AC and DC conductivity correlation: The coefficient of Barton--Nakajima--Namikawa relation

TL;DR

This paper derives a theoretical relation linking AC and DC conductivity using Havriliak--Negami functions, revealing how the coefficient depends on material parameters and temperature, with validation through experiments on polymers.

Contribution

It provides a new theoretical derivation of the Barton--Nakajima--Namikawa relation, detailing how the coefficient depends on dielectric shape parameters and ion dynamics.

Findings

The coefficient depends on Havriliak--Negami parameters and ion time scales.

Theoretical predictions align well with experimental data.

The coefficient decreases gradually with increasing temperature.

Abstract

It has been some time since an empirical relation, which correlates DC with AC conductivity and contains a loosely defined coefficient thought to be of order one, was introduced by Barton, Nakajima and Namikawa. In this work, we derived this relation assuming that the conductive response consists of a superposition of DC conductivity and an AC conductivity term which materialized through a Havriliak--Negami dielectric function. The coefficient was found to depend on the Havriliak--Negami shape parameters as well as on the ratio of two characteristic time scales of ions motion which are related to ionic polarization mechanism and the onset of AC conductivity. The results are discussed in relation to other relevant publications and they also applied to a polymeric material. Both, theoretical predictions and experimental evaluations of the BNN coefficient are in an excellent agreement, while this coefficient shows a gradual reduction as the temperature increases.