Adsorption in Controlled-Pore Glasses: Comparison of Molecular Simulations with a Mean-Field Lattice Gas Model
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Adsorption in Controlled-Pore Glasses: Comparison of Molecular Simulations with a Mean-Field Lattice Gas Model LEV D. GELB∗ AND RAFAEL SALAZAR† Center for Materials Innovation and Department of Chemistry, Washington University in St. Louis, St. Louis, MO 63130 [email protected]
Abstract. We consider the possible quantitative application of a lattice-gas model approach to the calculation of adsorption isotherms. In order to validate such application, we use the lattice-gas approach to solve for the adsorption and desorption isotherms in model controlled-pore glasses that have previously been the subject of an extensive series of Grand Canonical Monte Carlo simulations. We find that the lattice-gas model augmented with longer-ranged interactions provides a quite good account of adsorption in some of these systems for appropriate choice of several system parameters, but that the quality of agreement depends on the pore size of the material. Keywords: molecular simulation, statistical mechanics, capillary condensation
Introduction Analysis of the adsorption isotherms of simple liquids such as argon and nitrogen remains the most commonly used method to obtain the porosity, surface area and pore size distribution of microporous and mesoporous materials (Gregg and Sing, 1982; Rouquerol et al., 1999). Methods for gas adsorption analysis involve fitting (either implicitly or explicitly) the morphological properties of an idealized model of the material (for instance, a collection of cylinders of varying size) to the measured adsorption data, and then reporting the fitted quantities (Gelb and Gubbins, 1998, 1999). For amorphous materials with a range of pore sizes and shapes connected in a “tortuous” network topology, it is not always clear how to construct such an idealized model. We are working towards the extraction of structural data from adsorption isotherms by fitting the adsorption in an arbitrary three-dimensional porous matrix to experimental data. Such an extraction could ∗ To
whom correspondence should be addressed. Nacional Mayor de San Marcos. Fac. F´ısica, A.P. 140149, Lima 14, Per´u.
† Universidad
in principle be accomplished using the same sort of integral equation as in standard analyses (Gregg and Sing, 1982; Rouquerol et al., 1999). This would require a fluid model for which the isotherm can be very quickly and cheaply calculated, since an iterative procedure with many thousands of model isotherm determinations would be required. Latticegas models (as described below) may be suitable for this purpose, but must first be tested and parameterized against adsorption data in nontrivial, threedimensional structures before they could be applied reliably. In this paper we perform such a parameterization, using molecular simulations of xenon adsorption in controlled-pore glass materials as our reference data.
Models and Simulation Methods The original preparations and characterizations of controlled pore glasses were done by Haller (1965). The starting material is 50–75% SiO2 , 1–10% Na2 O, and the remainder B2 O3
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