Analytic scaling functions applicable to dispersion measurements in percolative metal-insulator systems

Scaling functions, F+(omega/omega(c)(+)) and F-(omega/omega(c)(-)) for phi>phi(c) and phi<phi(c), respectively, are derived from an equation for the complex conductivity of binary conductor-insulator composites. It is shown that the real and imaginary parts of F+/- display most properties required for the percolation scaling functions. One difference is that, for omega/omega(c)<1, Re F-(omega/omega(c)) has an omega dependence of (1 + t)/t and not omega(2) as previously predicted, but never conclusively observed. Experimental results on a graphite-Boron nitride system are given, which are in reasonable agreement with the omega((1 +t)/t) behavior for Re F-. Anomalies in the real dielectric constant just above phi(c) are also discussed. [S0163-1829(98)07443-8].