Phase diagram isobaric

As an example of more complex systems and descriptions, the Ni-Mg system is shown in Fig. 2.32 (adapted from Levinsky 1997). In (a) an isobaric section of the diagram is shown (a low pressure has been considered in order to have a certain extension of the gas phase which consists essentially of Mg vapour). In Fig 2.32(b) there is an isothermal section of the diagram at 700°C. Notice, for different values of pressure, the change in the sequence of phases stable at different compositions. A value of the pressure close to atmosphere is approached at the top of the figure. In Fig 2.32(c) the usual Tlx diagram is shown. This can be considered an isobaric phase diagram if pressure is relatively low but still higher than the sum of the equilibrium partial pressures of the components. 

Area within the coexistence curve of an isobaric phase diagram (temperature vs. composition) or an isothermal phase diagram (pressure vs. composition). 

Fig. 8.2. Simulation of the isobaric phase diagram for the reacting system methylphosphinic acid + butanol -+ methylphosphinic acid butyl ester plus water based on COSMO-RS predictions [C28].

Because of its high dimensionality, it is difficult - or even impossible - to view the phase diagram of a multicomponent system in its entirety. For example, an isobaric phase diagram for four components would involve a four-dimensional space. To... 

Fig. 11.7. Isobaric phase diagram of a binary system where the following reaction takes place A + B — C resulting in (a) a congruent melting compound and (b) an incongruent melting compound.

FIG. 13-57 Schematic isobaric-phase diagrams for binary azeotropic mixtures. (a) Homogeneous minimum-boiling azeotropes. 

The results obtained in the first paragraph of this chapter may now be applied to binary mixtures. The isobaric phase diagram is then of the form shown diagrammatically in fig. 22.3. 

The isobaric phase diagrams of three-component systems are determined by four variables three concentration coordinates and the temperature. With regard to the condition that the sum of mole or mass fractions equals one, it is possible to show these phase diagrams in three-dimensional space, where the concentration coordinates are shown in the x-y plane and the temperature on the z axis. 

Fig. 9. Temperature-composition isobaric phase diagram for the fully hydrated dipal-mitoylphosphatidylcholine/dipalmitoyl-phosphatidylethanolamine system constructed using the temperature gradient method. The notation used is that of Luzzati [8] and is as follows Lc, lamellar crystalline (also referred to as the subgel phase) L f, lamellar gel phase with hydrocarbon chains tilted with respect to the bilayer normal P)el, ripple phase L. lamellar liquid crystal phase. Insert bold line in graph as indicated...

Fig. 11. Temperature-composition isobaric phase diagram for the monolinolein/water system constructed using the lyotrope gradient method. See ligand to Fig. 3 for notation. Hn, inverted hexagonal phase CP4, cubic, primitive (aspect 8) BCC12, cubic, body-centered (aspect 12) Isotropic,...

For computation of an isobaric phase diagram the temperature dependence of the association constants has to be known K (T), Kg(T), and K (T). An Arrhenius-type dependence has been assumed ... 

Miscibility of polymer blends is usually presented as an isobaric phase diagram with the lower critical solution temperature, T = LCST (see Figure 16.5). The binodals indicate limits of miscibility, while the spinodals the boundary between the meta-stable and spinodal regions. Thus, polymer blends are usually miscible at lower temperature, outside the binodal and are immiscible at higher temperature inside the spinodal region. 

As most experiments are carried out at atmospheric pressure, a planar diagram, using temperature and composition as variables, is sufficient for many purposes. These sections at a fixed pressure are called isobaric phase diagrams. In these constant-pressure diagrams a single phase occurs over an area in the figure, and phase boundaries are drawn as hues. A point in such a binary phase diagram defines the temperature and composition of the system. 

Fig. 18. Isobaric phase diagram of a LC main chain polyester and a small molecule nematogen. From ref. 55-...

The binary, isobaric phase diagram for a mixture of ethyl 4-dodecyloxybenzylidene-4 -aminobenzoate(A) and 4-octyloxybenzylidene-4 -trifluoromethylaniline(B) is presented in Fig. 2. This mixture has a mildly enhanced smectic A phase. 

Fig. 2. Isobaric phase diagram for the binary pair of azobenzenes 4-ethoxy-4 - -pentanoyloxyazobenzene and 4-ethoxy-4 - -nonanoyloxyazobenzene, Ref. 7.

FIGURE 1.16. The isobaric phase diagram of mixtures HOPDOB-HBAB (a simplified version of [42]). Dashed lines correspond to monotropic transitions. 

To determine miscibility, usually isobaric phase diagrams are constructed. An example of... 

By following the contact method ,Noel and co-workers " " have reported the isobaric phase diagrams of mixtures of optically active compounds with thermotropic liquid crystal polymers and copolymers, such as those represented by structures 1-5... 

Fig. 10. Isobaric phase diagram of an LC main-chain polymer and a reference compound. From Ref. 59.

Fig. 11. Isobaric phase diagram of poly(terphenyl 4,4"-dicarboxylate) and...

Fig. 2.29. Isobaric phase diagram of a MCLC polyester and a LMM reference compound. (From Ref 164.)...

Fig. 2.31. Isobaric phase diagram of a SCLCP and a reference compound, (a) Freshly prepared samples and (b) after annealing...

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