A concentration-dependent diffusion coefficient model for water sorption in composite

The phenomenon of diffusion coefficients depending on concentration has been observed and studied experimentally for many years. This is particularly the case for the inter-diffusion in metals [1] but has also been observed on various polymeric systems [2]. This study presents a concentration-dependent diffusion coefficient model for water sorption in a polymer matrix composite. It has been developed by studying the water uptake of a polyphthalamide short glass fiber reinforced material. According to experimental data, we postulate that the diffusion coefficient follows a modified Arrhenius equation with a concentration dependence of the pre-exponential factor but also of the activation energy. This choice is related to the evolution of the glass transition temperature during sorption, which has a profound influence on transport properties. The coupled partial differential equation of the model is solved for some applied examples by using an easy-to-implement finite difference scheme.