MSA and GMSA for charged hard spheres of different diameters: Comparison with RHNC and MC calculationsa)

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Abstract
The excess internal energies and the radial distribution functions of systems of charged hard spheres with two species of different diameters are calculated by using the mean spherical approximation (MSA) and the generalized mean spherical approximation (GMSA). The results obtained are compared with reference hypernetted chain (RHNC) and Monte Carlo (MC) calculations performed by other authors. The MSA estimates of the excess internal energies are often very close to the computer simulation values. The MSA radial distribution functions, on the whole, compare qualitatively well with the MC gij(r), being less satisfactory when the difference in the diameters of the particles is large. The GMSA appears to improve in a systematic manner over the MSA and, when the whole range of the physical situations investigated in this paper is considered, the agreement of this theory with the MC simulation can be considered very good. Similar remarks apply to the RHNC, so that it is possible to conclude that the GMSA and the RHNC, in the present case, are more or less equally accurate. Different possibilities both to improve upon some still unsatisfactory aspects of the GMSA, and to apply this approximation in the future in order to describe the physical properties of real ionic liquids, are also discussed.