Phase Behavior Of Binary Mixtures Research Articles

On the liquid mixtures of xenon, alkanes and perfluorinated compounds

The fluid phase behaviour of binary mixtures of xenon and the lighter perfluoro-n-alkanes, CF4 and C2F6, and of propane and sulfur hexafluoride (SF6) has been examined using the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR). We found that the binary interaction parameters calculated in previous work for (n-alkane + perfluoro-n-alkane) systems and for (Xe + SF6), can be used to predict the existing phase diagrams of (Xe + perfluoro-n-alkane) and (propane + SF6) mixtures, respectively. These results are consistent with the view that mixtures of (xenon + perfluorinated-compound) can be regarded as a special case of mixtures of (n-alkane + perfluorinated-compound) and provide another example of the “alkane-like ” behaviour of xenon previously reported.

Phase Behavior of Multicomponent Phospholipid Mixtures with Cholesterol

Previous work has shown that mixtures of multiple phospholipids with cholesterol exhibit phase behavior which may be approximately modeled by a hypothetical binary mixture of cholesterol and an “average”-phospholipid.1 This study presents a detailed thermodynamic model of such multicomponent mixtures based on regular-solution theory. When the individual phospholipids are treated independently, calculated phase behavior shows systematic deviations from the average-phospholipid model. These deviations may be expressed concisely in terms of the distribution of binary critical parameters of the individual phospholipids, and the deviations are small for mixtures in which the individual phospholipids exhibit similar phase behavior in binary mixtures with cholesterol.

Closed-loop liquid-liquid equilibria and the global phase behaviour of binary mixtures involving hard-sphere + van der Waals interactions

Calculations of the critical properties of binary mixtures of components of equal size are reported using the Guggenheim equation of state. The calculations are used to determine the global phase diagram of binary mixtures. Type VI phase behaviour is predicted successfully indicating that closed-loop liquid-liquid equilibria can be obtained from hard-sphere + van der Waals interactions. Closed-loop liquid-liquid equilibria occur in the region of the global phase diagram characterized by moderately strong unlike interactions and components with very dissimilar critical temperatures. The Guggenheim equation can predict all experimentally known phase behaviour types. In addition, other hypothetical phase behaviour types are also predicted.

Closed-loop liquid-liquid equilibria and the global phase behaviour of binary mixtures involving hard-sphere + van der Waals interactions

Closed-loop liquid-liquid equilibria and the global phase behaviour of binary mixtures involving hard-sphere + van der Waals interactions

Fluid-phase and crystallization equilibria of (dimethylether + nitrogen, or argon, or krypton, or xenon) at temperatures fromT = (270 to 110) K and at pressures up to 200 MPa

The phase behaviour of binary mixtures of dimethyl ether with nitrogen, or argon, or krypton, or xenon as the second non-polar component has been investigated at temperatures from T= (270 to 110) K and at pressures up to 200 MPa. The measurements were performed in an optical high-pressure cell, fitted with sapphire windows and a magnetic stirrer. The compositions were determined by on-line gas chromatography. Phase separation was observed according to the synthetic method. The measured p(T) isopleths and the interpolatedT (x) isobars are presented and discussed. In the classification of van Konynenburg and Scott, the phase behaviour of (dimethyl ether + nitrogen) and (dimethyl ether + argon) corresponds to type III, (dimethyl ether + krypton) to type II, and (dimethyl ether + xenon) to type I (being close to a type II system). In (dimethyl ether + krypton) a quadruple point (solid + solid + fluid + fluid) occurs at about T= 133 K and p= 70 MPa.

Application of fluid opacity for determining the phase behavior of binary mixtures near their critical loci - CO 2 plus ethane and CO 2 plus propane

The rapid determination of critical data of binary mixtures of carbon dioxide plus propane and carbon dioxide plus ethane has been carried out using the opalescence effect of pure substances or mixtures near their critical loci. The experiments have been performed applying a heatable stainless-steel vessel equipped with two sapphire windows for optical observation of changes of state. The initial two-phase mixture is continuously heated and pressurized. The vessel content increasingly becomes opalescent and the critical point is characterized by a total opacity. Beyond this point the fluid instantly becomes clear; the one-phase supercritical state is reached.

Fundamental measure theory for mixtures of parallel hard cubes. II. Phase behavior of the one-component fluid and of the binary mixture

A previously developed fundamental measure functional [J. Chem. Phys. 107, 6379 (1997)] is used to study the phase behavior of a system of parallel hard cubes. The single-component fluid exhibits a continuous transition to a solid with an anomalously large density of vacancies. The binary mixture has a demixing transition for edge–length ratios below 0.1. Freezing in this mixture reveals that at least the phase rich in large cubes always lies in the region where the uniform fluid is unstable, hence suggesting a fluid–solid phase separation. A method is developed to study very asymmetric binary mixtures by taking the limit of zero size ratio at fixed solvent fugacity. With this procedure the mixture is exactly mapped onto a one-component fluid of parallel adhesive hard cubes. At any density and solvent fugacity the large cubes are shown to collapse into a close-packed solid. Nevertheless the phase diagram contains a large metastability region with fluid and solid phases. Upon introduction of a slight polydispersity in the large cubes, the system shows the typical phase diagram of a fluid with an isostructural solid–solid transition (with the exception of a continuous freezing). Consequences about the phase behavior of binary mixtures of hard core particles are then drawn.

Effect of PEG-lipid conjugates on the phase behavior of phosphatidylethanolamine dispersions

The phase behavior of binary mixtures of hydrated dielaidoylphosphatidylethanolamine (DEPE) with two different PEG-lipid conjugates at a molar fraction below 0.2 has been studied by using time-resolved X-ray diffraction, and partial phase diagrams have been constructed. The studied conjugates comprise two saturated hydrocarbon acyl chains 14 carbon atoms long and PEG550 or PEG5000 chains covalently attached to a phosphoethanolamine polar head group, DMPE(PEG550) and DMPE(PEG5000), respectively. When added in small amounts (10–20 mol%) to DEPE aqueous dispersions, both PEG-lipids favor the lamellar liquid crystalline (L α ) phase at the expense of the lamellar gel (L β ) and the inverted hexagonal (H II) phases. One of the conjugates, DMPE(PEG550), shifts the L α –H II transition of DEPE to higher temperatures by 2.5°C per mol% PEG-lipid, and induces the spontaneous formation of a cubic phase of space group Im3m in the DEPE dispersions. The cubic phase intrudes between the lamellar liquid crystalline and the inverted hexagonal phases in the DEPE/DMPE(PEG550) phase diagram. Low amounts of the DMPE(PEG5000) conjugate only shift the L α –H II transition of DEPE to higher temperatures, at 5.2°C per mol% PEG-lipid, but does not promote the formation of additional phases. The respective slopes for the L β –L α transition temperature depression are 10–15 times smaller. At >15 mol% DMPE(PEG550) and at >5 mol% DMPE(PEG5000), the non-lamellar phases are eliminated from the phase diagrams. Structural data on the organization of the pure hydrated PEG-lipid conjugates are also provided, suggesting that these lipids form micelles and lamellae.

The global phase behaviour of binary mixtures of chain molecules: theory and application

In this work the global phase behaviour of binary fluid mixtures of chain molecules is investigated. The underlying model employed for the investigation is based on our recently developed equation of state for chain molecules. This equation is based on the statistical associating fluid theory for chains of attractive hard spheres. It is an optimized equation of state for chain molecules which can be rearranged into a fourth order polynom in the molar volume. With this equation of state the global phase diagram for several mixtures of spherical molecules with non-spherical molecules has been investigated. The non-spherical molecules range from small non-spherical over short chain molecules to long chain polymer molecules. Special attention is paid to mixtures of small spherical molecules with long chain molecules. Such mixtures are employed to model polymer–solvent mixtures. Based on the calculated global phase diagram for polymer solutions, several processes such as co- or anti-solvent processes and polymerisations are discussed. These processes are represented by paths in the global phase diagram.

The stability of binary alkane blends

The phase behaviour of binary mixtures of normal alkanes, CnH2n+2–C36D74, for 20⩽n⩽34, was investigated by SAXS, SANS and DSC. The systems can be classified as forming solid solutions, metastable solid solutions leading to the formation of alternating lamellar (micro)phase structures, or eutectics. Microphase formation is more general than reported previously and can be induced by changing both the temperature of the system and chain-length difference. Current methods of classifying phase behaviour are shown to be problematic and an alternative is proposed.

Phase behavior of binary mixtures of thick and thin hard rods

Using a straightforward extension of the Onsager-theory for hard rods, we consider the thermodynamic stability of the isotropic (I) and nematic (N) phase of binary mixtures of thick and thin hard rods of the same length. We show that such mixtures not only exhibit the expected I–N ordering transition and the previously predicted depletion driven I–I demixing transition, but also a N–N demixing transition driven by the orientation entropy of the thinner rods. For various values of the diameter ratio of the two species we present the phase diagrams, which exhibit I–N, I–I and N–N coexistence, I–N–N and I–I–N triple points, and I–I and N–N critical points. We also present the results of computer simulations of the I–I and I–N coexistence for diameter ratio 1 : 10, which are in good agreement with the theory.

Solid-Liquid Phase Behavior of Binary Mixture of Tetraethylene Glycol Decyl Ether and Water

Solid-liquid phase behavior of binary mixture of nonionic surfactant, tetraethylene glycol decyl ether (C10E4), and water was examined by means of differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FT-IR), polarized optical microscopy (POM), and visual observation in the temperature range −40–70°C. The DSC experiments allowed us to determine many phase boundaries among various phases appearing in this mixture system, including mesomorphic phases. TheT-Xphase diagram for fluid phases of C10E4/H2O mixture constructed from the results of DSC and visual observation was in good agreement with that previously reported by Lang and Morgan for the same mixture system except for the occurrence of a dilute lamellar phase (Lang, J. C. and Morgan, R. D., J. Chem. Phys., 73, 5849 (1980). The FT-IR spectra obtained for the mixture in a solid state demonstrated that the phase compound expressed by C10E4· 6H2O is formed in the solid phase, which indicates that there is a strong interaction in the solid state between water and the hydrophilic polyoxyethylene chain of the surfactant. The FT-IR results also suggested that the strength of the hydrogen bond between water and the polyoxyethylene chain of C10E4differs among the phase states of the mixture, and increases in the orderL2<L1<Lα≈H1< solid, whereL2refers to the inverted micellar phase,L1the normal micellar phase,Lαthe lamellar phase, andH1the normal hexagonal phase.

Crossover Leung–Griffiths model and the phase behavior of binary mixtures with and without chemical reaction

A new theoretical crossover model for the phase behavior of binary mixtures is presented that corresponds to the Leung–Griffiths model in the critical region and is transformed into the regular classical expansion far away from the critical point. The model is optimized to, and leads to good agreement with, experimental vapor–liquid equilibrium data for CO 2+ n-butane, CO 2+propane, ethane+benzene, CO 2+methanol, and dilute aqueous solutions of NaCl in the extended critical region. Phase behavior of mixtures in the presence of chemical reaction and a possibility to incorporate this phenomenon into the model are also discussed.

Simulation of Vapor−Liquid Equilibria for Alkane Mixtures

A newly proposed united-atom force field is used to predict the phase behavior of binary mixtures of long and short alkanes over wide ranges of temperature and pressure. Given the chemical similarity of the components, no adjustable binary parameters are introduced. In general, agreement with experiment is satisfactory. Two commonly used equations of state are also used to describe experimental coexistence curves. In the absence of binary data, it is found that molecular simulations provide a fairly reliable means of estimating thermodynamic properties for the highly asymmetric mixtures of short and long alkanes studied in this work.

Using Molecular Orbital Calculations To Describe the Phase Behavior of Cross-associating Mixtures

In previous studies, we have used molecular orbital calculations to determine the thermodynamic changes of dimerization for a number of pure and cross-associated species. We have shown that by using these results in a physical equation of state, the statistical associating fluid theory (SAFT), we are able to accurately model the phase behavior of pure self-associating compounds and binary mixtures of a self-associating compound and a nonassociating compound with a reduction in the number of adjustable parameters. In this study, we consider the phase behavior of binary mixtures in which cross-associated species may occur. To determine the equation of state parameters describing cross association, we introduce a mixing rule based on the results of the molecular orbital calculations. We show that using information derived from the quantum-mechanical calculations results in correlations of mixture vapor-liquid equilibrium data with fewer adjustable parameters and no loss of accuracy, indeed frequently with improved accuracy, compared to the original SAFT model.

Thermodynamics of fluid mixtures near to and far from the critical region

AbstractA theory for an equation of state for simple fluid mixtures valid both near to and far from critical points is presented. The base equation of state obtained from integral‐equation theory using the mean‐spherical approximation is used to compute the contribution of short‐wavelength fluctuations to the free energy of the fluid mixture. Wilson's phase space cell approximation, as extended by White, is used to compute the contribution of long‐wavelength fluctuations. The resulting theory possesses nonclassic critical exponents similar to those observed experimentally. Far from the critical region, where long‐wavelength fluctuations are not important, the theory reduces to that corresponding to the base equation of state. The complete theory is used to represent the thermodynamic properties and phase behavior of binary mixtures of methane, carbon dioxide, and n‐butane. In the critical region, agreement with experiment is dramatically improved upon, adding to the base equation of state corrections from long‐wavelength fluctuations.

Effect of Three-Body Interactions between Dissimilar Molecules on the Phase Behavior of Binary Mixtures: The Transition from Vapor−Liquid Equilibria to Type III Behavior

An investigation is reported of the effect of three-body interactions between dissimilar molecules on the phase behavior of binary mixtures. The Gibbs ensemble algorithm is implemented to determine phase coexistence of binary mixtures interacting via a two-body Lennard−Jones + three-body Axilrod−Teller potential. The contributions of both two-body and three-body interactions are calculated exactly. Calculations are reported with three-body interactions of varying strength. It is demonstrated that three-body interactions can result in a transition from vapor−liquid equilibria to type IIIb behavior (gas−gas immiscibility of the second kind). This is the first time that three-body interactions have been linked rigorously to type III behavior.

Thermodynamic properties of R32 + R134a and R125 + R32 mixtures in and beyond the critical region

A parametric crossover equation of state for pure fluids is adapted to binary mixtures. This equation incorporates scaling laws asymptotically close to the critical point and is transformed into a regular classical expansion far away from the critical point. An isomorphic generalization of the law of corresponding states is applied to the prediction of thermodynamic properties and the phase behavior of binary mixtures over a wide region around the locus of vapor-liquid critical points. A comparison is made with experimental data for pure R32, R 125 and R 134a, and for R32 + R 134a and R 125 + R32 binary mixtures. The equation of state yields a good representation of thermodynamic property data in the range of temperatures 0.8 T c ( x) ≤ T ≤ 1.5 T c ( x) and densities 0.35 ϱ c ( x) ≤ ϱ ≤ 1.65 ϱ c ( x).

Extended law of corresponding states and thermodynamic properties of binary mixtures in and beyond the critical region

A parametric crossover equation of state for pure fluids which incorporates the scaling laws asymptotically close to the critical point and is transformed into the regular classical expansion far away from the critical point is adapted to binary mixtures. An isomorphic generalization of the law of corresponding states is applied to the prediction of the thermodynamic properties and the phase behavior of binary mixtures over a wide region around the locus of vapor-liquid critical points. Methane-ethane and methane-propane are used as reference mixtures, and model parameters for other mixtures are determined completely from excess critical compressibility factors. A comparison is made with the experimental data for twelve binary mixtures. The crossover equation yields a satisfactory representation of the thermodynamic property data in a large range of temperatures and densities. Results for the ammonia-water mixture are consistent with an independent classical correlation.

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.