High performance of polymer-electrolyte fuel cells requires rapid cation conduction through perflurosulfonic-acid (PFSA) membranes. Consequently, understanding water and aqueous cation transport in aqueous nanoscale domains (nano length scale) and connectivity and tortuosity of the microscale domains (meso length scales) is critical to optimizing PFSA membrane design. Due to transport coupling, membrane ionic conduction depends not only on electrostatic potential gradients but also on water content gradients (i.e. electro-osmosis). In this work, we model coupled cation and water transport in PFSA membranes at the nano- and mesoscale and predict macroscopic properties.

We adopt a mean-field local-density theory for cation and water chemical potentials to predict transport in the nanoscale PFSA aqueous domains. Cation-polymer electrostatic interactions and solvation energy are included. Concentrated solution transport theory (Stefan-Maxwell formulation) models diffusion and specifically accounts for dielectric friction induced by the strong electrostatic fields of charged polymer groups. To model the mesoscale, a resistor network that includes Stefan-Maxwell coupling quantifies transport along the segments of the collection of aqueous domains in PFSA membranes. The nanoscale model parameterizes the properties of each segment of the resistor network.

With this methodology, we decouple the influences of nano- and mesoscale resistances on macroscopic water and cation transport and electro-osmosis. At the nanoscale there is coupling between water and cation transport from both diffusional drag and electrostatic-driven convection. Electrostatic and pressure forces on the membrane are countered by immobilization of the polymer matrix. The models show the nature of electro-osmosis depends on water content and the vapor and electrostatic potential boundary conditions of the membrane. This work provides a compelling approach to elucidate the multiscale resistances to water and cation transport in PFSA membranes.