A study of the size dependence of self diffusivity across the solid-liquid transition

The present study investigates the effect of temperature-induced change of phase from face centred cubic solid to liquid on the size dependence of self diffusivity of solutes through detailed molecular dynamics simulations on binary mixtures consisting of a larger solvent and a smaller solute interacting via Lennard-Jones potential. The effect of change in density during the solid-liquid transition as well as in the solid and the liquid phase itself have been studied through two sets of simulations one at fixed density (NVE simulations) and another at variable density (isothermal-isobaric ensemble). A size dependent diffusivity maximum is seen in both solid and liquid phases at most densities except at low liquid densities. Two distinct regimes may be identified : linear and anomalous regimes. It is seen that the effect of solid to liquid transition is to shift the diffusivity maximum to smaller sizes of the solutes and decrease the height of the maximum. This is attributed to the predominant influence of disorder (static and dynamic) and relatively weaker influence of density. The latter shifts the diffusivity maximum towards larger solute size while the former does exactly the opposite. Interestingly, we find that lower densities lead to weaker diffusivity maximum. We report for the first time for systems with large solute-solvent interaction strength, ǫuv, multiple diffusivity maximum is seen as a function of the solute size. The origin of this is not clear. A remarkable difference in the ballistic-diffusive transition is seen between solutes from the linear regime and anomalous regime. It is found that this transition is sharp for solutes from anomalous regime. Negative exponent α in dependence of mean square displacement on time u(t) ∼ t is seen for linear regime solute in solid phase during ballistic-diffusive transition which is completely absent for a solute from anomalous regime. This provides interesting insight into motion of anomalous regime solutes. Apart from these, we report several properties which are different for the linear and anomalous regime solutes.