Diffusion in Polymers with Concentration Dependent Diffusivity

Diffusion coefficients of several solute-polymer systems can be characterized by an exponentially dependent function D = D 0Exp(AC). The cumulative mass uptake after a step increase of the solute concentration at the surface was considered using a film with a finite thickness and a semi-infinite domain. For finite film the diffusion equation was solved numerically by the Crank—Nicholson method. The results showed that at the beginning stage the mass uptake is proportional to √ for both constant diffusivity and concentration dependent diffusivity. For a semi-infinite domain a transformation of variables led to a nonlinear second order ordinary differential equation which can be solved numerically to obtain the concentration function. The results of mass uptake using the Crank—Nicholson calculation on a finite thickness agree with the results of a semi-infinite calculation in the short time region. It is concluded that the diffusion coefficient as a function of concentration can be determined experimentally from the results of short-term absorption using a series of solute concentrations.