Reply to comments on the need to reconsider traditional free volume theory for polymer electrolytes

Abstract

New aspects of the defect diffusion model (DDM) are presented. First, it is shown that if the correlation volume exhibits two dimensional scaling, e.g. grows in two dimensions more rapidly than in a third orthogonal direction, the standard Vogel relation is obtained. Second, it is pointed out that, independent of the dimensionality, ∂ ln σ/∂ P should be proportional to ∂ ln σ/∂ ln T where the proportionality constant is −∂ ln T c/∂ P. It is shown that both of these results are consistent with the temperature and pressure variation of the electrical conductivity for 20:1 PPG:LiCF 3SO 3 below about 1.3 times the glass transition temperature, T g. Finally, the DDM is compared with the free volume theory (FVT) of Dlubek et al. who have reconsidered “traditional” FVT and presented a formalism where the free volume is not proportional to the macroscopic volume. One aspect of the new FVT, which is difficult to understand is that the compressibility of the occupied volume is larger than the compressibility of the free volume.