Frequency-dependent diffusion in a spherical cavity: The effects of domain structure on ionic conduction in polymer electrolytes

The effects of domain structure on the low-frequency conductivity response of a polymer electrolyte having low carrier concentration are investigated by modeling the domains as spheres. For zero leakage (no dc conductivity), the diffusion equation is solved exactly. The results are also extended approximately to the case of small but nonzero leakage by imposing physically reasonable approximate boundary conditions together with an ad hoc procedure for treating the diffusion in the less conductive exterior. Interaction between charge carriers in different domains is taken into account in the Maxwell-Garnet approximation and found to have only a small effect for physically reasonable parameter values. The predicted diffusive behavior is studied and the results are applied to examine the predicted behavior of the frequency-dependent conductivity.