# Comments on frequency dependent ac conductivity in polymeric materials at low frequency regime

## TL;DR

This paper analyzes dielectric spectroscopy data of polymeric materials at low frequencies, clarifying the origins of the apparent power exponent values and their relation to charge dynamics and molecular relaxations.

## Contribution

It provides a detailed interpretation of the frequency-dependent AC conductivity and dielectric loss, explaining the occurrence of power exponents greater than 1 in terms of molecular dipolar relaxations.

## Key findings

- Apparent power exponent n ranges from 0 to 1, related to charge mobility.
- Values of n between 1 and 2 are due to molecular dipolar relaxations.
- Minimum in dielectric loss plots indicates separation of conduction and relaxation mechanisms.

## Abstract

The AC conductivity response in a broad frequency range of disordered materials is of great interest not only for technological applications, but also from a theoretical point of view. The Jonscher power exponent value, and its temperature dependence, is a very important parameter in dielectric data analysis as well as the physical interpretation of conduction mechanisms in disordered materials. In some cases the power exponent of AC conductivity has been reported to be greater than 1 at the low frequency regime. This fact seems to contradict the universal dynamic response. The present work focuses on the analysis of dielectric spectroscopy measurements in polymeric materials, below 100 MHz. The apparent power exponent n gets values in the range (0,1) and is directly related to the characteristics of mobile charges at shorter time scales, in the case of the occurrence of DC conduction and the slowest polarization mechanism that is due to the charge motions within sort length scales, in log(epsilon'')-log(frequenvy) plot. The emergence of apparent n values in the range [1,2], for a relatively narrow frequency range, may be attributed to an additional molecular dipolar relaxation contribution at higher frequencies, in log(epsilon'')-log(frequency) plot. The appearance of apparent n values in the range (1,2], can be assigned to the existence of a well defined minimum between DC conductivity contribution and a molecular dipolar dispersion or between two well separated dielectric loss mechanisms, in log(epsilon'')-log(frequency) plots, above the crossover frequency. In these latter cases, the apparent power exponent n is merely related to the Havriliak-Negami equation shape parameters of the higher frequencies molecular dipolar relaxations.

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Source: https://tomesphere.com/paper/1803.08133