Toward a predictive understanding of water and charge transport in proton exchange membranes.

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 H(3)O(+) 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.

Applications of a general random-walk theory for confined diffusion.

A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.