Ion Pairing and Solvent Shell Polarization in Aqueous Solutions of Divalent Metal Sulfates

The interactions of divalent metal cations with other species in aqueous solution are important in contexts such as the basic functioning of living cells. Recent evidence suggests that contact ion pairs are virtually absent in magnesium sulfate solutions and that solvent-shared ion pairs predominate. It is still unclear whether this is the case for divalent metal salts, in general. The polarization energy of the water molecules of the first solvation shell of divalent metal cations is known to be essential to correctly calculating the ionic solvation energy. Here, we show that the same type of solvent shell polarization is important for ion pairing in metal sulfate model electrolytes. The polarization energy of the solvating water molecules makes them harder to replace with ions compared to nonpolarizable models and therefore suppresses ion contact. As this polarization energy increases strongly with the electric field strength at the position of solvating water molecules, which, in turn, depends on cation size, this introduces an ion size dependence. With a polarizable water model, contact ion pairing is completely suppressed for cations below a certain minimum size. No corresponding tendency is seen with a nonpolarizable water model, for which direct contacts between cations and anions are prevalent for all cation sizes considered. This observation may explain the previously noted tendency of extremely small ions in certain respects to behave as large ions. While this effect has previously been ascribed to a strongly bound solvation shell around small ions, the current results provide a mechanism for why small ions are disproportionately strongly solvated.