Extension of the SAFT-VR Mie EoS To Model Homonuclear Rings and Its Parametrization Based on the Principle of Corresponding States

The statistical associating fluid theory of variable range employing a Mie potential (SAFT-VR-Mie) proposed by Lafitte et al. (<i>J. Chem Phys.</i> <b>2013</b>, <i>139</i>, 154504) is one of the latest versions of the SAFT family. This particular version has been shown to have a remarkable capability to connect experimental determinations, theoretical calculations, and molecular simulations results. However, the theoretical development restricts the model to chains of beads connected in a linear fashion. In this work, the capabilities of the SAFT-VR Mie equation of state for modeling phase equilibria are extended for the case of planar ring compounds. This modification proposed replaces the Helmholtz energy of chain formation by an empirical contribution based on a parallelism to the second-order thermodynamic perturbation theory for hard sphere trimers. The proposed expression is given in terms of an extra parameter, χ, that depends on the number of beads, <i>m</i>_s, and the geometry of the ring. The model is used to describe the phase equilibrium for planar ring compounds formed of Mie isotropic segments for the cases of <i>m</i>_s equals to 3, 4, 5 (two configurations), and 7 (two configurations). The resulting molecular model is further parametrized, invoking a corresponding states principle resulting in sets of parameters that can be used indistinctively in theoretical calculations or in molecular simulations without any further refinements. The extent and performance of the methodology has been exemplified by predicting the phase equilibria and vapor pressure curves for aromatic hydrocarbons (benzene, hexafluorobenzene, toluene), heterocyclic molecules (2,5-dimethylfuran, sulfolane, tetrahydro-2<i>H</i>-pyran, tetrahydrofuran), and polycyclic aromatic hydrocarbons (naphthalene, pyrene, anthracene, pentacene, and coronene). An important aspect of the theory is that the parameters of the model can be used directly in molecular dynamics (MD) simulations to calculate equilibrium phase properties and interfacial tensions with an accuracy that rivals other coarse grained and united atom models, for example, liquid densities, are predicted, with a maximum absolute average deviation of 3% from both the theory and the MD simulations, while the interfacial tension is predicted, with a maximum absolute average of 8%. The extension to mixtures is exemplified by considering a binary system of hexane (chain fluid) and tetrahydro-2<i>H</i>-pyran (ring fluid)

Comparison of United-Atom Potentials for the Simulation of Vapor–Liquid Equilibria and Interfacial Properties of Long-Chain <i>n</i>-Alkanes up to <i>n</i>-C₁₀₀

Canonical ensemble molecular dynamics (MD) simulations are reported which compute both the vapor–liquid equilibrium properties (vapor pressure and liquid and vapor densities) and the interfacial properties (density profiles, interfacial tensions, entropy and enthalpy of surface formation) of four long-chained <i>n</i>-alkanes: <i>n</i>-decane (<i>n</i>-C₁₀), <i>n</i>-eicosane (<i>n</i>-C₂₀), <i>n</i>-hexacontane (<i>n</i>-C₆₀), and <i>n</i>-decacontane (<i>n</i>-C₁₀₀). Three of the most commonly employed united-atom (UA) force fields for alkanes (SKS: Smit, B.; Karaborni, S.; Siepmann, J. I. <i>J. Chem. Phys</i>. <b>1995,</b> <i>102</i>, 2126–2140; <i>J. Chem. Phys</i>. <b>1998,</b> <i>109</i>, 352; NERD: Nath, S. K.; Escobedo, F. A.; de Pablo, J. J. <i>J. Chem. Phys</i>. <b>1998</b>, <i>108</i>, 9905–9911; and TraPPE: Martin M. G.; Siepmann, J. I. <i>J. Phys. Chem. B</i> <b>1998</b>, <i>102</i>, 2569–2577.) are critically appraised. The computed results have been compared to the available experimental data and those fitted using the square gradient theory (SGT). In the latter approach, the Lennard–Jones chain equation of state (EoS), appropriately parametrized for long hydrocarbons, is used to model the homogeneous bulk phase Helmholtz energy. The MD results for phase equilibria of <i>n</i>-decane and <i>n</i>-eicosane exhibit sensible agreement both to the experimental data and EoS correlation for all potentials tested, with the TraPPE potential showing the lowest deviations. However, as the molecular chain increases to <i>n</i>-hexacontane and <i>n</i>-decacontane, the reliability of the UA potentials decreases, showing notorious subpredictions of both saturated liquid density and vapor pressure. Based on the recommended data and EoS results for the heaviest hydrocarbons, it is possible to attest, that in this extreme, the TraPPE potential shows the lowest liquid density deviations. The low absolute values of the vapor pressure preclude the discrimination among the three UA potentials studied. On the other hand, interfacial properties are very sensitive to the type of UA potential thus allowing a differentiation of the potentials. Comparing the interfacial tension MD results to the available experimental data and SGT results, the TraPPE model exhibits the lowest deviations for all hydrocarbons

Resolving Discrepancies in the Measurements of the Interfacial Tension for the CO₂ + H₂O Mixture by Computer Simulation

Literature values regarding the pressure dependence of the interfacial tension of the system of carbon dioxide (CO₂) + water (H₂O) show an unexplained divergence and scatter at the transition between low-pressure gas–liquid equilibrium and the high-pressure liquid–liquid equilibrium. We employ the Statistical Associating Fluid Theory (SAFT) and canonical molecular dynamics simulations based on the corresponding coarse grained force field to map out the phase diagram of the mixture and the interfacial tension for this system. We showcase how at ambient temperatures a triple point (gas–liquid–liquid) is expected and detail the implications that the appearance of the third phase has on the interfacial tensions of the system

Force Fields for Coarse-Grained Molecular Simulations from a Corresponding States Correlation

We present a corresponding states correlation based on the description of fluid phase properties by means of an Mie intermolecular potential applied to tangentially bonded spheres. The macroscopic properties of this model fluid are very accurately represented by a recently proposed version of the Statistical Associating Fluid Theory (the SAFT-γ version). The Mie potential can be expressed in a conformal manner in terms of three parameters that relate to a length scale, σ, an energy scale, ε, and the range or functional form of the potential, λ, while the nonsphericity or elongation of a molecule can be appropriately described by the chain length, <i>m</i>. For a given chain length, correlations are given to scale the SAFT equation of state in terms of three experimental parameters: the acentric factor, the critical temperature, and the saturated liquid density at a reduced temperature of 0.7. The molecular nature of the equation of state is exploited to make a direct link between the macroscopic thermodynamic parameters used to characterize the equation of state and the parameters of the underlying Mie potential. This direct link between macroscopic properties and molecular parameters is the basis to propose a top-down method to parametrize force fields that can be used in the coarse grained molecular modeling (Monte Carlo or molecular dynamics) of fluids. The resulting correlation is of quantitative accuracy and examples of the prediction of simulations of vapor–liquid equilibria and interfacial tensions are given. In essence, we present a recipe that allows one to obtain intermolecular potentials for use in the molecular simulation of simple and chain fluids from macroscopic experimentally determined constants, namely the acentric factor, the critical temperature, and a value of the liquid density at a reduced temperature of 0.7

Vapor–Liquid Equilibrium, Densities, and Interfacial Tensions of the System Ethanol + Tetrahydro-2<i>H</i>-pyran

Isobaric vapor–liquid equilibrium (VLE) data have been measured for the binary system ethanol + tetrahydro-2<i>H</i>-pyran at (50, 75, and 94) kPa and over the temperature range (331 to 358) K using a vapor–liquid equilibrium still with circulation of both phases. Mixing volumes were also determined at 298.15 K and atmospheric pressure with a vibrating tube densimeter, while a maximum differential bubble pressure tensiometer was used to measure atmospheric interfacial tensions at 303.15 K. According to experimental results, the mixture exhibits positive deviation from ideal behavior, and minimum boiling point azeotropy is present at mid-range concentrations (0.55 < <i>x</i>₁^Az < 0.67). VLE measurements show also that the azeotropic mole fraction impoverishes in ethanol as pressure (or temperature) increases. The mixing volumes of the mixture evolve from positive to negative deviations as the concentration of ethanol increases. Finally, it is experimentally observed that the interfacial tensions exhibit positive deviations from the linear behavior. The VLE data of the binary mixture satisfy Fredenlund's consistency test and were well-correlated by the Wohl, nonrandom two-liquid (NRTL), Wilson, and universal quasichemical (UNIQUAC) equations for all of the measured isobars. The mixing volumes and interfacial tensions, in turn, were satisfactorily correlated using the Redlich–Kister equation

Surface Tension of 1‑Ethyl-3-methylimidazolium Ethyl Sulfate or 1‑Butyl-3-methylimidazolium Hexafluorophosphate with Argon and Carbon Dioxide

Surface tensions of two ionic liquids (IL): 1-ethyl-3-methylimidazolium ethyl sulfate and 1-butyl-3-methylimidazolium hexafluorophosphate in pressurized atmospheres of argon and carbon dioxide have been measured over the temperature range (303 to 366) K and over the pressure range (0.1 to 15) MPa for the case of argon atmosphere and (0.1 to 5) MPa for the case of carbon dioxide atmosphere by using a pendant drop tensiometer. Based on the experimental measurements, the isothermal surface tension of all IL–gas systems studied decreases as the pressure increases, evidencing a gas adsorption at the IL interface. Isobaric surface tension of an IL–gas does not show a general pattern as the temperature increases. In order to verify the isothermal surface behavior, the relative Gibbs adsorption isotherms have been calculated from the surface tension data by using the theoretical Guggenheim model, corroborating the gas adsorption processes at the IL interface. Comparing the relative Gibbs adsorption isotherms, it is possible to conclude that the ILs studied have the capability to adsorb more carbon dioxide than argon. This fact provides relevant information to use the IL as a capturing agent for carbon dioxide and the use of argon to store pure ILs

Comprehensive Characterization of Interfacial Behavior for the Mixture CO₂ + H₂O + CH₄: Comparison between Atomistic and Coarse Grained Molecular Simulation Models and Density Gradient Theory

The accurate description of the phase equilibria and interfacial behavior of the ternary mixture H₂O + CO₂ + CH₄ is of fundamental importance in processes related with enhanced natural gas recovery, CO₂ storage, and gas-oil miscibility analysis. For this reason, the physical understanding and theoretical modeling of this remarkably complex mixture, in a wide range of thermodynamic conditions, constitutes a challenging task both for scientists and engineers. This work focuses on the description of the interfacial behavior of this mixture, with special emphasis on several regions that yield different scenarios (vapor–liquid, liquid–liquid, and vapor–liquid–liquid equilibria) and in pressure and temperature ranges related with the practical applications previously mentioned. A comparison between three alternative approaches has been performed: atomistic Monte Carlo simulations (MC), coarse grained molecular dynamics (CG-MD) simulations, and density gradient theory (DGT) have been used to characterize the interfacial region, describing in detail complex phenomena, including preferential adsorption and wetting phenomena even in the ternary triphasic region. Agreement between the results obtained from different methods indicate that the three alternative approaches are fully equivalent to analyze the interfacial behavior. It has been also found that the preferential adsorption of CO₂ over H₂O interface is greater if compared to CH₄ in all conditions characterized. In fact, we have also demonstrated that CH₄ under triphasic conditions has very limited influence on the complete wetting of the binary system H₂O + CO₂