Determination of a distribution of relaxation frequencies using a combination of time and frequency dielectric spectroscopies

Recently it has been shown that the natural scale for a distribution of relaxation frequencies is a logarithmic one, provided that there is a distribution of activation energies and that these energies are related to frequency through an Arrhenius type equation under isothermal conditions. Under those conditions a new approach to dielectric relaxation has been formulated, enabling the numerical calculation of the distribution of relaxation frequencies underlying the experimental data taken from the time and/or from the frequency domains. In this communication we try to solve the following practical problem: suppose that measurements of permittivity are performed in a certain frequency range [f_i, f_f] while depolarization current measurements are obtained in a given data window [t_i, t_f]. These experimental windows are such that there is a superposition regarding the corresponding windows of the distribution function of relaxation frequencies. We will propose a procedure to extract the overall underlying distribution of relaxation frequencies consistent with both sets of experimental data. It should be pointed out that, while using this approach, careful attention should be paid to the contribution of the conduction current to the imaginary part of dielectric constant which does not appear in a discharge current type of measurement