Studies in Surface Science and Catalysis 128 K.K. Ungeret al. (Editors) 9 2000 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 . 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 . 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 . 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 . 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) . 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 . 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 . In a previous study , 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  (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) . 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 . 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 . 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 . It will be very valuable to compare those intrinsic specific surface values with that obtained from adsorption isotherms applying the usual BET method . 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  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 . 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 .
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 ) 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
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  (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  (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) . 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  while for the Xe/vycor system, Ssp=106 m2/g . 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
the Institut du D6veloppement et des Ressources en Informatique Scientifique, (CNRS, Orsay, France) for the computing grant 98/99281.
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