Breakdown of the Stokes-Einstein relationship: role of interactions in the size dependence of self-diffusivity

Abstract

Einstein and others derived the reciprocal dependence of the self-diffusivity D on the solute radius r_u for large solutes based on kinetic theory. We examine here (a) the range of r_u over which Stokes-Einstein (SE) dependence is valid and (b) the precise dependence for small solutes outside of the SE regime. We show through molecular dynamics simulations that there are two distinct regimes for smaller solutes: (i) the interaction or Levitation effect (LE) regime for solutes of intermediate size and (ii) the D α1/r_u² for still smaller solutes. We show that as the solute-solvent size ratio decreases, the breakdown in the Stokes-Einstein relationship leading to the LE regime has its origin in dispersion interaction between the solute and the solvent. These results explain reports of enhanced solute diffusion in solvents existing in the literature seen for small solutes for which no explanation exists.