Dimensions of the distribution of dielectric relaxation time: 1D versus 2D

The extraction of the relaxation time distribution, G(ln(tau)), from Broad Band Dielectric Spectroscopy can be done in two ways. A one dimensional (1D) distribution is extracted from the variation of epsilon*(omega) as a function of frequency, omega, at constant temperature, T. epsilon*(omega) is considered as the sum of elementary Debye functions, each one characterized by a single relaxation time, tau, and contributing according to G(ln(tau)) to the global spectrum. On the other hand, if the variation of epsilon*(omega, T) with the temperature T is performed, a temperature dependence for the relaxation time with temperature has to be considered which can be either Arrhenius, which is appropriate for secondary relaxations in polymers or Vogel-Fulcher, mostly used for the segmental relaxation. A two dimensional (2D) distribution, G(E, tau(0)), is then obtained where E is the reorientation energy and tau(0) a pre-exponential factor and each (E, tau(0)) pair defines a Debye function. In this work, the Monte Carlo Simulated Annealing Direct Signal Analysis (SADSA) procedure is used to extract the 1D and/or 2D relaxation time distribution. The SADSA procedure finds the best and less structured set of Debye functions that describes the experimental data in the isothermal case and when both w and T are variable. The method is applied to simulated data generated with Gaussian distributions in E and tau(0) and the 1D and 2D distributions obtained are compared in their capacity to model the data.