Adsorption, diffusion and permeation of gases in microporous membranes. III. Application of percolation theory to interpretation of porosity, tortuosity, and surface area in microporous glass membranes

Abstract

The dependencies of porosity, surface area, and a tortuosity factor in microporous membranes on the porous membrane structure were considered. it was shown that the porosity and tortuosity in silica glasses could be described within the framework of the percolation theory. Tortuosity factors were influenced not only by the elongation of the diffusion path but also by the amount of throughout porosity. Mathematical medoling of gas diffusion processes in microporous glasses was performed by the MonteCarlo method. The simulation results were in good agreement with experimental observations for Vycor glass membranes. Dependence of the surface area per unit volume, S V, on pore size was represented by a simple power law of the type S V∼ f (θ) d −1 P with O < f(θ) < 1.23, where d P is the pore diameter. Experimental data from literature on surface area and porosity in porous carbons, alumina, silica, glasses, silver, nickel, and polymeric membranes were used to verify the relationship. As a first approximation, the surface area per unit volume in porous materials with porosity 0.4 < θ < 0.6 can be estimated as S V ≈ 1.23/ d P.