Strong dependence of percolation thresholds on polydispersity

Monte Carlo simulations for a large family of discretized Boolean models exhibit complex dependencies of the percolation threshold not only on shape and correlations but also on the polydispersity of the constituents (pores). A pronounced peak of the critical volume fraction as a function of the density fraction is found for large-size ratios of the pores. Such an increase of more than 10% even for small changes in composition of less than 1% is important in material science, where the accurate prediction of percolation thresholds for arbitrary shaped pores plays a fundamental role. A topological percolation criterion works well for dependence on shape and correlation. But none of the known explicit estimates for percolation thresholds is in reasonable quantitative agreement with the numerical data for polydisperse systems presented here