Vapor–liquid equilibria and phase densities at saturation of carbon dioxide + 1-butanol and carbon dioxide + 2-butanol from 313 to 363 K

Experimental vapor–liquid equilibria for the systems carbon dioxide + 1-butanol and carbon dioxide + 2-butanol were obtained from 313 to 363 K via a static-analytic set-up. A vibrating U-tube densitometer was coupled to this apparatus to perform simultaneous measurements of both saturated densities of the vapor and liquid phases. The suitability of this apparatus was checked by comparing the experimental vapor–liquid equilibrium and saturated density results with the literature data. The experimental vapor–liquid equilibrium data were correlated using the Peng–Robinson equation of state coupled to the Wong–Sandler mixing rules with good agreement; however densities using the same model were not satisfactorily represented.     

Modeling of three-phase vapor–liquid–liquid equilibria for a natural-gas system rich in nitrogen with the SRK and PC-SAFT EoS

In this work, we present the modeling of three-phase vapor–liquid–liquid equilibria for a mixture of natural gas (Hogback gas) containing high concentrations in nitrogen (51.8 mol%) with the SRK and PC-SAFT equations of state. The interest of studying this mixture is due to the experimental evidence of the occurrence of multiple equilibrium liquid phases for this mixture over certain ranges of temperature and pressure. The calculation of the multiphase equilibria was carried out by using an efficient numerical procedure based on the minimization of the system Gibbs energy and thermodynamic stability tests to find the most stable state of the system. The results of the calculated vapor–liquid–liquid equilibria (VLLE) show that the PC-SAFT equation of state predicts satisfactorily the phase behavior that experimentally exhibits this mixture, whereas the SRK equation of state predicts a three-phase region wider than the experimentally observed. The two-phase boundary for this mixture was also calculated through flash calculations, and the results showed that this mixture does not present any gas-liquid critical point.     

Isobaric vapor–liquid and vapor–liquid–liquid equilibrium data for the water–ethanol–hexane system

Isobaric vapor–liquid and vapor–liquid–liquid equilibria were measured for the water–ethanol–hexane system at normal atmospheric pressure. The apparatus used for the determination of vapor–liquid–liquid equilibrium data was an all-glass dynamic recirculating still with an ultrasonic homogenizer coupled to the boiling flask.     

Measurement and correlation of vapor–liquid equilibria for methanol + methyl laurate and methanol + methyl myristate systems near critical temperature of methanol

A flow-type method was adopted to measure the vapor–liquid equilibria for methanol + methyl laurate and methanol + methyl myristate systems at 493–543 K, near the critical temperature of methanol (T_c = 512.64 K), and 2.16–8.49 MPa. The effect of temperature and fatty acid methyl esters to the phase behavior was discussed. The mole fractions of methanol in liquid phase are almost the same for both systems. In vapor phase, the mole fractions of methanol are very close to unity at all temperatures. The present vapor–liquid equilibrium data were correlated by PRASOG. A binary parameter was introduced to the combining rule of size parameter. The binary parameters of methanol + fatty acid methyl ester systems were determined by fitting the present experimental data. The correlated results are in good agreement with the experimental data. The vapor–liquid equilibria for methanol + methyl laurate + glycerol and methanol + methyl myristate + glycerol ternary systems were also predicted using the methanol + fatty acid methyl ester binary parameters. The mole fractions of methanol in vapor phase are around unity even if glycerol is included in the systems.     

Closed-packed lattice model for polymer solution systems considering the chain length dependence effect: Correlating LLE,VLE, and gel swelling behaviors using identical interaction energy parameters

We propose a new Helmholtz energy of mixing equation following the original Flory–Huggins (F–H) closed-packed lattice model. Also, to overcome F–H mean-field approximation, we introduce new universal constants to consider chain length dependence of polymer in solvent and consider specific interactions to describe strongly interacting polymer systems. Our proposed model successfully describes liquid–liquid equilibria (LLE) for binary polymer–solvent systems using identical interaction parameters which do not depend on the polymer molecular weight. We also describe vapor–liquid equilibria (VLE) for polymer/solvent systems and swelling equilibria of thermosensitive hydrogel systems using the same energy parameters obtained from LLE calculations.     

Phase behavior of the system hyperbranched polyglycerol + methanol + carbon dioxide

Phase equilibrium data have been measured for the ternary system hyperbranched polyglycerol + methanol + carbon dioxide at temperatures of 313–450 K and pressures up to 13.5 MPa. Phase changes were determined according to a synthetic method using the Cailletet setup. At elevated temperatures the system shows a liquid–liquid–vapor region with lower solution temperatures. Besides the vapor–liquid and liquid–liquid equilibria, the vapor–liquid to vapor–liquid–liquid and vapor–liquid–liquid to liquid–liquid phase boundaries are reported at different polymer molar masses and can serve as test sets for thermodynamic models. A distinct influence of the polymer molar mass on the vapor–liquid equilibrium can be noticed and indicates the existence of structural effects due to the polymer branching. Modeling the systems with the PCP-SAFT equation of state confirms these findings.     

Effect of pressure on rotational isomers in solution: infrared and Raman spectroscopy

The effect of pressure on the conformational equilibria between rotational isomers in solution has been studied by the infrared and Raman spectroscopy. The experimental volume changes for the transformation are explained theoretically by the three effects contributing to these volume changes, namely the overlap of the atoms with the internal rotation angle, the change of local packing of the solute and solvent, and the change of the electrostatic interaction with the solvent. The purpose of this paper is to review what is known about the volume changes for small molecules with internal rotation angles.     

New analytic apparatus for experimental determination of vapor–liquid equilibria and saturation densities

A new experimental apparatus for performing simultaneous determination of high-pressure vapor–liquid equilibria (VLE) and saturated densities was developed in this work. The experimental methodology was verified by measuring these properties for the carbon dioxide + 1-propanol and carbon dioxide + 2-propanol systems from 313 to 363 K. The apparatus is based on the static-analytic method for VLE determinations and was slightly modified by coupling a vibrating U-tube densitometer to obtain saturated densities for both vapor and liquid phases. VLE measurements agreed with previous literature data and were correlated with the Peng–Robinson equation of state coupled to the Wong–Sandler mixing rules. Saturation densities at temperatures above 313 K have not been published up to now.     

Molecular modelling of liquid crystal systems: An internal coordinate Monte Carlo approach

A Monte Carlo scheme is presented which is designed to provide a convenient mechanism to model accurately the internal molecular structure of liquid crystalline molecules. The technique stores atomic positions in terms of bond lengths, bond angles and dihedral angles within a Z-matrix, and the Monte Carlo scheme involves generating trial configurations from changes to the Z-matrix using the MM2 molecular mechanics potential to describe energy changes between different molecular conformations. The technique is applied to the liquid crystal molecule 4-n-pentyl-4'-cyanobiphenyl (5CB), and results are presented for the conformational populations and dihedral angle distributions of 5CB in the gas phase at 300 K. The effect of a nematic mean field on the distribution of molecular conformations is also examined via the addition of a conformation-dependent potential of mean torque to the internal energy.     

Phase equilibria of imidazolium ionic liquids and the refrigerant gas, 1,1,1,2-tetrafluoroethane (R-134a)

A number of applications with ionic liquids (ILs) and hydrofluorocarbon gases have recently been proposed. Detailed phase equilibria and modeling are needed for their further development. In this work, vapor–liquid equilibrium, vapor–liquid–liquid equilibrium, and mixture critical points of imidazolium ionic liquids with the hydrofluorocarbon refrigerant gas, 1,1,1,2-tetrafluoroethane (R-134a) was measured at temperatures of 25 °C, 50 °C, 75 °C and pressure up to 143 bar. The ionic liquids include 1-hexyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)amide ([HMIm][Tf₂N]), 1-hexyl-3-methyl-imidazolium hexafluorophosphate ([HMIm][PF₆]), and 1-hexyl-3-methyl-imidazolium tetrafluoroborate ([HMIm][BF₄]). The effects of the anion and cation on the solubility were investigated with the anion having greatest impact. [HMIm][Tf₂N] demonstrated the highest solubility of R-134a. The volume expansion and molar volume were also measured for the ILs and R-134a. The Peng–Robinson Equation of State with van der Waals 2-parameter mixing rule with estimated IL critical points were employed to model and correlate the experimental data. The models predict the vapor–liquid equilibrium and vapor–liquid–liquid equilibrium pressure very well. However, the mixture critical points predictions are consistently lower than experimental values.     

A simplified approach to vapor–liquid equilibria calculations with the group-contribution lattice-fluid equation of state

Equations of state that are based on the lattice-statistics approach use Guggenheim's quasi-chemical approximation to describe the non-randomness in the mixture due to the energetic interactions between the molecules. For ternary and higher-component systems the non-randomness expression is complex and requires an iterative calculation procedure. We have shown that the non-randomness parameters play a negligible role in the application of the GCLF-EoS model (based on the Panayiotou–Vera EoS) for predicting vapor–liquid equilibria. Omission of the non-randomness parameters from such calculations can significantly improve the computation efficiency. Binary, ternary, and quaternary vapor–liquid equilibria predictions were made including polystyrene, polyvinyl acetate, polyethylene, and polypropylene in polar and non-polar solvents to test the theory.     

Torsional potential of 4,4'-bipyridine: ab initio analysis of dispersion and vibrational effects

Ab initio calculations using restricted Hartree-Fock, second-order M?ller-Plesset perturbation theory (MP2), density-functional theory (DFT), and coupled-cluster methods have been done to obtain the torsional potential-energy profile of the aza-aromatic molecule 4,4'-bipyridine. The torsional potential is evaluated adiabatically by fixing the normalized sum of the dihedral angles through the C-C inter-ring bond at several values along the torsional path and relaxing the remaining degrees of freedom. Previous discrepancies between MP2 and DFT internal rotation barrier heights are removed, and seen to be mostly due to the underestimation of the dispersion energy in the coplanar conformer by MP2 when using relatively small basis sets. The calculations indicate that the barrier height between the twisted global minimum and the 0 degrees conformer is around 1.5-1.8 kcal mol-1 while that corresponding to the 90 degrees one is about 2.0-2.2 kcal mol-1. This same relative energy ordering of the coplanar and perpendicular conformers was experimentally derived from nuclear magnetic resonance (NMR) measurements of 1H dipolar couplings on 4,4'-bipyridine solutions in a nematic liquid crystal, although the barrier heights are much lower than those estimated from NMR experiments in the gas phase. The DFT infrared spectrum and zero-point vibrational energy corrections to the torsional energy profile have also been calculated, the latter having a small influence on the torsional potential-energy profiles.     

Isobaric vapor–liquid–liquid equilibrium and vapor–liquid equilibrium for the system water–ethanol-1,4-dimethylbenzene at 101.3 kPa

An all-glass, dynamic recirculating still equipped with an ultrasonic homogenizer has been used to determine vapor–liquid (VLE) and vapor–liquid–liquid (VLLE) equilibria. Consistent data have been obtained for the ternary water + ethanol + p-xylene system at 101.3 kPa for temperatures in the range of 351.16–365.40 K. Experimental results have been used to check the accuracy of the UNIFAC, UNIQUAC and NRTL models in the liquid–liquid region of importance in the dehydration of ethanol by azeotropic distillation.     

Classical and recent free-volume models for polymer solutions: A comparative evaluation

In this work, two “classical” (UNIFAC-FV, Entropic-FV) and two “recent” free-volume (FV) models (Kannan-FV, Freed-FV) are comparatively evaluated for polymer–solvent vapor–liquid equilibria including both aqueous and non-aqueous solutions. Moreover, some further developments are presented here to improve the performance of a recent model, the so-called Freed-FV. First, we propose a modification of the Freed-FV model accounting for the anomalous free-volume behavior of aqueous systems (unlike the other solvents, water has a lower free-volume percentage than polymers). The results predicted by the modified Freed-FV model for athermal and non-athermal polymer systems are compared to other “recent” and “classical” FV models, indicating an improvement for the modified Freed-FV model for aqueous polymer solutions. Second, for the original Freed-FV model, new UNIFAC group energy parameters are regressed for aqueous and alcohol solutions, based on the physical values of the van der Waals volume and surface areas for both FV-combinatorial and residual contributions. The prediction results of both “recent” and “classical” FV models using the new regressed energy parameters are significantly better, compared to using the classical UNIFAC parameters, for VLE of aqueous and alcohol polymer systems.     

Analyse conformationnelle théorique des molécules de benzylidène-aniline, stilbène et azobenzène : Partie II. Résultats de la méthode PCILO et ajustement d''un potentiel empirique

A conformational study of the benzylidene-aniline stilbene and azobenzene isoelectronic molecules has been carried out by the PCILO method in terms of torsional angles, bond lengths and valence angles. Initially, the conditions of application of this method to highly conjugated molecules were defined. The optimized geometries are in good agreement with those determined in the gas phase. Furthermore the rotation around a Ф—N or Ф—C bond can be specifically related to the variation of the second-order correction to the energy. This term was used to adjust the torsional potential in an empirical method adapted to this kind of molecule and able to account for both theoretical and experimental results.     

Free energy surfaces for the alpha(1 --> 4)-glycosidic linkage: implications for polysaccharide solution structure and dynamics

We present a potential of mean force surface for rotation about phi and psi dihedral angles of the alpha(1 --> 4)-glycosidic linkage in the maltose disaccharide (4-O-alpha-d-glucopyranosyl-d-glucopyranose) in aqueous solution. Comparison of the vacuum and solution free energy surfaces for maltose shows the principal effects of water to be an increase in the rotational freedom of the alpha(1 --> 4) linkage brought about by lowering the energy barrier for syn to anti conformational changes as well as expansion of the range of low-energy phi,psi conformations. This free energy analysis thus provides a thermodynamic and conformational rationale for the effects of water on alpha(1 --> 4)-linked polysaccharides and carbohydrate glasses.     

High-pressure vapor–liquid and vapor–liquid–liquid equilibria in the carbon dioxide + 1-heptanol system

Vapor–liquid equilibria (VLE) and vapor–liquid–liquid equilibria (VLLE) data for the carbon dioxide + 1-heptanol system were measured at 293.15, 303.15, 313.15, 333.15 and 353.15 K. Phase behavior measurements were made in a high-pressure visual cell with variable volume, based on the static-analytic method. The pressure range under investigation was between 0.58 and 14.02 MPa. The Soave–Redlich–Kwong (SRK)-EOS coupled with Huron–Vidal (HV) mixing rules and a reduced UNIQUAC model, was used in a semi-predictive approach, in order to represent the complex phase behavior (critical curve, LLV line, isothermal VLE, LLE, and VLLE) of the system. The topology of phase behavior is qualitatively correct predicted.     

Equation of state for square-well chain molecules with variable range. I: Application for pure substances

An equation of state (EOS) for square-well chain molecules with variable range developed on the basis of statistical mechanics for chemical association in our previous work is employed for the calculations of pVT properties and vapor–liquid equilibria (VLE) of pure non-associating fluids. The molecular parameters for 73 normal substances and 46 polymers are obtained from saturated vapor pressure and liquid molar volume data for normal fluids or pVT data for polymers. Linear relations are found for the molecular parameters of normal fluids with their molecular weight of homologous compounds. This indicates that the model parameters of homologous series, subsequently pVT and VLE, can be predicted when experimental data are not available. The predicted saturated vapor pressures and/or liquid volumes are satisfactory through the generalized model parameters. The calculated VLE and pVT for normal fluids and polymers by this EOS are compared with those from other engineering models, respectively.     

Prediction of solubilities of salts,osmotic coefficients and vapor–liquid equilibria for single and mixed solvent electrolyte systems using the LIQUAC model

The electrolyte model LIQUAC has been used up till now to predict osmotic coefficients, mean ion activity coefficients, the vapor–liquid equilibrium (VLE) behavior, the solubility of gases in single and mixed solvent electrolyte systems, and solubilities of salts in aqueous solutions. In this paper, the required expressions for the calculation of salt solubilities not only in aqueous systems, but also in organic solvents and water–solvent electrolyte systems were deduced in detail based on the LIQUAC model with a fixed reference state and thermodynamic relations. Four salts (NaCl, KCl, NH₄Cl and NaF) and two solvent (water and methanol) were selected to test the derived expressions. The results show that the LIQUAC model with a fixed reference state can be used to predict osmotic coefficients, solubilities of salts in aqueous solutions, vapor–liquid equilibria, and the solubilities of salts in water–organic solvent systems with strong electrolytes.