Mechanics-based model for non-affine swelling in perfluorosulfonic acid (PFSA) membranes

A mechanics-based model is developed to predict the swelling pressure in perfluorosulfonic acid (PFSA) ionomer membranes during water uptake. The PFSA membrane is represented as a two-phase system, where the water-filled hydrophilic domains are dispersed throughout the hydrophobic polymer matrix. Two representative volume elements (RVEs) are used to represent the nanostructure: (i) a spherical RVE with a spherical hydrophilic domain at the center, and (ii) a cylindrical RVE with a cylindrical hydrophilic domain. The model starts with the non-affine swelling behavior of the membrane and interprets this as a structural reorganization of the RVEs to characterize the microscopic deformation. Swelling pressure is then determined as a function of water volume fraction and temperature for both RVEs. Using the resulting relationship between the swelling pressure and water volume fraction, theoretical sorption isotherms are generated. The results suggest that with increasing temperature, the constraining pressure due to the deformation of the polymer region decreases and therefore, water uptake in a vapor-equilibrated PFSA membrane increases. This relationship is consistent with previously-reported experimental data. The model can also account for the effect of residual water in the membrane - which is associated with the membrane's thermal history - on the sorption behavior. The proposed continuum mechanics model can serve as a tool for deeper understanding of the sorption behavior of PFSA by bridging the gap between the molecular level descriptions and the experimental observations of macroscopic swelling.