Modelling percolation in fibre and sphere mixtures: Routes to more efficient network formation

Mixtures of perfectly conducting fibres and spheres, as well as mixtures of fibres of different aspect ratios, were simulated using a Dissipative Particle Dynamics (DPD) method, and the connectivity of the resulting assemblies was analysed using a Monte Carlo algorithm to predict the threshold volume fraction of filler material required for electrical percolation. For both isotropic and uniaxially oriented fibre–sphere mixtures, it was found that gradually replacing fibres with an equivalent volume of spheres increased the percolation threshold. By contrast, in aligned mixtures of fibres of two different aspect ratios, replacing a small fraction of higher aspect ratio fibres with shorter fibres led to a reduction in the percolation threshold, since the shorter fibres orient less well and provide bridging links between the highly oriented longer fibres. These theoretical results suggest that mixtures of fibres of different aspect ratio may be helpful in reducing the volume fraction of high aspect ratio filler particles (such as multi-wall carbon nanotubes) required to achieve significant electrical conductivity in composite materials.