Integral Equation Theory of Continuum Percolation

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When designing composite materials, it is often useful to know whether the individual components form a system spanning network along which heat or charges can be transported through the material – i.e. it is useful to know under which conditions a given component of a composite percolates. Most theoretical approaches to the percolation transition can predict critical exponents accurately, but they give only rough estimates for the percolation thresholds of complex interacting systems (apart from some special cases such as fibres). We have recently developed a new theoretical approach, which allows to compute percolation thresholds and network structures with high accuracy. Here, we propose to apply this approach to a set of systems with non-trivial interactions and particle geometries, which are of experimental interest. We will study hard spheres, spheres with van der Waals interactions, spheres with screened Coulomb interactions and hard platelets and consider size polydispersity in all cases. We will predict percolation thresholds, network structures and conductivities for direct comparison with experiments on suspensions of colloidal metallic particles.