Determination of a distribution of relaxation frequencies based on experimental relaxational data

A possible explanation for the relaxation behavior of many phenomena, and in particular of dielectric polarization phenomena, has been to assume the existence of a distribution of relaxation frequencies instead of a single relaxation frequency. It has been demonstrated that the natural scale for the distribution of relaxation frequencies is logarithmic in frequency axis. This assertion should be valid provided that there is both a relationship, between the frequency and the activation energy, of an exponential type like in an Arrhenius equation, and that a distribution exists in the domain of activation energies. These activation energies could possibly correspond to the energy states of the relaxing entities. A theory is then here presented to show that the product of the elapsed time by the depolarization current is a convolution of the distribution function of relaxation frequencies by a weight function of an asymmetric bell shape. A similar relationship is also shown to exist for the permittivity of a dielectric. Various consequences can be deduced from this theory, among them the determination of a similar relationship to that of the Hamon approximation. In the second part of this paper a deconvolution procedure has been proposed to find the distribution function of relaxation frequencies from experimental data, based on the above theory. Tests for this deconvolution procedure and its associated theory are reported, based on theoretical distribution functions as well as on data taken from previous published work.