Table Of Contentiiix
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 partici-
pants from 52 countries enjoyed a very successful meeting with 32 lectures and 551 poster
presentations.
The Symposium started with a highly stimulating lecture by Sir John Meurig Thomas, Cam-
bridge, highlighting the recent developments ni 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 ni composing a scientific programme of outstand-
ing 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 12 grants to students to
participate.
It has been decided that COPS-VI will be held on May 8 - ,11 2002 in Alicante, Spain.
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XV
Scientific Committee
.J Rouquerol, CTM du CNRS, Marseille, France
.R Rodriguez-Reinoso, Universidad de Alicante, Spain
K.S.W. Sing, Universities of Exeter und Bristol, United Kingdom
K.K. Unger, Universitat Mainz, Germany
Organising Committee
.F Schuth, MPI fur Kohlenforschung, Mulheim na der Ruhr, Germany
.U Muller, BASF Aktiengesellschafi, Ludwigshafen, Germany
.L Nick, DECHEMA e.V., Frankfurt ma Main, Germany
Financial Support
The organisers gratefully acknowledge the financial support of the following sponsors:
B FSA 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 ma Main, Germany
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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 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 591 K) in a mesoporous silica
Controlled Porous Glass (CPG) by means of Grand Canonical Monte-Carlo (GCMC) simula-
tion. Several numerical samples of the CPG adsorbent have been obtained by using an off-
lattice reconstruction method recently introduced to reproduce topological and morphological
properties of correlated disordered porous materials. The off-lattice functional of Vycor is ap-
plied 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 ob-
tained by saturating all oxygen dangling bonds with hydrogen. All numerical samples have
similar textural and structural properties in terms of intrinsic porosity, density, specific sur-
face 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 591 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 polariz-
ability 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. INTRODUCTION
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 ra-
dius of about 30-35 A (assuming a cylindrical geometry) and are spaced about 200 A apart 2-
3. 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 re-
construction procedure gives a connectivity similar to experiment. One challenge was to de-
fine 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 par-
ticular 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 nu-
merical sample is contained in a box of about 701 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 do-
main. The atomistic pseudo-vycor porous medium has been obtained by applying the off-
lattice functional to a box containing the silicon and oxygen atoms of 351 unit cells of cubic
cristoballite (a siliceous non-porous solid). This allows to cut out portions of the initial vol-
ume 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 morphologi-
cally and topologically equivalent numerical samples of pseudo-vycor. Periodic boundary
conditions are applied in order to simplify the Grand Canonical Monte-Carlo (GCMC) ad-
sorption procedure. In order to model the surface in a realistic way and to ensure electroneu-
trality, 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 (qo--le and qsi=-2e
respectively) and a polarizability of 0.58 ~3. the adsorbate/H repulsive contribution (Born-
Mayer term) is adjusted on the experimental low coverage isosteric heat of adsorption (13.5
and 71 kJ/mol for argon 7,8 and xenon 9,10 respectively). The adsorbate-adsorbate poten-
tial 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 in-
dependent variables are the chemical potential, the temperature and the volume 11 . At equi-
librium, the chemical potential of the adsorbed phase equals that of the bulk phase which con-
stitutes 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 inde-
pendent variables in a GCMC simulation of adsorption ni vycor are the temperature, the pres-
sure of the bulk gas and the volume of the simulation cell containing the porous sample as de-
fined above. The adsorption isotherm can be readily obtained from such a simulation tech-
nique 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 ni 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 poros-
ity 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 nu-
merical 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 re-
constructed 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 mak-
ing 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 al-
most 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 cor-
responding porosities are 0.344, 0.378, 0.301,0.298 and 0.291). Globally, large values of spe-
cific surface are obtained for high value of porosity although the intrinsic specific surface ex-
hibits a maximum value for a porosity around 0.344. Note that the values of the intrinsic spe-
cific 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 spe-
cific 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 intrin-
sic 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 51 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 pseudo-
vycor 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 adsorp-
tion 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 591 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 con-
sidered 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.
Figure "2 Xenon adsorption isotherm at 591 K
Most important is the adsorption mechanism as seen from equilibrium configuration snap-
shots (Figures 3 and 4). At 591 K, xenon does not wet the vycor surface: adsorption and con-
densation 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 re-
gions of the pores are filled with condensate while other parts of the interface remain uncov-
ered. 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 iso-
therms (using the BET equation with cross-section values of 8.31=rAYC ~2 and 0.71=eXYC ~2
[17]) are 731 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 ni 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 ni 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 spe-
cific 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 homo-
geneous 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 con-
tinuous film on the inner surface 18]. [ Therefore, one can infer that there are different adsorp-
tion mechanism depending on the adsorbate (and on the temperature). Note that a similar wet-
ting behavior to that presented in this work for xenon was found in a GCMC study of adsorp-
tion 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 de-
serves 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 poten-
tial 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 con-
ditions, the adsorbate does not wet the surface. Of course, wetting has the status of a thermo-
dynamic 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 po-
rous 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
