Micromechanical analysis of ionic clustering in Nafion perfluorinated membrane

Abstract

The cluster morphology in a water-swollen Nafion perfluorinated membrane is studied using a micromechanics approach. The cluster size is determined from the minimization of the free energy as a function of the equivalent weight of Nafion, the volume fraction of water, and the temperature, taking into account the electrostatic dipole interaction energy, the elastic polymer chain reorganization energy, and the cluster surface energy, leading to results which are in accord with experimental observations. By minimizing the sum of: (1) the electro-elastic interaction energy between an ionic cluster and the fluorocarbon matrix, and (2) the cluster surface energy, it is concluded that the effective cluster shape is spherical in the absence of an electric field, and becoming an oblate spheroid when an electric field is applied. The effect of cluster morphology on the effective electro-elastic moduli and the effective ionic conductivity is then studied by a micromechanical multi-inclusion model. The result seems to describe the available empirical relation when a spherical cluster shape is assumed. It correctly predicts the insulator-to-conductor transition which occurs in Nafion, as the water volume fraction is increased.