Theory and simulation of percolation in dispersions of colloidal platelets

We will address the problem of percolation in suspensions of hard platelets theoretically and by Monte Carlo simulations. Recently, many experiments have been conducted on composite materials containing plate-like filler particles such as graphene. When an insulating matrix is filled with a conductive filler, the composite itself becomes conductive at the percolation transition. Hence the question of percolation, which has been of fundamental mathematical interest for a long time, is also of high relevance for technological applications in light-weight conductive composites. Using Monte--Carlo techniques, we will investigate in this project the effects of effective attractions between the filler particles, external fields and filler polydispersity on the percolation transition. Complementing the simulations, we will employ an integral equation approach to clustering. The project is at the interface of statistical physics and materials science.