Theoretical studies of the available volume for adsorption in a random quenched and depleted disordered medium

Abstract

The use of a removable template during synthesis of a disordered porous material can result in a material of greatly differing pore structure. We present here a theoretical study of the influence of a template on the material’s available volume. We model the material as a medium formed by quenching and depleting an equilibrium fluid and develop a theoretical method by which the available volume for adsorption in this model material may be investigated. This method makes use of the known relationship between the direct correlation function and the available volume. An analysis of the diagrams contributing to the available volume shows that two types of field points are present: those corresponding to the density of the medium following depletion (ρ) and those corresponding to the density of the original quenched fluid (ρq). A perturbation term to the available volume is derived that accounts for the diagrams containing ρq field points. The resulting expression contains only the direct and total correlation function; these quantities are known exactly for a hard sphere system within the Percus–Yevick approximation. Using this approach, we show that for materials of a given density, those formed by depletion can possess available volumes enhanced by up to an order of magnitude.