Varying the charge of small cations in liquid water: structural, transport, and thermodynamical properties

In this work, we show how increasing the charge of small cations affects the structural, thermodynamical, and dynamical properties of these ions in liquid water. We have studied the case of lanthanoid and actinoid ions, for which we have recently developed accurate polarizable force fields, and the ionic radius is in the 0.995-1.250 Å range, and explored the valency range from 0 to 4+. We found that the ion charge strongly structures the neighboring water molecules and that, in this range of charges, the hydration enthalpies exhibit a quadratic dependence with respect to the charge, in line with the Born model. The diffusion process follows two main regimes: a hydrodynamical regime for neutral or low charges, and a dielectric friction regime for high charges in which the contraction of the ionic radius along the series of elements causes a decrease of the diffusion coefficient. This latter behavior can be qualitatively described by theoretical models, such as the Zwanzig and the solvated ion models. However, these models need be modified in order to obtain agreement with the observed behavior in the full charge range. We have thus modified the solvated ion model by introducing a dependence of the bare ion radius as a function of the ionic charge. Besides agreement between theory and simulation this modification allows one to obtain an empirical unified model. Thus, by analyzing the contributions to the drag coefficient from the viscous and the dielectric terms, we are able to explain the transition from a regime in which the effect of viscosity dominates to one in which dielectric friction governs the motion of ions with radii of ca. 1 Å.