Adsorption of fluids in disordered porous media from integral equation theory

Abstract

We consider the application of the integral equation theory developed by Madden and Glandt to a recently developed model of methane adsorbed in a silica xerogel. At higher temperatures, above the bulk fluid critical temperature, the theory yields very good predictions of the adsorbate–matrix and adsorbate–adsorbate distribution functions. At lower temperatures, where the attractive intermolecular forces play a more dominant role in determining the microstructure, the agreement between simulation and theory deteriorates somewhat. It also becomes increasingly difficult to obtain solutions of the integral equations at low temperatures. We have found that for this system and others where the matrix particles are much larger than the adsorbate particles the adsorbate–matrix and adsorbate–adsorbate correlation functions differ only slightly from those of an equilibrium mixture of matrix and adsorbate particles. We offer an explanation for this result on the basis of cancellation of diagrams in the cluster expansion of the total correlation function. We discuss the determination of adsorption isotherms from integral equation theory using expressions developed in the context of density functional theory.