0.3 V appearing in the CV can be ascribed to quinone/hydrochinone-like groups in different chemical enviroments [5]. In addition the time constant of the charging process is almost the same for the activated and non-activated sample. Since for practical purposes a high volumetric capacitance of the electrode is an important requirement, the corresponding data are also given in tab. 2. Unlike the increase
Table 2 Density, BET-surface area and surface capacitance of two non-activated aerogels with different densities and their activated derivatives. The index (0) corresponds to the reference, (*) to the electrochemically, (**) to the thermally activated samples, respectively. 5-10% error must be assumed for the evaluated data. sample number Fo F* F** Go G* density (gcm -3) 0.30 0.36 0.16 0.68 0.85 BET-surface area (m 2g-1) 660 647 2 5 1 0 739 733 surface capacitance (#Fcm -2) 14.1 26.9 7.2 1 3 . 8 24.2 volumetric capacitance (Fcm -3) 28.0 63.5 28.6 69.2 141.8
378
- - - - - - - Fo
2.0
--o--
,~
F*
F**
1.5
. . . .
A," /
.-'-/
1.0 v
u~
0.5
E
0.0
t'-
,0
-0.5
-1.0 -1.5 I
-0.2
~
I
0.0
,
I
0.2
,
I
~
0.4
v o l t a g e vs. A g / A g C I
I
0.6
,
l
0.8
(V)
Figure 4. Cyclic voltanamograms of the activated aerogels recorded with a scan rate of 5mV/s. The current is normalized to Ig of the samples and therefore proportional to the mass specific capacitance of the samples as described in eq. 2).
in mass specific capacitance (fig. 4), the volumetric capacitance of the CO2- activated sample F** remains almost unchanged due to the reduced density. On the other hand an anodic oxidation obviously increases both the volumetric and specific capacitance. This effect is strongly, pronounced in the case of the high density sample (G*). However in order to ensure a fast current response as required for supercapacitors in high frequency applications the C02-activated sample should be prefered because the anodic oxidation introduces a higher time constant and therefore limits the fast availability of the stored charge (fig. 4). 4. C o n c l u s i o n The applicatioll of electrochemical investigations is an efficient method to characterize the microstructure of porous electrically conducting materials. Modifications in the chemical constitution of the skeleton which do not change the BET values can be identified by the electrochemically derived surface capacitance, as demonstrated in the case of anodically oxidized carbon aerogels. The capacitance of the aerogels can be improved via thermal and electrochemical activation procedures. For high frequency applications the first activation procedure is to
379 be preferred. Interesting topics for further investigations are the maximum increase in capacitance which can be reached with these methods and the influence of a combination of both activation procedures on the capacitive response of carbon aerogels. Acknowledgement This work was supported by the European Commision in the frame of a Brite Euram Project. REFERENCES ~
2. 3. 4. 5. .
7. 8.
10. 11. 12. 13. 14. 15. 16. 17. 18.
R. W. Pekala, J..~Iat. Sci.. 24 3221 (199.5) S.T.Mayer, R.W. Pekala. J.L. Kaschmitter, J. Electrochem.Soc., 140 446 (1993) H. Shi, Electrochimica Acta, 41 1633 (1996) K. Kinoshita, Proc. Electrochem. Soc. Meeting, Chicago 95-29 171 (1995) K. Kinoshita, Carbon: Electrochemical and Physicochemical Properties, John Wiley Sons, New York (1988) B.E. Conway, J. Electrochem. Soc., 138 1539 (1991) R.W. Pekala, F. M. I{ong, J. Phys. (Paris) Colloq. C 4 (1989) 33 R. Saliger, H. Pr6bstle, G. Reichenauer. J. Fricke. Proc. of the 9th CIMTEC, Part L. Innovative Materials in Advanced Energy Technology, ed. P. Vincencini (1999) F. Rouquerol, J. Rouquerol, K. Sing, Adsorption by Powders & Porous Solids, Academic Press, Lon(lon (1999) B.V. Tilak, C.-P. Chen. S.K. Rangarajan, J. Electroanal. Chem. 324 405 (1992) F.M. Delnik,C.D. Jaeger, S.C. Levy, Chem.Eng. Commun., 55 29 (1985) I. D. Raistrick. in Electrochemistry of Semiconductors and Electronics, ed. by J. Mc Hardy and F. Ludwig. Noyes publications, New Jersey (1992) H. Keiser, K.D. Beccu. M.A. Gutjahr, Electrochimica Acta, 21 539 (1976) A. Bard, L. R. Faulkner, Electrochemical Methods, John Wiley & Sons, New York (1980) K. Kaneko, C. Isllii. ~I. Ruike. H. Kuwabara, Carbon, 30 1075 (1992) N. L. Weinberg, T. B. Reddy, J. Eppl. Electrochem., 3 73 (1973) H. Binder, A. I{Shlillg. K. Richter, G. Sandstede, Electrochimica Acta, 9 255 (1964) R. Safiger, U. Fischer. C. Herta. J. Fricke, J. Non-Cryst. Solids 225 81 (1998)
This Page Intentionally Left Blank
Studies in Surface Scienceand Catalysis 128 K.K. Unger et al. (Editors) 92000 Elsevier Science B.V. All rights reserved.
381
EVOLUTION OF MICROPOROSITY UPON CO2-ACTIVATION OF CARBON AEROGELS R. SALIGER, G. Reichenauer 1, j. Fricke Physikalisches Institut der Universit/it W t i r z b u r g and Bavarian Center for Applied Energy Research (ZAE Bayern) A m Hubland, D-97074 W(irzburg, G e r m a n y
Carbon aerogels are derived via the pyrolysis of resorcinol-formaldehyde (RF) aerogels. The stoichiometry of the reactants in the solution determines the mesostructure of RF aerogels and their pyrolyzed derivatives. The micropore structure in C-aerogels on the other hand can be tailored by the pyrolysis conditions, i.e. temperature and atmosphere. A high accessible surface area of the material is needed for applications in supercapacitors and waste water treatment, a large micropore volume is a prerequisite when used as a host for gases. Comparing N2-adsorption and small angle X-ray scattering (SAXS) data, complementary information can be obtained for the accessible surface area and the overall porosity. The porosity that is not accessible for N2 at 77 K can be considered as a surface area reservoir that can be made accessible via activation. The carbon bum-off is an indicator for the micropore volume and surface area obtained during activation. Via CO2-activation of C-aerogels the BET surface area can be increased from 500 m 2/g to more than 2000 m 2/ g with a carbon bum-off of only 50%. The micropore volume detected by N2-adsorption increases to more than 1 cm 3/g. This is due to an opening of initially inaccessible micropores plus the creation of new voids. For C-aerogels with different mesopore structures (particle sizes and densities) the effect of pyrolysis temperature and CO2-activation is reported.
1
INTRODUCTION
C a r b o n (C)-aerogels have been investigated for one decade as a promising material for electrochemical applications in supercapacitors, fuel cells and waste w a t e r treatment [1,2]. C-aerogels are nanoporous, electrically conducting and monolithic materials that provide the unique possibility to tailor the carbon properties on a molecular scale. The surface area and the degree of microporosity can be adjusted almost i n d e p e n d e n t l y of the overall porosity for which mainly meso- and macropores are responsible. Whereas the mesostructure is d e t e r m i n e d by the stoichiometry of the reactants in the precursor solution, the pyrolysis conditions control the micropore structure of the material [3,4]. H i g h pyrolysis t e m p e r a t u r e s will increase the electrical conductivity [5], an i m p o r t a n t p r o p e r t y for m a n y electrochemical applications. The derived carbon materials consist of particles (diameter 5 n m - 1 #m) w h i c h contain micropores w i t h radii of 0.3-0.5 nm. The particles are interconnected by smaller necks 1 currently Dept. Civil Eng. & Oper. Res., Princeton University, USA
382 and build up an open porous network (mesopores from 5 nm to several ~m) [4,6]. Most of the surface area is located in micropores within the particles. These pores are partly inaccessible for molecules, as shown previously via comparison of N2-sorption and SAXS data [7]. Thus CO2-activation gives the possibility to increase accessible surface areas considerably.
2
EXPERIMENTAL A N D DATA ANALYSIS
C-aerogels are obtained upon pyrolysis of resorcinol-formaldehyde (RF) aerogels. The samples are labeled by their resorcinol to catalyst (R/C) molar ratio and the mass percentage of the reactants resorcinol+formaldehyde in solution. The R / C ratio controls the particle size, the mass ratio determines the density of the aerogel. In this work two types of aerogels with different R / C and mass ratios were investigated, giving rise to a wide structural variation: one aerogel is synthesized with a R / C ratio of 200 and a mass ratio of 45% (briefly termed 200/45), leading to fine structures (mesopores and particles in the 10nm range) and high densities (0.7 g/cm3). The other composition 1500/30 produces coarse structures (particles 100 nm, pores 500 nm) at low density (0.3 g/cm3). Detailed structural data are given in ref. [7,8]. Compared to the synthesis conditions described in ref.[9] some simplifications were introduced: Gelation and aging time was reduced to a total of 3 days and drying of the samples was performed subcritically with respect to acetone [7]. The RF aerogels were cut into slices of about 2 m m and placed in a tube furnace. The pyrolysis program was shortened to about 6 h [10]. This was achieved by increasing the heating rates and cutting the isothermal phases to 1.5 h. C-aerogels were characterized by N2-adsorption at 77 K and small angle X-ray scattering (SAXS) measurements. The adsorption analysis was performed using a Micromeritics ASAP 2000 instrument. Prior to the adsorption runs the samples were baked under vacuum at 300~ in order to remove physisorbed species from the micropores. From the N2- adsorption data the BET surface area (S/m)BET was obtained [11]. Linearity of the BET transformation was given in a relative pressure region between 0.001 and 0.1. It was shown by Kaneko et al. that even though not developed for microporous materials, the BET transformation is applicable when the range of linearity is obeyed [12]. In order to get detailed information on the micropore range, the adsorption data were replotted using the Dubinin-Raduchkevitch (DR) transformation [13]. From the slope in the DR diagrams the specific energy of adsorption E0 was derived and with the equation of Stoeckli et al. [14] 1 10.8 L/2(nrn) - ~ E o ( k d / r n o l )
-
11.4
(1)
the micropore half width L/2 of slit-shaped micropores was calculated. SAXS experiments were performed at the synchrotron radiation facility HASYLAB/ Hamburg. The scattering data were evaluated using the two-phase media model (TPM)
383
[3 . . . . -EJ C 200/45 o ......... e C 1500/30
1000 '7 I,,,,,
100
!
04
E
v
o
sharp bend 10
"t3 o
". d%o. . . . . . . .
..........................................................
I(q) = A , / (1+1.414/3*R2*q2) 2
"',,,,
"........ "4
meso porosity .1
....,.\
1
micro porosity 10
scattering vector q / nm 1
Fig. 1. Scattering cross sections for the investigated C-aerogels C 200/45 and C 1500/30. The d a s h e d / d o t t e d lines correspond to scattering patterns for pure meso- and microporous materials, respectively. [16] and a fit routine for the microstructures as illustrated in fig.1. As long as the sharp bend towards homogeneous scattering is within the range of scattering angles (which is the case for mesostructures < 50 nm), the complete curve can be evaluated according to the TPM model with a Porod slope of-4, corresponding to smooth particle surfaces of the smallest probed structures. Hereby the total surface area (S/m)tot and the skeletal carbon density pc can be derived as well as the chord length of the micrographitic regions lc. For mesostructures > 50 nm the carbon density pc must be known to derive the total surface area (e.g. for the 1500/30 aerogel). By subtraction of the microstructure contribution (dashed curve) the TPM model yields values for the mesostructure, like particle density ps, particle size Is and surface area (S/m)m~o [7]. In addititon the shoulder for large scattering vectors is fitted with an equation for spherical particles/voids (dotted line) to derive an average radius R, of the microstructures [7]. The constant A, is proportional to the height of the shoulder. I do
m d~
A, (1 + v
/a,
9
(2)
384 3
RESULTS and DISCUSSION
3.1
Effect of pyrolysis temperature
In order to analyze the effect of temperature on the microstructure, slices of both types of RF aerogels were pyrolyzed at temperatures between 500 and 1000~ The scattered intensity times q2 for the 1500/30 samples pyrolyzed at different temperatures is plotted in fig.2. Obviously significant changes take place at large q vectors (i.e. small length scales), which is due to structural rearrangement within the particles. The micropore volume increases continuously with rising pyrolysis temperature while the mesostructure remains unchanged. Additionally a shift towards larger microstructures can be observed, as indicated by the arrow. A fit to the scattering patterns according to eq.2 reveals an increase of the microstructure radius from R, = 0.33 to 0.41 nm. This effect is consistent with the tendency found by Reichenauer et al. [15] that larger pyrolysis temperatures result in an increase of the micropore radius (up to I nm at 2100~ The observations made for our samples can be interpreted as the initial stages of the pyrolysis, where originally non-porous RF particles become porous upon removal of oxygen-containing linkages. Fig.3 shows the DR-transformations of the N2-adsorption data of the same samples. Linear regions can be observed in the low pressure region between p/p0 0.001 and 0.05 (see upper scale), the range of linearity becoming larger with higher pyrolysis temperatures. The accessible micropore volume, as reflected by the y-intercept of the fit lines, increases up to temperatures of 700~ With still higher temperatures it is decreasing again. This effect has also been reported by Jenkins & Kawamura [17] for the pyrolysis of phenolic resins. They argued that a closing of pore entrances above temperatures of 700~ reduces the accessible volume. This can be explained by the persisting loss of hydrogen at temperatures above 500~ leaving larger pores behind; but due to the creation of new links between condensed aromatic carbon ribbons, closing of pores occurs at the same time. The apparent discrepancy between SAXS and DR analysis is therefore not unexpected. The energy of adsorption E0 calculated from the slope of the fit curves (with the affinity coefficient fl - 0.33) is decreasing with increasing pyrolysis temperature, indicating a pore widening. According to eq.1 the micro-pore half width L/2 increases from 0.26 nm at 600~ to 0.31 nm at 1000~ The deviation of the experimental data from the fit lines at higher relative pressures can be attributed to secondary micropore filling [18]. The data for the 1000~ sample in fig.3, exhibit an additional linear region for p/po between 0.17 and 0.45, corresponding to a half width of 0.53 nm. The value derived from the fit of the SAXS data averages over all pore sizes assuming a spherical shape which leads to an intermediate radius. In addition closed micropores are included. The evaluation of the data for adsorption of the nano-structured aerogel 200/45 was difficult because of the superposition of monolayer adsorption on the mesopore surface. Linearity of the DR plots was observed in a smaller pressure region, leading
385
Fig. 2. Change in microstructural features for the sample 1500/30 as a function of pyrolysis temperature, as indicated by the arrow. A fit line according to eq.2 is included. to half-widths L/2 of 0.55 to 0.67nm. No ultramicropores with radii < 0.35 nm are detected. Also the fit to the SAXS data gives rise to larger microstructures (0.45 nm) compared to the 1500/30 aerogel. A possible explanation for the different microstructures in both aerogels is the larger amount of residual sodium from the synthesis in the 200/45 sample, which acts as a catalyst for the pyrolysis and creates larger pores [19]. A comparison of BET and SAXS measurements with respect to surface area reveals a large difference of 500-700m2/g which is due to the presence of closed pores in the particles [10].
3.2
C02-activationof carbon aerogels
The discrepancy between BET and SAXS surface areas has been attributed to the existence of pores which are inaccessible for N2 at 77 K. In a previous publication it could be shown that via CO2-activation of C-aerogels the accessible surface area could be increased significantly [10]. This was attributed to the opening of closed pores and a widening of formerly inaccessible pores. Here a detailed analysis of the effect of CO2-
386
Fig. 3. Dubinin-Radushkevich plots for C-aerogel 1500/30 as a function of the pyrolysis temperature. activation on the structure of C-aerogels will be presented. Our experiments reveals that the mass loss of carbon upon CO2-activation depends strongly on the mesostructure of the samples. Aerogels with higher densities exhibit a smaller burn-off than low density aerogels. This can be attributed to the limited accessibility of CO2 to the interior of dense monolithic samples and a slower diffusion rate of the reaction products (e.g. CO) to the outside, thus changing the reaction rates as the process is diffusion limited. The mass loss was recorded right after the pyrolysis and compared to the non-activated sample. The low density aerogel 1500/30 could be activated to 50% burn-off and even higher, whereas for the high density aerogel a maximum of 29% burn-off was achieved. The activation conditions were varied with respect to temperature (between 850~ and 1000~ gas flow of CO2 (between 30 and 60ml/min) and activation time (1 or 2h). Higher activation temperatures result in a larger burn-off, whereas the flow of CO2 has only a minor influence. The homogeneity of activation of dense samples could be increased by reducing the temperature and prolonging the time of activation. In fig.4 BET and SAXS total surface areas are plotted vs. burn-off. It has to be noted that in order to
387
Fig. 4. Comparison of the total surface areas derived from BET and SAXS measurements versus the carbon burn-off. calculate the total SAXS surface area of the coarse structured samples, the skeletal density at each stage of burn-off is required. Based on the SAXS measurements for a series of activated C-aerogels, a linear relationship between skeletal density pc and burn-off was found: pc(hg/rrt 3) 1855 + 4.15 x (burn-off in %). The surface area increases with the burn-off, the BET surface area starting from a lower level but showing a steeper increase than the SAXS data. The discrepancy in surface areas from N2-adsorption and SAXS that is evident after pyrolysis in inert atmosphere is diminishing with progressing burn-off. For burn-offs above 50% both experimental techniques yield the same surface area. Accessible surface areas of 2500m 2/g can be achieved at a burn-off of only 50% for the 1500/30 aerogels. This as well as the increase in skeletal density can be explained in terms of pore opening by the removal of less ordered carbon in the initial stages. At the same time new pores are generated as indicated by the increasing surface area derived from the SAXS data. The flattening of the SAXS curve towards higher burn-offs shows that a limit in surface area for the material and this activation method is reached. In addition it can be seen that both aerogels give comparable BET and SAXS surface areas for the same burn-off. The remaining large difference in SAXS and BET surface area for the fine structured samples can be attributed to the limited accessibility through small mesopores (7nm), which leads to a gradient in accessible micropores over the sample cross section. (fig.5). It should also be noted that the ac=
388
Fig. 5. Illustration of the diffusion limited activation in monolithic aerogel slices with different mesostructures. tivation is not affecting the mesostructures. Only at very high degrees of burn-off a degradation of the particle size can be detected. Fig.6 shows the evolution of micropore volume and adsorption energy for different degrees of burn-off for the low density aerogel. The micropore volume is strongly increasing from 0.24 cm 3/g for the reference sample to 1.0 cm 3/g for the sample with a mass loss of 51%. At low degrees of burn-off only one linear region corresponding to a micropore width L of 0.6 nm is measured. With larger carbon burn-off the slope increases, indicating the widening of micropores to 1.3 nm. At some degrees of activa-
Fig. 6. N2-adsorption isotherms (left) and the corresponding DR plots for aerogel C 1500/30 with the burn-off as a parameter.
389 tion, a second linear region with a larger slope is developing, which can be attributed to the appearance of larger micropores of up to 2 nm. Further information about the microstructural changes upon CO2-activation was gathered for the 200/45 sample where a complete evaluation of the scattering data was performed. Tab.3.2 shows a marked decrease of the particle density and an increase of the carbon density with progressing burn-off. This can be interpreted in terms of hollowing out of the primary particles by removing less ordered carbon and leaving more resistant microcrystallites behind. Particle porosities of up to 50% are obtained. The BET surface area increases in accordance with larger accessible micropore volumina. In contrast to the coarse structured aerogel, the micropore width remains unchanged upon activation. Further experiments on very thin monoliths have to be done in order to completely understand the different behaviour upon activation of both types of aerogels. Table 1 Change of the microstructure of C-aerogel C 200/45 with the degree of burn-off, measured by SAXS and N2-adsorption.
(S)tot
(pc)
(ps)
(S)BET
L , / 2 (DR)
Vmic.
(m2/g)
(g/cm 3)
(g/cm 3)
(m2/g)
(nm)
cm3/g
ref.
1450
1.89
1.37
705
0.65
0.281
13.4%
1800
1.93
1.27
1080
0.56
0.434
29.2%
2150
2.02
1.12
1320
0.64
0.521
17Z
SAXS
4
T/Z
N2-adsorption
CONCLUSION
A large amount of microporosity that is hidden in carbon aerogels can be made accessible by activation methods without loss of monolithicity. To understand the differences between a very fine and a coarser aerogel with respect to microstructural changes upon pyrolysis and activation further investigations are necessary. ACKNOWLEDGEMENT This work was supported by the European Commission in the frame of a Brite Euram Project.
REFERENCES
[1] S. T. Mayer, R. W. Pekala, J. L. Kaschmitter, J. Electrochem. Soc. 140 (1993) 446
390 [2] R. W. Pekala, S. T. Mayer, J. F. Poco, J. L. Kaschmitter Mat. Res. Soc. Symp. Proc. 349 (1994) 79 [3] D. W. Schaefer, R. W. Pekala, G. Beaucage, J. Non-Cryst. Solids 186 (1995) 159 [4] R. Saliger, V. Bock, R. Petricevic, T. Tillotson, S. Gels, J. Fricke, J. Non-Cryst. Solids 221 (1997) 144 [5] G. A. M. Reynolds, A. W. P. Fung, Z. H. Wang, M. S. Dresselhaus, R. W. Pekala J. NonCryst. Solids 188 (1995) 27 [6] X. Lu, R. Caps, J. Fricke, C. T. Alviso, R. W. Pekala, J. Non-Cryst. Solids 188 (1995) 226 [7] R. Saliger, U. Fischer, C. Herta, J. Fricke J. Non- Cryst. Solids 225 (1998) 81 [8] V. Bock, A. Emmerling, J. Fricke, J. Non-Cr~dst. Solids 225 (1998) 69 [9] R. W. Pekala and F. M. Kong, J. de Physique, Colloque C4 (1989) 33 [10] R. Saliger, H. Pr6bstle, G. Reichenauer, J. Fricke, Proc. of the 9th CIMTEC, Part L: Innovative Materials in Advanced Energy Technologies, ed. P. Vincenzini (1999) [11] S. Brunauer, P. H. Emmett, E. Teller, J. Am. Ceram. Soc 60 (1938) 309 [12] K. Kaneko, C. Ishii, M. Ruike and H. Kuwabara, Carbon Vol.30, No.7 (1992) 1075 [13] M. M. Dubinin and L. V. Radushkevich, Proc. Acad. Sci. USSR 55 (1947) 331 [14] H. F. Stoeckli P. Rebstein, L. Ballerini, Carbon 28 (1990) 907 [15] G. Reichenauer, A. Emmerling, J. Fricke and R. W. Pekala, J. Non- Cryst. Solids 225 (1998) 210 [16] A. Emmerling, J. Fricke, J. Non-Cryst. Solids 145 (1992) 113 [17] G. M. Jenkins and K. Kawamura, Polymeric c a r b o n s - carbon fibre, glass and char, Cambridge University Press 1976 [18] F. Stoeckli, D. Huguenin, A. Greppi, J. Chem. Soc. Faraday Trans. 89 (1993) 2055 [19] F. Rodriguez-Reinoso and M. Molina-Sabio, Carbon Vol.30, No.7 (1992) 1111 [20] K. Kinoshita, Carbon, Electrochemical and Physicochemical Properties, John Wiley & Sons, New York, 1988
Studies in SurfaceScienceand Catalysis 128 K.K. Ungeret al. (Editors) 92000ElsevierScienceB.V.All rightsreserved.
391
On the determination of the micropore size distribution of activated carbons from adsorption isotherms D. L. Valladares a, G. Zgrablich a and F. Rodriguez Reinoso b aLaboratorio de Ciencias de Superficies y Medios Porosos, Universidad Nacional de San Luis, Chacabuco 917, 5700 San Luis, Argentina bDepartamento de Quimica Inorganica, Universidad de Alicante, Alicante, Espafia The effects of the adsorption mechanism, the pore geometry and the energetic heterogeneity of the pore walls on the determination of the micropore size distribution of activated carbons from adsorption isotherms are evaluated by means of Monte Carlo simulation. Results are applied to the characterization of two series of activated carbons with different burn-off degrees. 1. INTRODUCTION The problem of the characterization of the microporous structure of activated carbons from adsorption isotherms, in particular the determination of the Micropore Size Distribution (MSD), is a long standing one [1-15]. The advancement of experimental techniques and the possibility of performing massive computer simulations have raised a renewed interest in the subject and made possible improvements on classical methods, like Dubinin-Stoekli [1-3] or Horvath-Kawazoe [5] methods, which have played a pioneer and important role in the past. It is by now clear that several mechanisms and phases are present in the adsorption process in micropores, due to the interplay between gas-gas and gas-solid interactions, depending on their geometry and size. For this reason all those methods assuming a particular pore-filling mechanism, or adsorption model, should show shortcomings in some regions of the relevant parameters and their predictions should be compared with those based on more fundamental formulations of the adsorption process, like Density Functional Theory (DFT) [13] or Monte Carlo simulation [13,15]. Then, one question that arises is: how the adsorption model affects the determination of the MSD? A second important and unanswered question is the influence of the assumed pore geometry. The slit geometry is usually accepted to represent the microporous structure of activated carbons. However, there is no firm evidence that this would be the best choice for the pore geometry and that it would be enough to account for the important decrease of the isosteric heat of adsorption with adsorbed volume usually observed [6]. Therefore, a comparative study using well differentiated geometries, like for example slit and triangular pores, under the same conditions and with a complementary analysis of the behavior of the isosteric heat of adsorption, is necessary to shed light on this issue Finally, a third unanswered question, in our opinion, is the extent to which it is important to take into account the possible surface energetic heterogeneity contribution of the pore graphite walls. In the present work we attempt a systematic investigation of the influence of these three factors in the determination of the MSD of activated carbons. In Section 2, we present a Monte Carlo simulation method for the adsorption process, which is based on realistic
392 interparticle interactions and does not assume any specific filling mechanism, and the characterization method to obtain MSD. In Section 3, predictions of Monte Carlo simulation and classical methods are compared and discussed. The influence of the geometry of pores is studied in Section 4 and the effects of surface energetic heterogeneity are addressed in Section 5. Finally, in Section 6, we give the conclusions. 2. SIMULATION M O D E L AND CHARACTERIZATION METHOD In what follows we describe the simulation model for N2 adsorption in activated carbons for slit-like and triangular section pores and the characterization method to find the MSD from adsorption data by fitting simulated isotherms to experimental ones.
2.1. Simulation Model: Slit Geometry The structure of activated carbon is assumed to be represented by a collection of independent slit-like pores, with a distribution of pore sizes f(d), d being the separation between the two parallel walls. The distance d used here to characterize the pore size refers to the available space for gas adsorption and differs from the distance, dr, between the centers of carbon atoms of opposite walls. Each wall of a pore is composed by several layers of graphite planes, taken as 4 in our simulations as explained below. For a single pore with a given size d, the adsorption process is simulated in the Grand Canonical Ensemble. The simulation volume is a continuum 3-dimensional space defined by x ~ (0,L) ; y ~ (0,L) ; z ~ (0,d), the pore walls being parallel to the (x,y) plane, and periodical boundary conditions are applied in x and y directions. L = 10.3 nm was taken for all pores. The gas-solid interaction for an adsorbate molecule with a pore wall is taken as the wellknown Steele potential for graphite [ 16]: U,. (z)
4 "rCCgsPa~
5(z +dp )Io
_ 2(z+idp)4 , }
(1)
where z is the distance between the adsorbate molecule and the wall, p~ is the surface density of a graphite basal plane, dp is the distance between basal planes, ~g., and O-~s are the wellknown Lennard-Jones interaction parameters and n is the number of basal planes forming the wall. It is found that the variations in the potential from N-3 to 4 are very small and negligible for higher values, so that n - 4 is assumed in our simulations. For the adsorbate-adsorbate interaction, Ugg, the usual Lennard-Jones potential for two gas molecules separated a distance r is assumed with a cutoff at 3 molecular diameters in order to speed up calculations. The total potential energy for a molecule at position F, -- (x, y,, z, ) is then given by: - Ugs (Z,) + X Vgg
-
l
where Ug, (z,) = U, (z,) + U,. (d:- - z, ). Following the method proposed by Adams [17] and by Soto and Myers [18], three elementary events are considered in the simulation: a) displacement of a molecule from position F, to /:1, with a transition probability
393
1t
love. n,,,,f, , expI_
(3)
b) addition of a molecule to the adsorbed phase, with a transition probability
pV exp P~dd -- mm 1, (N + 1)k~T
(4)
kBT
c) subtraction of a molecule from the adsorbed phase, with a transition probability
Ps,~ - rain 1, Nk~ T exp pV
(5)
ksT
For all events, U, and Uf are the initial and final total energies of the adsorbed phase, respectively, N is the number of adsorbed molecules, p the equilibrium pressure in the gas phase, T the temperature and k8 the Boltzman constant. For a given pore of size d, the adsorption isotherm is obtained by Monte Carlo simulation of the adsorption process in the continuum, following the usual grand canonical ensemble algorithm [ 15, 17,18]. 2.2. Simulation Model- Triangular Geometry For the triangular geometry, we consider the adsorption space as being a prism, whose cross section is an equilateral triangle, formed by three semi-infinite walls, each wall consisting of 4 graphite planes. The size of the pore, d, is taken as the diameter of the inscribed circle. The axis of the pore runs along the x ~ (0, L) coordinate, with L =21 nm and periodic boundary conditions in x. In the same way as the Steele potential, eq. (1), is obtained by integrating the LennardJones gas-solid potential for an infinite graphite plane and then summed up for n planes, to find the interaction of a gas molecule with a semi-infinite wall we integrate the Lennard-Jones gassolid potential for a semi-infinite graphite plane and then sum it for n planes in a wall. To do this, in addition to the already defined x coordinate, we define for each wall the y coordinate as the distance from the edge of the wall and the z coordinate as the distance of the gas molecule from the wall. Then, the potential energy for a semi-infinite graphite plane is given by: Up -
(6)
4rcp,,[U 1(y', y,z)-Uz(y',y,z)]i'ii-~o
where 63
12 2(y'-y) (
U, (y', y, z) - -~Crg,
~/s
3cr6 2 ( y ' - y ) (
U2(y',Y,Z)- 8 gs
~
1
4
8
32
L| 8Z2S9 + 63Z 4S7 + ~10526S 5 + 8s---------315z ~ 1
1 )
6zZs 3 +~z 4
1 ") + 315z 1~J
(7)
(8)
394 with s - z: + (y'-y) 2 The interaction energy of a molecule with a single wall having n graphite planes is then n-1
(9)
U,.(y,z)- ~~Up(y,z +idp) t=0
Of course, given a molecule in the pore volume, its total gas-solid interaction with the pore, Ugs, must be calculated by summing up its interaction energy with the three pore walls. The rest of the simulation procedure is the same as for the case of slit geometry. 2.3. Characterization Method
In order to characterize the micropore structure by obtaining the MSD from adsorption isotherm data, it is necessary to obtain a collection of simulated isotherms for different size d, (i = 1, ..., n), in the form of adsorbed volume of gas at STP as a function of p: I.~ (d,, p). Then, assuming the hypothesis of independent pores as valid, as commonly done, the global theoretical isotherm for a microporous material having a size distribution/" (d,) can be written as
(10)
V,heo - S f ( d , ) V s ( d , , p ) t:l
Finally, given the experimental isotherm I exF (P), the micropore size distribution is obtained by finding those f ( d , ) values, which minimize the mean square deviation
A-Z{V~•
2
(11)
J
3. INFLUENCE OF THE ADSORPTION MODEL IN THE PREDICTION OF MSD
Our characterization method, based on Monte Carlo simulation in the continuum, was applied to predict the MSD of two series of activated carbons, obtained by carbonization of olive stone. For series D, the activation step took place in a flow of carbon dioxide at 1098 K, while for series H a flow of water vapor at 1023 K was used. Activated carbon samples D8, D19, D52, D70 and H8, H22, H52 and H74 were obtained, where the number represents the burn-off degree. Details concerning the preparation of the samples and the measurement of N2 adsorption isotherms at 77 K are given in [ 19-22]. Figures 1 a and b show the experimental adsorption isotherms for both series (lines) and the theoretical fitted isotherms (symbols). Figures 2 a and b show the predicted MSD for series D and H, respectively. Results for series D suggest that the microporosity for these carbons resides mainly in the range 1-1.5 nm. The increase in the activation degree with CO2 does not extend the microporosity toward smaller micropores but only modifies the micropore volume associated with each value of d . By comparing the experimental adsorption isotherms in the very low-pressure range with Monte Carlo simulations we conclude that these carbons do not have micropores with sizes less than 1 nm. In contrast to this behavior, for series H, we find that activation with H20 vapor generates an important amount of micropores smaller than 1 nm. The main porosity resides in the range from 0.8 to 1.3 nm, with a maximum near 1.0 nm, when the burn-off degree is 8%. At this low burn-off, some porosity is also observed in the range from 1.3 to 2.3 nm. Increasing in the burn-off degree causes the porosity to develop more or less evenly in the whole range, with a shift in the maximum of the distribution
395 toward 1.3 nm. Also, an important amount of porosity near the beginning of the mesopore region is developed. The distribution changes very little from H37 to H52 and remains unchanged from H52 to H74.
a)
25 "b)
20
20
~15
15
~'10
10 <>
,,~--~
. . . . . . -,
. . . . . -~
...... ,
..... -,
s 10-4 10-3p/Po10-2 10'
,,,7
0
~
10~ 10" 10;~""10s'"'10;;i:~'"'10:'"'1(..) "'"10"
Figure 1. N2 adsorption isotherms for series D (a) and series H (b) carbons: lines are experimental data, symbols are MC calculations with slit geometry. (O) D8 and H8, (A) D19 and H22, (V1), D52 and H52, (0) D70 and H74. 4
1,5
1,0
-
5"
0,5
,
~
':
10
,
'.:--~,--'>-'-'-
d 1(rim)
20
;!! ~4 i'i !i C ;
I
<:
l 2,5
i
-
,,:..._.. ,
, I
d;~)
2'o
2,5
Figure 2. MSD for series D (a) and H (b) obtained with slit geometry MC simulations ( .... ) D8 and HS, ( ...... ) D19 and H22, (-.-.-) D52 and H52, ( - - - ) D70 and H74.
396 When classical methods, like Dubinin-Stoekli (DS) [1-3], or Horvath-Kawazoe (HK) [5], are applied to the same carbon series to obtain the MSD, a main and important difference appears in the distribution as compared to the Monte Carlo method, namely, the prediction of an important amount of micropores in the region below l nm for both series (results not shown). In a recent paper [15], DS and HK methods were tested against ideal theoretical isotherms generated by Monte Carlo simulation using a given gaussian MSD as an input. The output MSD obtained by DS and HK methods where found always shifted to the left of the input MSD. For DS the shift was bigger the wider was the input MSD, while for HK the shift was bigger the narrower was the input MSD, for distributions centered in the region above 1.0 nm. Both methods gave acceptable outputs only when the input MSD was narrow and centered in the ultramicropore region, say 0.5 nm. Shortcomings of these methods were attributed to the pore-filling mechanism assumed in each of them: Dubinin plot was shown to be strongly non-linear for ideal simulated isotherms corresponding to slit pores of given sizes, while the assumption that at a given pressure a pore is either completely full or completely empty, implicit in the derivation of the HK equation, is not in accordance with simulation results. These considerations explain the differences in the prediction of MSD observed in applying DS and HK methods to the carbons analyzed here and suggest that the MSD predicted by Monte Carlo simulations should be more reliable. 4. INFLUENCE OF PORE G E O M E T R Y The pore geometry is an important factor affecting the distribution of gas-solid interaction energy through the pore space, and therefore the adsorption isotherm and the determination of MSD. It is generally believed that the slit geometry must be present in a great extent in the structure of activated carbons, since pore walls are made of graphite basal planes. However, a question that immediately arises is to what extent these planes intersect each other to form closed ends or acute corners where adsorption would be greatly enhanced. Two pore geometries that could be tested to study this effect are the rectangular and the triangular section pores. The greatest differences with the slit geometry should be find for the latter, while the former should give an intermediate behavior with the disadvantage that in a rectangular section pore it is impossible to define a pore size with only one parameter. Therefore, in this section we apply our simulation method for triangular pores to the series H carbon, which presented a more interesting and regular behavior, and compare the results with those obtained with a slit geometry. Figure 3 (a) and (b) show the results for the adsorption isotherms and MSD, respectively, for series H. We see that, while the model again gives a good fit to experimental adsorption isotherms, the predicted MSD differ substantially from the ones obtained for slit geometry. The main difference is the disappearance, or strong decrease, of micropores below 1.0 nm for all carbons. For H52 and H74 the distribution is enhanced toward larger pores. This result can be understood by considering that in the triangular geometry corners provide high adsorptive energy making unnecessary the presence of small micropores to fit the adsorption isotherm in the low pressure region. At the same time greater sizes than those required for slit geometry are necessary to account for the slow increase of the adsorption isotherm in the high-pressure region.
397
600
1,5
b)
a)
5oo
.I '.i
i~
i
Ii t~ 9I~ tl
I:
:~ i ~ :, i', '1 l,
ii
~
20o
.. !
: !
':
;/
:
3,5
1 oo
,i~ i
o,~. 0
30
10 .7 10 .6 10 -S 104
10 -~ 10 z
P/Po
10'
10 ~
05
1,0
,5
d
i ,
2 0
nm)
2.5
3,0
Figure 3. Results for triangular geometry, a) Adsorption isotherms for series H lines are experimental data, symbols are MC calculations (O) H8, (A) H22, (~) H52, (0) H74. b) MSD for series H ( .... ) H8, ( ...... ) H22, (-.-.-) H52, ( - - ) H74.
3
a)
2-
0.000
0.C)02 "0,()04"0.(~06'0.()08
V a:
(moles/g)
'0,()I0
3
o.oooo.do~ o ~o, o.do~o do~o d,o V~_
(mmoles/g)
Figure 4. Isosteric heat of adsorption for H22 obtained with slit (a) and triangular (b) geometry. Both the behavior of MSD predicted by the slit geometry and the one predicted by the triangular geometry are generally consistent with the increase in burn-off degree for all carbons of the series, so that this analysis is not sufficient to decide which geometry is more appropriate to describe the structure of activated carbons. However, our simulation and characterization method allows us also to obtain the behavior of the isosteric heat of
398 adsolption, q~t as afunction of adsorbed volume [23 ], shown in Figure 4 (a) and (b) for slit and triangular geometry, respectively, for carbon H22. As we see, the two geometries predict qualitatively different behaviors of q.~, and this could provide a strong test if microcalorimetric measurements were available for these carbons. 5. SURFACE E N E R G E T I C H E T E R O G E N E I T Y E F F E C T S In addition to structural (geometric) heterogeneity, characterized by different pore shapes and sizes, activated carbons like all porous solids may present surface energetic heterogeneity (SEH). This heterogeneity is mainly due to the presence of functional groups and strongly bound impurities on the surface of pores, whose characteristics depend on the type of row material used and the conditions of carbonization and activation processes. SEH effects in microporous materials are very difficult to separate from the global heterogeneity effects. The question we try to address here is to what extent it is necessary to take into account SEH in formulating the adsorption process in order to obtain reliable MSD. A second question related to this is to what extent SEH is necessary to account for the steady decrease of about 2.5 Kcal/mol in qs,, as adsorbed volume increases, with an initial value near 5.5 Kcal/mol, observed in some activated carbons with very high surface area (reported BET area near 3000 mZ/g) [24]. Our calculations of q.,t for H22 (Fig. 4) show that slit geometry accounts for a decrease of about 2.5 Kcal/mol, while triangular geometry only accounts for less than 1 Kcal/mol, both with an initial value near 3 Kcal/mol. However H22 only presents micropores greater than 0.7 nm (its BET surface area is about 1200 m2/g). Simulations of the adsorption process for slit pores in the ultramicropore region, Figure 5, show that a maximum q.~t above 5 Kcal/mol is reached for pore size of 0.4 nm. It is then feasible to account for the behavior of q.~t in a very high surface area activated carbon considering only the effect of geometric heterogeneity. 5,5
5,o-
4,5-
4,0-
3,5-
3,0-
2,5
I
0,40
,
i
0,45
,
i
0,50
,
i
0,55 d
,
'i
0,60
,
~
0 5
9
i
0 70
(rim)
Figure 5. Minimum (circles) and maximum (triangles) values of qst as a function of d for slit geometry pores An independent test we performed consisted in obtaining the MSD of series D carbons by formulating the adsorption process in a lattice-gas scheme [25]. In this way it was possible to
399 take into account the SEH through a gaussian distribution of adsorptive energy whose parameters were fixed by fitting an adsorption isotherm obtained for a non-microporouse sample of the same carbon of series D. Results of this test indicate that we obtain essentially the same MSD for series D as the one obtained in the present work. These results seem to indicate that the SEH plays a secondary role in the determination of the MSD, even though it may become important for the characterization of the solid in the mesoporous region. 6. CONCLUSIONS We have presented a simulation method to obtain the MSD of activated carbons, and have analyzed the influence of the adsorption model, pore geometry and surface energetic heterogeneity on this determination, in particular for two series of activated carbons. Classical methods, like DS and HK, show shortcomings in the determination of MSD due to the assumptions involved in their formulation of the adsorption process. Dubinin equation does not show linearity in the Dubinin plot for single slit pores and Horvath-Kawazoe equation assumes that at a given pressure a pore is either completely filled or completely empty, which is contrary to the behavior observed in computer simulations. Resulting MSD are shifted respect to those obtained by Monte Carlo simulations, by amounts that vary with the actual distribution, and too small micropores are predicted. The effect of a pore geometry, different from the usually assumed slit-like one, is studied by considering triangular section pores. This can account for probably occurring pore walls intersections in the activated carbon structure providing high-energy adsorption regions in the corners. It is found that the assumption of triangular geometry changes drastically MSD. However, predicted MSD are consistent with the activation process of the carbons in the series analyzed and this analysis alone is insufficient to decide which geometry should be assumed preferentially or to what extent both geometries contribute to represent the structure of activated carbons. Further analysis based on the behavior of the isosteric heat of adsorption may give some clues about this matter and q~t measurements on the analyzed carbon series are encouraged. Finally, we found that surface energetic heterogeneity effects are secondary, at least for the characterization of the porous structure in the micropore range. All the studies presented here omit connectivity effects due to the micropore network.
Acknowledgments This work was supported in part by CONICET (Consejo Nacional de Investigaciones Cientificas y Tecnicas) of Argentina. REFERENCES 1. M.M. Dubinin, in Progress in Surface and Membrane Science, J.F. Danielli, M.D. Rosenberg and D.A. Cadenhead (eds.), Vol. 9, Academic Press, New York, 1975 2. H.F. Stoekli, J. Colloid Interface Sci., 59 (1977) 184 3. M.M. Dubinin and H.F. Stoekli, J. Colloid Interface Sci., 75 (1980) 34 4. S.J. Gregg and K.S.W. Sing, Adsorption, Surface Area and Porosity, Academic Press, New York, 1982 5. G. Horvath and K. Kawazoe, J. Chem. Engng. Japan, 16 (1983) 470
400 6. F. Rodriguez Reinoso and A. Linares Solano, Microporous Structure of Activated Carbons as Revealed by Adsorption Methods, in Chemistry and Physics of Carbon, P.A. Thrower (ed.), Vol.21, Marcel Dekker, NewYork, 1988. 7. M. Molina Sabio, F. Rodriguez Reinoso, D L. Valladares and G. Zgrablich, in Characterization of Porous Solids III, J. Rouquerol, F. Rodriguez Reionoso, K.S.W. Sing and K.K. Unger (eds.), Elsevier, Amsterdam, 1994 8. F. Rodriguez Reinoso, M. Molina Sabio and M.T. Gonzalez, Carbon, 33 (1995) 15 9. M.T. Gonzalez, A. Sepfilveda Escribano, M. Molina Sabio and F. Rodriguez Reinoso, Langmuir, 11 (1995) 2151 10. N. Setoyama and K. Kaneko, J. Phys. Chem., 100 (1996) 10331 11. F. Ehrburger-Dolle, M.T. Gonzb.lez, M. Molina Sabio and F. Rodriguez Reinoso, in Characterization of Porous Solids IV, J. Rouquerol, F. Rodriguez Reionoso, K.S.W. Sing and K.K. Unger (eds.), Elsevier, Amsterdam, 1996 12. M. Jaroniec and J. Chorea, in Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, W. Rudzirrski, W.A. Steele and G. Zgrablich (eds.), p. 715, Elsevier, Amsterdam, 1997 13. C.M. Lastoskie, N. Quirke and K.E. Gubbins, in Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, W. Rudzinski, W.A. Steele and G. Zgrablich (eds.), p. 745, Elsevier, Amsterdam, 1997 14. K. Kaneko, in Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, W. Rudzinski, W.A. Steele and G. Zgrablich (eds.), p. 679, Elsevier, Amsterdam, 1997 15. D.L. Valladares, F. Rodriguez Reinoso and G. Zgrablich, Carbon, 36 (1998) 1491 16. W.A. Steele, The Interaction of Gases with Solid Surfaces, Pergamon Press, New York, 1974, p.53 17. D.J. Adams, Molec. Phys. 28 (1974) 1241 18. J.L. Soto and A.L. Myers, Molec. Phys. 42 (1981) 971 19. F. Rodriguez Reinoso, J.M. Martin Martinez, M. Molina Sabio, R. Torregrosa and J. Garrido Segovia, J. Colloid. Interface Sci., 106 (1985) 315 20. J. Garrido, A. Linares Solano, J.M. Martin Martinez, M. Molina Sabio, F. Rodriguez Reinoso and R. Torregrosa, Langmuir, 3 (1987) 76 21. J. Garrido Segovia, A. Linares Solano, J.M. Martin Martinez, M. Molina Sabio, F. Rodriguez Reinoso and R. Torregrosa, J. Chem. Soc., Faraday Trans. I, 83 (1989) 1081 22. F. Rodriguez Reinoso, J. Garrido, J.M. Martin Martinez, M. Molina Sabio and R. Torregrosa, Carbon, 27 (1989) 23 23. D.L. Valladares, F. Rodriguez Reinoso and G. Zgrablich, to be published 24. S. Manzi, D.L. Valladares, J. Marchese and G. Zgrablich, Adsorption Science & Tech., 15 (1997) 301 25. D.L. Valladares, M.Sc. Thesis, Universidad Nacional de San Luis, Argentina (1997).
Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (F_Aitors) 92000 Elsevier Science B.V. All rights reserved.
401
Role of Pore Size Distribution in the Binary Adsorption Kinetics of Gases in Activated Carbon Shizhang Qiao and Xijun Hu* Department of Chemical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
A heterogeneous multicomponent adsorption model is presented to study the adsorption equilibrium and kinetics of mixed gases in activated carbon (AC). The model utilizes a micropore size distribution concept to interpret the solid structural heterogeneity. The pore size is related to the adsorbate-adsorbent interaction energy by the Lennard-Jones potential. The size exclusion effect is taken into account in the competition of different species for a given pore. Both pore diffusion of free species and surface diffusion of adsorbed species are considered in the theory. The driving force for surface diffusion is the chemical potential gradient in the adsorbed phase. Isothermal and kinetics parameters extracted from singlecomponent data fittings are used to predict multicomponent adsorption kinetics. Single and binary experimental adsorption and desorption data of ethane and propane in Norit activated carbon are collected to validate the model. The agreement between the model results and experimental data is good in general.
1. I N T R O D U C T I O N The structure of activated carbon is highly heterogeneous. The adsorption kinetics of gases in activated carbon cannot be interpreted well by a simple homogeneous model without properly addressing the surface heterogeneity of activated carbon. Various models for the adsorption kinetics in a heterogeneous porous particle has been reviewed [1]. There are two methods to interpret the structure heterogeneity of the adsorbent. One approach assumes an energy distribution to follow either uniform or binomial form, where the matching energies between different species in the adsorbed phase is described by the cumulative energy matching scheme [2-4]. The other method uses a micropore size distribution (MPSD) and the Lennard-Jones potential [5] to study the surface heterogeneity [6,7]. The approach using energy distribution to describe the system heterogeneity is reasonable for a single-component adsorption system since the micropore size is related to the adsorbate-adsorbent interaction energy. For multicomponent adsorption system, the cumulative energy matching approach does not bring out the feature of competition of different adsorbates residing in a pore, and may match the energy of one species in one pore to the energy of another species in another *This project is supported by the Croucher Foundation and the Research Grants Council of Hong Kong.
402 pore of different size, which is physically impossible. One more disadvantage associated with the energy distribution concept is that the size exclusion effect can not be incorporated, which is important in dealing with mixtures of large and different molecule sized molecules. In order to overcome these drawbacks of energy distribution and to describe the physical adsorption phenomenon coherently, investigation has been carried out using the micropore size distribution (MPSD) and the Lennard-Jones potential methodology to study adsorption equilibrium [6,8] and kinetics [7,9] of single component system. This approach was extended to study multicomponent adsorption equilibrium [10, I1 ]. In this study, the MPSD method is further extended to study multicomponent adsorption kinetics in a large activated carbon particle. The micropore size distribution is treated as the intrinsic property of adsorbent. The competition of all adsorbates exists in all micropores, except those micropores having a width less than the molecular diameter of a specified species (Exclusion phenomenon). Experimental data of adsorption kinetics of ethane and propane and their binary mixture on Norit activated carbon under various conditions are measured using a differential adsorption bed (DAB) rig. These data are used to validate the predictive capability of the kinetic model. For comparison purpose, another model based on a uniform energy distribution [12] is also used to predict the same system.
2. T H E O R Y Let us consider a gas mixture stream containing NC components flowing at very high velocity. At time t - 0 a large microporous particle is exposed to this environment. The flow rate of the gas stream is so high that the gas concentration can be considered constant and the system can be assumed isothermal because the heat released from adsorption is dissipated quickly by the flowing gas. The adsorbent particle is assumed large enough so that the mass transfer resistance is along the particle coordinator.
2.1. Slit-pore potential and adsorption energy The gas-solid potential of a molecule confined in two parallel lattice planes, Up, is given by the well-known Lennard-Jones 10-4 potential [5]: 9 5 2 Up (k,z) - u s (k)-~- ~-
-r~
z
+
5
2rp - z
[2r-~-z
(1)
where rp is the length between the pore center and a given atom of pore surface layer, i.e., the pore half-width plus the lattice half-space between graphite planes, z is the distance between the molecule and a given atom of a pore surface layer separated by a distance of 2rp, and ro is the collision diameter of gas [5]: 1 1 ro - -~-[ro(bulk gas)+ (lattice spacing between graphite planes)] = ~-[rg + 3.40 A] the parameter u~ is the depth of the Lennard-Jones potential minimum for a single lattice plane and this depth occurs at the position ro . The adsorbate-adsorbent interaction energy can be taken as the negative of the potential energy minimum inside the pore [6,7]. Solving Eq. l for the minimum potential energy, the
403 relationship between the interaction energy and the pore half-width can be obtained as following: , E(k, rp) - u p (k,rp) (2) where Up is the depth of the potential minimum.
2.2. Adsorption Isotherm and Micropore Size Distribution For multicomponent systems, the local adsorption isotherm for a given micropore is assumed to follow the extended Langmuir equation, b0(k)e
Cu(k,rp)=Cg,.(k)
E(k ,re, )/R~,T
CI,(k)
NC
l+Eb0(j)e
E( j,rp )/ R~T C
j=l
(3)
p(j)
where Cr(k,rp) is the adsorbed phase concentration of species k at an adsorbate-adsorbent interaction energy level of E, Cr~ is the maximum adsorbed phase concentration (saturation capacity), Cp is the gas phase concentration, Rg is the gas constant, T is temperature, NC is the number of components, b0 is the affinity constant at zero energy level and can be treated as temperature independent over a limited temperature interval. If the micropore size distribution of the activated carbon follows some kind of distribution function, for example, the non-negative gamma distribution: qV+lrp v e -qrv F(rp) : (4)
F(v + 1)
the observed isotherm on the activated carbon is then the integral of the local adsorption isotherm over the accessible micropore size distribution range, i.e.:
bo (k)eE(k.r,,)lR~.rCl, (k) uc F(rt,)ds, ")e E( ),rt, ) / ReT r,.,.(*) 1 + Z ~ (j)bo (J C,, (j)
Cu(k)-Cg"(k) I
(5a)
j=l
where
{(j)_{;if
r> rn~,,(j) if
(5b)
rmi. (k) < r < r.,, (j)
rn~n is the minimum accessible half-width of the pore for a given species and is assumed to be 0.8584ro, corresponding to a zero potential energy with the 10-4 potential.
2.3. The Local Surface Diffusion Flux The driving force for the diffusion of adsorbed species is assumed as the chemical potential gradient, hence the local surface diffusion flux of species k, Jr(k, rp), can be written as" Cr(k, rp) ~ /)Cp(k) 0Cr(j,r p) (6) J r ( k ' r p ) - - D r(k,rp) ~ii(7 J=' 0C. (j, rp) 0r where r is the coordinate in the particle and D r is the zero coverage surface diffusivity and related to the micropore half width by"
404
Du(k, rp) = Duo(k)ex p
-
a E(k. rp)
R.T
)
(7)
where a is the ratio of surface activation energy to the adsorption energy, D.o is the zero coverage surface diffusivity at zero energy level, and the adsorption energy is calculated from the micropore half width rp.
2.4. Mass Balance Equations Since the particle is large, the mass transfer can be assumed to be under pore and surface diffusion control, so the mass balance equation in the particle is:
Ofr
CM 3Cp(k_~) 3t + (1 - CM)-~~E M
,,,(k,C " (k, rp )F(rp )drp
(8)
71 ~3 (r~j p ( k ) ) - (1- c M)17 3---r3( r~r[=~," (k)J. (k, rp )F(rp )drp )
where c M is the macropore porosity, s is the particle geometric factor having a value of O, 1 or 2 for slab, cylinder or sphere, respectively, and Jp is the macropore diffusion flux" Jp (k) - -Dp (k) 0Cp (k) 3r
(9)
where Dp is the pore diffusivity, calculated from the combined molecular and Knudsen diffusivities and the tortuosity of the adsorbent. Eq. (8) states that the accumulation of mass in both free and adsorbed form (LHS) is balanced by the diffusion rate into the particle of gas (first term in RHS) and the adsorbed species (second term in RHS). The diffusion rate of adsorbed species in particle is related to the observed adsorbed concentration C, (Eq. 6) so that the effect of size exclusion (Eq. 5) has been accounted for in the mass balance equation. One of the boundary conditions of Equation (8) is the zero flux at the particle center: OC (k) ~)C (k) r - 0 ; P--------L----= ~---------~--= 0 3r 3r Another boundary condition is at the particle exterior surface: r = R; EMJ v(k) +(1 - c M)I~, .(k) J.(k'rv)F(rv)drv = k
m (k)[Cp(k)-Cb(k)
l
(10)
(11)
where R is the radius (half width) of the particle and C b is the adsorbate concentration in the bulk phase. The initial conditions of the model equations are: t = 0; Cp (k) = C p i (k); C" (k) - C"s(k)
....(k)
b0 (k)e E(rp)/R'TCpi (k) NC
1 + ~_~(j)bo(j)eE(J.rr,,R.V Cp,(j) j=l
q ~+'rp v e -qrp F(V + 1)
drp
(12)
405
2.5. Solution Methodology The integrals over the required micropore size distribution is evaluated by the orthogonal collocation technique and the adsorption energy is found from gas-solid potential energy minimum inside the pore by a univariate minimization routine DUMING [13]. Since the model equation are coupled partial differential equations, they are solved numerically by using a combination of the orthogonal collocation technique [14] and an ODE integrator [ 15].
3. EXPERIMENTAL Norit Row activated carbon (type 0.8 supra) is supplied by Norit Company (USA) in the form of 0.8 mm (diameter) cylindrical extrudate. The physical and structural properties of the adsorbent and the measurement procedures of adsorption isotherm and kinetics were given in our previous work [ 16].
4. RESULTS AND DISCUSSION
4.1. Micropore size distribution of the activated carbon The micropore size distribution of Norit carbon is shown in Figure 1. The optimal 1.s micropore size distribution parameters are q = 21.01 /k-i, v = 98.14. The molecule diameter of adsorbate dictates the accessibility of that species in the micropore network of the adsorbent. In this paper the values reported by Breck [17] are used. The molecule diameters of ethane and propane are 3.9 and 4.3 /k, respectively, which are also shown in Figure 1. Only a small portion of pores is excluded for ethane and propane molecules.
Pore accessibility cut off ethane propane
o~1.o O -.,~.,
= ~ 0.s c3 00
1
0
2
I
~
f
4 6 Pore half width (,~,)
I
8
10
Fig. 1. Micropore size distribution of Norit activated cabon
4.2. Adsorption isotherm The pure component adsorption equilibrium of ethane and propane are measured on Norit AC at three temperatures (30, 60 and 90 ~ All experimental data of two species at three temperatures are employed simultaneously to fit the isotherm equation to extract the isothermal parameters. Since an extended Langmuir equation is used to describe the local multicomponent isotherm, the maximum adsorbed capacity is forced to be the same for ethane and propane in order to satisfy the thermodynamic consistency. The saturation capacity was assumed to be temperature dependent while the other parameters, b0 and u~, are temperature independent but species dependent. The derived isotherm parameters for ethane and propane are tabulated in Table 1. The experimental data (symbols) and the model fittings (solid lines)
406 Table 1. Isothermal parameters, pore and surface diffusivities of ethane and propane in Norit activated carbon (pore size distribution model) T Duo x 10 6 Dt, xlO 6 C,, b,, x 10 4 ll.,. (~ (m2/s) (m2/s) (kmol/m3) (kPa-l) (kJ/mol) C2 3O 60 90 C2: ethane;
[ C3
C2
C3 ,,,
5.1958 1.679 4.4792 3.8125 C3: propane
1.964
C2
11.39
C2
C3
C2
C3 1.75 1.86 1.97 , ,
2.12 12.30 2.26 2.38
C3
0.383 0.294
0.5
Table 2. Isothermal parameters, pore and surface diffusivities for ethane and propane in Norit activated carbon (uniform energy distribution model ) Dl, X106 Duo x 10 6 " Emax Emin T C~.~ b • 10 4 (kJ/mol) (kJ/mol) (m2/s) (m2/s) (~ (kmol/m 3) (kPa -l) ,,
C2
~30 60 90
]
C3
5.3090 4.7867 4.2789
C2
0.08
C3
0.77
C2 27.3
C3 26.9
are shown in Figures 2a and 2b for ethane and propane, respectively. For comparison the isotherm fitting using a uniform energy distribution [12] is also plotted in Figure 2 as dashed lines. The corresponding parameters are tabulated in Table 2. The model fitting using a uniform energy distribution is slightly better than that utilizing a pore size distribution.
C2 14.5
The pore size distribution is converted into adsorbate-adsorbent interaction energy via the Lennard-Jones potential. The converted energy distribution from the above gamma pore size distribution is shown as solid lines in Figures 3a and 3b for ethane and propane, respectively. Although the pore size distribution is the same for ethane and propane, the energy distributions of them are different. The reason is that the pore size distribution is the intrinsic property of adsorbent but the energy distribution is related with the interaction of adsorbate and adsorbent. Also plotted in Figure 3 as dashed
C2
9.71
2.12 2.26 2.38
C3
C3
1.75 1.86 1.97
1.81
0.47
(a) Ethane
0.5
,.O.- ~ ~ ~
32 Ur~ 1
vE .El O
4.3. A d s o r p t i o n e n e r g y distribution
C3
< CO O
z~
0 0
5
[]
60 ~
A
90 ~
I
1
I
I
1
20
40
60
80
100
120
(b) Propane
43-
-
0
[]
60 ~
A
90 ~
I
I
1
1
1
20
40
60
80
100
120
Pressure (kPa) Fig. 2. Adsorption isotherm data and model fitting of ethane and propane in Norit activated carbon MPSDmodel Energy distributionmodel
407 lines are uniform energy distributions for the same adsorption systems. The uniform energy distribution has a higher mean energy compared to that derived from pore size distribution for ethane. 4.4. Single component adsorption kinetics Single component adsorption kinetics data of ethane and propane are measured on Norit AC of 4.41mm half-length slab under various experimental conditions. The pore diffusivity of each species is computed from the combined molecular and Knudsen diffusivities and a tortuosity of three. The ratio of the activation energy for surface diffusion to the local interaction energy, a, is taken as 0.5. With these parameters defined, the only parameter to be extracted from the kinetics data fitting is the surface diffusivity at zero loading and zero energy level (D~0), which is
0.30
0.20 0.15 0.10 -
f. . . .
I] 1|
0.05 O
E
o.oo
~"
0.20
v
10
t
i
I
15
20
25
30
(b) Propane 0.15 -
I ~
0.10 -
0.05
-
---]
0.00
5
.
)
.
.
.
.
-[
I
10
i
i
15
20
I 1 I
r
25
30
35
Energy (kJ/mol)
independent of concentration and temperature. Figure 4 shows the adsorption dynamics of ethane in a 4.41 mm half length slab of Norit activated carbon at 30 ~ 1 atm. The results are shown as the fractional uptake versus time. The fractional uptake is defined as the uptake
~+1~ ~ [~MCp+(1-~;M)C~]dr
(a) Ethane
0.25 -
Fig. 3. Adsorption energy distribution of ethane and propane in Norit activated carbon MPSD
Energy
model
distribution
model
at any time 0.8
divided by its value at final equilibrium (time - ~). The experimental data of ethane at three bulk phase concentrations (2, 5, 10%) are first utilized to optimize the kinetics parameter (D~,,) for the MPSD model. The kinetics parameters of ethane adsorption are listed in Table 1. Figure 4 shows that the model fittings (solid lines) are in good agreement with the experimental data (symbols). For comparison, the fitting of heterogeneous macropore and surface model using a uniform energy distribution [12] is also plotted in Figure 4 as dashed line. Both models can adequately describe the concentration dependence of adsorption kinetics.
ethane
Y
'1~ ,//
~.0.6 "~ .O 0.4
v
v
O [3
2% 5%
A V
10% 5%
I1 0.2
0.0
0
~
t
500
1000
.... 1500
T i m e (Seconds) Fig. 4. Adsorption and desorption kinetics of ethane at different bulk gas concentrations in Norit activated carbon of 4.41 m m haft-length slab at 30 ~ MPSD
model ....
1 atm.
Energy distribution model
408
With the zero coverage surface diffusivity at zero energy level obtained from the above fitting of the adsorption data, the MPSD model is used to predict the desorption kinetics of 5% ethane on the same activated carbon particle at a temperature of 30 ~ The result is also plotted in Figure 4. It is seen that the model can reasonably predict the experimental data although the simulated uptake is a little bit faster than the experimental data, and the MPSD model prediction is slightly better than the model prediction using uniform energy distribution. The single component adsorption kinetics of propane is measured on the same adsorbent and at the same experimental conditions as those of ethane, so our simulation also follows the same procedures as described above. The kinetics parameter, Duo, for propane is first optimized by fitting
,oI
0.8
(D
-
4.5. Binary adsorption kinetics Having obtained the adsorption equilibrium and mass transfer parameters of single component systems (Tables 1 to 2), we are ready to examine the predictability of the model in simulating the sorption kinetics of multicomponent systems on Norit activated carbon. The adsorption kinetics of the binary mixtures of ethane and propane is first measured on Norit AC of 4.41 mm half
y,/j
-
[] =O,o
t1<-,t' \ v
r-
v S'Jo
"4...
I/
.0 0 . 4 U..
0.2-
0.0 0
i
l
1
i
500
1000
1500
2000
2500
Time (Seconds) Fig. 5. Adsorption and desorption kinetics of propane at different bulk gas concentration in Norit activated carbon of 441 mm half-length slab at 30 ~ MPSD model
1.4 1.2
1 atm.
Energy distribution model
O/~~..~
0
1.0
the model equation to the experimental data of three bulk concentrations (2, 5 and 10%) at 30 ~ simultaneously. The optimization results (lines) and the experimental data (symbols) are presented in Figure 5 while the optimized value of Duo for propane is listed in Tables 1 and 2. Both models fit the data well. The desorption kinetics of 5% propane at 30 ~ is predicted with the extracted surface diffusivity and the result is also shown in Figure 5. Some deviations are observed for the desorption simulation of propane.
o
k./V/ 0.6
-Q
0.8 0.6
0.4
O A
0.2 0.0 0
,
,
)
j
)
500
1000
1500
2000
2500
1.2
3000
2
0.8
A
0.6
LI~
2% C 2 5% C 3
02
A
0.0
oc,
'
z
)
)
~
I
0
500
1000
1500
2000
2500
1.4 1.2 1.0 08 06 '& O.4 _~/z, I/z..~ 02 - ~ 0 . 0 L~
0
O A ~ 500
T
3000
I0%C 5% C 3
~
)
I
i
1000
1500
2000
2500
3000
Time (Seconds)
Fig. 6. Binary adsorption dynamics of ethane and propane onto Norit activated carbon of 4.41 mm half-length slabs at 30~ 1 atm. MPSD model Energy distribution model
409 length slab at three bulk phase compositions: (1) ethane (2%) - propane (5%); (2) ethane (5%)- propane (5%); and (3) ethane (10%) - propane (5%). The bulk phase total pressure is 1 atm and the temperature is 30 ~ Figure 6 shows these adsorption experimental data (symbols) and the corresponding model predictions (lines). Since the system consists of a fast-moving/less-strongly-adsorbed species (ethane) and a slower-moving/more-stronglyadsorbed species (propane), the typical overshoot maximum in the ethane uptake curve is observed. The predictions of the MPSD model (solid lines) are in very good agreement with the experimental data (symbols). The predictions of the uniform energy distribution model are plotted in Figure 6 as dashed lines, which 1.0 { are also in good agreement with experimental 0 5% C 2 data. As propane is the slow-diffusing/more0.8strongly-adsorbed species, it behaves like 0.6single-component so that both model 0.4predictions on propane uptake are \ ~ 0 ~ 0 ~-0.2superimposed to each other. ,4,--' s
E3
4.6. Binary desorption kinetics The desorption kinetics of two binary mixtures of ethane (5%) - propane (5%) and ethane (5%) - propane (10%) on Norit AC of 4.41 mm half-length slab at 30 ~ is measured and compared with the model simulations to examine the model potential. Figure 7 shows the model predictions (lines) and the experimental data (symbols) of these two gas mixtures. Some deviations are observed between the model predictions and the experimental data, especially when desorption has progressed to a longer time. The model prediction for ethane using the MPSD model gives a marginally better result than the model using uniform energy distribution. For the propane uptake rate prediction, both models give similar results. The binary desorption kinetics of 5% ethane and 5% propane in the same particle is investigated at a higher temperature of 60 ~ 1 atm. The desorption kinetics predicted by the models (lines) and the experimental data (symbols) are presented in Figure 8. Similar phenomena as above are observed. The simulated uptake using the MPSD model agrees well with the experimental data of ethane. Some deviations are observed for the propane uptake.
cO
0.0 0
s
1.0
f
r
5O0
1000
0.8-LI..
,--,
0.6-
1500
0
5% C 2
[]
10% C 3
[]
0.4"~... 0
0.2-
0
"
0.0
1
0
~
~
400
o
1
I
800
1200
1600
Time (Seconds) Fig. 7. Binary desorption kinetics of ethane and propane onto Norit activated carbon of 4.41 mm half-length slab at 30 ~ MPSD model ....
1 atm.
Energy distribution model
1.0 {
0.8-
A
5% C 2
V
5% C 3
.1..., r
S306c. _O ,,.., (3
0.4-
It_ 0 . 2 0.0 0
i
i
500
1000
Time
1500
(Seconds)
Fig. 8. Binary desorption kinetics of 5% ethane and 5%propane onto Norit activated carbon of 4.41 mm half-length slab at 60~ 1 atm. Energy distribution model MPSD model
410 5. CONCLUSIONS A kinetics model has been formulated using a micropore size distribution concept to study multicomponent adsorption kinetics on a large activated carbon. In the model, the pore size distribution of slit-shaped micropores is considered as the main source of surface heterogeneity, which governs the adsorption equilibrium and kinetics through the dispersive force represented by the Lennard-Jones potential theory. The MPSD model can coherently address the energy-matching between various adsorbate molecules via their own interaction strength with the local micropores. In comparison, when an energy distribution is used, the traditional cumulative energy-matching scheme is arbitrary and lacks of the fundamental ground since the matching does not bring out the feature of competition of adsorbates residing in a pore. Experimental kinetics data of single-component and binary mixtures of ethane and propane on commercial Norit activated carbon under various experimental conditions are measured and employed to examine the prediction capacity of the models. With the parameters extracted from single component systems, both MPSD model and that using uniform energy distribution show reliable concentration dependence and possess good predictive capability for single and multicomponent adsorption kinetics. Some deviations are observed between the model simulation and desorption kinetics data. It is difficult to tell which model is better by comparing the model predictions with the experimental data, but the MPSD model is inherently more plausible since a uniform energy distribution is incompatible with a MPSD.
REFERENCES 1. D.D. Do, Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces (eds. W. Rudzinski, W. Steele, and G. Zgrablich), Elsevier, Amsterdam, 777-835 (1997). 2. D.P. Valenzuela, A.L. Mayers and I. Zwiebel, AIChE J, 34, 397 (1988) 3. A. Kapoor, J.A. Ritter and R.T. Yang, Langmuir, 6, 660-664 (1990). 4. X. Hu and D.D. Do, AIChE J. 41, 1585-1592 (1995). 5. D.H. Everett and J.C. Powl, J. Chem. Soc. Faraday Trans. I. 72, 619-636 (1976). 6. J. Jagiello and J.A. Schwarz, Langmuir, 9, 2513-2517 (1993). 7. X. Hu and D.D. Do, Langmuir, 10, 3296-3302 (1994). 8. K. Wang and D.D. Do, Langmuir, 13, 6226-6233 (1997). 9. D.D. Do and K. Wang, Carbon, 36, 1539-1554 (1998). 10. X. Hu and D.D. Do, Fundamentals of Adsorption, (ed. LeVan, M. D.), Kluwer Academic Publishers, Boston, Massachusetts, 385-392 (1996). 11. X. Hu, Chem. Eng. Comm., in press (1999). 12. X. Hu and D.D. Do, Langmuir, 9, 2530-2536 (1993). 13. IMSL Library, version 1.1 (1989). 14. J. Villadsen and M.L. Michelsen, Solution of Partial Differential Equation Models by Polynomial Approximation, Prentice-Hall, Englewood Cliffs, NJ (1978). 15. L.R. Petzold, Sandia Technical Report: SAND 82-8637, Livermore, CA (1982). 16. S. Qiao and X. Hu, Sep. Purif Technol., 16, 261-271 (1999). 17. D.W. Breck, Zeolite Molecular Sieves: Structure, Chemistry. and Use; John Wiley & Sons: New York (1974).
Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) o 2000 Elsevier Science B.V. All rights reserved.
411
C o n f i n e d State o f A l c o h o l in C a r b o n M i c r o p o r e s as R e v e a l e d by In Situ X - R a y Diffraction T. Ohkubo, T. liyama, T. Suzuki, and K. Kancko Physical Chemistry, Material Science, Graduate School of Nature Science and Technology, Chiba University, Yayoi 1-33, Inagc, Chiba 263-8522, Japan The X-ray diffraction (XRD) of ethanol and methanol molecules confined in carbon micropores was measured at 303 K.
The effect of the pore width in the range of 0.7-1.1 nm
on the molecular assembly structure of ethanol and methanol in the micropores was examined. The XRD patterns were analyzed by use of the electron radial distribution function (ERDF) analysis.
The density of alcohol molecular assemblies in micropores was determined by
using ethanol or methanol adsorption at 303 K and nitrogen adsorption at 77 K.
The density
of alcohol molecular assemblies in pores of 1.1 nm was close to the solid density of alcohol, whereas that in micropores of 0.7 nm was almost equal to the bulk liquid density.
However
the amplitudes of the ERDFs of alcohol in both micropores were much greater than that of bulk liquid, indicating that the serious confinement in micropores gives rise to their solid-like ordering even at 303 K.
1. I N T R O D U C T I O N The potential in micropores gives a deep potential well because of the overlapping of the interaction potentials.
Molecules tend to be adsorbed in the deep potential well. ~2 The
classical Gurvitch rule ~guarantees a liquid-like structure formation of the adsorbed molecules in micropores.
Wc can control the structure of the liquid-like molecular assembly of
adsorbed molecules in micropores because of the asymmetric molecular field. The authors have studied the molecular structure adsorbed in micropores about various molecules such as CC143'4, N2,~, 0 6 NO 7, SO), He 9, and H,O"' ~' using activated carbon fiber (ACF) which has considerably uniform slit-shaped hydrophobic micropores.
Polar molecule,
for example, H~O molecule in carbon micropore interacts strongly between H20 molecules than between H20 and carbon walls.
Iiyama et al. reported that H_,O molecules confined in
412 hydrophobic nanospaces have the solid-like specific structure even at 303 K using in situ Xray diffraction experiment. ~~ ~
H~O molecules confined in carbon micropores whose pore
width is less than 0.8 nm cannot freeze even below 150 K. ~' ~
On the contrary a CC14
molecule interacts strongly with the carbon micropore, CC14 can be adsorbed even at very low pressure to form a dense adsorbed phase in the higher pressure. 3' 4 The adsorbed CC14 in hydrophobic micropore shows an unusual elevation of the melting temperature. ~3 An alcohol molecule has both polar and nonpolar groups.
The hydrophilic groups tend to
gather each other in a hydrophobic nanospace by hydrogen bonds, whereas hydrophobic groups are adsorbed on hydrophobic surfaces in a flat orientation. ~4 ~~ The hydrocarbons are more stabilized in carbon microporcs by increasing the chain length. ~
Ethanol molecules
confined in slit-shaped graphitic micropores have a specific structure depending on the pore width. 17 This paper describes the comparison of ethanol and methanol molecular assembly structures in the hydrophobic slit-shaped micropores.
2. EXPERIMENTAL 2.1 Adsorption isotherms Two kinds of pitch-based ACFs (P5 and P2(); Osaka Gas Co.) were used.
The
microporous structure was determined by high-resolution N2 adsorption isotherms at 77 K using a gravimetric method.
The micropore structual parameters were obtained from high-
resolution a s-plot analysis with subtracting pore effect (SPE) method. '8' 19 The average slit pore width w was determined from the microporc volume and the surface area.
The
adsorption isotherms of methanol and ethanol on carbon samples were gravimetrically measured at 303 K.
The sample was preevacuated at 10 mPa and 383 K for 2h.
2.2 In situ X-ray diffraction The X-ray diffraction of methanol and ethanol adsorbed in microporcs of ACF samples was measured at 303 K by the transmission method using an angle-dispersivc diffractometer (MXP3 system, MAC Science) in the scattering parameter s (= 4 n sin 0/,~ ) range of 3.1 to 125 nm -~. The monochromatic Mo Ka at 50 kV and 30 mA was used for the diffraction measurement.
We used an in situ XRD chamber with Mylar film windows, which was
shown in the preceding paper. 4 measurement.
The ground ACF samples were used for the XRD
The XRD data were analyzed with the ERDF method. -~~
413
3. RESULTS AND DISCUSSION 3.1 Adsorption isotherms and adsorbed densities of alcohol The
N 2
adsorption isotherms at 77 K were of Type I.
The adsorption isotherms of
N 2 were
analyzed by the SPE method using the high resolution a s-plots, as shown in Figure 1.
The
adsorption isotherm of N2 on nonporous carbon black (Mitsubishi Chemical Co. #32B) was used as the standard isotherm.
The fcaturcs of the a s-plots were similar to that published in
the preceding paper. 21 We can dctcrmine the micropore volume W0, total surface area a,,, and the external surface area a~x, from the c~s-plots.
The average pore width w can be
evaluated from both the surface area and pore volumc of slit-shaped micropores. summarizes these pore parameters.
,...,
600 E
[_] 7
0 J_)
E 400
?.
u
LJ
0 0
'2 200
0 O
O
0
()
0
O
C
0
O
E < I
1
0.5
1 Ct
I
1
1.5
2
2.5
S
Figure 1. High resolution t~ s-plots for N2 adsorption isotherms on P5 and P20.
O" P5, [-]" P20
Table 1 Pore parameters of P5 and P20. W0/ ml g-i
a ,, / m 2 ,,-~
a~,,, / m 2 ,, ,-,
w/nm
P5
0.26
790
10
0.7
P20
0.79
1430
25
1.1
Table 1
414
The adsorption isotherms of methanol and ethanol on ACF samples at 303 K were shown in Figure 2.
The horizontal axes arc expressed by the logarithm of P/Po to show explicitly
the adsorption in the low relative pressure range.
The adsorption isotherms of ethanol on
both P5 and P20 have a greater uptake in the lower relative pressure than those of methanol. Theretbre, the interaction of an ethanol molecule with the micropore is much greater than that of a methanol molecule.
However, the methanol molecule can interact more strongly than a
H20 molecule, because almost no water molecule is adsorbed below P/P0 = 0.3-2~ The density of confined methanol and ethanol can be determined using the micropore volume from the N2 adsorption at 77 K and the saturated amount of adsorbed methanol and ethanol which was obtained from the Dubinin-Radushkevich (DR) plots. adsorbed density of methanol and ethanol on ACE
Table 2 shows the
The solid density at 113 K 2_, and liquid
density at 303 K of bulk methanol are 0.98 and ().79 ~ c m 3, respectively.
On the other hand,
the solid density at 87 K 2., and liquid density at 3()3 K of bulk ethanol are 1.025 and 0.7868 e," /cm 3, respectively.
The adsorbed density values indicate that methanol and ethanol confined
in P20 have their solid-like structures and those of P5 have less-packed structures.
200
10()0
(b)
(a) E
,=.
9 c9 o ~
_~ 150
" 800
9
F
_
e,-,
r~
d
9
6O0
9
.~ loo
9 9
4OO
,i
o
50 9
<
2()o
,,-~ ~
oO0
-
Ul
nll~
<
~
r
-
--
i
-4
-3
-_"
-I
0
-4
-3
-2
-1
log (P /P())
log (P /Po)
Figure 2. Adsorption isotherms of methanol and ethanol on P5 (a) and P20 (b)at 303 K.
O and [-]" Methanol
I L. - .
9 and n . Ethanol
415 Table 2 Adsorbed density of methanol and ethanol at 303 K. 9
11
,
Amount of adsorbcd /mgg
Adsorbed density
-1
/gem
-3
Methanol
Ethanol
Methanol
Ethanol
P5
183
185
().7
0.7
P20
762
867
1.()
1.1
3.2 X-ray diffraction patterns of confined alcohol molecules Figure 3 shows the XRD patterns of ethanol-adsorbed P20 and pure P2() at 3()3 K. Though the XRD pattern of P2() has a weak peak of (002) reflection near s = 15 nm -~, the diffraction pattern of ethanol-adsorbed P2() has a broad pcak duc to the adsorbed ethanol in the (002) reflection area.
The subtraction of I t ( s ) -
I(.(s) leads to the approximated
diffraction of adsorbed ethanol in carbon micropores, where I,(s) and It(s) are the total scattering intensity of ethanol-adsorbed P20 and the intensity of pure P20, respectively. Figure 4 shows the corrected XRD patterns of adsorbed ethanol on P5 and P20.
6000
4000 d ,,..q
2. = 2000
I
0
2()
s / nm
-1
I
I
4{)
60
Figure 3. X-ray diffraction patterns of P2() (fine line) and ethanol-adsorbed P20 (bold line) at 303 K.
416
'100 90
300
d
Oa
200
...q m |
0
201
~
...
,
.
A 50
lO0
60
mS
9
9
I
0
. . . .
-,,ow
,..
2o
,. . . .
I
40 s/nm
"
60
-1
Figure 4. Corrected X-ray diffraction pattcrns of adsorbcd ethanol on P5 (bold solid line), P20 (fine solid line) and bulk liquid ethanol (dotted line).
Thc scale is magnificd in the
insct. (O" on P5, A. on P20, [--]"bulk liquid ethanol).
The XRD of bulk liquid ethanol is also shown for comparison. observed in the s range from 10 to 30 nm-'. at s = 35 nm -1 in the inset. in narrow spaces.
The slight diffcrcncc is
Thc pcak of ethanol confincd in P5 can bc sccn
This can bc attributcd to thc spccific structurc of adsorbcd ethanol
However, these diffraction pattcrns cannot providc thc dctailcd structure
of adsorbed molecule.
Thcn wc transformed thc structure function dcrivcd from XRD
patterns into electron radial distribution lhnction (ERDF) by Fouricr translbrmation. 3.3 Effect of pore width and chain length of an alcohol molecule on ERDF
Figure 5 shows the ERDFs of methanol on ACFs and bulk liquid methanol at 303 K.
The
peak positions of ERDFs adsorbed on both P5 and P20 arc similar to those of bulk liquid methanol.
However, the nearest neighbor peak of the ERDF lbr liquid methanol at 0.46 nm
is shifted to a smaller distance for adsorbed methanol on P5, at 0.44 nm, although the peak of adsorbed methanol on P20 is the same as that of bulk liquid.
Moreover, the nearest peak of
adsorbed methanol on P5 has a weak shoulder peak (a) near 0.38 nm.
Taucr el al. reported
that the intermolecular distances between neighboring molecules for solid methanol at 113 K are 0.364 nm tbr CH3-CH3, 0.40 nm tbr O-O, and ().41 and 0.42 for CH3-O. 2-~ This peak means the formation of the solid-like structure in microporcs of P5.
In addition, the
amplitudes of ERDFs of confined methanol arc grcatcr than thosc of bulk liquid methanol. These results suggested that adsorbed mcthanol molcculcs should lbrm an ordcrcd structurc in
417 -) 4
I
Figure 5. ERDFs of methanol on
2
ACFs and bulk liquid at 303 K.
V/"
0 ~L
Bold solid line: P5. P20.
Fine solid line"
Dotted line" bulk liquid.
-4 J
0
i
A
0.5
,,
~.,
I
A
~
L.____~__
1.0
1.5
r / nm
~-
Figure 6. ERDFs of ethanol on
2
i
ACFs and bulk liquid at 303 K. 0
Bold solid line: P5.
Fine solid line:
v.,i
R ~
P2().
Dotted line" bulk liquid.
-2
-4
~
0
0.5
1.0
1.5
r/nm
carbon micropores having less-mobility comparcd with liquid methanol. Figure 6 shows the ERDFs of ethanol on ACFs and bulk liquid ethanol at 303 K.
The
peak position of adsorbed ethanol at 0.49 nm on P20 arc close to that of crystalline slate at 0.47 nm (b). ~7 On the other hand, the peak of adsorbed ethanol at ().44 nm on P5 is different from peak of bulk liquid and solid ethanol,
Also, the peak position of second neighbors of
adsorbed ethanol on P5 shifts to a smaller distance by 0.11 nm compared with bulk liquid ethanol more drastically.
This result indicates that a serious restriction of ethanol molecules
in the narrow space of P5 and adsorbed ethanol molecules cannot form the ordinary solid structure because of the serious confinement.
3.4 Ordered structure of confined alcohol The adsorbed density of methanol and ethanol molecules confined in P20, i.e. in larger micropores is not close to that of bulk liquid but to that of bulk solid.
The results of ERDF
analysis strongly support the ordered structurc lbrmation of adsorbed methanol and ethanol.
418 Morishige et al. showcd that cthanol and mcthanol molcculcs adsorbed on thc graphite surface have a hydrogen-bonded spccific structure at low tcmpcraturc. -'4 -'~ The hydrogcn bonds should play an important rolc for thc structure of adsorbcd mcthanol and ethanol molecular assemblies evcn at 303 K. Methanol molecules confined in microporcs can form thc close packcd structurc in larger micropores, though they cannot form in narrowcr microporcs bccausc of thc misfit spacc sizc for formation of the solid-likc structure of the high packing density.
On the othcr hand, thc
close packed structure like bulk liquid can bc formcd in short distance still in narrower micropores.
Ethanol molecules adsorbed in carbon microporcs can lbrm the solid-likc
ordered structure in widcr microporcs but cannot Ibrm in narrowcr microporcs. molecules should be oricntcd parallcl to thc porc walls in wider microporcs.
Ethanol
In narrower
microporcs, cthanol molecules form a specific ordered structurc diffcrcnt from bulk solid. The model having a flat oricntation lbr thc surfacc of narrowcr microporcs can support the results of adsorbed density and ERDF of adsorbcd cthanol on P5. So far, wc cannot dctcrminc the atomic position using these analyscs.
In situ X-ray
diffraction and adsorption isotherm studies showcd thc adsorbcd statc of molccular asscmblics for alcohol molecules confincd in graphitic microporcs and thc formation of ordcrcd structurc even at 303 K.
Acknowledgement This work was funded by the Grant-in-Aid for Scientific Rcscarch on Priority Arcas No. 288 "Carbon Alloys" from Japanese Govcrnmcnt and Japan Intcraction in Science and Technology Forum.
Reti~rences 1. S. J. Gregg, K. S. W. Sing, Adsorption, Surface Area and Porosity, Academic Prcss, London, 1982. 2. K. Kaneko, J. Membrane Sci., 26 (1994) 59. 3. T. Iiyama, T. Suzuki, and K. Kancko, Chem. Phys. Lctt., 259 (1996) 37. 4. T. liyama, K. Nishikawa, T. Suzuki, T. Otowa, M. Hijiriyama, Y. Nojima, and K. Kancko, J. Phys. Chem. B, 101 (1997) 3037. 5. K. Kancko K. Shimizu, and T. Suzuki, J. Chem. Phys., 98 (1992) 8705.
419 6. H. Kanoh, and K. Kaneko, J. Phys. Chem., 99 (1995) 5746. 7. K. Kaneko, Colloids Surt., 109 (1996) 319. 8. Z. M. Wang, and K. Kaneko, J. Phys. Chem., 99 (1995) 155. 9. N. Setoyama, K. Kaneko, and E Rodrigucz-Rcinoso, J. Phys. Chem., 100 (1996) 1(7331. 10. Iiyama, K. Nishikawa, T. Otowa, and K. Kancko, J. Phys. Chem., 99 (1995) 10075. 11. T. Iiyama, K. Nishikawa, T. Suzuki, and K. Kancko, Chem. Phys. Lctt., 274 (1997) 152. 12. K. Kaneko, J. Miyawaki, A. Watanabc, and T. Suzuki, Fundamentals of Adsorption, E Meunier (eds.), Elsevier, Amsterdam, 1998. 13. K. Kaneko, A. Watanabe, T. liyama, R. Radhakrishnan, and K. E. Gubbins, J. Phys. Chem. in press. 14. J. H. Clint, J. Chem. Sot., Faraday Trans. I, 68 (1972) 2239. 15. Y. Du, H. Yuan, D. Wu, and Y. Kong, Magn. Reson. Chem., 27 (1989) 987. 16. X. L. Cao, B. A. Colenutt, and K. S. W. Sing, J. Chromatogr., 555 (1991) 183. 17. T. Ohkubo, T. Iiyama, K. Nishikawa, T. Suzuki, and K. Kancko, J. Phys. Chem. B, 103 (1999) 1859. 18. K. Kaneko, and C. Ishii, Colloids Surf., 67 (1992) 203. 19. N. Setoyama, T. Suzuki, and K. Kaneko, Carbon, 36 (1998) 1459. 20. K. Nishikawa, and T. Iijima, Bull. Chem. Soc. Jpn., 57 (1984) 1750. 21. J. Miyawaki, T. Kanda, T. Suzuki, T. Okui, Y. Macda, and K. Kancko, J. Phys. Chem. B, 102(1998)2187. 22. K. J. Tauer, and W. N. Lipscomb, Acta Crysl., 5 (1952) 606. 23. P. G. J6nsson, Acta Crystallogr. B, 32 (1976) 232. 24. K. Morishige, K. Kawamura, and A. Kose, J. Chem. Phys., 93 (1990) 5267. 25. K. Morishige, J. Chem. Phys., 97 (1992) 2(784.
This Page Intentionally Left Blank
Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) 92000 Elsevier Science B.V. All rights reserved.
421
Critical appraisal o f the use o f n i t r o g e n a d s o r p t i o n for the characterization o f porous carbons P. L. Llewellyn, F. Rouquerol, J. Rouquerol and K.S.W. Sing CTM du CNRS, 26 rue du 141 eme RIA, 13331 Marseilles cedex 3, France I. Introduction The introduction of a range of user-friendly equipment and software has accompanied the present widespread use of low-temperature nitrogen adsorption. Advances have been made in the development of both routine experimental procedures and on-line processing of the adsorption isotherm data. However, there is now a risk that an unskilled operator may gain the impression that with the aid of a manufacturer's user-friendly software it is relatively easy to evaluate the specific surface area and the pore size distribution of the material under examination. Furthermore, the ready access to sophisticated computational procedures may tend to obscure the limitations of the theoretical models on which they are based. The aims of this paper are to draw attention to these problems and to indicate how further progress can be made in the analysis of nitrogen isotherms on porous carbons. The surface properties of most adsorbent carbons are exceedingly complex. For example, there is generally an initial decline in the differential energy of adsorption with increasing surface coverage. This form of energetic heterogeneity is usually attributed to the heterogeneous nature of the surface structure [1]; but the interpretation of the adsorption energy data is complicated by the fact that most high-area carbons contain ultramicropores (ie pores of molecular dimensions). At the operational temperature of 77K, ultramicropore filling by nitrogen begins to occur at very low relative pressures (at p/pO < 105), but it is not easy to obtain accurate adsorption data at such low p/pO [ 1]. Physisorption in the wider micropores (ie the supermicropores of w i d t h - 1 - 2nm) occurs over a range of higher relative pressures (eg at p/pO ~ 0.01 - 0.2) and in this range the experimental measurements are evidently less demanding. At p/pO> .~ 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 