Modeling of Proton Conductivity through Perfluorosulfonate Acid Electrolyte Membranes

Proton conductivity (σ) through perfluorosulfonate acid (PFSA) polymer electrolyte membranes was modelled from the unsaturated hydraulic conductivity, which was described as a power-law function of water content; i.e.,λ^q, where λ is the water content and the exponent q is a porosity factor. In this study, the membrane was modeled as a network of nanopores with the anionic groups (i.e., –SO₃^–) assumed to be fixed along the pore wall according to an indeterminate distribution consistent with the material’s equivalent weight (EW) and dry membrane density. The transport of the hydronium ions inside the porous network was expressed using the extended Nernst-Einstein equation, which was modified using continuum percolation theory to reveal the relevant transport mechanisms at different water contents and temperatures. The power q in the modification was compatible with the critical path analysis simulation results; i.e., q=1.28±0.07 in two dimensions and q=1.86±0.19 in three dimensions, depending singularly on the dimensionality of the transport system. The average electrical conductivity of the membrane was deduced in terms of the following quantities: water content, equivalent weight, and the nature of the perfluorosulfonate acid polymer side chain.  Theoretical predictions of this model were compared against experimental data of conductivity for four different membranes: DuPont’s Nafion 117 (EW = 1100), Membrane C (EW = 900) of Chlorine Engineers Corp., Japan, Dow Chemical’s XUS 13204.10 (EW = 800), and a 3M membrane developed by 3M Corp. (EW = 1000) for different water contents and temperatures. The theoretical predictions of the model matched the experimental data with reasonable quantitative accuracy in most cases.