Two-dimensional radial distribution functions via integral-equation perturbation theory

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Abstract
The radial distribution function (RDF) for a two-dimensional Lennard-Jones fluid is calculated by a statistical-mechanical perturbation scheme originally developed by Madden and Fitts [4] for three-dimensional fluids. This perturbation method requires the solutions of the Percus-Yevick (PY) and hypernetted-chain (HNC) integral equations for the repulsive part of the Lennard-Jones potential and the solution of the HNC equation for the full Lennard-Jones potential. In addition, the RDF and the solution of the PY equation for the hard-disk potential are needed. Various criteria for the selection of the hard-disk diameter are studied. The RDF's calculated by the Madden-Fitts scheme at four thermodynamic states are in excellent agreement with computer simulations.