FREQUENCY-DEPENDENCE OF THE CONDUCTIVITY AND DIELECTRIC-CONSTANT OF A CARBON BLACK-EPOXY PERCOLATION SYSTEM

Abstract

The a.c. conductivity SIGMA(omega, theta) and the a. c. dielectric constant epsilon(omega, theta) near the percolation threshold of carbon black-epoxy bulk composites were measured in the frequence range from 100 Hz to 10 GHz. The power-low dependence of the a. c. conductivity, SIGMA(omega, theta(c)) approximately omega(x), was observed at the percolation threshold in the frequency range up to 10 GHz, but that of the a. c. dielectric constant, epsilon(omega, theta(c)) approximately omega(-gamma), was valid in the bound frequency range of 2 kHz approximately 1.5 MHz and the three-stage variation of the dielectric constant with frequency was apparent at the percolation threshold. The critical exponents x = 0.65 +/- 0.05 and y = 0.26 +/- 0.01 obtained in the power-law frequency range are close to the theoretical predictions of intercluster polarization. Our observation of the critical exponents satisfies the general universality relation x + y = 1. The critical volume fraction theta(c) = 0.18 obtained at the divergence of the dielectric constant is close to that of a continuous percolation system.