Relations between the Fractional Stokes−Einstein and Nernst−Einstein Equations and Velocity Correlation Coefficients in Ionic Liquids and Molten Salts

Abstract

It is often asserted that deviation from the Nernst-Einstein relation (NE) between the molar conductivity (Lambda) and ion self-diffusion coefficients (D(i)) in ionic liquids (ILs) and molten salts is evidence for ion pairing. The NE was originally derived for noninteracting ions, as in an infinitely dilute electrolyte solution. In reality, mass, charge, momentum, and energy transport processes in ILs and molten salts involve correlated interionic collisions, caging, and vortex motions, as in any other dense liquid. Phenomenological theory using nonequilibrium thermodynamics and literature molecular dynamics simulations shows that deviations from the simple NE expression occur due to differences in cross-correlations of ionic velocities. ILs have also been shown, like molecular liquids generally, and model fluids such as the Lennard-Jones, to fit the fractional form of the Stokes-Einstein relation, D(i)/T proportional to (1/eta)(t) and Lambda proportional to (1/eta)(t), where eta is the shear viscosity. Here, it is shown that when this is the case, the NE deviation parameter Delta is then a constant, independent of temperature and pressure (consistent with experiment) and the value of the parameter t; it is a function of the ionic charges and volumes, but not the masses. Therefore, Delta is not a measure of "ionicity": it is necessary to seek other independent evidence to determine whether ion pairing is present in a given ionic liquid or molten salt. The use of "apparent" transport numbers derived from self-diffusion coefficients to describe charge transport in pure salts is argued to be unnecessary.