Analytic Scaling Functions Applicable to Dispersion Measurements

Abstract

Scaling functions, $F_+(ω/ω_c^+)$ and $F_-(ω/ω_c^-)$ for $ϕ>ϕ_c$ and $ϕ<ϕ_c$, 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 $ω/ω_c<1$, $\Re F_-(ω/ω_c)$ has an $ω$-dependence of $(1+t)/t $ and not $ω^2$ as previously predicted, but never conclusively observed. Experimental results on a Graphite-Boron Nitride system are given which are in reasonable agreement with the $ω^{(1+t)/t}$ behaviour for $\Re F_-$. Anomalies in the real dielectric constant just above $ϕ_c$ are also discussed.