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

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 D 0 = D PBC + 2.837297 k B T /(6πη L ), where D PBC is the diffusion coefficient calculated in the simulation, k B 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.