Test of Stokes-Einstein Formula for a Tracer in a Mesoscopic Solvent by Molecular Dynamics Simulation

Abstract

particles interact through multi-particle collision events which take place at discrete time intervals. Between such collision events the particles undergo free streaming motion. The dynamics conserves mass, momentum and energy and yields the exact hydrodynamic equations of motion for the conserved fields on long distance and time scales. One may consider the dynamics of solute molecules in this mesoscopic solvent and because the solvent is described at an effective particle level the solute and solvent molecules interact through intermolecular forces rather than through boundary conditions. This leads to a hybrid description of the dynamics where solute molecules evolve by Newton’s equations of motion but the solvent evolves through the multi-particle mesoscale dynamics. 2,3 Calculations of the diffusion and friction coefficients by molecular dynamics (MD) simulations are well-studied problems that have been addressed many times. Nevertheless, the computation of the friction coefficient from MD simulations involves a number of subtle issues for finite-size systems as discussed in several recent papers. 4-6 The problems center around the definition of the friction coefficient in terms of the projected dynamics and its relation to the fixed-particle friction coefficient for a massive Brownian particle. The estimates of the friction coefficients have been shown to depend on the order in which the mass of the tracer and the solvent particle number N are taken to infinity. For finite-size systems one must investigate how large N must be to obtain a reliable estimate of the friction; this typically requires very large MD simulations. Similarly, the estimate of the diffusion coefficient from the velocity autocorrelation function requires large scale simulations, especially for large tracers, due to the importance of hydrodynamic contributions. In recent papers, 7-9 the friction and diffusion coefficients of a tracer in a Lennard- Jones (LJ) solvent were evaluated by equilibrium molecular dynamics simulations in a microcanonical 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. These works were motivated by determination of the diffusion (D) and friction (ζ) coefficients of the tracer in the thermodynamic limit (N→∞) and by test of the Stokes-Einstein (SE) formula: D =