Two recent and fully open source COSMO-SAC models are assessed for the first time on the basis of very large experimental data sets. The model performance of COSMO-SAC 2010 and COSMO-SAC-dsp (2013) is studied for vapor−liquid equilibrium (VLE) and infinite dilution activity coefficient (γ i ∞) predictions, and it is benchmarked with respect to the group contribution models UNIFAC and mod. UNIFAC(DO). For this purpose, binary mixture combinations of 2 295 components are investigated. This leads to 10 897 γ i ∞ and 6 940 VLE mixtures, which correspond to 29 173 γ i ∞ and 139 921 VLE data points. The model performance is analyzed in terms of chemical families. A MATLAB program is provided for the interested reader to study the models in detail. The comprehensive assessment shows that there is a clear improvement from COSMO-SAC 2010 to COSMO-SAC-dsp and from UNIFAC to mod. UNIFAC(DO). The mean absolute deviation of γ i ∞ predictions is reduced from 95% to 86% (COSMO-SAC 2010 to COSMO-SAC-dsp) and from 73% to 58% (UNIFAC to mod. UNIFAC(DO)). A combined mean absolute deviation is introduced to study the temperature, pressure, and vapor mole fraction errors of VLE predictions, and it is reduced from 4.77% to 4.63% (COSMO-SAC 2010 to COSMO-SAC-dsp) and from 4.47% to 3.51% (UNIFAC to mod. UNIFAC(DO)). Detailed error analyses show that the accuracy of COSMO-SAC models mainly depends on chemical family types, but not on the molecular size asymmetry or polarity. The present results may serve as a reference for the reliability of predictions with COSMO-SAC methods and provide direction for future developments.
For the first time, the Fick diffusion coefficient matrix of a quaternary liquid mixture is sampled consistently by means of molecular dynamics simulation. The required phenomenological diffusion coefficient and thermodynamic factor matrices of the mixture water + methanol + ethanol + 2-propanol are determined following the Green–Kubo formalism and Kirkwood–Buff theory. Further, a system size correction methodology for the Fick diffusion coefficient of multicomponent mixtures is proposed. Ten compositions are studied under ambient conditions and validated by analyzing the ternary limits of the quaternary Fick diffusion matrix. Because of complex intermolecular interactions due to the presence of hydrogen bonding, the elements of the Fick diffusion coefficient matrix exhibit a significant composition dependence. The magnitude of several cross coefficients indicates important coupling effects mainly affecting the diffusive flux of water. These effects are explained in the light of the structural information given by the radial distribution functions of the mixture. This work that solely rests on molecular dynamics simulation techniques to predict the Fick diffusion coefficient matrix of quaternary mixtures is expected to be a significant step forward for the understanding of multicomponent diffusion.
Kirkwood-Buff integration (KBI) is implemented into the massively-parallel molecular simulation tool ms2 and assessed by molecular dynamics simulations of binary liquid mixtures. The formalism of Krüger et al. (P. Krüger et al., J. Phys. Chem. Lett. 4: 235-238, 2013) that adopts NVT ensemble data to the μVT ensemble is employed throughout. Taking advantage of its linear scaling with inverse system size, the extrapolation to the thermodynamic limit is analyzed. KBI are calculated with standard radial distribution functions (RDF) and two corrected RDF forms. Simulations in the NVT ensemble are carried out in the entire composition range for four Lennard-Jones mixtures, studying system size dependence by varying N = 4000, 8000 and 16000 molecules. Moreover, four mixtures of "real" components are considered with N = 4000. Thermodynamic factor, partial molar volumes and isothermal compressibility are calculated from KBI and compared with benchmark data from NpT ensemble simulations. The assessment shows that the formalism of Krüger et al. greatly improves KBI and that extrapolation is important, particularly for smaller systems.
A new version release (4.0) of the molecular simulation tool ms2 (Deublein et al., 2011; is presented. Version 4.0 of ms2 features two additional potential functions to address the repulsive and dispersive interactions in a more versatile way, i.e. the Mie potential and the Tang-Toennies potential. This version further introduces Kirkwood-Buff integrals based on radial distribution functions, which allow the sampling of the thermodynamic factor of mixtures with up to four components, orientational distribution functions to elucidate mutual configurations of neighboring molecules, thermal diffusion coefficients of binary mixtures for heat, mass as well as coupled heat and mass transport, Einstein relations to sample transport properties with an alternative to the Green-Kubo formalism, dielectric constant of non-polarizable fluid models, vapor-liquid equilibria relying on the second virial coefficient and cluster criteria to identify nucleation.
Expressions for the thermodynamic factor matrix Γ of quaternary mixtures are derived in terms of Kirkwood-Buff integrals and implemented into the massivelyparallel simulation tool ms2. To assess these expressions, a liquid-like supercritical quaternary Lennard-Jones mixture is sampled throughout its entire composition range, employing molecular dynamics in the canonical ensemble. Good agreement is found between numerical chemical potential derivatives and the results from the present Kirkwood-Buff integral expressions. Moreover, the limits of the thermodynamic factor matrix for pure, binary and ternary subsystems are discussed.
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