Connecting systems with short and long ranged interactions: local molecular field theory for ionic fluids

摘要

Structural and thermodynamic properties of ionic fluids are related to thoseof a simpler ``mimic'' system with short ranged intermolecular interactions ina spatially varying effective field by use of Local Molecular Field (LMF)theory, already successfully applied to nonuniform simple fluids. Byconsistently using the LMF approximation to describe only the slowly varyingpart of the Coulomb interaction, which we view as arising from a rigid Gaussiancharge distribution with an appropriately chosen width $\sigma$, exceptionallyaccurate results can be found. In this paper we study a uniform system ofcharged hard spheres in a uniform neutralizing background, where these ideascan be presented in their simplest form. At low densities the LMF theoryreduces to a generalized version of the Poisson-Boltzmann approximation, butthe predicted structure factor satisfies the exact Stillinger-Lovett momentconditions, and with optimal choice of $\sigma$ the lowest order approximationremains accurate for much stronger couplings. At high density and strongcouplings the pair correlation function in the uniform mimic system with shortranged interactions is very similar to that of the full ionic system. A simpleanalytic formula can then describe the difference in internal energy betweenthe ionic system and the associated mimic system.