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

Scaling functions, F₊(ω/ωc⁺) and F_-(ω/ωc^-) for φ>φc and φ<φc, 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 ω/ωc<1,ReF_-(ω/ωc) has an {ω} dependence of $(1+t)/t$ and not ω² as previously predicted, but never conclusively observed. Experimental results on a graphite--Boron nitride system are given, which are in reasonable agreement with the ω(1+t)/t behavior for ReF_-. Anomalies in the real dielectric constant just above φc are also discussed.