Electron transport and ac electrical properties of carbon black polymer composites

The dielectric behaviour of various carbon black polymer composites has been characterized by the critical frequency ω_c denoting the crossover from the dc plateau of the conductivity to its frequency dependent ac behaviour. The critical frequency can be related to the dc conductivity using a power law, ω_c∝σ_dc^z, with the exponent z. Presently accepted models predict z to be greater than one when varying the filler content. However, in accordance with published experimental results this work shows that z is rather close to one indicating a nearly constant static permittivity. Furthermore, the above power law makes it possible to describe all investigated compounds using a single master curve ranging over ten decades of dc conductivity. These findings are explained by a qualitative percolation model based on electron tunnelling. Increasing the dc conductivity along the percolation curve does not require the establishment of more physical links between carbon black aggregates. Rather, new conduction paths of nearly the same lengths but with higher tunnelling probability due to smaller gaps satisfy the percolation theory. This scenario allows the number of capacitive gaps to be nearly constant making z near one.