Relaxation spectra of the Warburg impedance and the constant-phase elements

It is shown that there is indissoluble connection of impedances of constant-phase elements (CPE) with the presence, in a system, of a continuous spectrum of intrinsic frequencies inside a region where an impedance of CPE is observed. Such a connection exists in objects of any nature. As a result, the inevitable presence of the minimum limiting relaxation frequencies in real systems distorts the frequency characteristics of an ideal impedance of CPE in the zone where intrinsic frequencies are absent (restricts CPE). A transition zone of frequency characteristics of restricted CPE is studied. A false effect of the deviation of the CPE power index determined experimentally from a Nyquist plot from its true value is shown. A technique is proposed for restoring true values of CPE power indices and estimating limiting frequencies of relaxation spectra lying by many orders of magnitude lower than the minimum frequencies available for an experimental setup.