Calculation of surface tension of metals using density gradient theory and PC-SAFT equation of state

The Cahn-Hilliard theory was combined with PC-SAFT equation of state (EOS), in order to describe both the phase behaviors and the surface tension of different types of metals (Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Fe, Zn, Cd, In, Sn, Pb, and Bi). The only two inputs of the theory are the Helmholtz free-energy density and the influence parameter. The PC-SAFT equation of state was applied to determine Helmholtz free-energy density and bulk properties. The influence parameter is obtained by fitting to the experimental data of surface tension. The results show a useful possibility to calculate surface tensions which are in satisfactory agreement with experimental data.     

Bulk and Interfacial Properties for CO2-SO2 Binary Mixtures

The perturbed‐chain statistical associating fluid theory (PC‐SAFT) and density‐gradient theory (DGT) were used to construct an equation of state (EOS) for the phase behaviors of carbon dioxide (CO₂)‐sulfur dioxide (SO₂) binary mixtures. The p‐x diagrams at 263 and 333 K, and the p‐T diagrams corresponding to x=0.8871 and 0.6213 were satisfactorily calculated as compared to the experimental data. With the influence parameters of pure components and the equilibrium bulk properties of mixtures as input, the interfacial properties of CO₂‐SO₂ binary mixtures in a wide temperature range were predicted, and the influences of temperature, pressure and bulk properties on the surface tension were discussed.     

Application of the Perturbed-Chain SAFT equation of state to polar systems

The Perturbed-Chain SAFT (PC-SAFT) equation of state is applied to pure polar substances as well as to vapor–liquid and liquid–liquid equilibria of binary mixtures containing polar low-molecular substances and polar co-polymers. For these components, the polar version of the PC-SAFT model requires four pure-component parameters as well as the functional-group dipole moment. For each binary system, only one temperature-independent binary interaction k_ij is needed. Simple mixing and combining rules are adopted for mixtures with more than one polar component without using an additional binary interaction parameter. The ability of the model to accurately describe azeotropic and non-azeotropic vapor–liquid equilibria at low and at high pressures, as well as liquid–liquid equilibria is demonstrated for various systems containing polar components. Solvent systems like acetone–alkane mixtures and co-polymer systems like poly(ethylene-co-vinyl acetate)/solvent are discussed. The results for the low-molecular systems also show the predictive capabilities of the extended PC-SAFT model.     

Vapor–liquid equilibrium measurements and modeling of the n-butane + ethanol system from 323 to 423 K

Vapor–liquid equilibrium (VLE) data are presented for the n-butane + ethanol system in the temperature range from 323 to 423 K. Measurements were performed using a “static-analytic” apparatus, equipped with two electromagnetic ROLSI™ capillary samplers, and thermally regulated via an air bath. This work presents vapor compositions which have not been explicitly measured previously. The modeling of the data was performed using two models: the Peng–Robinson equation of state with the Wong and Sandler mixing rule and NRTL excess function (PR/WS/NRTL); and the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. To assess the effect of dipole–dipole interactions present, a dipolar contribution developed by Jog and Chapman (1999) [20] was tested with the second model. Temperature dependent binary interaction parameters have been adjusted to the new data. The PR/WS/NRTL equation of state shows good correlation with the results, while the PC-SAFT is slightly less accurate.     

Vapor–liquid equilibrium in the n-butane + methanol system,measurement and modeling from 323.2 to 443.2 K

New experimental vapor–liquid equilibrium (VLE) data for the n-butane + methanol binary system are reported over a wide temperature range from 323.2 to 443.2 K and pressures up to 5.4 MPa. A static–analytic apparatus, taking advantage of two pneumatic capillary samplers, was used. The phase equilibrium data generated in this work are in relatively good agreement with previous data reported in the literature. Three different thermodynamic models have been used to represent the new experimental data. The first model is the cubic-based Peng–Robinson equation of state (EoS) combined with the Wong–Sandler mixing rules. The two other models are the non-cubic SAFT-VR and PC-SAFT equations of state. Temperature-dependent binary interaction parameters have been adjusted to the new data. The three models accurately represent the new experimental data, but deviations are seen to increase at low temperature. A similar evolution of the binary parameters with respect to temperature is observed for the three models. In particular a discontinuity is observed for the k_ij values at temperatures close to the critical point of butane, indicating the effects of fluctuations on the phase equilibria close to critical points.     

One parameter friction theory models for viscosity

In this work the friction theory (f-theory) for viscosity modeling is used in conjunction with the SRK, PR and PRSV cubic equations of state in order to develop three one parameter general models for viscosity prediction. The models are considered one parameter models because they only require a characteristic critical velocity, which is a parameter normally not tabulated. The models use these rather simple cubic equations of state as a basis to obtain accurate modeling of the viscosity of fluids for wide ranges of temperature and pressure. The general models presented in this work are based on the viscosity behavior of n-alkanes from methane to n-octadecane. Although best performance is obtained for the considered n-alkanes, a good model performance is also obtained for other systems. Thus, recommended characteristic critical viscosity values for several systems are also reported in this work. However, in the case of n-alkanes, an empirical equation for the characteristic critical viscosity is provided so that no additional parameters are required. In addition, with the use of simple mixing rules, the viscosity of several binary to quaternary n-alkane mixtures can also be predicted with a satisfactory accuracy.     

Parameters estimation and VLE calculation in asymmetric binary mixtures containing carbon dioxide + n-alkanols

In the present work, the estimation of the parameters for asymmetric binary mixtures of carbon dioxide + n-alkanols has been developed. The binary interaction parameter k₁₂ of the second virial coefficient and non-random two liquid model parameters τ₁₂ and τ₂₁ were obtained using Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules. In all cases, Levenberg–Marquardt minimization algorithm was used for the parameters optimization employing an objective function based on the calculation of the distribution coefficients for each component. Vapor–liquid equilibrium for binary asymmetric mixtures (CO₂ + n-alkanol, from methanol to 1-decanol) was calculated using the obtained values of the mentioned parameters. The agreement between calculated and experimental values was satisfactory.     

Viscosity of heavy n-alkanes and diffusion of gases therein based on molecular dynamics simulations and empirical correlations

The viscosity of pure n-alkanes and n-alkane mixtures was studied by molecular dynamics (MD) simulations using the Green–Kubo method. n-Alkane molecules were modeled based on the Transferable Potential for Phase Equilibria (TraPPE) united atom force field. MD simulations at constant number of molecules or particles, volume and temperature (NVT) were performed for n-C₈ up to n-C₉₆ at different temperatures as well as for binary and six-component n-alkane mixtures which are considered as prototypes for the hydrocarbon wax produced during the Gas-To-Liquid (GTL) Fischer–Tropsch process. For the pure n-alkanes, good agreement between our simulated viscosities and existing experimental data was observed. In the case of the n-alkane mixtures, the composition dependence of viscosity was examined. The simulated viscosity results were compared with literature empirical correlations. Moreover, a new macroscopic empirical correlation for the calculation of self-diffusion coefficients of hydrogen, carbon monoxide, and water in n-alkanes and mixtures of n-alkanes was developed by combining viscosity and self-diffusion coefficient values in n-alkanes. The correlation was compared with the simulation data and an average absolute deviation (AAD) of 11.3% for pure n-alkanes and 14.3% for n-alkane mixtures was obtained.     

Measurements and equation-of-state modelling of thermodynamic properties of binary mixtures of 1-butyl-1-methylpyrrolidinium tetracyanoborate ionic liquid with molecular compounds

This paper presents a comprehensive thermodynamic study of binary mixtures formed by 1-butyl-1-methylpyrrolidinium tetracyanoborate ionic liquid and hydrocarbons (n-heptane, benzene, toluene, ethylbenzene), thiophene and alcohols (methanol, ethanol, 1-propanol, 1-butanol, 1-hexanol, 1-octanol, 1-decanol and 1-dodecanol). An impact of chemical structure of molecular compounds on their solubility in the ionic liquid and excess enthalpies of mixing is discussed. Furthermore, modelling of the measured properties by using perturbed-chain statistical associating fluid theory (PC-SAFT) is presented. The theory is applied in both correlative and semi-predictive mode involving temperature-dependent binary corrections fitted to infinite dilution activity coefficients. Solubility curves and excess enthalpies are captured by the model with a reasonable accuracy, when semi-predictive strategy is adopted. Moreover, (liquid + liquid) equilibrium phase diagram in ternary system composed of the investigated ionic liquid, thiophene and n-heptane is predicted with PC-SAFT and then the calculations are confronted with available experimental data. The results indicate that the approach proposed can be perceived as an interesting tool for reproducing the thermodynamic behaviour disclosed by such complex systems as those based on ionic liquids.     

Interfacial properties of water + alcohol mixtures

Mixtures of water with alcohol are important in numerous engineering applications. Caused by the polarity of water and alcohol self-association of water and alcohol as well cross-association between water and alcohol appear in such complex mixtures. These features show significant impact on physical and chemical properties, especially phase equilibrium behaviour and hence interfacial properties. The Cahn–Hilliard theory was combined with original statistical associated fluid theory equation of states (SAFT EOS) in order to describe both the phase behaviour and interfacial properties with respect of association. The paper focuses on theoretical investigations of surface tension, density profiles, surface thickness in vapour–liquid or vapour–liquid–liquid equilibrium of mixtures of water with ethanol or 1-butanol. Results of vapour–liquid equilibrium surface tension calculations were compared with experimental data taken from the literature.     

Predicting Excess Enthalpies of Ether and/or Hydrocarbon Binary Mixtures

Previous applications of the Flory–Patterson theory in the analysis of the excess molar enthalpies at 25°C for some binary mixtures composed of ethers, n-alkanes, br-alknes, and cycloalkanes are reviewed. The possibility of correlating the Flory interaction parameters X _ij in terms of the acentric factors of the components is examined. For selected ether (1) + n-alkane(2) mixtures, a set of linear relations between X ₁₂ and the acentric factors of the n-alkanes are reported.Visiting Professor on sabbatical leave from the     

Prediction of the second cross virial coefficients of nonpolar binary mixtures

The binary interaction parameter, k_ij, of 268 nonpolar mixtures were determined from the database of second cross virial coefficients containing 1728 experimental data points by fitting the second cross virial coefficients with a new correlation for pure compounds [L. Meng, Y.Y. Duan, L. Li, Fluid Phase Equilib. 226 (2004) 109–120] and classical mixing rules. Regularity distributions were found for both n-alkane/n-alkane binaries and fluorocarbon/fluorocarbon binaries. Correlations were developed following Tsonopoulos’ ideas [C. Tsonopoulos, Adv. Chem. Ser. 182 (1979) 143–162] with the quantity of binary compounds enlarged using Dymond's latest complication [J.H. Dymond, K.N. Marsh, R.C. Wilhoit, Virial Coefficients of Pure Gases and Mixtures, Subvolume B, Virial Coefficients of Mixtures, Series IV/21B, Landolt-Börnstein, 2002]. Correlations were also developed for inorganic/n-alkane binaries using new k_ij values. The predictions do not need any thermodynamic property parameters besides the carbon number. Comparisons with the existing correlations show that the present work is more accurate for nonpolar binary mixtures.     

Liquid–liquid equilibrium data for binary perfluoroalkane (C6 and C8) + n-alkane systems

This study aims to make detailed measurements of the solubility data for perfluoroalkane + n-alkane systems. Using a laser-scattering technique developed in our laboratory, we determined the liquid–liquid equilibria (LLE) for three binary mixtures: perfluorohexane + n-hexane, perfluorohexane + n-octane, and perfluorooctane + n-octane. The experimental LLE data were represented by the NRTL equation. In addition, the activity coefficients obtained from the experimental LLE data were compared with those obtained from the vapor–liquid equilibrium (VLE) data.     

Excess enthalpies of binary mixtures of n-octane with each of the hexane isomers at 298.15 K

Excess molar enthalpies, measured at 298.15 K in a flow microcalorimeter, are reported for the five binary systems formed by mixing n-octane with n-hexane, 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane and 2,3-dimethylbutane. The results for equimolar mixtures, together with similar data for other n-alkane + hexane isomer mixtures, are correlated in terms of the acentric factors of the n-alkanes.     

Density-functional theory for polymer-carbon dioxide mixtures: A perturbed-chain SAFT approach

We propose a density-functional theory (DFT) describing inhomogeneous polymer-carbon dioxide mixtures based on a perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The weight density functions from fundamental measure theory are used to extend the bulk excess Helmholtz free energy to the inhomogeneous case. The additional long-range dispersion contributions are included using a mean-field approach. We apply our DFT to the interfacial properties of polystyrene-CO(2) and poly(methyl methacrylate) CO(2) systems. Calculated values for both solubility and interfacial tension are in good agreement with experimental data. In comparison with our earlier DFT based on the Peng-Robinson-SAFT EOS, the current DFT produces quantitatively superior agreement with experimental data and is free of the unphysical behavior at high pressures (>35 MPa) in the earlier theory.