A study was made of the diffusion of solute particles in the limit of infinite dilution in a solvent. An estimate was made of the solute concentration below which this limit was attained. The range of the size and mass values of the solute particles were determined for where the solute diffusion coefficient was well estimated from the Stokes-Einstein formula. To this aim, extensive molecular-dynamics simulations were carried out for a model tracer-solvent system made up of 5324 molecules including solvent and tracer molecules interacting through Lennard-Jones potentials. The values of the viscosity coefficient, corrected for long time tail contributions, and the diffusion coefficients were obtained with high precision. Positive deviations from the Stokes-Einstein formula were observed as the size ratio or the mass ratio of the tracer to solvent molecules was lowered. For equal solvent and tracer molecular masses, the crossover to the hydrodynamics regime was found to occur when the size ratio was ~4. The results showed a strong coupling between the size and mass effects on the tracer diffusivity, with the latter being predominant. An analysis of the molecular-dynamics data in the hydrodynamic regime showed that the Stokes-Einstein formula holds for this system with slip boundary conditions and the hydrodynamic radius equal to the cross radius between the tracer-solvent molecules. The friction coefficient was evaluated from the computed autocorrelation function of the force exerted by the fluid on the tracer molecule, following a scheme proposed by Lagarkov and Sergeev; it was found that the latter criterion gave the correct diffusion coefficient only in the limits of high sizes and high masses.

Molecular-Dynamics Investigation of Tracer Diffusion in a Test of the Stokes-Einstein Law. Ould-Kaddour, F., Levesque, D.: Physical Review E, 2001, 63[1], 0112051-9