Analytic Scaling Functions Applicable to Dispersion Measurements

Abstract

Scaling functions, $F_{+}(\omega /{\omega }_c^{+})$ and $F_{-}(\omega /{\omega }_c^{-})$ for $\varphi >{\varphi }_c$ and $\varphi <{\varphi }_c$, 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 ${\varphi }_c$ are also discussed.

26 pages, Latex, 5 postscript figures, to appear November 15 in PhysRev B15