Phase Diagrams for Ternary Mixtures

The isothermal ternary diagrams will get stacked one on top the other to build a prism that shows the effect of pressure on the phase behavior. The three sides of the prism are, in fact, the P-x diagrams for each binary pair at the system temperature. The ternary diagrams in this chapter always put the SCF in the lower right-hand corner of the triangle. A, the component least soluble in the SCF, is always placed in the lower left-hand corner B, the third component, is placed at the top of the triangle. We will assume that components A and B have vapor pressures that are less than 5 bar at modest temperatures, typical of organic solvents. 

A schematic representation of type-I ternary phase behavior is shown in figure 3.29. The three diagrams in this figure represent mixtures at a fixed temperature slightly higher than the critical temperature of the SCF but at three different pressures. The distinguishing feature of type-I ternary phase behavior is the absence of LLV immiscibility regions within the ternary 

In figure 3.29b the pressure of the system has been increased to a point slightly below the critical pressure of the SCF. At this pressure the SCF still remains virtually insoluble in component A but its solubility in B has increased markedly, i.e., the tie line for the SCF-B mixture has gotten smaller to reflect the increased solubility of component B in the SCF-rich phase and of the SCF in the B-rich phase. The binodal curve in the ternary diagram now bends further toward the SCF apex. The vapor phase composition remains essentially pure SCF since, at this temperature, we are assuming that the vapor pressures of components A and B are extremely low. 

In figure 3.29c the pressure has now been increased to a value greater than the critical pressure for the SCF-B mixture. The SCF is now miscible in all proportions with B, and the binodal curve no longer intersects the SCF-B binary axis of the ternary diagram. Even at this elevated pressure, the SCF still remains virtually insoluble in A, as would be the case if the supercritical fluid were a low molecular weight hydrocarbon and component A were water (Culberson and McKetta, 1951). As shown in figure 3.29c, the binodal curve intersects the SCF-A binary axis in two locations. The tie lines for the ternary system now indicate that a liquid phase, mostly a mixture of A and B, is in equilibrium with a fluid phase, mainly the SCF with component B. 

An isothermal pressure-composition phase diagram is shown in figure 3.29d (Elgin and Weinstock, 1959 Treybal, 1968). As mentioned previously. 

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Eig. 14. Schematic isobatic phase diagrams for ternary azeotropic mixtures, (a) Homogeneous Hquid phase at all boiling points (b) heterogeneous... 

Schematic phase diagrams for binary mixtures of water with a strong amphiphile, and for ternary mixtures containing oil, water, and amphiphile, are shown in Fig. 3 (adapted from Refs. 7,8). Among the many interesting...

Figure 3A.1 Ternary phase diagram for two mixtures of hydrogen sulfide + carbon dioxide + methane [data from Robinson and Bailey (1957) and curves from the Peng-Robinson equation of state].

The equilibrium composition of phases can be represented vividly with the help of the diagram for ternary mixture. As seen in fig,4 points 1, 2, 3 of intersection of connecting line with binodales describing the composition of the rubber phase of POO-... 

But some double-chain cationic surfactants form microemulsions when mixed with only water and oil over a large region of the ternary phase triangle [38, 39]. These surfactants are virtually insoluble in both water and oil and therefore are located exclusively at the oil-water interface. This aids structural analyses significantly. We shall focus on mixtures containing DDAB. Some typical phase diagrams for these mixtures are reproduced in Fig. 4.19. 

Phase diagrams for multicomponent mixtures possess additional degrees of freedom and are inherently multidimensional. In practice, construction and interpretation of phase diagrams of multicomponent mixtures are similar to, and based on, those of binary mixtures. " " The phase behavior of multicomponent mixtures can also be depicted as sections in PTxiX2-space, keeping one or more of the variables constant. A widely used section for ternary mixtures is an equilateral triangle composition diagram at fixed pressure and temperature (Fig. 7). 

Phase equilibria for ternary mixtures are conventionally represented on equilateral triangular diagrams. Such diagrams provide a convenient way to present basic material balance relations these are reviewed in Appendix H. Triangular diagrams are T diagrams, and for C = 3 components, (9.1.12) gives... 

Figure 9.25 Six common types of isothermal-isobaric triangular diagrams for ternary mixtures that exhibit liquid-liquid equilibria. Filled circles locate consolute points. Numeral 3 inside a triangle identifies three-phase LLLE the compositions of the three phases are given by the vertices of the triangles. These six diagrams are arranged by the number of two-phase regions (a) and (b) each have one, (c) has two, and (d)-(f) each have three. Adapted from Walas [5].

Similarly to the phase diagrams for binary systems, the main types for fluid phase diagrams of ternary mixtures should not have an intersection of critical curves and inunis-cibUity regions with a crystallization surface in them. Combination of four main types of binary fluid phase behavior la, lb, Ic and Id (Figure 1.2) for constituting binary subsystems gives six major classes of ternary fluid mixtures with one volatile component, two binary subsystems (with volatile component) complicated by the immiscibility phenomena and the third binary subsystem (consisted from two nonvolatile components) of type la with a continuous solid solutions. These six classes of ternary fluid mixtures can be referred as ternary class I (with binary subsystems Ib-lb-la), ternary class II (with binary subsystems Ic-lc-la), ternary class III (with binary subsystems Id-ld-la), or ternary class IV (with binary subsystems Ib-ld-la), ternary class V (with binary subsystems Ib-lc-la) and ternary class VI (with binary subsystems Ic-ld-la). 

Figure 6 Hypothetical ternary phase diagram for a mixture of polymer A with another polymer B at two molecular weights, Bl and B2. A mixture at X will not phase separate into compositions Y and Z but into V and W with fractionation of polymer B. In the psuedobinary phase diagram below, on cooling a mixture to V one might expect the coexistent phase U to separate but in fact the coexisting phase is at W with a different distribution of Bl and B2...

Figure A2.5.30. Left-hand side Eight hypothetical phase diagrams (A through H) for ternary mixtures of d-and /-enantiomers with an optically inactive third component. Note the syimnetry about a line corresponding to a racemic mixture. Right-hand side Four T, x diagrams ((a) tlirough (d)) for pseudobinary mixtures of a racemic mixture of enantiomers with an optically inactive third component. Reproduced from [37] 1984 Phase Transitions and Critical Phenomena ed C Domb and J Lebowitz, vol 9, eh 2, Knobler C M and Scott R L Multicritical points in fluid mixtures. Experimental studies pp 213-14, (Copyright 1984) by pennission of the publisher Academic Press.

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. 

Compositional phase diagrams for three-component mixtures must be plotted in such a way that the compositions of all three components can be displayed. Diagrams formed from equilateral triangles are convenient. for this purpose. These are called ternary diagrams. 

Fig. 6.43 Phase diagram for a ternary mixture of equal concentrations of A and B homopolymers and symmetric AB diblock (all with equal degrees of polymerization) computed by Holyst and Schick (1992). The Lifshitz tricritical point is shown at L, the line CL is that of continuous transitions from the disordered phase to coexisting A-rich and B-rich phases, and LG is the line of continuous transitions from the disordered to the lamellar phase. LD is the disorder line.

Figure 4 Some phase diagrams for lipid bilayers in excess water prepared from binary and ternary lipid mixtures, a) Multibilayer lipid vesicles prepared from binary mixtures of DMPC and DPPC (24) b) Multibilayer lipid vesicles prepared from binary mixtures of DMPC and DSPC [adapted by Reference (25) from data for perdeuterated lipids published by Knoll et al. (26)] c) Multibilayer lipid vesicles prepared from binary mixtures of diCi/.QPC and C22 oCi2 oPC (27) d) Multibilayer lipid vesicles prepared from binary mixtures of DMPC and cholesterol (28) e) Multibilayer lipid vesicles prepared from ternary mixtures of palmitoyl sphingomyelin, POPC, and cholesterol [adapted by Reference (29), from data published by De Almeida et al. (30)] Lipid bilayers prepared from ternary mixtures of DSPC, DOPC, and cholesterol (31).

Fig. 5 Ternary phase diagram for oil, water, and surfactant mixtures showing micellar, microemulsion, and multiphase macroemulsion regions with schematic representations of various structures.

The phase diagrams for some systems are quite simple, like the solubility curve for binary mixtures, whereas for some complex mixtures, it is dilScult to define the degree of supersaturation owing to the large number of crystallizing components present. So it is necessary to make an approximation and represent a complex system on the basis of a ternary phase diagram of only three prominent components. The phase boundaries obviously depend on the number of components present, and these are explained in the sections that follow. 

Figure 9m3 Simplified schematic ternary phase diagram for the system Na20-Si02- H2O. Commercially important areas are shaded. (1) anhydrous NaiSiO- and its granular mixtures with NaOH ...

Figure 3.29 Schematic phase diagrams for a type-I ternary mixture (Weinstock, 1952).

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