Percolation exponents and threshold in two nearly ideal anisotropic continuum systems

Compressed discs made from graphite and, its mechanical but not electrical isomorph, boron nitride, as well as graphite-boron nitride powders, undergoing compression, are nearly ideal continuum percolation systems; as the ratio of their conductivities is 10−18 and the scatter of the experimental points near the critical volume fraction φc is very small. The following measurements, with the characteristic exponent(s) in brackets, are made on some or all of the samples in (axial) and at right angles (radial) to the direction of compression, as a function of the volume fraction of graphite (φ): DC conductivity (s and t), complex dielectric constant (s and t), magnetoresistivity (t ) and noise power (κ and w). The φcʹs obtained for all measurements are virtually the same in the axial and radial directions. The results for the exponents are less well understood. Where possible, these results are compared with theoretical predictions and previous experiments.