Percolation cluster statistics of Lennard-Jones fluids

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Abstract
The percolation and cluster characteristics of the 3D Lennard-Jones, LJ, fluid have been determined by molecular dynamics computer simulation. The continuous nature of the LJ potential has a pronounced effect on the percolation threshold when compared with a nearest equivalent hard-sphere fluid. In the hard-core limit, percolation takes place at a higher equivalent hard-sphere density than for the hard-sphere fluid. In the soft-core regime the reverse trend is observed. The distribution of clusters is analysed using the cluster number distribution function, ns , above and below the percolation threshold. Its variation with density is statistically the same as for lattice percolation. The pair correlation within the percolating cluster is measured using the pair connectedness function, p(r). It can be used to obtain, at short range the coordination number within the cluster and at long range the fractal dimension, D f, of the percolating cluster. The radius of gyration, R g, of the non-percolating clusters is calculated separately as a function of cluster size, s. Using R g, the D f of these non-percolating clusters at the percolation threshold is statistically the same as that of the percolating cluster. The critical exponents, τ, σ, α, β, δ v and the fractal dimension of the non-percolating and percolating clusters at the percolation threshold, p c, have been determined. They were found to be essentially state point independent. The values for v, τ, σ and γ (in the soft-core regime) were statistically the same as for random static lattice percolation whereas β and α were considerably lower than the lattice values. This is attributed to the finite-size of the periodic cell, which suppresses the number of non-percolating clusters above p c. In the hard-core limit, the susceptibility manifests a deviation from universality.