Mobility of large ions in water

Mobility of ions in polar liquids is diminished when the ionic charge is increased. This phenomenon, known as dielectric friction, is caused by the retarded response of the liquid's dipoles to the charge movement. Linear response theories predict linear scaling of the inverse diffusion coefficient with the squared ionic charge. This prediction is analyzed here by molecular dynamics simulations of model ions with fractional charge q in the simple point charge water and by microscopic theory formulated in terms of the dynamic electric-field susceptibility of the solvent. The results of the analytical theory, and of its dielectric continuum limit, are in excellent agreement with simulations at sufficiently small charges q < 0.5 when linear response holds. At higher ionic charges, the hydration shell contracts, resulting in deviations from linear response in both static and dynamic properties of the electric field produced by water at the ion. Nevertheless, dielectric friction continues to rise in the nonlinear regime, resulting in an overall factor of 3.7 slower diffusion upon placing a single charge q = 1 on the solute. An approximately linear scaling of the inverse diffusion coefficient with the squared ionic charge comes from a mutual compensation between nonlinear solvation and correlations between non-electrostatic and electrostatic forces. Mobility of common electrolyte ions in water is predicted to occur in the regime of nonlinear dielectric friction.