Analytic Scaling Functions Applicable to Dispersion Measurements

TL;DR

This paper derives and analyzes scaling functions for dispersion measurements in conductor-insulator composites, showing their properties align with percolation theory and providing experimental validation with graphite-boron nitride systems.

Contribution

It introduces analytic scaling functions applicable to dispersion measurements and demonstrates their properties and experimental relevance near the percolation threshold.

Findings

Real and imaginary parts of the scaling functions exhibit properties consistent with percolation theory.

Experimental data on graphite-boron nitride systems support the predicted frequency dependence.

Anomalies in dielectric constants near the percolation threshold are discussed.

Abstract

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.