Non-Debye and CPA Behaviors of Ionic Materials

Abstract

Non-Debye and constant-phase-angle (CPA) behaviors associated with the bulk and interfacial processes involving ionic materials are discussed in terms of complex impedance, admittance, and dielectric spectra. The yielding of a CPA and/or a broad non-Debye dielectric loss peak in a spectrum from fractal, pore, and ion-hopping models are compared and reviewed. The observed wide frequency ranges of the CPA behavior suggest that the fractal and pore models, which require a wide range of special structures down to very fine scales, may not be realistic. The ion-hopping model treats the bulk and interfacial processes as a chemical reaction having a thermally-activated Arrhenius form. Because of thermal fluctuations, the activation energies for ion hopping (e.g., in a potential double-well) have a double-exponential distribution which yields a non-Debye dielectric loss peak and a CPA spectrum over a wide frequency range above the loss peak. The distribution also has a special temperature dependence which may explain the invariance of dielectric spectral shapes with temperature, an observation by Joscher. The construction of CPA elements (in a generalized Warburg impedance form) using three distinct types of resistor-capacitor networks are presented and used to aid the discussion.