An analytical model for water and charge transport in highly acidic and highly confined systems such as proton exchange membranes of fuel cells is developed and compared to available experimental data. The model is based on observations from both experiment and multiscale simulation. The model accounts for three factors in the system including acidity, confinement, and connectivity. This model has its basis in the molecular-level mechanisms of water transport but has been coarse-grained to the extent that it can be expressed in an analytical form. The model uses the concentration of H3O+ ion to characterize acidity, interfacial surface area per water molecule to characterize confinement, and percolation theory to describe connectivity. Several important results are presented. First, an integrated multiscale simulation approach including both molecular dynamics simulation and confined random walk theory is capable of quantitatively reproducing experimentally measured self-diffusivities of water in the perfluorinated sulfonic acid proton exchange membrane material, Nafion. The simulations, across a range of hydration conditions from minimally hydrated to fully saturated, have an average error for the self-diffusivity of water of 16% relative to experiment. Second, accounting for three factors—acidity, confinement, and connectivity—is necessary and sufficient to understand the self-diffusivity of water in proton exchange membranes. Third, an analytical model based on percolation theory is capable of quantitatively reproducing experimentally measured self-diffusivities of both water and charge in Nafion across a full range of hydration.
Available at: http://works.bepress.com/david_keffer/12/