A number of models for CPA impedances of conductors and for relaxation in non-Debye dielectrics

Abstract

The impedance, admittance, or permittance diagrams of materials, when presented in the complex plane, are often well defined straight lines, or well defined semi-circles with axes depressed below the real axis. Using a general theoretical approach, it is suggested that this behavior is not characteristic of a single particular phenomenon or theory (hence, not characteristic of fractal geometry for example). The potential difference, V( t), causing a current, I( t), to flow in any type of electrical circuit, can be expressed in terms of the ‘fractional derivative’ of the current: V = Pfrsol| Pd vgn I/ dt ν where P (‘phasance’, magnitude) and ν (degree of fractional derivation) depend on the physical properties. A particular case corresponds to constant P and ν, to a constant energy efficiency, to a straight line on the complex impedance diagram and to the ‘constant phase angle’ (CPA) behavior. As an example, the direct application of the mathematical theory leads to several simple and exact distribution functions of relaxation times and a number of models for non-Debye dielectrics.