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

Abstract

A study of the soft-core to hard-core percolation properties of the hard-sphere fluid as a function of hard core (sphere) packing fraction, ζ, has been made using the Molecular Dynamics computer simulation method. The interparticle separation between the soft shells to achieve percolation, σ p , exhibits a monotonic decrease with ζ from the permeable spheres limit to approximately the glass transition, where σ p tends to the hard-sphere radius, σ. σ p was fitted to a semi-empirical function of ζ, which has the exact low density limiting behaviour. The ζ-dependence of the corresponding packing fraction of the permeable shells, 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 σ p as a function of ζ. The hard-sphere percolation distance dependence on packing shows a similar behaviour to that of rescaled Weeks–Chandler–Andersen (WCA) fluids, but not the same, which is consistent with the conclusions of that previous study.