The dielectric properties of random R-C networks as an explanation of the 'universal' power law dielectric response of solids

Simulations of the AC electrical characteristics of 2D square networks randomly filled with resistors or capacitors exhibit many features in common with experimental dielectric responses of solids. These include the 'universal' fractional power law dispersions in permittivity and dielectric loss characterized by the Cole-Davidson response function. Simulations are presented of networks containing different proportions of resistors and capacitors which show that the power law frequency response is accounted for well by the logarithmic mixing rule. Limiting high and low frequency characteristics are found to be controlled by percolation paths of either resistors or capacitors. It is suggested that the power law response of a solid could be an indication that it is microscopically inhomogenous, containing an effective microscopic random network of conducting and dielectric insulating islands.