The radial distribution function in fluid mixtures: Conformal solution theory and molecular dynamics results

The conformal solution approach is used to relate the distribution functions g αβ (r) for a fluid mixture to those of a pure fluid, g x (r). The procedure is to expand g αβ (r) about the corresponding function for an ideal solution, using σ αβ 3 and ε αβ σ αβ 3 as expansion parameters; the expansion of the function y αβ (r) is also considered. Molecular dynamics results are reported for the tg αβ for argon-krypton liquid mixtures using the Lennard-Jones (12, 6) potential. These results are used to test the conformal solution expansions to first order; the g αβ expansion is found to be superior to that for y αβ for most r values of interest. The second order term in the conformal solution expansion for the Helmholtz free energy is also calculated for argon-krypton mixtures, and found to be about 10 per cent of the value of A E given by the van der Waals 1 theory.