Analysis of polarization dynamics by singularity decomposition method.
The driving point immittance (impedance or admittance) function is commonly used in electrical characterization of polarized materials and interfaces. The immittance function typically attenuates following a power function dependence on frequency. This fact has been recognized as a macroscopic dynamical property manifested by strongly interacting dielectric, viscoelastic and magnetic materials and interfaces between different conducting substances. Linear interfacial polarization processes which occur at metal electrode-electrolyte interfaces have been represented by the Fractional Power Pole [FPP] function in single or multiple stages. The FPP function is referred to as the Davidson-Cole function in the dielectrics literature. A related function widely used in mathematical modeling of dielectric and viscoelastic polarization dynamics is the Cole-Cole function. The fractional power factor which parametrizes the FPP or the Davidson-Cole function has been shown earlier to equal the logarithmic ratio of the locations of the pole-zero singularities. In this paper we first review a modified form of the singularity decomposition of the FPP function accomplished within a prescribed error range. The distribution spectrum and the corresponding simulation by a cascade R-C network, as opposed to the synthesis by a ladder R-C network, are readily obtained as the next step in the simulation. The method is then applied to decompose the Cole-Cole function; the pole-zero placement of the singularity function is determined and the equivalent cascade R-C network is synthesized.