Direct determination of concentration-dependent diffusion coefficient in polymeric membranes based on the Frisch method

Abstract

In addition to gas permeation simulation in polymeric membranes, much progress has been attained on the theories whereby the mechanisms of transport are described. In this way, numerous studies are assigned to achieve methods for determination of diffusion coefficient. Consequently, some correlated equations are obtained which consider diffusivity dependency on concentration, position or time, or any conjunction of them. Compared to the traditional time lag, a comprehensive approach developed by Frisch gives a general mathematical procedure for achieving the concentration dependent diffusion coefficient, disregarding the effect of membrane physical properties. In this study, a comprehensive algorithm is presented for direct determination of diffusion coefficient. It determines diffusion coefficient by two approaches: first, through the traditional time lag method, and second, considering the concentration dependent system. A comprehensive mathematical model was developed and solved for CO 2 gas permeation through a nonporous polymeric membrane. The results showed that considering the concentration dependent system (CDS) for diffusion coefficient led to the small deviation of about 13%, while the deviation of 360% by the concentration independent system (CIS) was acquired. Finally, a reasonable conformity between the predicted values based on concentration dependant method and experimental data was perceived.