Isotopic mass dependence of metal cation diffusion coefficients in liquid water

Isotope distributions in natural systems can be highly sensitive to the mass (m) dependence of solute diffusion coefficients (D) in liquid water. Isotope geochemistry studies routinely have assumed that this mass dependence either is negligible (as predicted by hydrodynamic theories) or follows a kinetic-theory-like inverse square-root relationship (D ∝ m−0.5). However, our recent experimental results and molecular dynamics (MD) simulations showed that the mass dependence of D is intermediate between hydrodynamic and kinetic theory predictions (D ∝ m−β with 0 ⩽ β < 0.2 for Li+, Cl−, Mg2+, and the noble gases). In this paper, we present new MD simulations and experimental results for Na+, K+, Cs+, and Ca2+ that confirm the generality of the inverse power-law relation D ∝ m−β. Our new findings allow us to develop a general description of the influence of solute valence and radius on the mass dependence of D for monatomic solutes in liquid water. This mass dependence decreases with solute radius and with the magnitude of solute valence. Molecular-scale analysis of our MD simulation results reveals that these trends derive from the exponent β being smallest for those solutes whose motions are most strongly coupled to solvent hydrodynamic modes.