The nature of proton transport in fully hydrated Nafion®

The diffusion of protons has been studied in fully hydrated Nafion® with a recently constructed non-equilibrium statistical mechanical transport model. Radial cross-sectional profiles of the effective friction and diffusion coefficients were computed in an electrolyte membrane pore with a hydration of 22.5 water molecules per sulfonic acid fixed site. Input parameters were taken from recent SAXS measurements of the hydrated membrane and electronic structure calculations of water clusters with CF3SO3H, the associated acid for the side chain termination. The calculations revealed that the effective friction coefficient increases by more than two orders of magnitude as the proton is brought from the center of the pore to within 4 Å of the fixed sites. The model calculated a diffusion coefficient of 1.92 × 10−9 m2 s−1, without ‘fitting’ any parameters, for a proton moving along the pore center, in good agreement with experimental measurements. In addition, the model also identified a predominantly vehicular transport mechanism in regions of the cross section of the pore where the proton is within 12 Å of the pore wall. This was distinguished from the central region of the pore (within 4 Å of the center axis) where a component of the conduction is via the Grotthuss mechanism. This investigation has demonstrated the applicability of this transport model in the prediction of diffusion coefficients in fully hydrated membranes.