Hydration and Proton Conductivity of Ionomers: The Model Case of Sulfonated Aromatic Polymers

The hydration of proton-conducting ionomers is described in terms of a simplified model, where only osmotic and elastic contributions to the Gibbs free energy of hydration are considered. Although only two physically meaningful parameters are used - the deformation parameter, inversely proportional to the elastic modulus of the ionomer, and the free volume parameter – simulated hydration isotherms are in good agreement with the experiment. The proton mobility u inside the electrolyte solution of the ionomer is calculated from the proton conductivity determined at various hydration numbers. Its variation with the proton concentration c reveals the percolation threshold of hydrated nanometric channels and the tortuosity of the membrane. Above the percolation threshold, a power law u ~ c-3 is observed, in agreement with the “universal” law for 3-dimensional percolation. The proton conductivity  shows at 100°C a maximum of 0.2 S/cm at a hydration number ~90. The  = f(c) plot allows to predict which hydration conditions are necessary for a desired area specific resistance.