Experimental study of the three-dimensional ac conductivity and dielectric constant of a conductor-insulator composite near the percolation threshold

Abstract

We measured the ac conductivity and dielectric constant of a three-dimensional randomly mixed conductor-insulator system consisting of amorphous carbon and Teflon powder in the frequency range from 10 Hz to 13 MHz. Near the percolation threshold, these two quantities varied as a power of \ensuremath{\omega}, such as \ensuremath{\sigma}\ensuremath{\sim}${\ensuremath{\omega}}^{x}$, and \ensuremath{\epsilon}\ensuremath{\sim}${\ensuremath{\omega}}^{\mathrm{\ensuremath{-}}y}$. The values of x and y were found to be 0.86\ifmmode\pm\else\textpm\fi{}0.06 and 0.12\ifmmode\pm\else\textpm\fi{}0.04, respectively. These values are compared to the present percolation theories. We also measured the dc conductivity exponent t and dielectric constant exponent s to complete the study. Our data yielded t=1.85\ifmmode\pm\else\textpm\fi{}0.25 and s=0.68\ifmmode\pm\else\textpm\fi{}0.05.