Exploring the universal nature of electrical percolation exponents by genetic algorithm fitting with general effective medium theory

Abstract

This paper considers the nature of the electromagnetic response of percolating conductor–insulator composites in the critical region near the percolation threshold. It is demonstrated how the filler fraction and frequency dependence of the complex permittivity for these composites can be matched to McLachlan's general effective medium theory using a genetic algorithm fitting process to obtain values for the percolation threshold, percolation exponents, s and t, and the filler particle conductivity. Good estimates of these parameters can be obtained from broadband permittivity spectra of, as few as, two composite formulations. The use of genetic algorithm techniques enables the uniqueness of the fit parameters to be considered, as the genetic algorithm method is robust in terms of finding globally optimum solutions. It was hypothesized that non-universal exponents could be offset by ambiguity in the filler conductivity. For example, contact resistance effects could reduce filler conductivities below their bulk values. The genetic algorithm technique employed is described and it is demonstrated that the best fit values for fit parameters are unique. Thus, confidence can be placed in non-universal values of the percolation exponents.