Proton transfer in a single pore of a polymer electrolyte membrane

We discuss the principles determining the activation of proton hops in pores of polymer–electrolyte membranes and calculate the electrostatic contributions to the activation Gibbs energy. For this purpose, we explore a model of a flat water filled pore with charged sulfonic groups on the surfaces. We find that when the proton transport takes place along the array of sulfonic groups, the contribution of the work terms due to the proton charge interaction with sulfonic groups is large. In the central region of the pore, where the proton transport proceeds in a bulk-like fashion the work terms vanish. Moreover, the activation energy of the hopping along the surface increases considerably with the average distance between the sulfonic groups. Squeezing the pore leaves no room for bulk like proton transfer and, though the effect on the solvent reorganization energy may be small, the overall effective activation energy increases strongly. This is in line with the observed effect of decreasing water content on membrane conductivity.