The dielectric behaviour of various carbon black polymer composites has been characterized by the critical frequency ωc 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, ωc∝σdcz, 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.

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Local variations in filler particle concentration and/or shape and orientation in static filler/polymer composites are modelled as distributions of percolation thresholds. The concentration variations can be due to insufficient mixing, formation of semicrystalline voids during cooling from the melt, shrinkage during polymer curing, flow during physical compression or the like. Irregular filler shapes, especially elongated shapes, reduce the percolation threshold; thus, natural variations in the shapes and orientations of filler particle aggregates lead to locally varying percolation thresholds. A distribution of percolation thresholds leads to an apparent average percolation threshold based on the conductivity below the mean percolation threshold. For filler concentrations above the apparent percolation threshold, the dielectric constant continues to increase before reaching a lowered peak value at the mean percolation threshold and then decreasing. This can explain some ‘anomalous’ published experimental results concerning the dielectric constant just above the percolation threshold. In the frequency plane, the percolation threshold distribution can lead to a slight reduction of the apparent critical exponents x and y of the frequency dependencies of the conductivity and relative dielectric constant, respectively. Our experimental results on ethylene butylacrylate copolymer/carbon black composites support the theory.

The ac electrical properties of acetylene black composites mixed into ethylene butylacrylate copolymer (EBA) and into poly (methyl methacrylate) (PMMA) have been measured in thermal cycling and isothermal annealing experiments. The results show that changes in electrical properties are due to rearrangement of gaps between the carbon black aggregates. This has been concluded using an exponent z that relates the critical frequency ωc denoting the crossover of the conductivity from the dc-plateau to its frequency-dependent part to the dc conductivity, σdc, according to ωc ∝σdcz. Below the melting range of EBA and the glass transition of PMMA z is about one corresponding to strong variation of the conductivity and weak dependence of the permittivity on the gaps. Above the melting range of EBA z is about 1.5, indicating strong dependence of both the conductivity and the permittivity on the gaps, as predicted by percolation theory. This was not found in the PMMA composites above the glass transition. We conclude that the polymer matrix affects the nature of the gaps between carbon black aggregates, either allowing their size to vary continuously (z about 1) or letting them open and close (z about 1.5).

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