Proton friction and diffusion coefficients in hydrated polymer electrolytemembranes: Computations with a non-equilibrium statistical mechanical model

A recently derived mathematical model to compute the effective friction and diffusion coefficients of hydronium ions in hydrated polymer electrolyte m embranes is described and tested for dependence on membrane-specific parame ters. Contributions to the friction coefficient due to water-polymer, water -hydronium, and hydronium-polymer interactions are determined through compu tation of force-force correlation functions. The conventional Stokes law fr iction coefficient of the hydronium ion in bulk water is then "corrected" w ith these statistically derived contributions and the corresponding diffusi on coefficient calculated. For a Nafion(R) membrane pore with an hydration level of six water molecules per sulfonic acid functional, the model was us ed to compute friction coefficients for various distributions of the fixed sites, and for different side chain lengths. The model showed substantial s ensitivity to these parameters and predicted that for pores of fixed volume and a constant total number of sulfonate groups, the friction on the hydra ted proton is the greatest for distributions with high local anionic charge density. In a second series of computations where the radius and length of the pore were varied, the model demonstrated that the proton diffusion inc reases with increasing channel diameter. These calculations, therefore, dem onstrate the important predictive capability of this molecular-based, noneq uilibrium statistical mechanical model. (C) 2001 American Institute of Phys ics.