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. B20041081587315879). 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.

We present a new plugin for LAMMPS for on-the-fly computation of transport properties (OCTP) in equilibrium molecular dynamics. OCTP computes the self- and Maxwell–Stefan diffusivities, bulk and shear viscosities, and thermal conductivities of pure fluids and mixtures in a single simulation. OCTP is the first implementation in LAMMPS that uses the Einstein relations combined with the order-n algorithm for the efficient sampling of dynamic variables. OCTP has low computational requirements and is easy to use because it follows the native input file format of LAMMPS. A tool for calculating the radial distribution function (RDF) of the fluid beyond the cutoff radius, while taking into account the system size effects, is also part of the new plugin. The RDFs computed from OCTP are needed to obtain the thermodynamic factor, which relates Maxwell–Stefan and Fick diffusivities. To demonstrate the efficiency of the new plugin, the transport properties of an equimolar mixture of water–methanol were computed at 298 K and 1 bar.

The number of molecules used in a typical Molecular Dynamics (MD) simulations is orders of magnitude lower than in the thermodynamic limit. It is therefore essential to correct diffusivities computed from Molecular Dynamics simulations for finite-size effects. We present a comprehensive review on finitesize effects of diffusion coefficients by considering self-, Maxwell-Stefan, and Fick diffusion coefficients in pure liquids, as well as binary, ternary, and quaternary mixtures. All finite-size corrections, both analytical and empirical, are discussed in detail. The finite-size effects of rotational and confined diffusion are also briefly discussed.

A method is proposed for calculating the shear viscosity of a liquid from finite-size effects of self-diffusion coefficients in Molecular Dynamics simulations. This method uses the difference in the self-diffusivities, computed from at least two system sizes, and an analytic equation to calculate the shear viscosity. To enable the efficient use of this method, a set of guidelines is developed. The most efficient number of system sizes is two and the large system is at least four times the small system. The number of independent simulations for each system size should be assigned in such a way that 50%–70% of the total available computational resources are allocated to the large system. We verified the method for 250 binary and 26 ternary Lennard-Jones systems, pure water, and an ionic liquid ([Bmim][Tf2N]). The computed shear viscosities are in good agreement with viscosities obtained from equilibrium Molecular Dynamics simulations for all liquid systems far from the critical point. Our results indicate that the proposed method is suitable for multicomponent mixtures and highly viscous liquids. This may enable the systematic screening of the viscosities of ionic liquids and deep eutectic solvents.

The system-size dependence of computed mutual diffusion coefficients of multicomponent mixtures is investigated, and a generalized correction term is derived. The generalized finite-size correction term was validated for the ternary molecular mixture chloroform/acetone/methanol as well as 28 ternary LJ systems. It is shown that only the diagonal elements of the Fick matrix show system-size dependency. The finite-size effects of these elements can be corrected by adding the term derived by Yeh and Hummer (J. Phys. Chem. B 2004, 108, 15873–15879). By performing an eigenvalue analysis of the finite-size effects of the matrix of Fick diffusivities we show that the eigenvector matrix of Fick diffusivities does not depend on the size of the simulation box. Only eigenvalues, which describe the speed of diffusion, depend on the size of the system. An analytic relation for finite-size effects of the matrix of Maxwell–Stefan diffusivities was developed. All Maxwell–Stefan diffusivities depend on the system size, and the required correction depends on the matrix of thermodynamic factors.