Conductivity critical exponents lower than the universal value in continuum percolationsystems

Abstract

A simple model was developed which explains how a continuumpercolation system can attain a conductivity critical exponent,t, lower than the universal value. In this model, a structure parameter,κ, was developed to evaluate the geometry of the original conductor shape. Another parameterη accounts for the average backbone probability density of the conductive phase within the percolation system. The structure parameterκ was used to evaluate the ‘sensitivity’ of the critical exponentt to the average backbone probability density . As increased, a lower t could be obtained. To test this model experimentally, aCu–Cu2O conductor–insulator material was developed and tested. In this conductor–insulator material, C was usedto reduce Cu2O into Cu and CO, which produced a material with an optimum and allowed the critical exponentt = 0.87 ± 0.1 atpc = 0.23 ± 0.01 to be achieved.