Analytic Scaling Functions Applicable to Dispersion Measurements

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 $F_{\pm}$ 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 $\omega ^{(1+t)/t}$ behaviour for $\Re F_-$. Anomalies in the real dielectric constant just above $\phi_c$ are also discussed.