Electrophysical Properties of Polymer Electrolyte Membranes: A Random Network Model

Abstract

A random network model of charge transport in porous polymer membranes is proposed and investigated by means of an effective medium theory. Specific conductivity and geometrical capacity (dielectric constant) of membranes are calculated in dependence of water content, taking swelling effects into account. The conductivity shows a quasi-percolation type dependence, growing above a certain critical water content, while taking below it a value typical of residual conductivity in dry membranes. The geometrical capacity can show an increase with water content or it can undergo a maximum at the percolation threshold, depending on the model parameters. The theoretical findings are in line with experimental observations of the membrane complex impedance as a function of water content. The results suggest a frame for classification of different types of polymer membranes with regard to their performance, depending on swelling properties.