Phase Diagrams for Binary Mixtures

Constituents from a particular homologous series, such as the normal paraffins, usually deviate from type-I phase behavior only when the size difference between them exceeds a certain value. This is because the constituents are so close in molecular structure that they cannot distinguish whether they are surrounded by like or unlike species. It is important to remember that the critical curve depicted in figure 3.1a is only one possible representation of a continuous curve. It is also possible to have continuous critical mixture curves that exhibit pressure minimums rather than maximums with increasing temperature, that are essentially linear between the critical points of the components (Schneider, 1970), and that exhibit an azeotrope at some point along the curve. 

Now let us progress to the construction of the general three-dimensional P-T-x diagram for type-I binary mixtures, shown in figure 3.2. The P-T-x 

As the pressure is further increased at this fixed overall composition, the amount of the liquid phase increases while the amount of the vapor phase shrinks until only a small bubble of vapor remains. If the pressure is still further increased, the bubble of vapor finally disappears, then a single liquid phase exists. The locus of points that separates the two-phase vapor-liquid region from the one-phase liquid region is called the bubble point curve. This vapor-liquid envelope can now be inserted into the three-dimensional P-T-x diagram in figure 3.2a. 

If an experiment is performed at an overall composition equal to x in figure 3.2d, the vapor-liquid envelope is first intersected along the dew point curve at low pressures. The vapor-liquid envelope is again intersected at its highest pressure, which corresponds to the mixture critical point at T2 and x. This mixture critical point is identified with the intersection of the dashed curve in figure 3.2b and the vertical isotherm at T2. At the critical mixture point, the dew point and bubble point curves coincide and all the properties of each of the phases become identical. Rowlinson and Swinton (1982) show that P-x loops must have rounded tops at the mixture critical point, i.e., (dPldx)T = 0. This means that if the dew point curve is being experimentally determined, a rapid increase in the solubility of the heavy component will be observed at pressures close to the mixture critical point. The maximum pressure of the P-x loop will depend on the difference in the molecular sizes and interaction energies of the two components. 

Type-I phase behavior is probably the type of behavior most familiar to chemical engineers, since the description of this phase behavior can be found in many undergraduate thermodynamic textbooks. Rowlinson and Swinton (1982) present compilations of type-I mixtures as well as other types of mixtures. Hicks and Young (1975) also present an extensive compilation of P-T-x information on a wide variety of solvent-solute pairs from which the specific type of each system can easily be determined. Two examples of type-I P-x diagrams are shown in figure 3.3 (Li, Dillard, and Robinson, 1981 Ng and Robinson, 1978). For these two examples, the P-T traee of the critieal mixture curve exhibits a maximum in pressure. 

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Phase Diagrams. For binary mixtures, it is weU known that when a Hquid—Hquid envelope merges with a minimum boiling vapor—Hquid-phase envelope the resulting azeotropic phase diagram has the form shown in Figure 13. When the Hquid composition, as in Figure 13a, then the vapor... 

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 2 shows a spin-label-derived phase diagram for binary mixtures of (II) and (IV), dipalmitoylphosphatidylcholine and dielaidoylphosphatidylcholine. It will be seen that the diagram describes miscibility of these two lipids in both the solid and solution phases. (Other binary mixtures of lipids show immiscibility in the solid as well as the fluid phases.45,54)... 

In Fig. 3.2, we show the pressure-temperature view of the phase diagram for binary mixtures of methane and ethane. The point Ci represents the critical point of pure methane, and the point C2 represents the critical point of pure ethane. The curve connecting the points A and Ci is the vapor pressure curve for pure methane the curve connecting points B and C2 is the vapor pressure curve for pure ethane. The dotted curve connecting the points C and C2 is the critical locus. The critical points of the mixtures, where the coexisting liquid and vapor phases become identical, lie on this critical locus. 

Fig. 38. Phase diagram for binary mixtures of compounds 13 and 14 as function of the increasing content of compound 13 (after Vill, lunger and Peters [57])...

To begin to understand such behaviour at least qualitatively we should first consider the case of an ideal binary mixture of nematogens for which ATsc = 0. Within the framework of a molecular field theory developed to predict phase diagrams for binary mixtures of nematogens, three intermolec-ular energy parameters, Eaa> bb and the mixed parameter Eab. must be defined... 

Figure 9.29 One of the many isomorphisms that exist between vapor-liquid and liquid-solid phase diagrams for binary mixtures. (1(0) An isobaric Txy diagram with a minimum boiling-point azeotrope and a miscibility gap above an LLE situation (right) an isobaric Txx diagram with a minimum melting-point solutrope and a miscibility gap above an SSE situation.

Figure 30 p-T-x surfaces and p(T) projections of phase diagrams for binary mixtures of HgO with hydrocarbons (HC) schematic representation see text, a and c. Type found for naphthalene + H O, biphenyl + HgO b and d, type found for benzene + HgO and aqueous solutions of methylsubstituted benzenes e, no aqueous hydrocarbon system known f, type found for cyclohexane + HjO, butane + HjO... 

Fig. 3. Calculated and observed nematic-isotropic phase diagrams for binary mixtures of homologous 4,4 -di-n-alkyloxyazoxybenzenes. Solid line is calculated by regular solution approximation. A denotes point calculated assuming ideal solution. denotes experimentally observed point. 3-6 means 4,4 -di-n-propyloxy in mixture with 4,4 -di-n-hexyloxyazoxybenzene. X is mole fraction of ith component.

Fig. 5. Calculated phase diagrams for binary mixtures of -nitrobenzalaminocinnamic acid 2-methyl hexyl ester(I) with cholesterol nonanoate(II) (a) cholesterol tetradecanoate(III) (b) cholesterol octadecanoate(IV) (c). Dashed lines indicate observed temperatures.

Lamm MJ, Hall CK (2001) Molecular simulation of complete phase diagrams for binary mixtures. AIChE J 47 1664-1675... 

Experimentally, polymer solutions as well as mixtures of small molecules may show a wide range of phase behavior. A schematic representation of possible phase diagrams for binary mixtures of small molecules and polymers in solution is given in Figure 6. For some systems, eg water/triethylamine solutions, miscibility decreases with increasing temperature, phase separation taking place above a... 

Fig. 6. Schematic representation of possible phase diagrams for binary mixtures the shaded areas indicate two phase regions (a) upper critical solution temperature behavior (UCST) (b) lower critical solution temperature behavior (LOST) (c) combination of LOST and UCST, mostly observed in nonpolar polymer solutions (d) phase diagram showing upper, lower, and quasilower critical phase boundaries (e) immiscibility loop and (f) hourglass-shaped phase boundary obtained by convergence of upper and lower critical boundaries.

A large number of phase diagrams for binary mixtures combining cholesterol with different saturated and unsaturated phosphatidylcholines have been established. Cholesterol at different bilayer concentrations can promote or suppress lateral segregation of phospholipids of differing acyl chain length. 

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