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 sphere fluid. These data were fitted to the relationship D = D-infinity - AN(-alpha), where the parameters D-infinity, A and alpha were all allowed to be density dependent. The self-diffusion coefficient in the thermodynamic limit was obtained for both fluids. The Stokes - Einstein (SE) relationship stick - slip parameter, c = k(B)T/pi D eta(s), where k(B) is Boltzmann's constant, T is the temperature and eta(s) is the shear viscosity, was calculated for the two fluids at each state point as a function of N. Because of the relatively strong N dependence of D, the parameter c is also shown to be sensitive to N. It is shown that data taken for a few hundred particles can significantly overestimate the value of c. At liquid-like densities, with increasing system size, c tends towards the slip value of 2. The same trend is observed for hard spheres and WCA particles. Therefore for any study of the SE stick - slip parameter it is important to perform several simulations for different system sizes and extrapolate the self-diffusion coefficient to the thermodynamic limit, and it is this value which should be used to compare with theory. At the same packing fraction the self-diffusion coefficient of the WCA fluid is larger than the value for the hard sphere fluid in the thermodynamic limit by, for example, 10% at a packing fraction of 0.3 and 60% at a packing fraction of 0.49. The trend for the shear viscosity is the reverse, both of which could be attributed to the softness of the potential in the WCA case and its effect in inducing more cooperative interparticle trajectories than for the hard sphere.
