Percolation threshold of hard-sphere fluids in between the soft-core and hard-core limits

A study of the soft-core to bard-core percolation properties of the hard-sphere fluid as a function of hard core (sphere) packing fraction, zeta, has been made using the Molecular Dynamics computer simulation method. The interparticle separation between the soft shells to achieve percolation, up, exhibits a monotonic decrease with zeta from the permeable spheres limit to approximately the glass transition, where sigma(p) tends to the hard-sphere radius, sigma. sigma(p) was fitted to a semi-empirical function of zeta, which has the exact low density limiting behaviour. The zeta-dependence of the corresponding packing fraction of the permeable shells, zeta(p) = zeta(sigma(3)(p)/sigma)(3) P. is discussed. The local coordination number at the percolation threshold showed a transition between the soft-core and hard-core limits from ca. 2.74 to 1.51, as found in previous studies. A reasonably accurate simple analytic expression is given for the packing fraction dependence of the coordination number up to the percolation distance. Various key length scales of the hard-sphere system are compared with sigma(p) as a function of zeta. The hard-sphere percolation distance dependence on packing shows a similar behaviour to that of resealed Wee ks-Chandler-Andersen (WCA) fluids, but not the same, which is consistent with the conclusions of that previous study.