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

Abstract

Measurements of both components of the complex ac conductivity ${\ensuremath{\sigma}}_{m}^{*}(\ensuremath{\varphi},\ensuremath{\omega})$ 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 ${\ensuremath{\sigma}}_{m}^{*}({\ensuremath{\sigma}}_{\mathrm{mr}})$ above the critical volume fraction $({\ensuremath{\varphi}}_{c})$ and the imaginary component of ${\ensuremath{\sigma}}_{m}^{*}({\ensuremath{\sigma}}_{\mathrm{mi}})$ below ${\ensuremath{\varphi}}_{c}$ (\ensuremath{\equiv} dielectric constant ${\ensuremath{\varepsilon}}_{r}$) 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 ${\ensuremath{\varphi}}_{c}$ are found to be ${\ensuremath{\sigma}}_{\mathrm{mr}}$ and ${\ensuremath{\sigma}}_{\mathrm{mi}}\ensuremath{\propto}{\ensuremath{\omega}}^{u}$ ($\ensuremath{\equiv}{\ensuremath{\varepsilon}}^{\ensuremath{-}v},$ with $u+v=1$). The values of u and $v$ agree with the $R\ensuremath{-}C$ 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 ${\ensuremath{\omega}}_{c}(\ensuremath{\varphi}),$ found experimentally from the scaling plots, plotted against the dc conductivity ${\ensuremath{\sigma}}_{m}(\ensuremath{\varphi})$ agree well with theory, while others do not. Unfortunately the magnitudes of ${\ensuremath{\omega}}_{c}$ sometimes differ from the theoretical ones by orders of magnitude.