Primitive and non-primitive model electrolytes: Comparing ion-related Helmholtz energies using molecular simulations.

This article focuses on a rigorous comparison between primitive and non-primitive modeling frameworks for electrolyte solutions by evaluating Helmholtz energy contributions. Using molecular simulations of model electrolytes composed of charged and dipolar Lennard-Jones particles, the study isolates energy contributions from ion–ion, ion–dipole, and dipole–dipole interactions across various temperatures, densities, ion concentrations, and charges. The results show that classical primitive model expressions—specifically the Debye–Hückel (DH) equation, the primitive mean spherical approximation (MSA), and the Born theory of solvation—qualitatively capture trends but systematically underestimate Helmholtz energy contributions related to ion–solvent and ion–ion interactions. Quantitative agreement requires empirical adjustment of the Born radius, which yields values significantly larger than actual ion sizes, raising questions about the primitive model’s physical applicability. The study provides comprehensive molecular simulation data and benchmarks that can inform the refinement of existing electrolyte equations of state and guide the development of more accurate, physically rigorous models.