Scaling behavior of the complex conductivity of graphite-boron nitride percolation systems

Abstract

Measurements of both components of the complex ac conductivity ${\sigma }_m^{*}(\phi ,\omega )$ on continuum percolation systems, based on graphite and boron nitride (G-BN), between 30 Hz and 100 MHz are reported. The results for the real part of ${\sigma }_m^{*}\left({\sigma }_{\mathrm{mr}}\right)$ above the critical volume fraction $\left({\phi }_c\right)$ and the imaginary component of ${\sigma }_m^{*}\left({\sigma }_{\mathrm{mi}}\right)$ below ${\phi }_c$ (≡ dielectric constant ${\varepsilon }_r$) are shown to scale onto single curves and also to closely fit an analytic, but phenomenological, scaling function. The frequency dependences for high frequencies and close to ${\phi }_c$ are found to be ${\sigma }_{\mathrm{mr}}$ and ${\sigma }_{\mathrm{mi}}\propto {\omega }^u$ ($\equiv {\varepsilon }^{-v},$ with $u+v=1\mathrm{}$). The values of u and $v$ agree with the $R-C$ model, only if the values of s and t obtained from the previously reported dc conductivity and low-frequency ac conductivity measurements, as a function of the graphite volume fraction, are used. Some of the slopes of the critical or crossover frequencies ${\omega }_c\left(\phi \right),$ found experimentally from the scaling plots, plotted against the dc conductivity ${\sigma }_m\left(\phi \right)$ agree well with theory, while others do not. Unfortunately the magnitudes of ${\omega }_c$ sometimes differ from the theoretical ones by orders of magnitude.