Beyond the Virial Expansion: Microscopic Origins of Partial Molar Volumes in LiCl Solutions

Abstract

Although electrolyte density measurements have been reported for over a century, employing them to obtain accurate partial molar volume (PMV) profiles as a function of salt concentration has remained elusive. Obtaining such curves requires precise density measurements combined with a proper treatment of the associated virial expansion. In this work, we obtain PMV profiles for aqueous LiCl solutions. The resulting data enable the development of highly accurate force fields for Li$^+$ and Cl$^-$ ions, revealing a clear progression from isolated ions to ion pairs and ultimately to higher-order chain and ring structures. Because ion clustering emerges from complex, nonlocal interactions, it cannot be easily mapped onto specific virial terms. Instead, a direct structural and volumetric interpretation can be achieved by partitioning molecular dynamic (MD) simulation snapshots into three-dimensional polyhedral regions associated with individual salt ions and water molecules. The corresponding ionic and water volumes from this treatment quantitatively reproduce the experimental PMV curve. The results demonstrate that the PMV for salt increases (while that of water decreases) up to 6.7 M. Above this concentration, the direction reverses as three- and four-body interactions become prominent. Complementary multivariate curve resolution (MCR) Raman spectroscopy and density functional theory (DFT) calculations elucidate the molecular-level details of water electrostriction, which also persists up to 6.7 M. Significantly, the PMV data can be correlated with key thermodynamic properties, including the osmotic coefficient and the eutectic point. The procedures established here provide a general framework for modeling electrolyte solutions and enable the development of a new generation of accurate force fields for aqueous ions.