General Theory of Nonuniform Fluids: From Hard Spheres to Ionic Fluids

Abstract

The exclusion effects of repulsive intermolecular potential cores are often modeled by hard sphere fluids, for which an accurate Hydrostatic Linear Response (HLR) equation was previous developed by Katsov in 2001 for computing the density response to general external fields. In this dissertation the HLR equation is combined with various thermodynamic integration pathways to investigate the solvation free energy of cavity insertion which characterizes the entropic cost of solvating molecules in a fluid. A Shifted Linear Response (SLR) equation is developed to build in the exact limits of external fields varying in very small ranges and fluids confined in narrow spaces, where the HLR fails qualitatively. The SLR is derived from an expansion truncated at linear order about a reference density, and an Insensitivity Criterion (IC) is proposed for determining an optimal reference density. The slow 1/r decay of the Coulomb potential is characteristically long-ranged, but it also becomes strong at short distances. The structure of ionic systems exhibits an intricate interplay between the short and long length scales of their molecular potentials. A strategy is proposed for separating the Coulomb interaction between general charge distributions into a short-ranged piece u0(r) and a slowly varying piece u1(r). In the strong coupling states of the ionic systems that we have studied, mimic systems with only the short-ranged part u0(r) are found to show very similar correlation functions. The slow decays of ion-ion and ion-dipole interactions give rise to unique long-wavelength constraints on ionic fluid structure. Local Molecular Field Theory (LMF), which maps an external field in the full system to a mimic system in the presence of a renormalized field, can correct the mimic correlations by embodying contributions from u1(r). The LMF has been applied to both uniform and nonuniform model ionic systems, and accurate results for bulk correlation functions, internal energy and the density distribution in a confined system are obtained. For a system of counterions confined by charged walls, the LMF and the mimic system have especially helped shed light on many phenomena that had previously lacked coherent physical interpretations and consistent approximations.