Continuum percolation of congruent overlapping spherocylinders

Continuum percolation of randomly orientated congruent overlapping spherocylinders (composed of cylinder of height H with semispheres of diameter D at the ends) with aspect ratio α =H /D in [0 ,∞ ) is studied. The percolation threshold ϕ_c, percolation transition width Δ, and correlation-length critical exponent ν for spherocylinders with α in [0, 200] are determined with a high degree of accuracy via extensive finite-size scaling analysis. A generalized excluded-volume approximation for percolation threshold with an exponent explicitly depending on both aspect ratio and excluded volume for arbitrary α values in [0 ,∞ ) is proposed and shown to yield accurate predictions of ϕ_c for an extremely wide range of α in [0, 2000] based on available numerical and experimental data. We find ϕ_c is a universal monotonic decreasing function of α and is independent of the effective particle size. Our study has implications in percolation theory for nonspherical particles and composite material design.