Modelling the 0.6 - 0.7 power law of permittivity and admittance frequency responses in random R-C networks

Abstract

The dielectric response of complex materials is characterized, in many cases, by a similar power law frequency dependence of both the real and the imaginary parts of their complex dielectric constants. In the admittance representation, this power law is often shown as the constant phase angle (CPA) response. Apparently, the power that characterizes many different systems, when expressed as the frequency dispersion of conductivity (the real part of admittance) is often found to be in the range of 0.6 - 0.7 or having frequency independent, constant phase angles (CPA) of about 54 - 63 deg. The model suggested here is based on series-parallel mixing of resistors' and capacitors' responses in a random R-C network. A geometric mean evaluation of the effective resistivity of conductors having a uniform distribution of resistivity is used. In contrast to models based on percolation arguments, the model suggested here can be applied to both 2D and 3D systems.