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Measurement of AC conductance, and minima in loss tangent, of random conductor-insulator mixtures

The complex AC conductance of carbon-wax mixtures was measured as a function of angular frequency omega from 7 Hz to 100 kHz for different concentrations p of carbon near the percolation threshold pc. The scaling exponents x=0.72+or-0.01, y=0.23+or-0.05 were found to be remarkably close to the theoretical values expected from the intercluster polarization model. The characteristic frequency omega c at which the real part of the AC conductance deviates from its DC value scales with the DC conductance sigma DC as omega c approximately sigma DCz, where z approximately=1.1. The nature of the variation of loss tangent tan delta with frequency was studied in detail. It was found that tan delta went through a minimum at a frequency which increased with p. The increase of tan delta at higher frequencies cannot be explained by the usual RC model. The authors consider a modified version, the R-RC model in which a capacitor is always in series combination with a resistor, i.e. capacitors are lossy. This model is shown to reproduce the observed behaviour of tan delta and believed to be more realistic than the RC model hitherto considered in that series resistors may be a more effective representation of the dangling bonds in the system.