Ion transport properties including the friction coefficient, Walden product (product of conductivity and viscosity), and the limiting equivalent conductance are predicted in water at elevated temperatures using a semicontinuum model. Molecular dynamics computer simulation is used to determine water rotational reorientation times in the first coordination shell compared with the bulk, and the results are incorporated into a hydrodynamic expression for the ionic friction coefficient. Along the coexistence curve of water, the effective Stokes−Einstein radius implied by the model is relatively constant. However, for Cl-, K+, and Rb+, this radius increases at typical supercritical water conditions, where the motion of the first shell water molecules is coupled more closely to that of the ion. For Na+, the coupling is already quite strong at higher solvent densities. The increment to the friction coefficient in excess of the bare ion Stokes−Einstein result contributes a larger fraction of the total in supercritical water at typical densities (up to 0.29 g/cm3) than it does in higher density subcritical water, as a result of electrostriction. The limiting equivalent conductance increases approximately linearly with decreasing solvent density in the supercritical regime, in qualitative accord with the experimental extrapolations of Quist and Marshall (J. Phys. Chem. 1968, 72, 684−703) and in contrast to the plateau with decreasing density inferred from much more recent experiments by Zimmerman et al. (J. Phys. Chem. 1995, 99, 11612−11625).
We report the results of simulations of the ionic mobility of Na+ and Cl- in supercritical water at 673 K, including solvent densities below those previously considered in simulation or experimental data. By considering these results along with earlier published analyses, we find that the spatially inhomogeneous solvation structure around the ions and solvent dynamics are strongly coupled in determining transport rates. The appearance of a plateau in the infinite-dilution conductivity over a wide range of intermediate solvent densities is a result of a subtle balance of excess (dielectric) friction and a nonlinear variation in the viscous friction. The result is strongly influenced by the inhomogeneous solvent density around the ions, but cannot be rationalized on the basis of only structural criteria. A reduced effective ionic radius is introduced that is inversely proportional to the Walden product and can be trivially evaluated from experimental conductivity results. It is shown that when represented in this way, conductivity data smoothly and continuously vary with solvent density over the entire density range and are much more readily interpreted. In particular, this effective ionic size exhibits a maximum at a density of ca. 0.2 g/cm3, providing a natural division between high- and low-density solvents. At higher densities, the structure of the first hydration shell of the ions is only weakly dependent on solvent density, while at lower densities, entropic forces increasingly lead to the loss of this primary solvation shell. These results are consistent with the view that, with decreasing solvent density down to this natural division, an increasing imbalance between ion−water and water−water interactions produces an increasingly rigid ionic solvation shell and thus an increasing friction on the ion.
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