Mesoscopic non-equilibrium thermodynamics approach to non-Debye dielectric relaxation

TL;DR

This paper develops a mesoscopic non-equilibrium thermodynamics model for non-Debye dielectric relaxation, incorporating memory effects and fractional Fokker-Planck equations to analyze complex dielectric behaviors in glassy and polymer systems.

Contribution

It introduces a novel thermodynamic framework linking memory kernels with fractional Fokker-Planck equations for dielectric relaxation analysis.

Findings

Derived expressions for complex susceptibilities as functions of frequency and wave number.

Compared different memory kernels with experimental data on glassy dielectric relaxation.

Linked relaxation time distributions with segmental motions in polymer melts.

Abstract

Mesoscopic non-equilibrium thermodynamics is used to formulate a model describing non-homogeneous and non-Debye dielectric relaxation. The model is presented in terms of a Fokker-Planck equation for the probability distribution of non-interacting polar molecules in contact with a heat bath and in the presence of an external time-dependent electric field. Memory effects are introduced in the Fokker-Planck description through integral relations containing memory kernels, which in turn are used to establish a connection with fractional Fokker-Planck descriptions. The model is developed in terms of the evolution equations for the first two moments of the distribution function. These equations are solved by following a perturbative method from which the expressions for the complex susceptibilities are obtained as a functions of the frequency and the wave number. Different memory kernels are considered and used to compare with experiments of dielectric relaxation in glassy systems. For the case of Cole-Cole relaxation, we infer the distribution of relaxation times and its relation with an effective distribution of dipolar moments that can be attributed to different segmental motions of the polymer chains in a melt.