Statistical Mechanics of Charged Objects: General Method and Applications to Simple Systems

摘要

Real fluids are composed of molecules that are objects of complex geometries and charge distributions. In a previous note we have shown that, by studying the asymptotic high density limit (AHDL) and the asymptotic strong coupling limit (ASCL) one is able to reduce the problem of computing the thermodynamics and correlation functions of the system to a geometrical calculation involving overlap integrals between the objects. In previous work a simple geometrical, physically intuitive meaning of the direct correlation functions (dcf) I for point charges in a background (as interactions between smeared charges) and hard sphere (as overlap volumes) within the mean spherical approximation (MSA) was given, thus also revealing its analytic structure. A general variational approach to study system composed of complex charged molecules is discussed. In this approach the variational trial functions for the free energy functional are constructed from the asymptotic limiting (AL) forms of the direct correlation functions. A number of examples are discussed, and in each case the variational form of the direct correlation is given explicitly. The relation to Onsager's procedure of immersing the system in a infinite conducting fluid of obtaining an energy bound is discussed in detail.