Model melting diagrams of ternary systems with a lower critical liquid stratification point

Model melting diagrams of ternary systems with lower critical liquid stratification points in the initial binary systems are considered. Phase equilibria are analyzed, and polythermal and isothermal sections in various interinvariant intervals are presented.     

Phase equilibria and critical phenomena in a sodium nitrate-water-diethylamine ternary system

The phase equilibria and critical phenomena in a sodium nitrate—water—diethylamine ternary system were studied by the visual polythermal method at 10—150°C, where the frontier binary liquid system is characterized by delamination with the lower critical solution temperature (LCST). The introduction of sodium nitrate into the water—diethylamine system led to a significant decrease (from 146.1 to 22.9°C) in the LCST of the system and the mutual solubility of its components. The coefficients of the distribution of diethylamine between the water and organic phases of the monotectic equilibrium at different temperatures were calculated. The effect of the salting-out of diethylamine by sodium nitrate from aqueous solutions increased with temperature. The constructed isotherms of the phase states of the system confirmed the general scheme of the topological transformation of the phase diagrams of the salt—binary solvent ternary systems with salting-out. The results of the salting-out action of sodi um, potassium, and cesium nitrates on the water—diethylamine binary system were compared.     

Phenomenological theory of phase diagrams with multicritical points

The breakup of multicritical points is studied in detail within the phenomenological theory of second-order phase transitions for a thermodynamic potential invariant with respect to the C _3v (3m) group of transformations. The general conditions of this breakup are obtained and possible types of derived diagrams are plotted from a parent phase diagram containing a multicritical point. Examples of experimental phase diagrams are given that qualitatively confirm the results from theoretical and computer simulations of phase equilibria.     

Phase equilibria and critical phenomena in the cesium nitrate-water-diethylamine ternary system

Phase equilibria and critical phenomena in the cesium nitrate-water-diethylamine ternary system were studied by the visual-polythermal method over the temperature range 60–150 °C, where the boundary binary liquid system was characterized by stratification with a lower critical solution temperature (LCST). The introduction of cesium nitrate into the water-diethylamine system decreased the LCST of this system from 146.1 to 69.3°C and lowered the mutual solubility of the components. The diethylamine distribution coefficients between the aqueous and organic phases were calculated for monotectic equilibria at various temperatures. The salting out of diethylamine with cesium nitrate grew stronger as the temperature increased. The conclusion was drawn that the isotherms of the phase states of the system substantiated the generalized scheme of topological transformations of phase diagrams for salt-binary solvent ternary systems with salting out. The salting out effects of cesium and potassium nitrates on the water-diethylamine binary system were compared.     

A universal method for calculating isobaric-isothermal sections of ternary system phase diagrams

A method for calculating and constructing isobaric-isothermal sections of ternary system phase diagrams with the use of convex hulls was developed. The method is based on the projection of the singularities of the lower part of the Gibbs energy convex hull onto the plane of component mole fractions followed by a geometric analysis of the properties of this projection. The method is applicable to a wide range of ternary systems, it can be used to find tie-line coordinates and determine the phase compositions of all the diagram regions. The quality of the suggested algorithm was estimated, and examples of the construction of several phase diagrams are given.     

Phase separation of a liquid coexisting with vapor in ternary systems

Model T-x ₁-x ₂ diagrams are considered for ternary systems with liquid-liquid phase separation in cases where invariant equilibria between two liquids and vapor exist in binary subsystems. Original Russian Text ? K.A. Khaldoyanidi, 2009, published in Zhurnal Neorganicheskoi Khimii, 2009, Vol. 54, No. 6, pp. 1052–1056.     

Phase transfer catalytic system with the third liquid phase

Phase transfer catalysis, a technique to bring the reactants in two immiscible phases together by adding a phase transfer agent, has been employed in the production of fine chemicals and pharmaceuticals in the last few decades. The third liquid phase (catalytic phase) may be formed when phase transfer catalysts (PTC), cannot be dissolved in either organic or aqueous phase. The third phase catalytic systems have the following three advantages, that is, (1) high activity (2) repeated use and (3) separation between the organic phase and the aqueous phase. It is expected that simple new processes can be constructed by applying these three advantages.     

Twist-grain-boundary phase diagrams in chiral liquid crystals

The experimental phase diagrams of several chiral systems are compared with a theoretical diagram based on the chiral Chen-Lubensky model, which predicts at least two kinds of twist-grain-boundary phase, TGBA and TGBC. Also shown for comparison are typical nonchiral phase diagrams that exhibit a nematic-smectic A-smectic C multicritical point. Several aspects of experiment and theory agree, but there appear to be common experimental features that differ from those predicted by current theory.     

Models of p-T diagrams for a ternary system with invariant equilibrium of three solid phases, liquid, and vapor

A version of a model of the p-T diagram for a ternary system in which three solid phases, liquid, and vapor are in invariant five-phase equilibrium is developed. The phase equilibria and phase transitions in the isobaric T-x-y diagram are analyzed, and isothermal and polythermal sections are presented.     

Complete phase diagrams of mixtures of a nematic liquid crystal with n-alkanes

The full experimental phase diagrams of mixtures of the nematic liquid crystal 4.4'-azoxyanisole, (PAA), and n-tetracosane and of PAA and n-octadecane are given. Equilibria of a nematic phase with an isotropic phase, of two isotropic phases, and a reentrant isotropic phase could be observed directly. The experimental phase diagram is in qualitative agreement with the result derived from the Flory lattice model adopted for thermotropic systems.     

Phase diagrams of degenerate states in ternary metal and metal chalcogenide systems with solid solutions

Models with a good-fit have been developed for the phase diagrams of ternary systems with intermediate solid phases of variable and fixed compositions, including diagrams with limited or degenerate solid solutions in subsystems.     

Diffusion in a ternary system and the critical mixing point

Diffusion coefficients were measured for the ternary system water-chloroformacetic acetic acid at 25°C and at five concentrations approaching the critical mixing point. The relationship D₁₁D₂₂–D₁₂D₂₁=0 holding at the critical mixing point has been proven experimentally. By choosing water as solvent instead of acetic acid, negative main diffusion coefficients were found for chloroform, showing an interesting case of incongruent diffusion.     

Construction of solid-liquid phase diagrams in ternary systems by titration calorimetry

Titration calorimetry was used to construct the solid-liquid equilibrium line in ternary systems containing the solute and an aqueous mixed solvent by measuring the heat of dissolution of the solid solute during successive additions of the liquid solvent. The plot of cumulated heats versus the mole ratio, n_solvent/n_solute, yields two (almost) linear increases of different slopes. These two lines represent successively the enthalpy of dissolution then the enthalpy of dilution of the medium; their intersection gives the solubility and the enthalpy of dissolution of the solute. Phase diagrams have been established over the whole concentration range for o-anisaldehyde, 1,3,5-trimethoxybenzene and vanillin, in water + methanol, +ethanol, or +n-propanol at 303, 313 and 318 K.     

Phase diagrams of cholesteric liquid crystals obtained with a generalized Landau-de Gennes theory

Phase diagrams of chiral nematic liquid crystals are studied within the framework of a generalized Landau-Ginzburg-de Gennes theory. Using the parametrization of Grebel, Hornreich, and Shtrikman for the tensor order parameter Q, all relevant elastic terms are included for the helicoidal phase and the blue phases of chiral nematic liquid crystals up to fourth order in Q and its gradient ∂Q. The influence of the additional elastic terms on the phase diagrams of the chiral nematic phases is then investigated. The theory correctly describes the variation of the pitch with temperature and the induced biaxiality of the cholesteric phase. The results resolve the discrepancies encountered by Hornreich and Shtrikman in the comparison of experiment and theory. New features in the topology of the phase diagrams of blue phases, like re-entrant phase transitions, are predicted.     

Phase diagrams of cholesteric liquid crystals obtained with a generalized Landau-de Gennes theory

Abstract

Phase diagrams of chiral nematic liquid crystals are studied within the framework of a generalized Landau-Ginzburg-de Gennes theory. Using the parametrization of Grebel, Hornreich, and Shtrikman for the tensor order parameter Q, all relevant elastic terms are included for the helicoidal phase and the blue phases of chiral nematic liquid crystals up to fourth order in Q and its gradient ?Q. The influence of the additional elastic terms on the phase diagrams of the chiral nematic phases is then investigated. The theory correctly describes the variation of the pitch with temperature and the induced biaxiality of the cholesteric phase. The results resolve the discrepancies encountered by Hornreich and Shtrikman in the comparison of experiment and theory. New features in the topology of the phase diagrams of blue phases, like re-entrant phase transitions, are predicted.     

Nonasymptotic critical behavior of a ternary ionic system

Refractive indices n and salt concentrations ms of coexisting phases of the ternary system 1,4-dioxane + water + potassium chloride were measured along the liquid-liquid-solid coexistence curve near the liquid-liquid critical end point. Refractive index measurements were carried out in the range 0.689 x 10-3 < t = (T - Tc)/Tc < 0.118 while salt concentrations were determined for the temperature range 1.84 x 10-3 < t < 8.07 x 10-2. From these experimental results, compositions fD (mass fraction of dioxane on a salt-free basis) and densities rho of coexisting phases were obtained. The shape of the coexistence curve was analyzed using alternatively n, ms, fD, and rho as order parameters. In all cases, the obtained coexistence curve displays, asymptotically, Ising behavior. Outside the asymptotic critical domain, n, ms, and rho show significant deviations of the effective critical exponent from its Ising value, while the concentration variable fD requires no corrections to simple scaling. On the basis of the present results, we conclude that this system shows no indication of multicritical behavior.     

Phase equilibrium of a water-n-pentane system in the upper locus region of critical points

Measurements of the p, V, T data and phase equilibrium of a water-n-pentane system were performed. It was established that the phase diagram of this system belongs to the third type in the Scott and Van Koninenburg classification. The intervals and parameters of the lower and upper branches of the critical line and the parameters of the upper critical endpoint and the double homogeneous point were determined.     

Phase equilibrium diagrams in a system of the Li-LiH type

The structure of the diagram of state for a binary solution of the Li-LiH type at phase equilibrium is analyzed in detail on the basis of the available literature. Characteristic dependences of the boundary curves on the temperature and composition of the solution for Li-LiH (LiD, LiT) systems are found.