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    Centre de Recherche sur la Matière Divisée, CNRS et Université d’Orléans 1b rue de la Férollerie, 45071 Orléanscedex 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 off-lattice 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 30 Å-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 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 radius of about 30-35 Å (assuming a cylindrical geometry) and are spaced about 200 Å 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 N2 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 Å in size, the calculated curve exhibits the experimentally observed correlation peak at 0.026 Å− 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 Å. 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 Å in size (see below). This transformation preserves the pore morphology but reduces the average pore size from 70 Å to roughly 30 Å. 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 off-lattice 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 Å 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 = -1e and qSi = -2e respectively) and a polarizability of 0.58 Å3; the adsorbate/H repulsive contribution (Born-Mayer 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 (ε = 120 K and σ = 3.405 Å for argon and ε = 211 K and σ = 3.869 Å 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/cm3. The average density and porosity values are 1.467 g/cm3 and 0.334 respectively (the values for real vycor are 1.50 g/cm3 and 0.30). Density and porosity exhibit fluctuations...