An analytic treatment of percolation in simple fluids

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Abstract
The percolation behavior of simple fluids, modeled by a pair potential with a hard core and Yukawa tail, is studied by solving the connectedness Ornstein–Zernike equation analytically in the mean-spherical approximation for two different connectedness models. The simplest connectedness model is defined by a ‘‘connectedness shell’’ concentric to the sphere that defines the hard core. The analytical solution applies to the case of the shell width less than the hard-core diameter, which is the case for most applications of physical interest. The percolation loci on the phase diagram have been determined along with the average coordination number, which is found to be essentially constant along each locus, but different for different loci. A second model is introduced in which direct connectedness-in-probability is defined and applied to the gelation problem. This model can be thought of as a continuum generalization of the lattice model of gelation introduced by Coniglio, Stanley, and Klein. In the mean-spherical approximation, the models have percolation exponents (β=1/2, δ=5, γ=2, η=0, fractal dimensionality=2.5) that for the most part are quite close to the best available estimates of these exponents.

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