Using molecular dynamics to obtain Maxwell-Stefan diffusion coefficients in liquid systems

Abstract

Two methods are compared for the calculation of Maxwell-Stefan diffusion coefficients. The first method is a non-equilibrium molecular dynamics (NEMD) algorithm, in which the system is driven away from equilibrium and the system response is monitored. The second method is the equilibrium molecular dynamics (EMD) calculation of the appropriate Green–Kubo equation. Simulations were performed for systems of 250 and 300 Lennard–Jones particles at various densities and temperatures. The systems were divided into two or three components by attaching a colour label to the particles. Since a colour label plays no role in the dynamics, the Maxwell-Stefan diffusion coefficients of the binary and ternary systems are equal to the self-diffusion coefficient. In dense fluids, the system response to an external perturbation is not a first-order process, and the diffusion coefficients cannot be determined from the short term response in the NEMD method. Only the long term response can be used, after a steady state has been reached. In binary systems the Maxwell–Stefan diffusion coefficients, determined by the Green–Kubo (EMD) method, are more accurate than the NEMD coefficients. Since in the NEMD method only the long term response can be used, the Green–Kubo method is also less time consuming and is therefore preferred for the calculation of the Maxwell–Stefan diffusion coefficients. In ternary systems the Green–Kubo method is tested for the 250 particle system. The Maxwell–Stefan diffusion coefficients agree well with the selfdiffusion coefficient. For low mole fractions of the coloured components the diffusion coefficients were less accurate.