Numerical simulation method for identification of experimental results according to frequency dispersion of dielectric permittivity by Havriliak-Negami

One of the problems physics of dielectrics which has not yet been completely solved the determination of the form of the frequency dispersion of the dielectric constant. For relaxation mechanisms of polarization of dielectrics, there are many mathematical models. In practice, when analyzing experimental results, parameters are selected that correlate the results obtained with the proposed models. The goal of this paper is to search for basic equations to create a rapid method for identifying experimental results with the Havriliak-Negami model. The paper analyzes the influence of the parameters alpha and beta in the dispersion model of Havriliak-Negami for relaxation dielectric permittivity by the method of numerical simulation. The tangents of the slope angle lg epsilon(rel)'' rel are analyzed as functions of log omega at omega <1/tau and omega > 1/tau, and resolving formulas for alpha and beta are obtained on the basis of these relationships. The relaxation time is found from the condition of independence from alpha and beta on the basis of the analysis of the function epsilon(rel)''/(epsilon'-epsilon(infinity)). The values of epsilon(S) and epsilon(infinity) are found on the basis of the polynomial representation of the Argand (Cole-Cole) diagrams.