Statistical reinterpretation of dielectric relaxation models

Abstract

Modeling the correct relaxation behavior of materials is of great importance to both pure and applied scientists. By considering that the electrical interaction between the relaxing species leads to a distribution of relaxation times (RT), it has been shown that the real part of the complex permittivity is linked to the survival function of the random variable RP2/RT, where RP2 follows a Dagum distribution. Also, we proved that the imaginary part of the complex permittivity is linked to the probability density (pdf) of the random variable IP/RT, where IP follows a One-sided Cauchy distribution. These results have been used to obtain general relations involving the distribution of relaxation times and the measured values of complex permittivities. A simple procedure has been proposed to obtain the pdf of RT by estimating the Mellin transform of the random variables involved from experimental data. Finally, Kramers–Kronig equations are deduced based on this new statistical framework. By relating complex permittivities to known random variables, a new understanding of these physical quantities is proposed.