Frequency dependence of ionic conductivity in lattice gas models

Abstract

The frequency dependence of the ionic conductivity has been treated based on the relaxation process of ionic current using the pair approximation of the path probability method (PPM) of irreversible statistical mechanics. In order to deal with the time development of the time correlation of the motion of particles, the formalism of the PPM which deals with the flow based on the averaged distribution of particles has been changed to follow the fluctuation of the system with time. This allows us to evaluate the development of the time correlation of the motion of particles in the pair approximation. The Kohlrausch-Williams-Watts type relaxation behavior of ionic current when a constant field is applied at time t=0 can be attributed to the change of the time correlation with time. The Jonscher power-law exponent p is thus derived for several important examples in the pair approximation. In the case of the motion of a tagged particle in the assembly of particles of the same species in a lattice gas model, the results show an excellent agreement with those obtained by the Monte Carlo simulation method.