System size dependence of the transport coefficients and Stokes–Einstein relationship ofhard sphere and Weeks–Chandler–Andersen fluids

Abstract

Molecular dynamics simulations have been used to calculate the self-diffusion coefficient,D, and other transport coefficients of the hard sphere and Weeks–Chandler–Andersen (WCA)fluids over a wide density range. Simulations were carried out with different numbers of particles,N, in the range between 500 and 273 375 for the WCA and up to 10 976 for the hard spherefluid. These data were fitted to the relationship , where the parameters , A and α were all allowed to be density dependent. The self-diffusion coefficient in the thermodynamiclimit was obtained for both fluids. The Stokes–Einstein (SE) relationship stick–slip parameter,c = kBT/πDηs, wherekB is Boltzmann’sconstant, T is thetemperature and ηs is the shear viscosity, was calculated for the two fluids at each state point as a function ofN. Because of therelatively strong N dependence of D, theparameter c is alsoshown to be sensitive to N. It is shown that data taken for a few hundred particles can significantly overestimate the value ofc. At liquid-like densities, with increasing system size,c tends towards the slip value of 2. The same trend is observed for hard spheresand WCA particles. Therefore for any study of the SE stick–slip parameter it isimportant to perform several simulations for different system sizes and extrapolate theself-diffusion coefficient to the thermodynamic limit, and it is this value which shouldbe used to compare with theory. At the same packing fraction the self-diffusioncoefficient of the WCA fluid is larger than the value for the hard sphere fluidin the thermodynamic limit by, for example, 10% at a packing fraction of0.3 and 60% at a packing fraction of 0.49. The trend for the shear viscosity is the reverse, bothof which could be attributed to the softness of the potential in the WCA case and itseffect in inducing more cooperative interparticle trajectories than for the hardsphere.