Relationship between Ionic Mobility and Segmental Mobility in Polymers in the Liquid State

Abstract

Temperature and pressure dependences of the ionic d.c. conductivity σ(∞σ) and the segmental mobility (∞τ−1) were analysed in terms of the WLF and the Ferry–Stratton(FS) equations, respectively, where τ is the dielectric relaxation time for the segmental motion above the glass transition. The WLF parameter C2 for σ is nearly equal to that for τ−1, and the FS parameter b2 for σ is also nearly equal to that for τ−1 in some cases. In the other cases, however, this does not hold. If τ−1 and the ionic mobility μ are assumed to be described by the same C2, the former cases correspond to a constant carrier density and the latter to variable carrier density. In the case of constant carrier density, the relation σ(T, P) [τ(T, P)]m=const. is derived from experimental results. This is designated as a “modified Walden’s rule.” The exponent m is given by the ratio C1(σ)/C1(τ−1) or b1(σ)/b1(τ−1). The physical meaning of m is the ratio of critical hole size for ionic charge transport to that for the segmental motion.