Ionic conductivity threshold in sulfonated poly (phenylene oxide) matrices: a combination of three-phase model and percolation theory

Abstract

In this paper, both the percolation theory and the three-phase model (TPM) are employed to study the ionic transport behavior in sulfonated poly(phenylene oxide) (SPPO) series membranes. The conductive fraction was obtained from TPM, which had considered contributions of both the functional group and the neutral electrolytes impregnated in the polymer gel. The critical threshold at which the ions can be transported through the membrane or the membrane transit from insulator to a conductor, was calculated by the experimental data of membrane conductivities with different sulfonation degrees. The results showed that the threshold changed slightly from 0.14 to 0.19 when the concentration ranges from 0.01 to 0.1. Since the threshold is mainly determined by the active group zone and distribution, so a geometrically average value 0.16 is reasonably assumed here. This assumption coincides with the TPM which states that inter-gel fraction is not related with external concentration but related with the membrane properties. This experimental threshold is a little greater than the ideal value of 0.15 for a complete random system, suggesting that these ion cluster phases containing functional groups are not randomly dispersed in a practical SPPO membrane. If contribution of inter-gel is not considered, we will get a slightly larger value 0.18 as described in the previous paper. Therefore, a combination of TPM and percolation theory can bring us more precise information on ionic transport in SPPO matrices.