Phase behavior ternary diagrams

Phase Behavior. One of the pioneering works detailing the phase behavior of ternary systems of carbon dioxide was presented ia the early 1950s (12) and consists of a compendium of the solubiHties of over 260 compounds ia Hquid (21—26°C) carbon dioxide. This work contains 268 phase diagrams for ternary systems. Although the data reported are for Hquid CO2 at its vapor pressure, they yield a first approximation to solubiHties that may be encountered ia the supercritical region. Various additional sources of data are also available (1,4,7,13). 

Case I. At sufficiently low pressures, the solubility curve does not intersect the coexistence curve. In this case, the gas solubility is too low for liquid-liquid immiscibility, since the coexistence curve describes only liquid-phase behavior. Stated in another way, the points on the coexistence curve are not allowed because the fugacity f2L on this curve exceeds the prescribed vapor-phase value f2v. The ternary phase diagram therefore consists of only the solubility curve, as shown in Fig. 28a where V stands for vapor phase. 

Much of what we need to know abont the thermodynamics of composites has been described in the previous sections. For example, if the composite matrix is composed of a metal, ceramic, or polymer, its phase stability behavior will be dictated by the free energy considerations of the preceding sections. Unary, binary, ternary, and even higher-order phase diagrams can be employed as appropriate to describe the phase behavior of both the reinforcement or matrix component of the composite system. At this level of discussion on composites, there is really only one topic that needs some further elaboration a thermodynamic description of the interphase. As we did back in Chapter 1, we will reserve the term interphase for a phase consisting of three-dimensional structure (e.g., with a characteristic thickness) and will use the term interface for a two-dimensional surface. Once this topic has been addressed, we will briefly describe how composite phase diagrams differ from those of the metal, ceramic, and polymer constituents that we have studied so far. 

A ternary system consisting of two polymer species of the same kind having different molecular weights and a solvent is the simplest case of polydisperse polymer solutions. Therefore, it is a prototype for investigating polydispersity effects on polymer solution properties. In 1978, Abe and Flory [74] studied theoretically the phase behavior in ternary solutions of rodlike polymers using the Flory lattice theory [3], Subsequently, ternary phase diagrams have been measured for several stiff-chain polymer solution systems, and work [6,17] has been done to improve the Abe-Flory theory. 

These phase diagrams were assessed accurately in preliminary studies, since the phase separation method is based on the precipitation of a shell material from the phase behavior of the ternary system. Actually, the core material served as a poor solvent for the shell polymer. During evaporation of the solvent, a precipitation of the shell polymer on the surface of core droplets occurs. 

Above this pressure, dot 6, all mixtures of methane and propane are single phase. Thus only the methane-n-pentane binaries have two-phase behavior, and only the methane-n-pentane side of the ternary diagram can show a bubble point and a dew point. The bubble-point and dewpoint lines of the saturation envelope do not intercept another side of the diagram, rather the two lines join at a critical point, i.e., the composition of the three-component mixture that has a critical pressure of 1500 psia at 160°F. 

On a ternary equilibrium diagram like that of Figure 14.1, the limits of mutual solubilities are marked by the binodal curve and the compositions of phases in equilibrium by tielines. The region within the dome is two-phase and that outside is one-phase. The most common systems are those with one pair (Type I, Fig. 14.1) and two pairs (Type II. Fig. 14.4) of partially miscible substances. For instance, of the approximately 1000 sets of data collected and analyzed by Sorensen and Arlt (1979), 75% are Type I and 20% are Type II. The remaining small percentage of systems exhibit a considerable variety of behaviors, a few of which appear in Figure 14.4. As some of these examples show, the effect of temperature on phase behavior of liquids often is very pronounced. 

A limited number of studies have considered the use of surfactant and cosolvent mixtures to enhance the recovery of NAPLs (Martel et al., 1993 Martel and Gelinas, 1996). Martel et al. (1993) and Martel and Gelinas (1996) employed ternary phase diagrams to select surfactant+cosolvent formulatons for treatment of NAPL-contaminated aquifers. The surfactant+cosolvent formulations used in their work, which included lauryl alcohol ethersulfate/n-amyl alcohol, secondary alkane sulfonate/n-butanol, and alkyl benzene sulfonate/n-butanol, were shown to be effective solubilizers of residual trichloroethene (TCE) and PCE in soil columns (Martel et al., 1993). However, very little information is available regarding the effect of cosolvents on the solubilization capacity and phase behavior of ethoxylated nonionic surfactants. 

In the previous section we have described the three types of phase behavior observed in the low-molecular-weight PMMA/PS system and reviewed the four types observed in the low-molecular-weight PS/PMMA system. These various phase relationships have been studied in terms of their dependence on the molecular weight (Mn) and weight percent (W) of the initial polymer present. Further, we have presented quantitative data concerning the sizes of the dispersed particles, again correlated to variations in Mn and W. In this section we will discuss the results in terms of the poly (methyl methacrylate )/polystyrene/styrene and poly-styrene/poly( methyl methacrylate)/methyl methacrylate ternary phase diagrams, whichever is appropriate. 

Finally, we note that type (4 ) behavior also can be discussed in terms of the appropriate ternary diagram and we have done so in an earlier report (18). However, since we did not observe this type of phase relationship in our present study, we will not pursue this point here. 

Although studies of the thermotropic phase behavior of singlecomponent multilamellar phospholipid vesicles are necessary and valuable, these systems are not realistic models for biological membranes that normally contain at least several different types of phospholipids and a variety of fatty acyl chains. As a first step toward understanding the interactions of both the polar and apolar portions of different lipids in mixtures, DSC studies of various binary and ternary phospholipid systems have been carried out. Phase diagrams can be constructed by specifying the onset and completion temperatures for the phase transition of a series of mixtures and by an inspection of the shapes of the calorimetric traces. A comparison of the observed transition curves with the theoretical curves supports... 

The phase behavior observed in the quaternary systems A and B is also evidenced in ternary systems. Figure 4 shows the phase diagrams for systems made of AOT-water and two different oils. The phase diagram with decane was established by Assih (14) and that with isooctane has been established in our laboratory. At 25°C the isooctane system does not present a critical point and the inverse micellar phase is bounded by a two-phase domain where the inverse micellar phase is in equilibrium with a liquid crystalline phase, as for system B or system A when the W/S ratio is below 1.1. In the case of decane, a critical point has been evidenced by light scattering (15). Assih and al. have observed around the critical point a two-phase region where two microemulsions are in equilibrium. A three-phase equilibrium connects the liquid crystalline phase and this last region. 

In conclusion, the same phase behavior is evidenced when we change the alcohol or the W/S ratio in a quaternary system, and the oil in a ternary system. This behavior can be characterized by two types of phase diagrams. In the first type no critical point occurs. In this case, the inverse micellar phase is bounded by a two-phase region where it is in equilibrium with a liquid crystalline phase. 

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). 

Some typical phase behavior that can be exhibited by ternary mixtures is shown in Fig. 3.11. Let us consider a situation where binary mixtures of component 1 and component 2 are only partially miscible, where two coexisting liquid phases may be formed one rich in 1 and the other rich in 2. This is represented by the base of the ternary phase diagram shown in Fig. 3.11a. In addition, let us assume that components 1 and 3 are completely miscible and components 2 and 3 are also completely miscible. For this case, one might expect that if enough of component 3 is added to the system, then components 1 and 2 can be made to mix with each other, due to their mutual solubility with component 3. This is type I phase behavior. 

The phase behavior of microemulsions is complex and depends on a number of parameters, including the types and concentrations of surfactants, cosolvents, hydrocarbons, brine salinity, temperature, and to a much lesser degree, pressure. There is no universal equation of state even for a simple microemulsion. Therefore, phase behavior for a particular microemulsion system has to be measured experimentally. The phase behavior of microemulsions is typically presented using a ternary diagram and empirical correlations such as Hand s rule. 

In a type 111 system, a left lobe or right lobe microemulsion cannot coexist with the middle-phase microemulsion. The total composition determines the existence of a lobe or the middle-phase microemulsion. Gary A. Pope (Personal communication on Febraary 17, 2009) pointed out that, as a practical matter, we rarely measure a sufficient number of points in the ternary system to clearly define two-phase and three-phase regions. When cosolvent and/or Ca is used, or when soap forms, a ternary diagram does not accurately represent the phase behavior. When typical salinity scans at WOR = 1 and a low surfactant concentration are performed, almost aU the cases in a type III environment will be three phases. So there is little, if any, practical issue involved in a typical phase behavior experiment. 

This section describes how to use Hand s rule to represent binodal curves and tie lines. The surfactant-oil-water phase behavior can be represented as a function of effective salinity after the binodal curves and tie lines are described. Binodal curves and tie lines can be described by Hand s rule (Hand, 1939), which is based on the empirical observation that equilibrium phase concentration ratios are straight lines on a log-log scale. Figures 7.15a and 7.15b show the ternary diagram for a type II(-) environment with equilibrium phases numbered 2 and 3 and the corresponding Hand plot, respectively. The line segments AP and PB represent the binodal curve portions for phase 2 and phase 3, respectively, and the curve CP represents the tie line (distribntion cnrve) of the indicated components between the two phases. Cy is the concentration (volnme fraction) of component i in phase) (i or j = 1, 2, or 3), and 1, 2, and 3 represent water, oil, and microemulsion, respectively. As the salinity is increased, the type of microemulsion is changed from type II(-) to type III to type II(-i-). C, represents the total amount of composition i. 

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