The Contribution of the Ion–Ion and Ion–Solvent Interactions in a Molecular Thermodynamic Treatment of Electrolyte Solutions

Abstract

Developing molecular equations of state to treat electrolyte solutions is challenging due to the long-range nature of the Coulombic interactions. Seminal approaches commonly used are the mean spherical approximation (MSA) and the Debye−Huckel (DH) theory to account for ion−ion interactions and, often, the Born theory of solvation for ion−solvent interactions. We investigate the accuracy of the MSA and DH approaches using each to calculate the contribution of the ion−ion interactions to the chemical potential of NaCl in water, comparing these with newly computer-generated simulation data; the ion−ion contribution is isolated by selecting an appropriate primitive model with a Lennard-Jones force field to describe the solvent. A study of mixtures with different concentrations and ionic strengths reveals that the calculations from both MSA and DH theories are of similar accuracy, with the MSA approach resulting in marginally better agreement with the simulation data. We also demonstrate that the Born theory provides a good qualitative description of the contribution of the ion−solvent interactions; we employ an explicitly polar water model in these simulations. Quantitative agreement up to moderate salt concentrations and across the relevant range of temperature is achieved by adjusting the Born radius using simulation data of the free energy of solvation. We compute the radial and orientational distribution functions of the systems, thereby providing further insight on the differences observed between the theory and simulation. We thus provide rigorous benchmarks for use of the MSA, DH, and Born theories as perturbation approaches, which will be of value for improving existing models of electrolyte solutions, especially in the context of equations of state.

Insight into the ionic atmosphere effect: Comparison of theories for electrolytes at the primitive level

“…In subsequent literature, a common value for a i has often been taken (an adjustable mean distance of approach, or the average diameter of the ions [13]). Sometimes, the individual diameter σ i has been used for a i [69].…”

Further reflections about the “Born” term used in thermodynamic models for electrolytes

“…In a very recent publication [20], the capability of the "Born" term was investigated using Monte Carlo simulations for the system NaCl+water. This is the first fundamental study dedicated to this issue since the publication of Ref.…”

“…19. An involved procedure was used in that valuable work [20] in order to attempt disentangling the various contributions to the mean salt chemical potential. However, because of uncertainties on the simulation results, and in the estimation of the ion-ion (MSA) contribution, it seems difficult to draw a clear and definitive conclusion about the suitability of the "Born" term from this study.…”