Predicting gas diffusion regime within pores of different size, shape and composition

The ability to separate mixtures of molecules is a vital technology in a world that emits excess carbon dioxide into the atmosphere, needs purified water, desires artificial kidneys and requires hydrogen for sustainable energy alternatives. Membranes are composed of angstrom and nanometer-sized pores which may be designed to separate a gas, vapor or liquid mixture. In this paper we employ mathematical modeling, using the Lennard-Jones interactions between the gas molecule and the pore wall, to determine the gas diffusion regime occurring within pores of different size, shape and composition. This novel approach is used to predict the transport of light gases, namely, He, H2, CO2, O2, N2 and CH4, through carbon tubes, carbon slits, silica tubes and silica slits. Minimum pore size for barrier-free transport (dmin) and the minimum pore size for Knudsen diffusion (dK) are calculated for each gas and a mechanism for the intermediate region is suggested in which the attractive van der Waals forces cause an accelerated entrance velocity of the gas at the pore opening. Experimental results for gas transport in carbon nanotube, carbon molecular sieving and molecular sieving silica membranes are explained well by the model. The aim of this work is to provide the guidelines for tailoring porosity in membranes and adsorbents, such that desired separations are achieved.