Hydrodynamic consideration of the finite size effect on the self-diffusion coefficient in a periodic rectangular parallelepiped system.

In the present study, we use molecular dynamics (MD) simulations to provide an insight into the system size effect on the self-diffusion coefficient of liquids in the periodic rectangular parallelepiped system, from the hydrodynamic perspective. We have previously shown that in the rectangular box system, the diffusivity exhibits anomalous behaviors, i.e., the diffusion tensor appears to be anisotropic despite the bulk liquid simulation and the diffusion component in the direction along the short side of rectangular box with a high aspect ratio exceeding the diffusivity in the infinite system [Kikugawa et al., J.Chem. Phys. 142, 024503 (2015)]. So far, the size effect on the diffusivity has been intensively studied in the cubic system and has been interpreted quite well by the theoretical considerations employing the hydrodynamic interaction. Here, we have extended the hydrodynamic theory to be applied to periodic rectangular box systems and compared the theoretical predictions with MD simulation results. As a result, the diffusivity predicted by the hydrodynamic theory shows good agreement with the MD results. In addition, the system size effect was examined in a rod-shaped rectangular box in which the two shorter side lengths were equivalent and a film-type rectangular box in which the two longer side lengths were equivalent. It is of interest that we found that the aspect ratio, at which the diffusivity coincides with that in the infinite system, is a universal constant independent of the cross-sectional area for the rod system or the thickness for the film system. By extracting the universal structure in the hydrodynamic description, we also suggested a simplified approximate model to accurately predict the size effect on the diffusivity over a practical range of aspect ratios.