Diffusion in bulk liquids: finite-size effects in anisotropic systems

Abstract

We investigate systematically the effect of the cell size and shape on the diffusion properties in molecular dynamics simulations. Specifically, we consider a bulk Lennard–Jones fluid in orthorhombic cells with one length differing from the other two. The components of the diffusion tensor display complex variations as a function of the two independent lengths and may even become in some cases larger than the macroscopic limit for a cubic cell. These results can be perfectly explained by a purely hydrodynamic theory, which extends results obtained previously for the isotropic case. We provide the explicit expression of the diffusion tensor, including the effect of the finite size of the diffusing particle. The simulation results follow a simple scaling as a function of box size and aspect ratio and the corresponding scaling functions are determined numerically. These findings should have implications for the practically more relevant case of confined fluids.

Keywords:

• diffusion
• hydrodynamics
• molecular dynamics
• anisotropy
• finite-size effects

Acknowledgements

The authors would like express their gratitude to Jean-Pierre Hansen for his guidance and their pleasure to enjoy him as a colleague at UPMC. Benjamin Rotenberg is particularly indebted to Jean-Pierre for his continuing scientific inspiration and friendship, from his first interactions with him as a visiting student in Cambridge to a shared office in Paris.

Disclosure statement

No potential conflict of interest was reported by the authors.