Continuum percolation of 2D Lennard-Jones and square-well phases

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Abstract
The percolation cluster characteristics of two-dimensional, 2D, Lennard-Jones, LJ, and square-well, SW, fluids have been determined by molecular dynamics and Monte Carlo computer simulation. In the soft-core and hardcore limits the LJ percolation threshold increases with a fall in temperature, whereas this trend is reversed in the intermediate fluid density regime. In the hard-core limit in the solid phase the percolation threshold increases with decrease in temperature. Despite these variations, the coordination number at threshold always increases as temperature decreases. The distribution of clusters is analysed using the cluster number distribution function ns . Pictures of instantaneous configurations clearly demonstrate the effect of interactions on the form of the percolating cluster. The pair distribution and pair radial connectivity functions are analysed. The fractal dimension of the clusters, D f, at the percolation threshold is 1·90 ± 0·07, consistent with the 2D universal value of 1·90.