Ludger Wolff

Finite-size Effects of Binary Mutual Diffusion Coefficients from Molecular Dynamics

Molecular dynamics simulations were performed for the prediction of the finite-size effects of Maxwell-Stefan diffusion coefficients of molecular mixtures and a wide variety of binary Lennard–Jones systems. A strong dependency of computed diffusivities on the system size was observed. Computed diffusivities were found to increase with the number of molecules. We propose a correction for the extrapolation of Maxwell–Stefan diffusion coefficients to the thermodynamic limit, based on the study by Yeh and Hummer (J. Phys. Chem. B, 2004, 108, 15873−15879). The proposed correction is a function of the viscosity of the system, the size of the simulation box, and the thermodynamic factor, which is a measure for the nonideality of the mixture. Verification is carried out for more than 200 distinct binary Lennard–Jones systems, as well as 9 binary systems of methanol, water, ethanol, acetone, methylamine, and carbon tetrachloride. Significant deviations between finite-size Maxwell–Stefan diffusivities and the corresponding diffusivities at the thermodynamic limit were found for mixtures close to demixing. In these cases, the finite-size correction can be even larger than the simulated (finite-size) Maxwell–Stefan diffusivity. Our results show that considering these finite-size effects is crucial and that the suggested correction allows for reliable computations.

Chapter 5:Diffusion in Liquids: Experiments, Molecular Dynamics, and Engineering Models

Diffusion in liquids is an old but still important field of research, since a sound understanding and predictive models are lacking. In this chapter, established and novel techniques to obtain concentration-dependent multicomponent diffusion coefficients are presented: (1) Experimental methods: we present established measurement methods but also recently developed techniques which allow for substantial reductions of measurement time and effort. (2) Molecular Dynamics simulations: we present methods for the successful and efficient determination of diffusion coefficients as well as the thermodynamic factor from equilibrium Molecular Dynamics simulations, which allow for prediction of diffusion based on force-field models. (3) Engineering models: established as well as improved, recently developed engineering models for the simple determination of multicomponent diffusion coefficients are described.