The transport of gases in a supported mesoporous silica membrane

Abstract

We investigate the low pressure transport of several gases in a disordered mesoporous silica membrane of mean pore diameter 3.70nm, deposited on a porous tubular asymmetric support. The transport data for the supported membrane is examined using three different diffusion models, the classical Knudsen model, a version corrected for finite molecular size, as well as the Oscillator Model developed in this laboratory, using a representative pore size in each layer. We show that the correlation by the Knudsen approach, or its modification for finite molecular size, overestimates the diffusion coefficient in the membrane layer, and yields unrealistically high tortuosities, which vary with temperature and gas species. The apparent tortuosity is significantly reduced to a more reasonable range based on the Oscillator Model, which accounts for dispersive fluid–solid interaction and the effect of adsorption on the transport. In order to overcome the lack of transferability associated with fitting of a variable tortuosity, effective medium theory is used to model the transport in the different layers, while considering the entire pore size distribution for each layer, using only fundamental structural parameters. It is found that the classical and corrected Knudsen models yield significant deviations even with an unrealistically high thickness for the membrane layer, due to the overestimation of the diffusivity. The most satisfactory results are obtained with the Oscillator Model, in which the fitting error is significantly reduced with acceptable membrane thickness. The results indicate that the Knudsen model fails to represent the transport for the mesopores of mean size of 3.70nm in silica, and that the Oscillator Model provides a more accurate apparent diffusivity which accounts for the effects of adsorption. We also show that use of the effective medium theory provides a satisfactory option to model the transport, using only fundamental structural parameters that are transferable.