Test of Stokes-Einstein Formula for a Tracer in a Large System by Molecular Dynamics Simulation

摘要

In recent papers, the friction and diffusion coefficients of a tracer in a Lennard-Jones (LJ) solvent (N=32,000) were evaluated by equilibrium molecular dynamics (MD) simulations in a micro-canonical ensemble. The solvent molecules of diameter σ1 interact with each other through a repulsive LJ force and the tracer of diameter σ2 interacts with the solvent molecules through the same repulsive LJ force except a different LJ size or diameter parameter. Positive deviation of the diffusion coefficient (D) of the tracer from a Stokes-Einstein behavior was observed and the plot of 1/D versus σ2 showed a linear behavior. It was also observed that the friction coefficient ζ, of the tracer varies linearly with σ2 in accord with the prediction of the Stokes law but showed a smaller slope than the Stokes prediction. When the values of ratios (σ2/σ1) of sizes between the tracer and solvent molecules are higher than 5 approximately, the behavior of the friction and diffusion coefficients is well described by the Einstein relation.