An analysis of dispersion measurements in percolative metal–insulator systems using analytic scaling functions

Abstract

Continuous analytic scaling functions F +( ω/ ω c+) and F −( ω/ ω c−) for φ> φ c and φ< φ c, are derived from a phenomenological equation for the complex conductivity of binary composites, which reduces to the standard percolation equations in most limits. These scaling functions and the real conductivity, for φ< φ c, are compared with experimental results for several continuum percolation systems. The dispersion exponent for the real conductivity is found to be somewhat greater than 1 and close to (1+ t)/ t. These results also show that the real dielectric constant, as a function of φ, has a frequency-dependent maximum at φ> φ c. These last two results are in conflict with the standard percolation theory.