Diffusion coefficients of conductive ions in a copolymer of vinylidene cyanide and vinyl acetate obtained from dielectric measurements using the model of Trukhan

Abstract

The dielectric dispersion measurements of Furukawa et al. are treated in the light of a previously proposed model of Trukhan. The latter describes the influence of mobile ions on the dielectric dispersion in a slab of material placed between polarizable electrodes. It is shown that the so-called ‘‘constant phase element’’ is just a crude approximation to the predictions of the theory of Trukhan, an approximation not valid at very low frequencies. At low frequencies macropolarizations appear analogous to the ones observed in asymmetric cellulose acetate membranes by Malmgren-Hansen et al. The polarizations are much larger in the present case, and this indicates that there are no microheterogeneities in the polymeric film of Furukawa et al. The diffusion coefficient of the most rapidly diffusing ion (presumably H+) may be found as a function of temperature within some uncertainty. The Arrhenius plot shows clearly the change in activation energy around the glass transition temperature (182 °C). Below the glass transition the activation energy for diffusion is much larger (∼50000 K) than above. The diffusion coefficients increase from ∼10−17 m2/s at 170 °C to ∼5.10−16 m2/s at 195 °C. The concentration of electrolyte present in the polymer increases from ∼15 to ∼200 mol m−3 in the same temperature interval.