System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions

TLDR

The study investigates how system size influences translational diffusion coefficients and viscosities in molecular dynamics simulations with periodic boundary conditions. A simple hydrodynamic correction that scales as N⁻¹/³ (or 1/L) is applied, expressed as D₀ = D_PBC + 2.837297 k_BT/(6πηL). Diffusion coefficients increase strongly with system size, but the correction accurately removes this dependence, whereas viscosities show no significant size dependence.

Abstract

We study the system-size dependence of translational diffusion coefficients and viscosities in molecular dynamics simulations under periodic boundary conditions. Simulations of water under ambient conditions and a Lennard-Jones (LJ) fluid show that the diffusion coefficients increase strongly as the system size increases. We test a simple analytic correction for the system-size effects that is based on hydrodynamic arguments. This correction scales as N-1/3, where N is the number of particles. For a cubic simulation box of length L, the diffusion coefficient corrected for system-size effects is D0 = DPBC + 2.837297kBT/(6πηL), where DPBC is the diffusion coefficient calculated in the simulation, kB the Boltzmann constant, T the absolute temperature, and η the shear viscosity of the solvent. For water, LJ fluids, and hard-sphere fluids, this correction quantitatively accounts for the system-size dependence of the calculated self-diffusion coefficients. In contrast to diffusion coefficients, the shear viscosities of water and the LJ fluid show no significant system-size dependences.