On the statistical thermodynamics of interacting charged particles of arbitrary shape and concentration

Publisher Website
Google Scholar
Abstract
A great deal of effort has been devoted for many years to the statistical thermodynamics of interacting charged particles having spherical symmetry, e.g., simple electrolyte solutions, fluid plasmas, and micellized suspensions of ionic surfactants. In the present work we provide a straightforward and physically suggestive scheme for treating the bulk properties of interacting particles characterized by arbitrary charge, axial ratio and concentration. The basic idea involves a marriage of Onsager’s charge ‘‘smearing’’ optimization with a variational statement of the mean spherical approximation. In particular the direct correlation function is shown to be described accurately by the pair interaction energy between smeared charge distributions. After illustrating this approach for point particles (one and multicomponent plasmas), we generalize it to line charges of arbitrary length l. A simple analytical theory of the isotropic→nematic transition in this system is presented for the large l, high density regime. Results are also discussed for the weak-coupling (Debye–Hückel) and ‘‘high salt’’ limits. Finally, we stress the special features of our theory which enable ‘‘crossover’’ between dimensionalities and inclusion of polydispersity in both charges and lengths.