Solution and thermodynamic consistency of the GMSA for hard sphere mixtures

Abstract

The explicit numerical solution of the Generalized Mean Spherical Approximation (GMSA) for a two-component hard sphere mixture is obtained by employing an iterative procedure which starts from the known analytic Percus-Yevick (PY) result. The parameters which enter the theory are fitted to a set of thermodynamic data generated from parametrized forms of computer simulation results, so as to ensure the thermodynamic consistency of the theory. The radial distribution functions so obtained compare very favourably with the available Monte Carlo results, and systematically improve on the PY g_ij (r). A possible scheme for obtaining the thermodynamic consistency without having recourse to external data sources is also proposed. The q → 0 limit of the concentration-concentration structure factor S _cc(q) is also investigated, this allowing a better understanding of the role played by the diameter ratio, R, and the concentration of the two species, in the enhancement or reduction of disorder in the mixture, especially near the freezing density. This analysis is furtherly supported by an explicit calculation of the partial structure factors S_ij (q) for two diameter ratios. The most favourable conditions for ordering seem to be met near R = 0·5 where, for geometrical packing reasons, both the two species, on the short distance scale, occupy well defined positions. The dependence of S _cc(0) on R and concentration also allows to verify the possibility of segregation of the two species. It seems excluded that such a segregation occurs.