Poroelectroelastic theory of water sorption and swelling in polymer electrolyte membranes

This paper presents a novel poroelectroelastic model of equilibrium water sorption and swelling in polymer electrolyte membranes. These phenomena determine transport properties, electrochemical performance, durability and lifetime of the membrane in a polymer electrolyte fuel cell. Based on a consistent treatment of thermodynamic equilibrium conditions, involving capillary, osmotic and elastic effects, we establish the equation of state of water in a single membrane pore. It relates the charge density at the pore walls to a microscopic swelling parameter. Extended to the water sorption equilibrium in a pore ensemble, the model reconciles microscopic swelling in a single pore with macroscopic swelling of the membrane. Theoretical relations are developed that rationalize the impact of external conditions, statistical distribution of anionic head groups and elastic properties of the polymer on water sorption and swelling. The model resolves Schröder's paradox and other unexplained phenomena related to water sorption equilibria, pressure distribution, and transport properties in PEM.