Physical interpretation of theories of homogeneous electrolytes in the primitive model

Abstract

The primitive model of ions is an important model system of electrolytes and ionic liquids because it is the simplest one to include both electrostatic and ion size effects. Here, two recent theories of the electrostatic excess chemical potential of homogeneous electrolytes modeled in the primitive model are analyzed. Both the Mean Countershell Approximation (MCSA) and the Extended Mean Spherical Approximation (MSAX) theories were already known to be accurate when compared to Grand Canonical Monte Carlo simulation results. The analysis here uncovers why these two seemingly very different theories agree very closely numerically. Moreover, knowledge of the physical meaning of the MCSA theory is used to define the MSAX theory’s terms as electrostatic interactions of ionic screening clouds. Lastly, a mathematical analysis of MCSA, MSAX, and a third theory is performed. This shows how all these theories—despite using very different mathematical and physical approximations—couple the distinct physical regimes of the low- and high-density limits to get accurate results at intermediate ion densities.