Evaluation of Molar Volume Effect for Calculation of Diffusion in Binary Systems

Abstract

This article relates the theoretical evaluation of the effect of a molar volume change in the diffusion profile of a binary system. This study is based on the regression fit of a diffusion profile using a selected function in an inverse form. For the calculation of concentration-dependent diffusivity according to the Sauer and Freise (and Wagner) treatment of the Boltzmann-Matano relation, this inverse regression function is further modified by the inclusion of molar volume, which is dependent on the molar composition of a diffusing two-component mixture. Following the conversion of the initial relation to the form that enables the direct integration of the used inverse function, which fits the diffusion profile, the formulas for the analytical calculation of diffusivity are obtained. These formulas are derived both for the linear change in molar volume in the diffusion profile corresponding to Vegard’s rule and for the case of the positive or negative deviations from the linearity representing the swell or shrink course V _m. The analysis results show that the drop and swell shapes of the course of molar volume in a diffusion profile of the binary system increase the resulting diffusivity. Conversely, the increase of V _m and its shrink course are factors that lower diffusivity. The regression function that was used in its inverse form was suitable for fitting the diffusion profile of any asymmetrical shape. The derived relations are therefore practically applicable for the direct analytical calculation of concentration-dependent diffusivity in binary systems.