Distribution function in the description of relaxation phenomena

The experimental results obtained in the field of dielectric spectroscopy a re often insufficiently explained under the assumption of a homogeneously r elaxing dipole system represented by one distinct correlation time. Even in cases where several dipole mobilities exhibit a dielectric relaxation with an exact Debye behaviour to be ascribed to the distinct species of differe nt permanent electric dipoles, respectively, a separation into two or more single contributions of dispersion and absorption responses of the electric permittivity may prove to be unsatisfying. Instead, as for the interlamell ar water adjacent to cell membranes, a distribution of correlation times ha s to be taken into account to describe the experimentally found additional line broadening in the absorption, the less steep slope in the dispersion c urves and the loss of symmetry. Appropiate distribution functions are intro duced and discussed as to their physical relevance. The application of thes e selected distribution functions results in transformed Debye equations. T hus, analogous analytical expressions are obtained that are well adapted fo r a numerical fitting of the parameters containing both the width and the a symmetry of the distribution functions.