Mechanism and temperature dependence of polymer electrolyte conductivity in terms of dynamic disorder

Abstract

The dynamic disorder theory previously developed for ionic transport in polymer electrolytes is extended to the case of two distinct sequential steps in the transport. It is shown how this can describe in greater detail than before a specific microscopic mechanism usually assumed for cation transport. Expressions are obtained for the frequency and temperature dependence of the charge transport, and various limits are delineated in which the model leads to the same temperature dependence for the cationic conductivity as applies also for the viscosity on a microscopic scale, thereby providing an improved justification within the context of dynamic disorder theory for application of the Vogel–Tamman–Fulcher equation to ionic conduction when it applies to appropriate mechanical properties. An analogous model based directly on the earlier dynamic disorder approach is presented, is shown to be a special case of that considered here, and is shown capable of fitting dc conductivity data for polymer electrolytes in various limiting cases, thereby clarifying the relation between the two models and showing the present theory to be similarly capable of explaining the dc conductivity data considered.