Thermodynamic ternary mixture

Petlyuk FB, Kievskii VY and Serafimov LA (1975) Thermodynamic and Topological Analysis of the Phase Diagrams of Polyazeotropic Mixtures II. Algorithm for Construction of Structural Graphs for Azeotropic Ternary Mixtures, Russ J Phys Chem, 49 1836. 

Nagata, L, On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols. Fluid Phase Equilib., 19,153, 1985. 

A promising way to create LLC systems with sufficient stability is the use of immiscible ternary mixtures to create what is called a dynamic (or solvent-generated ) LLC system. The principle of such a phase system is illustrated in figure 3.9. This figure shows an example of a thermodynamic phase diagram of a mixture of three components (A, B and C). Both the binary mixtures A + B and A + C are miscible in all proportions. 

The two liquids thus formed are immiscible, but in thermodynamic equilibrium. Therefore, we may speak of a dynamic system of two immiscible phases. Figure 3.10 shows an example of a practical system applied to create a dynamic LLC phase system. A practical phase system can be created by pumping a mobile phase through a column, the composition of which corrresponds to a ternary mixture that is in dynamic equilibrium with another mixture (the two mixtures can be connected by a nodal line). If the mobile phase is the more polar one of the two ternary mixtures in equilibrium, then a non-polar (hydrophobic) solid support must be used and a reversed phase system can be generated. If the mobile phase is the less polar of the two mixtures in equilibrium, a polar support is required. 

For a ternary mixture, equations above can describe thermodynamically and mathematically coupled mass and energy conservation equations without chemical reaction, and electrical, magnetic and viscous effects. To solve these equations, we need the data on heats of transport, thermal diffusion coefficient, diffusion coefficients and thermal conductivity, and the accuracy of solutions depend on the accuracy of the data. 

The full extent and variety of the phase behavior for water-isopropanol-C02 mixtures observed experimentally and calculated with the Peng-Robinson equation of state was not anticipated based on known phase behavior for the constituent binary mixtures or similar ternary mixtures. These results suggest that multiphase behavior for related model surfactant systems could also be complex. Measurements of all the critical endpoint curves, the tricritical points, and secondary critical endpoint for such systems would be tedious and are extremely difficult. However, by coupling limited experimental data with a thermodynamic model based on this cubic equation of state, complex multiphase behavior can be comprehensively described. 

The present paper is devoted to the local composition of liquid mixtures calculated in the framework of the Kirkwood—Buff theory of solutions. A new method is suggested to calculate the excess (or deficit) number of various molecules around a selected (central) molecule in binary and multicomponent liquid mixtures in terms of measurable macroscopic thermodynamic quantities, such as the derivatives of the chemical potentials with respect to concentrations, the isothermal compressibility, and the partial molar volumes. This method accounts for an inaccessible volume due to the presence of a central molecule and is applied to binary and ternary mixtures. For the ideal binary mixture it is shown that because of the difference in the volumes of the pure components there is an excess (or deficit) number of different molecules around a central molecule. The excess (or deficit) becomes zero when the components of the ideal binary mixture have the same volume. The new method is also applied to methanol + water and 2-propanol -I- water mixtures. In the case of the 2-propanol + water mixture, the new method, in contrast to the other ones, indicates that clusters dominated by 2-propanol disappear at high alcohol mole fractions, in agreement with experimental observations. Finally, it is shown that the application of the new procedure to the ternary mixture water/protein/cosolvent at infinite dilution of the protein led to almost the same results as the methods involving a reference state. 

It was shown previously [5,14] that the KB theory of solution can be used to relate the thermodynamic properties of ternary mixtures, such as the partial molar volumes, the isothermal compressibility and the derivatives of the chemical potentials to the KB integrals. In particular for the derivatives of the activity coefficients one can write the following rigorous relations [5] ... 

The purpose of this Appendix is to provide expressions for the KBIs for binary and ternary mixtures (Gn, G13, G12 and G23) in terms of measurable thermodynamic quantities such as the derivatives of the chemical potentials with respect to concentrations, the isothermal compressibility and the partial molar volumes. 

This paper is devoted to the verification of the quality of experimental data regarding the solubility of sparingly soluble solids, such as drugs, environmentally important substances, etc. in mixed solvents. A thermodynamic consistency test based on the Gibbs-Duhem equation for ternary mixtures is suggested. This test has the form of an equation, which connects the solubilities of the solid, and the activity coefficients of the constituents of the solute-free mixed solvent in two mixed solvents of close compositions. 

Of course, for real mixtures the left hand side of Eq. (11) is not exactly equal to zero it has certain finite values even for very accurate data. Let us denote that value with D. McDermott and Ellis (McDermott and Ellis, 1965) suggested that the vapor-liquid equilibrium data in a ternary mixture are thermodynamically consistent if D for Eq. (6) is smaller than Dmax = 0.01. Now we should find the value of Dmax for the solubility of poorly soluble substances in mixed solvents for Eq. (11). Of course, this value should differ from that for the vapor-liquid equilibrium. 

However, Eqs. 3 and 5 are different equations even though they are based on the same definition of the preferential binding parameter and have the same theoretical basis the Kirkwood-Buff theory of solutions. To make a selection between Eqs. 3 and 5 a simple limiting case, the ideal ternary mixture, will be examined using the traditional thermodynamics, and the results will be compared to those provided by Eqs. 3 and 5. 

An analysis of the cosolvent concentration dependence of the osmotic second virial coefficient (OSVC) in water—protein—cosolvent mixtures is developed. The Kirkwood—Buff fluctuation theory for ternary mixtures is used as the main theoretical tool. On its basis, the OSVC is expressed in terms of the thermodynamic properties of infinitely dilute (with respect to the protein) water—protein—cosolvent mixtures. These properties can be divided into two groups (1) those of infinitely dilute protein solutions (such as the partial molar volume of a protein at infinite dilution and the derivatives of the protein activity coefficient with respect to the protein and water molar fractions) and (2) those of the protein-free water—cosolvent mixture (such as its concentrations, the isothermal compressibility, the partial molar volumes, and the derivative of the water activity coefficient with respect to the water molar fraction). Expressions are derived for the OSVC of ideal mixtures and for a mixture in which only the binary mixed solvent is ideal. The latter expression contains three contributions (1) one due to the protein—solvent interactions which is connected to the preferential binding parameter, (2) another one due to protein/protein interactions (B p ), and (3) a third one representing an ideal mixture contribution The cosolvent composition dependencies of these three contributions... 

In the light of these considerations, a different approach based on ternary system thermodynamics could be considered. However, the phase behavior of temaiy systems could be very complex and there is a considerable lack of data on ternary systems containing a component of low volatility therefore, a possible compromise could be to consider that the solute addition can produce the shift of the mixture critical point (MCP) (i.e., the pressure at which the ternary mixture is supercritical) with respect to binary system VLEs and the modification of this kind of system that is formed according to the van-Konynenburg and Scott classification. ... 

The thermodynamics of ternary mixtures that form solid solutions may be obtained by writing Equation (2) for the two solutes A and B. Thus, for solute A ... 

Quinones et al. [17] measured by frontal analysis multisolute adsorption equilibrium data for the system benzyl alcohol, 2-phenylethanol and 2-methyl benzyl alcohol in a reversed-phase system. Data were acquired for the pure compoimds, for nine binary mixtures (1 3,1 1, and 3 1) and four ternary mixtures (1 1 3,1 3 1, 3 1 1, and 1 1 1). These data exhibited very good thermod5mamic consistency. The thermodynamic functions of adsorption were derived from the single-solute ad-... 

In tills section, we examine the thermodynamics of systems which contain a mixture of species. First, we generalize the thermodynamic analysis of the previous section to multicomponent systems, deriving the Gibbs phase rule. Then we describe the general phase behavior of binary and ternary mixtures. 

Takahashi, T., 320, 330, 331 Tea decaffeination plant, 7 Temperature-entropy diagram, 138 Temperature rising elution fractionation (TREF), 197, 202-203 Ternary mixtures, phase diagrams, 71-84 Testosterone, 340 Tetracyclic steroids, 293 Thermodynamic modeling, 99-134 Thies, M. C., 88-90... 

We start the chapter by explaining the graphical thermodynamic representations for ternary mixtures known as Residue Curve Maps. The next section deals with the separation of homogeneous azeotropes, where the existence of a distillation boundary is a serious obstacle to separation. Therefore, the choice of the entrainer is essential. We discuss some design issues, as entrainer ratio, optimum energy requirements and finite reflux effects. The following subchapter treats the heterogeneous azeotropic distillation, where liquid-liquid split is a powerful method to overcome the constraint of a distillation boundary. Finally, we will present the combination of distillation with other separation techniques, as extraction or membranes. 

Initial works on the phase equilibrium of polymer solutions were concerned with nonpolar solutions using carefully prepared quasi-monodisperse polymer fractions [78]. The theory and practice was later extended to molecularly heterogeneous polymers [84], multicomponent solutions (ternary mixtures) such as polymer/solvent mixture [16, 85] and polymer mixture/solvent [86], and polymer blends [79, 80], among others [87]. Improvements on predicting thermodynamic properties were particularly proposed for polymer solutions of industrial importance, including those having polar and hydrogen-bonded components [16]. 

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