A program for the fitting of Debye, Cole-Cole, Cole-Davidson, and Havriliak-Negami dispersions to dielectric data

Abstract

The description and interpretation of dielectric spectroscopy data usually requires the use of analytical functions, which include unknown parameters that must be determined iteratively by means of a fitting procedure. This is not a trivial task and much effort has been spent to find the best way to accomplish it. While the theoretical approach based on the Levenberg-Marquardt algorithm is well known, no freely available program specifically adapted to the dielectric spectroscopy problem exists to the best of our knowledge. Moreover, even the more general commercial packages usually fail on the following aspects: (1) allow to keep temporarily fixed some of the parameters, (2) allow to freely specify the uncertainty values for each data point, (3) check that parameter values fall within prescribed bounds during the fitting process, (4) allow to fit either the real, or the imaginary, or simultaneously both parts of the complex permittivity. A program that satisfies all these requirements and allows fitting any superposition of the Debye, Cole-Cole, Cole-Davidson, and Havriliak-Negami dispersions plus a conductivity term to measured dielectric spectroscopy data is presented. It is available on request from the author.