A novel transport model for sorption and desorption of penetrants in dense polymeric membranes

The transport of penetrants in polymeric membranes is assumed to be a process of mixing of penetrant and polymer molecules, in which a creep strain is induced concurrently. Based on the assumption and combined with the mass conservation equation and phenomenological diffusive flux expression, a new transport model of penetrant in polymeric membrane is established, in which the total change of excess Gibbs free energy is considered as a sum of three parts calculated by the modified Scatchard-Hildebrand model, Flory-Huggins theory and linear viscoelastic theory, respectively. The partial difference equations in the model are solved by implicit finite difference method of Crank-Nicolson form, and the model parameters are optimized by simplex algorithm. The model is used to calculate various diffusions (Fickian diffusion, and non-Fickian diffusion) of ethanol in polyphthalazine ether sulfone (PPES), and polyphthalazine ether sulfone ketone (PPESK) membranes at 293.15, 298.15, and 303.15 K. The calculated results are in agreement with the experimental data and the maximal relative deviation is no more than 10.54% and the average relative deviation is 4.35%.