Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering , Delft University of Technology , Leeghwaterstraat 39 , 2628CB Delft , The Netherlands.
Institute of Technical Thermodynamics , RWTH Aachen University , 52056 Aachen , Germany.
J Chem Theory Comput. 2018 May 8;14(5):2667-2677. doi: 10.1021/acs.jctc.8b00170. Epub 2018 Apr 30.
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.
采用分子动力学模拟的方法对 Maxwell-Stefan 扩散系数的有限尺寸效应进行了预测，研究对象涉及多种二元 Lennard-Jones 体系。模拟结果表明，计算得到的扩散系数与体系尺寸存在较强的依赖性，且随着分子数量的增加而增加。我们基于 Yeh 和 Hummer 的研究成果（J. Phys. Chem. B, 2004, 108, 15873 - 15879 ），提出了一种将 Maxwell-Stefan 扩散系数外推到热力学极限的修正方法。该修正方法是体系黏度、模拟盒尺寸和热力学因子的函数，其中热力学因子是混合物非理想性的度量。我们对 200 多种不同的二元 Lennard-Jones 体系以及甲醇、水、乙醇、丙酮、甲胺和四氯化碳等 9 种二元混合物体系进行了验证。结果表明，对于接近相分离的混合物，有限尺寸 Maxwell-Stefan 扩散系数与热力学极限下对应的扩散系数之间存在显著偏差。在这些情况下，有限尺寸修正甚至可能大于模拟的（有限尺寸）Maxwell-Stefan 扩散系数。我们的研究结果表明，考虑这些有限尺寸效应至关重要，并且建议的修正方法可以实现可靠的计算。
