Pseudo-Binary Diagrams

Therefore, the approach followed in this chapter considers pseudo-binary diagrams, i.e., equilibria involving the third component are, however, neglected, but modifications due to the presence of the solute are considered on the binary system. We will observe in the analysis of the experimental results that this approach can provide interesting information regarding the evolution of the SAS process, and the morphology and dimension of the precipitated particles. A rationalization of the experimental results is also proposed. 

Figure 5 Pseudo-binary diagram and the possible operating points for SAS...

A pseudo-binary diagram is shown in Figure 5 and can be used to locate the various cases discussed with respect to VLEs. 

The benzene recovery section, between the condenser and the solvent feed stage, is represented on a Y-X pseudo-binary diagram where the acetone and chloroform are lumped as one component in solution with the benzene. 

Drawing pseudo-binaryjy—x phase diagrams for the mixture to be separated is the easiest way to identify the distillate product component. A pseudo-binary phase diagram is one in which the VLE data for the azeotropic constituents (components 1 and 2) are plotted on a solvent-free basis. When no solvent is present, the pseudo-binaryjy—x diagram is the tme binaryjy—x diagram (Eig. 8a). At the azeotrope, where the VLE curve crosses the 45° line,... 

Fig. 8. Pseudo-binary (solvent-free)jy-x phase diagrams for determining which component is to be the distillate where (—) is the 45° line, (a) No solvent (b) and (c) sufficient solvent to eliminate the pseudo-a2eotiope where the distillate is component 1 and component 2, respectively (51) and (d) experimental VLE data for cyclohexane—ben2ene where A, B, C, and D represent 0, 30, 50, and 90 mol % aniline, respectively (52).

The phase diagram of the pseudo-binary Li-(Zn,Ge) was published more than twenty years ago [63]. It reports the existence of two intermetallic compounds ... 

If the presence of the other components does not significantly affect the volatility of the key components, the keys can be treated as a pseudo-binary pair. The number of stages can then be calculated using a McCabe-Thiele diagram, or the other methods developed for binary systems. This simplification can often be made when the amount of the non-key components is small, or where the components form near-ideal mixtures. 

Fig. 1.41 Phase diagram of the pseudo-binary ZrOj-CaO system. ...

To evaluate the phase equilibria of binary gas mixtures in contact with water, consider phase diagrams showing pressure versus pseudo-binary hydrocarbon composition. Water is present in excess throughout the phase diagrams and so the compositions of each phase is relative only to the hydrocarbon content. This type of analysis is particularly useful for hydrate phase equilibria since the distribution of the guests is of most importance. This section will discuss one diagram of each binary hydrate mixture of methane, ethane, and propane at a temperature of 277.6 K. 

Figure 5.15 is the pseudo-binary pressure versus excess water composition diagram for the methane+propane+water system at a temperature of 277.6 K. At 277.6 K the hydrate formation pressures are 4.3 and 40.6 bar for pure propane (sll) and pure methane (si) hydrates, respectively, as shown at the excess water composition extremes in Figure 5.15. As methane is added to pure propane, there will be a composition at which the incipient hydrate structure changes from sll to si as seen in the inset of Figure 5.15, this composition is predicted to be 0.9995 mole fraction methane in the vapor—a very small amount of propane added to a methane+water mixture will form sll hydrates.

Figure 5.16 is the pseudo-binary pressure versus excess water composition diagram for the methane + ethane + water system at a temperature of 277.6 K. In the diagram, pure ethane and pure methane both form si hydrates in the presence of water at pressures of 8.2 and 40.6 bar, respectively. Note that between the compositions of 0.74 and 0.994 mole fraction methane, sll hydrates form at the incipient formation pressure. Similar to the methane + propane + water system, only a small amount of ethane added to pure methane will form sll hydrates. 

FIGURE 7.10 Pseudo-binary phase diagram of the water, HNO3/DMDBTDMA, dodecane system to identify the third-phase limit. Experimental points (circles) and theory (lines) obtained from Baxter sticky hard-sphere approach. The theoretical line is obtained with the experimental determination of the linear variation of the stickiness parameter tt1 versus [HN03]/[DMDBTDMA]. The different lines illustrate the impact of the error in this T-1 experimental linear law. (From C. Erlinger, L. Belloni, T. Zemb, and C. Madic, Langmuir, 15 2290-2300, 1999. With permission). 

Furfiier evidence fiiat supports these calculations derives from studies of the ternary mixtures of the cationic double-chain surfactant DDAB (didodecyl dimethyl ammonium bromide), cyclohexane and water. Within the cubic mesophase region of fiiis surfactant-water-oil mixtiure, all the cyclohexane is adsorbed between the surfactant chains, so that the system is a pseudo-binary one, for which our theoretical analysis ought to hold. (The effective surfactant parameter for fliis surfactant in the presence of cyclohexane is slightly larger tiian unity.) Close scrutiny of the cubic phase region within this ternary phase diagram has revealed the presence of at least one - and... 

ALON is a solid solution region on the binary line of AIN-A1203, which is in reality a pseudo binary in the Al-O-N system. The first phase diagram to include ALON was reported by Lejus [40], whereas the first... 

As a result of the recent investigations of the pseudo-binary systems of the substance sulphur we obtain the diagram shown in Fig. 67. Here, the points A, D, and G represent the ideal freezing-points of monoclinic, rhombic, and nacreous sulphur respectively, or the temperatures at which these three crystalline forms are in equilibrium with pure molten Sa. The curve HEB represents the dynamic equilibrium curve for Sa, S i, and S,r in molten sulphur and the points B, E, and H, where this equilibrium curve cuts the freezing-point curves, represent the natural freezing-points of the three modifications of sulphur. 

There is a large body of literature on phase diagrams for pseudo-binary and pseudo-ternary polymer systems (pseudo- is to indicate polydispersity of molecular weights) with solvents [Flory, 1953 ... 

The phase diagrams of polymer blends, the pseudo-binary polymer/polymer systems, are much scarcer. Furthermore, owing to the recognized difficulties in determination of the equilibrium properties, the diagrams are either partial, approximate, or built using low molecular weight polymers. Examples are fisted in Table 2.19. In the Table, CST stands for critical solution temperature — L indicates lower CST, U indicates upper CST (see Figure 2.15). 

The determination of was examined by first considering the liquid solution behavior and then the solid mixture properties. The liquid phase properties are typically determined by using a solution model to interpolate between the binary limits. In general, the use of only the binary phase diagrams in the data base for model parameter estimation does not give good values for the ternary liquid mixture properties. The solid solution behavior is normally determined from an analysis of the pseudo-binary phase diagram. Extrapolation of the solid solution behavior determined in this manner to lower values of temperature should be undertaken with caution. 

Figure 9. A pseudo binary phase diagram which explains mesophase formation in a pitch.

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