Critical anomaly and finite size scaling of the self-diffusion coefficient for Lennard-Jones fluids by non-equilibrium molecular dynamic simulation

We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard-Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density rho* = rho sigma(3) = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T* = kT/epsilon = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N-alpha, where alpha is an adjustable parameter and N is the number of particles. It is observed that the values of alpha < 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations from the literature.