Phase Behavior Of Ternary Mixtures Research Articles

Solid–liquid phase behavior of ternary mixtures

AbstractThe Gibbs Duhem integration technique is extended to calculate ternary phase diagrams at constant temperature and pressure. The technique is used to calculate solid–liquid–vapor phase equilibria for a system selected to roughly model a mixture of two diastereomeric molecules of similar melting point and diameter immersed in a solvent with a lower melting point and a slightly smaller diameter. The cross‐species well‐depth and diameter between the two diastereomers are varied to determine their impact on the phase equilibria. We find that when the interspecies well‐depth is lowered to less than that of either of the diastereomers, the solid phase separates into two solid solutions and consequently there is a region of three‐phase coexistence in the ternary phase diagram. We then calculate ternary phase diagrams at a series of temperatures for one set of molecular parameters. For an equimolar mixture of diastereomers, there is a range of temperature and solvent concentration at which only one of the diastereomers will precipitate, thus effecting a separation of the diastereomers. As the temperature is decreased the purity of the precipitate increases. © 2008 American Institute of Chemical Engineers AIChE J, 2008

Lyotropic liquid crystalline phases formed in ternary mixtures of 1-cetyl-3-methylimidazolium bromide/ p-xylene/water: A SAXS, POM, and rheology study

The phase behavior of ternary mixtures of 1-cetyl-3-methylimidazolium bromide (C 16mim-Br)/ p-xylene/water is studied by small-angle X-ray scattering (SAXS), polarized optical microscopy (POM), and rheology measurements. Two types of lyotropic liquid crystalline phases are formed in the mixtures: hexagonal and lamellar. The structural parameters of the lyotropic liquid crystalline phases are calculated. Greater surfactant content in the sample leads to denser aggregation of the cylindrical units in the hexagonal liquid crystalline phase. The increase in lattice parameter and thickness of the water layer in lamellar phase are attributed to the increase of water content, and the area per surfactant molecule at the hydrophobic/hydrophilic interface for lamellar phase is found to be larger than that for hexagonal phase. The structural parameters of the liquid crystalline phases formed from the cetyltrimethylammonium bromide (CTAB) system are larger than those for the C 16mim-Br system. The rheological properties of the samples are also found to be related to the structure of the liquid crystalline phases.

High-pressure phase behavior of ternary mixtures with ionic liquids, part I: the system bmim[BF4]+4-isobutylacetophenone + CO2

Performing reactions in a homogeneous system is extremely important for the achievement of high reaction rates and yield. Since carbon dioxide can tune the miscibility of ionic liquid/organic mixtures, measurements on the phase behavior of these systems provide useful information for the selection of operational conditions for reactions and extractions. We investigated the phase behavior of ternary mixtures of the type bmim[BF4] + solute + CO2, in which the solute is an intermediary in the synthesis of ibuprofen. In this contribution, the influence of carbon dioxide pressure on the location of the homogeneous liquid phase region in the phase diagram of the ternary system bmim[BF4] + 4-isobutylacetophenone + CO2 is presented. We show that for CO2 concentrations above 60 mol%, a narrow three-phase region can be found in the pressure versus temperature diagram, and that a further increase in CO2 composition gradually reduces the extension and influences the location of the one-phase liquid region, finally resulting in its complete disappearance.

Complex Polyion−Surfactant Ion Salts in Equilibrium with Water: Changing Aggregate Shape and Size by Adding Oil

The phase behavior of ternary mixtures containing an alkyltrimethylammonium polyacrylate complex salt, water, and a nonpolar "oil" (n-decanol, p-xylene or cyclohexane) is investigated. The complex salts were prepared with short or long polyacrylates (30 or 6000 repeating units) and with hexadecyltrimethylammonium or dodecyltrimethylammonium surfactant ions. Phase diagrams and structures were determined by visual inspection and small-angle X-ray scattering analyses. Systems containing decanol display a predominance of lamellar phases, while hexagonal phases prevail in systems containing p-xylene or cyclohexane. The difference is interpreted as a result of the different locations of the oils within the surfactant aggregates. Decanol is incorporated at the aggregate interface, leading to a decrease in its curvature, which favors the appearance of lamellar structures. p-Xylene and cyclohexane, on the other hand, are mostly incorporated in the interior of the cylindrical aggregate, as reflected by its swelling as the oil content increases. The comparison of these results with those reported for similar systems with monovalent (bromide) counterions indicates a much more limited swelling of the lamellar phases with polymeric counterions by water. This limited swelling behavior is predominantly ascribed to bridging due to the polyions.

Solubility and immiscibility behavior in ternary hydrothermal systems with critical phenomena in saturated solutions

Liquid-liquid immiscibility occurs widely in water-salt systems as stable and metastable equilibria at sub- and supercritical conditions. The phase behavior of ternary mixtures complicated by metastable immiscibility and by a transition of the metastable immiscibility regions into the stable equilibria is discussed using the experimental data on water-salt systems and theoretically derived complete phase diagrams.

Phase behaviour of ternary mixtures: a theoretical investigation of the critical properties of mixtures with equal size components

Conformal solution theory in conjunction with the one-fluid model and the Guggenheim equation of state are used to calculate the critical properties of binary and ternary mixtures characterised by molecules of identical size (identical h conformal parameters) but different energy parameters (different f conformal parameters). When the geometric mean combining rule is used to obtain contributions from unlike interactions, binary mixtures of equal size components generate Type I, II and III phase behaviour. The critical properties of ternary mixtures composed of binary subsystems of different phase behaviour types are examined. Results are presented at different temperatures and pressures covering both vapour–liquid and liquid–liquid equilibria. The results illustrate the diversity of phenomena exhibited by ternary mixtures and the relationship of the behaviour exhibited to the relative strength of dissimilar interactions between different pairs of molecules. A progressive transition between vapour–liquid and liquid–liquid equilibria and higher order critical phenomena are likely to be common features of the phase behaviour of ternary mixtures.

A theoretical study of Gemini surfactant phase behavior

Gemini surfactants are a relatively new type of surface active material, characterized by multiple hydrophilic head groups. The phase behavior of a Gemini surfactant lattice model is studied by Monte Carlo simulations and quasichemical (QC) calculations. The predictions of these methods are in excellent agreement, justifying use of the analytical QC theory. The dependence on temperature, surfactant solubility, surfactant rigidity, and oil chain length of the global phase behavior of ternary mixtures of Gemini surfactant, oil, and water is investigated. Three-phase equilibrium exists only at low temperatures, with a transition to two-phase equilibrium as temperature is increased. Surfactants with moderate solubilities (i.e., those which do not have a strong preference for either solvent) exhibit three-phase equilibrium at low temperatures, while surfactants with extreme solubility preferences yield two-phase equilibrium only. When a flexible surfactant exhibits three-phase equilibrium, imposing rigidity promotes a transition from three- to two-phase equilibrium. Increasing molecular size of the hydrophobic solvent (oil) causes a transition from two- to three-phase equilibrium, and finally back to two-phase equilibrium, but with reversed relative surfactant solubility in the oil and water phases.

Mixtures of branched non-ionic oligo-oxyethylene surfactants in aqueous solutions ? the effect of molecular geometry on LC phase behaviour 4

The LC phase behavior of ternary mixtures of the two corresponding branched non-ionic surfactants 1,3-bis-(methoxy-tetraoxyethylene)-2-propoxy-tetradecane (Y-surfactant) and 1,3-bis-(heptyloxy)-2-propoxyoctaoxyethylene mono-methyl ether (V-surfactant) and water were studied by polarizing microscopy. The two branched surfactants, which have different molecular geometries but nearly the same hydrophilic-lipophilic volume ratio, exhibit extremely different phase behavior in binary surfactant/water systems. For the ternary mixtures of Y- and V-surfactant and water we found-according to established packing models-a continuous stabilization of the cubic and hexagonal phases and a destabilization of the lamellar phase with increasing amount of Y-surfactant. On the other hand, we observed a thermal stabilization of the lamellar phase. The maximal transition temperatures of the lamellar phase pass a maximum with increasing amount of Y-surfactant.

A theoretically correct mixing rule for cubic equations of state

AbstractA new mixing rule developed for cubic equations of state equates the excess Helmholtz free energy at infinite pressure from an equation of state to that from an activity coefficient model. Use of the Helmholtz free energy insures that the second virial coefficient calculated from the equation of state has a quadratic composition dependence, as required by statistical mechanics. Consequently, this mixing rule produces the correct low‐ and high‐density limits without being density‐dependent.As a test, the mixing rule is used for ternary mixtures of cyclohexane + benzene + water, ethanol + benzene + water and carbon dioxide + n‐propane + water, and all the constituent binaries. The new mixing rule and a simple cubic equation of state can be used for the accurate correlation of vapor‐liquid and liquid‐liquid equilibria for binary mixtures. Using the parameters obtained from binary systems, the phase behavior of ternary mixtures can be predicted. Also, unlike previous empirical mixing rules, this theoretically based mixing rule is equally applicable and accurate for simple mixtures containing hydrocarbons and inorganic gases and mixtures containing polar, aromatic and associating species over a wide range of pressures. This mixing rule makes it possible to use a single equation of state model with equal accuracy for mixtures usually described by equations of state and for those traditionally described by activity coefficient models. It is the correct bridge between these two classes of models.

Prediction of binary and ternary critical properties using deiters' equation, hard sphere and hard convex body equations of state

The use of recently developed equations of state for critical phenomena is examined. Deiters' equation is incapable of accurately predicting the gas-liquid critical properties of mixtures of dissimilar size molecules whereas a hard convex body equation does not yield significantly better results than a simple hard sphere equation. In many cases a ‘hard sphere + attractive term’ equation can predict the critical properties of Type II mixtures to within experimental error. This conclusion is valid for a wide range of component molecules. However, an adjustable parameter is usually required to optimise agreement. Type II liquid-liquid properties can also be accurately calculated but the same precision can not be obtained for Type III phenomena. Some calculations for CHF 3 + alkane mixtures are reported which exhibited Type III behaviour. It appears that the most significant improvement in a priori prediction of critical phenomena lies in developing better combining rules rather than ‘improved’ equations of state. Work on ternary critical phenomena has hitherto been largely limited to simple gas-liquid properties which are continuous with respect to composition. In this work the critical properties of CF 4 + CHF 3 + CH 4 over a wide range of temperature and pressure are calculated. The results illustrate the potential of theory to classify the phase behaviour of ternary mixtures.

Phase studies of the systems synthetic soap‐sodium chloride‐water

SummaryThe phase behavior of ternary mixtures of various synthetic soaps, sodium chloride, and water are described. Several mixed sodium alkyl sulphates were investigated in detail at two temperatures; pure alkyl sulphates and alkyl and alkylarene sulphonates were investigated only tentatively. The phase relations showed a striking resemblance with those of fatty acid soaps.