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

G Kikugawa and T Nakano and T Ohara, JOURNAL OF CHEMICAL PHYSICS, 143, 024507 (2015).

DOI: 10.1063/1.4926841

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. (C)
2015 AIP Publishing LLC.

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