Continuum Percolation of 2D and 3D Simple Fluids

We use Monte Carlo and Molecular Dynamics computer simulations to investigate the percolation threshold, ρ _p , of d-dimensional Lennard-Jones LJ, and square-well fluids. We find that when the range of the potential well is small compared to the hard-core diameter (in the so-called ‘hard-core’ limit), an attractive well decreases ρ _p below the high temperature limiting value. In contrast, a hard shoulder potential produces the opposite trend. We investigate the structure of the 2D percolating clusters, in particular, the effects of periodic boundaries. We examine the shapes of the 3D clusters at the percolation threshold, resolved as a function of the number of particles in a cluster, s. The asphericity parameter, A₃ , 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.

We focus especially on the relationship between long and short range structural order as probed by the coordination numbers of the molecules. We also use a cluster-resolution of the co-ordination number to indicate the degree of branching in the clusters, and how it is influenced by the number of atoms in the cluster and temperature for the different potentials. We look forward to future directions for simulation in investigating physical properties in the vicinity of the percolation threshold.