The mean spherical approximation for an arbitrary mixture of ions in a dipolar solvent: Approximate solution, pair correlation functions, and thermodynamics

Abstract

The previously obtained solution of the mean spherical approximation (MSA) for an arbitrary mixture of ions and dipoles is discussed in the case of the low ionic densities (up to 3 M however). In this case, the solution is obtained by solving a system of only three algebraic equations for three parameters, an ion–ion scaling parameter Γ, an ion–dipole scaling parameter B10, and finally a dipole–dipole parameter b2. The thermodynamic properties, however, are better expressed in terms of a shifted screening parameter Γsj. The pair correlation functions and thermodynamics are discussed. The thermodynamics is known to agree fairly with more accurate theories like the LHNC. An attempt to fit the experimental hydration free energies shows that this simple model overestimates the structure breaking effect of the ions. If we empirically adjust this effect for one ion, then we get a surprisingly good correlation for monovanlent ions. The results for the pair correlation functions for the dipole–dipole and ion–dipole are reasonable. However the ion–ion correlation function exhibits the low density pathology of the MSA.