Modelling Proton Conductivity in Perfluorosulfonate Acid Membranes

Abstract

Proton conductivity through perfluorosulfonate acid (PFSA) polymer electrolyte membranes was investigated using a nanoporous network model, which was developed for the purpose of quantitatively describing transport of charged species through typical PFSA fuel cell membranes. The membrane was modeled as a collection of random fractal nanopores with the anionic groups (i.e., –SO3–) assumed to be fixed along the pore wall according to a distribution determined by the equivalent weight and dry membrane density. The transport of the hydronium ions inside the pore was expressed using a simplified Nernst-Einstein equation. Continuum percolation theory and a fractal structural transport model were used to modify the diffusion coefficient and illustrate the transport mechanism. The conductivity of the membrane was deduced in terms of the following quantities: water content, equivalent weight, temperature, and the architecture of the PFSA polymer side chain. Theoretical predictions of the model for varying water content and temperature were compared against experimental data of conductivity for four membranes: Nafion 117 (EW = 1100, a long side chain with a pendant CF3 group), Membrane C (EW = 900, same side chain as Nafion, but with a shorter backbone repeat unit), a 3M membrane (EW = 1000, long side chain without a pendant CF3 group), and Dow's XUS 13204.10 (EW = 800, same as the 3M membrane, but with shorter backbone unit and side chain). The theoretical predictions of the model matched the experimental data with reasonable quantitative accuracy in most cases.