On the theory of the universal dielectric relaxation

TL;DR

This paper presents a unified theoretical framework for dielectric relaxation, proposing a universal law that encompasses various known relaxation models as specific cases within a hierarchical response system.

Contribution

It introduces a modified mean field theory that unifies different dielectric relaxation laws under a single universal law based on a hierarchical response model.

Findings

Universal dielectric relaxation law derived from hierarchical response theory

Various known relaxation models are special cases of the universal law

The theory explains the relationship between different relaxation behaviors

Abstract

Dielectric relaxation has been investigated within the framework of a modified mean field theory, in which the dielectric response of an arbitrary condensed matter system to the applied electric field is assumed to consist of two parts, a collective response and a slowly fluctuating response; the former corresponds to the cooperative response of the crystalline or noncrystalline structures composed of the atoms or molecules held together by normal chemical bonds and the latter represents the slow response of the strongly correlated high-temperature structure precursors or a partially ordered nematic phase. These two dielectric responses are not independent of each other but rather constitute a dynamic hierarchy, in which the slowly fluctuating response is constrained by the collective response. It then becomes clear that the dielectric relaxation of the system is actually a specific characteristic relaxation process modulated by the slow relaxation of the nematic phase and its corresponding relaxation relationship should be regarded as the universal dielectric relaxation law. Furthermore, we have shown that seemingly different relaxation relationships, such as the Debye relaxation law, the Cole-Cole equation, the Cole-Davidson equation, the Havriliak-Negami relaxation, the Kohlrausch-Williams-Watts function, Jonscher's universal dielectric relaxation law, etc., are only variants of this universal law under certain circumstances.