Cluster analysis and continuum percolation of 3D square-well phases MC and PY solutions

Abstract

An extensive study of the percolation threshold, ρp of three dimensional attractive and repulsive square well fluids is made by Monte Carlo computer simulation. We find that in the hard-core limit an attractive well decreases ρp below the high temperature limiting value. In contrast a hard shoulder potential produces the opposite trend. A numerical solution of the PY integral equations employing Hill's concept of bound and unbound pairs gives results qualitatively in agreement with MC. The PY solution overestimates ρp especially in the hard-core limit and at high temperature. We examine the shapes of all the clusters at the percolation threshold, resolved as a function of the number of particles in a cluster, s. The asphericity parameter, A 3, describing the instantaneous shape of the cluster decays slowly from unity, typically only achieving ∼ 0·3 by s ∼ 100, close to the estimated universal value of 0·312.