Trap-controlled fractal diffusion model of the Havriliak-Negami dielectric relaxation

Abstract

A new model of non-Debye dielectric relaxation, which leads to the popular in broadband dielectric spectroscopy Havriliak-Negami expression for two-power-law dielectric response, is proposed. The new model is based on the multiple trapping model and the fractal diffusion model. Explicit analytical expressions for experimentally measured values such as dielectric strength, characteristic relaxation time, and power-law exponents, which include the microscopic parameters of the medium, are obtain. The comparison of the expression for the relaxation time with the experiment is demonstrated. A clear physical interpretation of the power-law exponents of the Havriliak-Negami relaxation function is found, one makes it possible to extend the area application of this function and to use it for the fitting of dielectric data, which exhibit atypical relaxation behavior.