Fractal approach to the critical filler volume fraction of an electrically conductive polymer composite

Abstract

It has been known for quite a long time that polymers filled with electrically conductive particles, foils or fibres exhibit a distinctive dependence of conductivity on filler volume fraction. With a rise in filler content, there is always a drastic increase in composite conductivity by the order of ten magnitudes at a certain threshold, namely, the critical volume fraction. Such a transition-like change in conductivity is usually interpreted as percolation. Many models have been proposed for explaining the conduction mechanism involved, but often they possess evident drawbacks mainly due to the negligence of relative filler arrangements or the Euclidean geometric description of the arrays. The present work focused on the prediction of the critical volume fraction by a new electrical conductive model, based on the fractal technique and the generalized unit-cell method proposed by Pitchumani and Yao for modelling the thermal conductivity of fibrous composites. It was found that the electrical conduction behaviour of a polymer composite is governed by both a filler geometry factor and a material factor of the components. The critical volume fractions estimated by the model are in good agreement with experimental results taken from the literature. In addition, possible improvements of the present approach are discussed.