Generalized mean-spherical-approximation description of highly asymmetric hard-sphere mixtures

Abstract

We use thermodynamically self-consistent integral equation theories to determine the structure of binary hard-sphere mixtures in a regime of moderate to high size asymmetry, and for low concentration of the species with bigger particle size. Calculations are performed by applying the generalized mean-spherical approximation (GMSA) and the Rogers-Young (RY) approximation. The thermodynamic consistency of the GMSA is implemented in terms of adjustable parameters which are used in order to reproduce the Mansoori-Carnahan-Starling-Leland equation of state, and to impose the equality of the osmotic isothermal compressibilities estimated through the virial and fluctuation routes. The structural results obtained for a moderate size asymmetry of the particle species compare rather satisfactorily with the available Monte Carlo (MC) data and their parametrizations, and with previously reported modified hypernetted-chain results. The relative performances of the GMSA and of the RY approximations are also examined for strongly asymmetric mixtures. A regime of semi-dilute concentration for which no simulation data are available is investigated first and a very close agreement emerges between the RY and GMSA radial distribution functions. The case of very high dilution of the component with bigger particle size, for which RY and MC results already exist, is then considered, but it appears impossible to achieve a thermodynamically consistent solution for the GMSA according to the consistency prescriptions adopted. Other possible implementations of the thermodynamic consistency of the GMSA for HSMs and other multicomponent fluids are discussed.