Electron transport and ac electrical properties of carbon black polymer composites

The dielectric behaviour of various carbon black polymer composites has bee n characterized by the critical frequency omega (c) denoting the crossover from the dc plateau of the conductivity to its frequency dependent ac behav iour. The critical frequency can be related to the dc conductivity using a power law, omega (c) proportional to sigma (z)(dc), with the exponent z. Pr esently accepted models predict z to be greater than one when varying the f iller content. However, in accordance with published experimental results t his work shows that z is rather close to one indicating a nearly constant s tatic permittivity. Furthermore, the above power law makes it possible to d escribe all investigated compounds using a single master curve ranging over ten decades of dc conductivity. These findings are explained by a qualitat ive percolation model based on electron tunnelling. Increasing the dc condu ctivity along the percolation curve does not require the establishment of m ore 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 n umber of capacitive gaps to be nearly constant making z near one.