Model of Water Sorption and Swelling in Polymer Electrolyte Membranes: Diagnostic Applications

This work expands on the poroelectroelastic model of water sorption in polymer electrolyte membranes. It links membrane water sorption and the evolution of the pore size distribution with the microscopic charge density distribution at pore surfaces and the microscopic shear modulus of polymeric pore walls. We evaluate different deformation modes of polymeric pore walls to derive stress-strain relationships that determine the law of swelling. Thereafter, the model is applied to different sets of water sorption data for membranes that were submitted to either hygrothermal aging or chemical degradation. The model-based analysis relates the macroscopic state of swelling to the evolution of the statistical distribution of the pore radius as well as of the microscopic fluid and elastic pressures. Changes in the surface charge density at pore surfaces and elastic pressure of pore walls, induced by degradation, can be rationalized. These insights are useful in view of understanding degradation mechanisms and their structural effects.