On dielectric data analysis - Using the Monte Carlo method to obtain relaxation time distribution and comparing non-linear spectral function fits

In this paper, we present a technique for analyzing dielectric response data in the frequency domain, chi(omega) = epsilon(omega) - epsilon (infinity) = epsilon '(omega) - epsilon (infinity) - i epsilon "(omega). We use a predistribution of relaxation times and reconstruct the original data by single Debye relaxations using a box constraint, least squares algorithm. The resulting relaxation times tau (Di), and their amplitudes Delta epsilon (i), yield the relaxation time spectrum, where i is equal or less than the number of data points. Two different predistributions of relaxation times are considered, log-uniform and adaptive. The adaptive predistribution is determined by the real part of the dielectric susceptibility chi ', and it allows for the increase of the number of effective relaxation times used in the fitting procedure. Furthermore, since the number of unknowns is limited to the number of data points, the Monte Carlo technique is introduced. In this way, the fitting procedure is repeated many times with randomly selected relaxation times, and the number of relaxation times treated in the procedure becomes continuous. The proposed method is tested for 'ideal' and measured data. Finally, the method is compared with a nonlinear curve fitting by a spectral function which consists of three contributions, i.e. the Havriliak-Negami relaxation polarization, low frequency dispersion and de conductivity It has been found that more information can be obtained from a particular data set if it is compared with a nonlinear curve fitting procedure. The method also can be used instead of the Kramers-Kronig transformation.