Critical Behaviour of Conductivity and Dielectric Constant near the Metal‐Non‐Metal Transition Threshold

TLDR

The study examines a composite of randomly distributed metallic and dielectric regions, including cases with non‑zero dc conductivity in the dielectric phase. The authors introduce critical indices that characterize how conductivity and dielectric constant vary with volume fraction and frequency near the metal‑non‑metal transition. They analyze the transition occurring at the percolation threshold, define the critical indices, and evaluate results from Webman et al.’s computer simulations. They find that the static dielectric constant diverges at the threshold and that all critical indices for complex conductivity can be expressed using two indices derived from computer and model experiments.

Abstract

Abstract A system consisting of randomly distributed metallic and dielectric regions is considered. The metal‐non‐metal transition takes place when the volume fraction of the metallic phase approaches the percolation threshold. It is shown that the static dielectric constant diverges near the threshold. Critical indexes are introduced which describe the behaviour of the conductivity and the dielectric constant near the threshold as functions of the volume fraction and frequency. The case of non‐zero dc conductivity of dielectric regions is considered also. It is shown that all indexes describing the critical behaviour of complex conductivity can be expressed by two indexes which are known from computer and model experiments. The results of computer calculations of Webman et al. are analysed.