Phase Equilibria Of Binary Mixtures Research Articles

Solubility of CO 2 in some heavy alcohols and correlation of fluid phase equilibrium

The synthetic method was applied to measure the phase equilibrium of binary mixtures involving CO 2 and the following alcohols: undecan-2-ol, undecan-6-ol, undec-10-en-1-ol, and 2-methylpentan-2,4-diol. Measurements were performed at three different temperatures: 313.15, 323.15, and 333.15 K. The bubble points were measured at carbon dioxide mole fractions between 0.1 and 0.8 and at a pressure range of 13–160 bar. The results were correlated with the Peng–Robinson equation of state using the quadratic mixing rules.

Molecular Simulation of Vapor−Liquid Phase Equilibria of Hydrogen Sulfide and Its Mixtures with Alkanes

A new set of force field parameters for a three-point potential model of hydrogen sulfide (H2S) is proposed, based on fitting of the experimental saturation densities. The proposed model also reproduces well the critical properties and vapor-phase dipole moment of the substance. The new model is used to study vapor−liquid phase equilibria of binary mixtures of hydrogen sulfide with alkanes of various lengths. Results of binary phase equilibria simulations are found to be in good agreement with available experimental data.

Liquid—Liquid Phase Equilibria in Binary Mixtures under Negative Pressure

AbstractFor Abstract see ChemInform Abstract in Full Text.

(Solid + liquid) phase equilibria of binary mixtures containing N-methyl-2-pyrrolidinone and alcohol at atmospheric pressure

The (solid + liquid) equilibria of { N-methyl-2-pyrrolidinone + 1-propanol, or 2-propanol, or 1-butanol, or 2-methyl-1-propanol, or 2-methyl-2-propanol, or 1-pentanol} has been measured by a dynamic method. The experimental results have been correlated using the Wilson, UNIQUAC ASM and two modified NRTL equations. The root-mean-square deviations of the solubility temperatures for all the calculated values vary from (0.5 to 2.1) K and depend on the particular equation used. The specific interaction between the carbonyl group of the NMP molecule and the alcohol has been discussed.

Critical lines and phase coexistence of polymer solutions: A quantitative comparison between Wertheim’s thermodynamic perturbation theory and computer simulations

We consider the vapor–liquid phase equilibria of binary mixtures of a model bead–spring polymer dissolved in a solvent made of single monomers. We employ Wertheim’s thermodynamic perturbation theory of first order (TPT1), with the properties of the monomer fluid described by the mean spherical approximation and the effect of the attractions considered within a van der Waals one fluid approximation. The results of the TPT1 theory are quantitatively compared to grand canonical Monte Carlo simulations. To this end, we obtain full critical lines all the way from the critical point of the pure polymer to the critical point of the pure monomer. Pressure–composition and pressure–temperature slices are also obtained. At low pressures, we find rather good agreement between simulation and theory for the coexistence liquid densities and compositions. At higher pressures, however, the results are far less satisfactory, as the critical pressures are highly overpredicted.

(Solid + liquid) phase equilibria of binary mixtures containing N-methyl-2-pyrrolidinone and long-chain n-alkanols at atmospheric pressure

The (solid+liquid) equilibria for N-methyl-2-pyrrolidinone+ n-alkanols (1-hexanol, or 1-heptanol, or 1-octanol, or 1-decanol, or 1-undecanol, or 1-dodecanol, or 1-tetradecanol) systems have been measured by a dynamic method for the whole concentration region x 1=0–1. The experimental results have been correlated by four equations: Wilson, UNIQUAC ASM and two modified NRTL. The relative standard deviations of the solubility temperature correlation for all measured data vary from 0.1 to 1.4 K and depend on the particular equation used. In the calculations, the existence of two solid–solid first-order phase transitions in 1-tetradecanol has been taken into consideration.

Prediction of phase equilibria for binary mixtures by molecular modeling

AbstractTwo new procedures based on quantum/COSMO calculations and on molecular mechanics/dynamics simulations, respectively, for estimating the PHSCT EOS parameters and to predict VLE behavior for binary mixtures are presented. The quality of the predictions achieved with both methods, in conjunction with the confined computational time aspects involved, can be considered satisfactory so that these strategies can be judged as promising routes toward an on‐line coupling between molecular and process simulation.

Phase equilibria of binary mixtures by molecular simulation and cubic equations of state

Molecular simulation data were used to study the performance of equations of state (EoS) and combining rules usually employed in thermodynamic property calculations. The Monte Carlo method and the Gibbs ensemble technique were used for determining composition and densities of vapor and liquid phases in equilibrium for binary mixtures of Lennard-Jones fluids. Simulation results are compared to data in the literature and to those calculated by the t-PR-LJ EoS. The use of adequate combining rules has been shown to be very important for the satisfactory representation of molecular simulation data.

Critical properties ( pc, Tc, and ρc) and phase equilibria of binary mixtures of CO 2, CHF 3, CH 2F 2, and SF 6

Measurements of the critical properties p c, T c, and ρ c of the pure substances CO 2, CHF 3, CH 2F 2, SF 6 and their binary mixtures were performed by observing the critical opalescence in a static equilibrium cell. The experimental uncertainties of the critical properties are ±6 kPa, ±60 mK, and ±2% for the determination of the density. The composition was determined by gas-chromatographic analysis within ±0.3 mol%. The experimental results for the binary mixtures are described by several simple cubic equations of state with van der Waals mixing and combining rules, using only the experimental critical data of the pure components and those of an approximately equimolar mixture to fit the binary interaction parameters. The capability of the cubic equations of state with these binary interaction parameters not only to describe the critical loci but also to describe VLE data is demonstrated by additional VLE measurements for the binary systems (CHF 3+SF 6) and (SF 6+CH 2F 2). Furthermore, VLE data published by other authors for some of the systems investigated are considered.

Predicting the High-Pressure Phase Equilibria of Binary Mixtures of n-Alkanes Using the SAFT-VR Approach

The phase behavior of selected alkane binary mixtures is studied using SAFT-VR, a version of the statistical associating fluid theory for potentials of variable attractive range (SAFT). We treat the n-alkane molecules as chains formed from united-atom hard-sphere segments with square-well potentials of variable range to describe the attractive interactions. We use a simple relationship between the number of carbon atoms in the n-alkane molecule and the number of segments in the united atom chains in order to predict the phase behavior of n-butane with other n-alkanes. The calculated vapor pressures and saturated liquid densities of the pure components are fitted to experimental data from the triple point to the critical point. These optimized parameters are rescaled by the respective experimental critical points and used to determine the critical lines and phase behavior of the mixtures. We use the Lorentz-Berthelot combining rule for the unlike interactions. We predict the phase behavior of n-butane + n-alkane binary mixtures, concentrating mainly on the critical region. The gas-liquid critical lines predicted by SAFT-VR for the n-alkane mixtures are in excellent agreement with the experimental data, and improve significantly on the results obtained with the simpler SAFT-HS approach where the attractive interactions are treated at the mean-field level.

Shape Effects in Molecular Liquids: Phase Equilibria of Binary Mixtures Involving Cyclic Molecules

Using the statistical association fluid theory−hard spheres (SAFT-HS) equation of state for chain molecules and its recent extension to ring molecules, phase diagrams for model mixtures of types (m1-sphere chain + m2-sphere chain) and (m1-sphere chain + m2-sphere ring) have been calculated. The influence of chain length, relative sphere size, relative mean-field attraction, and reduced temperature has been investigated. In a first ever application of the SAFT-HS model to cyclic molecules, the theoretical predictions have been compared with experimental data for a variety of systems involving both chain and cyclic molecules. The experimental results confirm the predictions of the theory for the effect of a cyclic molecular structure on the phase behavior of binary mixtures.

Liquid−Liquid Phase Equilibria in Porous Materials

Theoretical and experimental results are presented for the effect of confinement on liquid−liquid phase equilibria for binary mixtures. Density functional theory calculations for a symmetric Lennard-Jones mixture in pores show the following qualitative features: a reduction in the critical mixing temperature, and a shift in the coexistence curve toward the component 1-rich side of the phase diagram when molecules of component 1 are more strongly attracted to the walls. These effects become more pronounced for smaller pores. Experimental results are presented for nitrobenzene/n-hexane mixtures in a controlled pore glass having pores of mean width 100 nm. Results for the liquid−liquid coexistence in the pores are obtained using nonlinear dielectric effect (NDE) and light transmission measurements. The effect of confinement is to produce a lowering of the critical mixing temperature by 0.05 ± 0.02 K and a shift in the critical mixing composition toward the nitrobenzene-rich side of the diagram by 0.04 ± 0.01 in mole fraction. Measurements near the pore critical point show that the NDE tends to a finite value at the critical point, apparently due to the constraint on the growth of the correlation length due to the pore walls.

Vapour-liquid and liquid-liquid phase equilibria of binary mixtures containing helium: comparison of experiment with predictions using equations of state

The unlike interaction parameters for binary mixtures of helium + non-polar gases are obtained by comparing experimental critical data with calculations using the Guggenheim and Heilig-Franck equations of state. These interaction parameters and equations of state are used to predict a priori both the vapour-liquid and liquid-liquid equilibria for helium + non-polar gas mixtures. The predicted phase diagrams are compared with experimental data for a wide range of pressure, temperature and composition. Good agreement between theory and experiment is obtained for the isobaric temperature-composition phase behaviour and isothermal pressure-composition phenomena can be predicted qualitatively.

Theory of phase equilibria and critical mixing points in binary lipid bilayers

The fundamental problem of determining the phase equilibria of binary mixtures is discussed in the context of two-component phospholipid bilayer membranes of saturated phospholipids with different acyl-chain lengths. Results are presented from mean-field calculations and Monte Carlo simulations on a statistical mechanical model in which the interaction between lipid acyl chains of different length is formulated in terms of a hydrophobic mismatch. The model permits a series of binary phase diagrams to be determined in terms of a single ‘‘universal’’ interaction parameter. The part of the free energy necessary to derive phase equilibria is determined from the simulations using distribution functions and histogram techniques, and the nature of the phase equilibria is determined by a finite-size scaling analysis which also permits the interfacial tension to be derived. Results are also presented for the enthalpy and the compositional fluctuations. It is shown, in accordance with experiments, that the nonideal mixing of lipid species due to mismatch in the hydrophobic lengths leads to a progressively nonideal mixing behavior as the chain-length difference is increased. Moreover, indications are found that a phase transition in a strict thermodynamic sense may be absent in some of the short-chain one-component lipid bilayers, but a transition can be induced when small amounts of another species are mixed in, leading to a closed phase separation loop with critical points. The physical mechanism of inducing the transition is discussed in terms of the molecular properties of the lipid acyl chains. The results of the numerical model study are expected to have consequences for the interpretation of experimental measurements on lipid bilayer systems in terms of phase diagrams.

Phase equilibria in binary mixtures of propane and triphenylmethane

This paper presents experimental results on the phase behavior of the binary system propane + triphenylmethane. Besides vapor-liquid equilibria, also equilibria in the presence of solid triphenylmethane have been determined experimentally. Special attention was given to determine the course of the various three-phase equilibria originating in the quadruple point solid triphenylmethane-liquid-liquid-vapor ( sB l 1 l 2g). The experimental work was performed in the temperature region 310 < T K < 450 , while pressures up to 11 MPa have been applied. Surprisingly, it was found that in this binary system the three-phase equilibrium liquid-liquid-vapor ( l 1 l 2 g) could be determined at supercooled conditions over a temperature range of about 25 K, i.e. some parts of the fluid phase behavior could be observed and measured at metastable conditions.

Phase equilibria in binary mixtures of ethane and propane with sunflower oil

The solubility of ethane and propane in sunflower oil has been measured at temperatures between 298 K and 373 K, and pressures up to 8.88 MPa. Partial liquid miscibility was observed, for mixtures of high hydrocarbon concentrations, in the near-critial region of the solvent; the compositions of the coexisting liquid phases were calculated from a mass balance in the equilibrimn cell.

Calculation of the critical high pressure liquid-liquid phase equilibria of binary mixtures containing ammonia Unlike interaction parameters for the Heilig—Franck equation of state

The critical transitions of 21 binary mixtures containing ammonia + either an n-alkane (methane to octadecane) or a gas (hydrogen, helium, nitrogen, argon, carbon monoxide and sulphur hexafluoride) are calculated using the Heilig-Franck equation of state with the aid of two adjustable combining rule parameters (ξ, ζ). The calculations are in very good agreement with experimental data in the pressure range 3 – 90 MPa. For Type II mixtures, a progressive decline in the ξ parameter is observed as the size difference between the component molecules is increased whereas the ζ value passes through a maximum. A disparity in molecular size between component molecules does not seriously deteriorate the quality of agreement between theory and experiment. The theoretical analysis of Type III systems is also quantitatively accurate. At high pressures, “gas-gas” immiscibility of the second kind is predicted for the ammonia + sulphur hexafluoride mixture.

Phase equilibria in binary mixtures of propane and hexacontane

Peters, C.J., de Roo, J.L. and de Swaan Arons, J., 1993. Phase equilibria in binary mixtures of propane and hexacontane. Fluid Phase Equilibria, 85: 301-312. This paper reports on the phase behaviour of binary mixtures of propane with hexacontane ( n-C 60H 122). The measurements cover a temperature range from about 310 K up to 430 K. Pressures up to 15 MPa were applied. In the binary propane + hexacontane, a three-phase equilibrium liquid + liquid + vapour (l 1l 2g) occurs in the near-critical region of propane. However, in this system the lower critical end point (LCEP) was hidden by solidification of hexacontane. The pressure-temperature coordinates of the upper critical end point were determined at 369.95 K and 4.275 MPa. Because the three-phase equilibrium l 1l 2g is interrupted by the three-phase equilibrium, solid hexacontane + liquid + vapour (S Blg), a Q-point solid hexacontane + liquid + liquid + vapour (S Bl 1l 2g) is present in this binary. Its pressure and temperature coordinates were located at 352.0 K and 3.05 MPa.

Excess Gibbs energies and excess enthalpies of liquid binary mixtures containing nitroalkanes

Abstract Marongiu, B., Monaci, R. and Porcedda, S., 1993. Excess Gibbs energies and excess enthalpies of liquid binary mixtures containing nitroalkanes. Fluid Phase Equilibria , 84:281-296. A head-space gas Chromatographie technique was used to determine vapour phase equilibria for binary mixtures of 1-nitroalkanes (1-nitropropane, 1-nitrobutane, 1-nitropentane) + n -heptane or cyclohexane. Excess molar Gibbs energies, G E , for the mixtures investigated were obtained. All systems exhibit positive deviations. The G E values decrease with increasing nitroalkane chain length. Activity coefficients at infinite dilution, γ ∞ t , were also evaluated. A flow microcalorimeter, Model 2277-LK.B, was used to determine excess enthalpies, H E , as a function of concentration at atmospheric pressure and 298.15 K, for binary liquid mixtures containing the same 1-nitroalkanes with tetrachloromethane. A tentative approach, based on an additivity scheme of surface interactions combined with the scaled particle theory, is presented to estimate and analyse group contributions to Δ G solv 0 and Δ H solv 0 , the energy and the enthalpy of solvation respectively.

Measurements and calculations of phase equilibria in binary mixtures of propane + tetratriacontane

Abstract Peters C.J., de Roo J.L. and de Swaan Arons J., 1992. Measurements and calculations of phase equilibria in binary mixtures of propane + tetratriacontane. Fluid Phase Equilibria , 72: 251-266. This paper reports on the phase behaviour of binary mixtures of propane and tetratriacontane ( n -C 34 H 70 ) in the near-critical region of propane. The measurements cover a temperature region from about 350 K up to 420 K. Pressures up to 10 MPa were applied. It has been found that in the binary mixture propane + tetratriacontane partial miscibility occurs in the liquid phase, i.e. in this binary a three-phase equilibrium liquid + liquid + vapour (1 1 1 2 g) with a lower and upper critical endpoint exists. As well as the measurement of this three-phase equilibrium, various types of two-phase boundaries and the three-phase equilibrium solid tetratriacontane + liquid + vapour (s B 1g) have been determined experimentally. In addition simplified-perturbed-hard-chain theory (SPHCT) was applied to model the vapour + liquid equilibrium data. The results obtained are compared with similar calculations, using the Peng-Robinson (PR) equation of state. The calculations established that when modelling vapour + liquid equilibria of binaries with molecules differing largely in chain-length, the SPHCT equation of state should be preferred over the PR equation.