Impact of Nano- and Mesoscales on Macroscopic Cation Conductivity in Perfluorinated-Sulfonic-Acid Membranes

A mean-field local-density theory is outlined for ion transport in perfluorinated-sulfonic-acid (PFSA) membranes. A theory of molecular-level interactions predict nano domain and macroscale conductivity. The effects of solvation, dielectric saturation, dispersion forces, image charge, finite size, and confinement are included in a physically consistent 3D-model domain geometry. Probability-distribution profiles of aqueous cation concentration at the domain-scale are in agreement with atomistic simulations using no explicit fitting parameters. Measured conductivities of lithium-, sodium-, and proton-form membranes with equivalent weights of 1100, 1000, and 825 g/mol(SO3) validate the macroscale predictions using a single-value mesoscopic fitting parameter. Cation electrostatic interactions with pendant sulfonate groups are the largest source of migration resistance at the domain-scale. Tortuosity of ionically conductive domains is the largest source of migration resistance at the macroscale. Our proposed transport model is consistent across multiple length scales. We provide a compelling methodology to guide material design and optimize performance in energy-conversion applications of PFSA membranes.