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

Measurements of both components of the complex ac conductivity σₘ*(φ,ω) 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 σₘ*(σₘᵣ) above the critical volume fraction (φc) and the imaginary component of σₘ*(σₘᵢ) below φc ({≡} dielectric constant εᵣ) 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 φc are found to be σₘᵣ and σₘᵢ∝ωᵘ (≡ε^-v, with $u+v=1$). 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 ωc(φ), found experimentally from the scaling plots, plotted against the dc conductivity σₘ(φ) agree well with theory, while others do not. Unfortunately the magnitudes of ωc sometimes differ from the theoretical ones by orders of magnitude.