Phase equilibria general diagrams

Figure 6 shows the phase diagrams plotting temperature T vs c for PHIC-toluene systems with different Mw or N [64], indicating c( and cA to be insensitive to T, as is generally the case with lyotropic polymer liquid crystal systems. This feature reflects that the phase equilibrium behavior in such systems is mainly governed by the hard-core repulsion of the polymers. The weak temperature dependence in Fig. 6 may be associated with the temperature variation of chain stiffness [64]. We assume in the following theoretical treatment that liquid crystalline polymer chains in solution interact only by hardcore repulsion. The isotropic-liquid crystal phase equilibrium in such a solution is then the balance between S and Sor, as explained in the last part of Sect. 2.2. 

Figure 13.15 is drawn for a single constant pressure equilibrium phase compositions, and hence the locations of the lines, change with pressure, but the general nature of the diagram is the same over a range of pressures. For the majority of systems the species become more soluble in one another as the temperature increases, as indicated by lines CG and DH of Fig. 13.15. If this diagram is drawn for successively higher pressures, the corresponding three-phase equilibrium temperatures increase, and lines CG and DH extend further and further until they meet at the liquid/liquid critical point Af, as shown by Fig. 13.16. The temperature at which this occurs is known as the upper critical solution temperature, and at this temperature the two liquid phases become identical and merge into a single phase.

The systems involving rigid-chain polymers and forming both the liquid-crystalline and the crystallosolvate phase are characterized by a complex phase equilibrium. The general principles of constructing phase diagrams (topological analysis) allow us to assume that the sequence of phase transfonnations in such systems has the... 

Finally, the inexperienced reader should note that phase equilibrium diagrams only tell what will eventually happen—at equilibrium. These diagrams do not contain information relating to the kinetics of the reactions. In general, however, reactions involving alkali oxides are relatively fast for ceramic systems. If, for example, the phase diagram reveals liquid... 

Fig. 4.28 Generalized phase diagram. Only a supercritical fluid exists above the critical temperature (T ) and critical pressure (p ), which has properties intermediate between liquid and gas. (Note water is unusual in having a negative slope for the solid-liquid phase equilibrium line.)...

Generally, liquid-liquid phase equilibrium (or phase separation) occurs only over certain temperature ranges, bounded above by the upper consolute or upper critical solution temperature, and bounded below by the lower consolute or lower critical solution temperature. These critical solution temperatures are indicated on the liquid-liquid phase diagrams given here. All partially miscible mixtures should exhibit either one or both consolute temperatures however, the lower consolute temperature may be obscured by the freezing of the mixture, and the upper consolute temperature will not be observed if it is above the bubble point temperature of the mixture, as vaporization will have instead occurred. ... 

In a ternary mixture there is also the possibility of three or more liquid phases in equilibrium, which is allowed by a generalization of the two-phase equilibrium analysis of this section (see Problem 11.2-1). Indeed, note that some of the phase diagrams in Fig. 11.2-11 show regions of liquid-liquid-liquid equilibrium. 

On the phase boundaries, two phases coexist indefinitely, ice and water, water and steam, or ice and steam. If a variable is changed, the two-phase equilibrium is generally lost. In order to preserve a two-phase equilibrium, one variable, either pressure or temperature, can be changed at will, but the other must also change, by exactly the amount specified in the phase diagram, to maintain two phases in coexistence and so to return to the phase boundary. 

In Figure 8.12 the outer envelope is the locus of saturated equimolar liquid states and saturated equimolar vapor states. However, note that Figure 8.12 is not a phase-equilibrium diagram in Figure 8.12 every point on the two-phase line represents an equimolar mixture, but phases in vapor-liquid equilibrium generally do not have the same composition. Consequently, Figure 8.12 contains no tie lines across the two-phase region. Outside the saturation envelope, the mixtures are stable one-phase fluids. Underneath that envelope, the mixtures may be metastable one-phase fluids or they may be unstable to one phase (that is, they may exist as two-phases). 

Let s examine now the structure of trajectory bundles of sharp reversible distillation for the intermediate (extractive) section of the column with two feedings at separation of different types of azeotropic mixtures, the way we did it for the top and the bottom sections (Fig. 4.21). While composing these diagrams, we used, just as we did before, the data on the phase equilibrium coefficients of present and absent components at the sides of the concentration triangle and the general regularities of the location of the trajectory bundles of sharp reversible distillation. 

The general principles and techniques used to establish phase equilibrium are common for both equilibrium and nonequilibrium diagrams. These can be divided into three categories. One pertains to the evaluation of the chemical aspects for the system, for example, composition and structure. The second concerns the determination of the physical conditions within the system, for example, temperature, total pressure, and time. The result of such studies is a description of the variations in... 

For further reading, readers are encouraged to consult the book by Koningsveld, Stockmayer and Nies, which contains an extensive list of phase diagrams for various binary polymer-solvent mixtures [100]. The book also contains a detailed review of the general thermodynamic principles of the phase equilibrium. 

Chapter 1 (Phase Equilibria in Binary and Ternary Hydro-thermal Systems, V. M. Valyashko, Russia) contains a description of the general trends of sub- and supercritical phase behavioin in binary and ternary systems taking into accoimt both stable and metastable equilibria. A presentation of the various types of phase diagrams aims to show the possible versions of phase transitions under hydrothermal conditions and to help the reader with the determination of where the phase equilibrium occurs in p-T-X space, and what happens to this equilibrium if the parameters of state are changed. Special attention is paid to continuous phase transformations taking place with variations of temperature. 

Furthermore, in sohd-phase reactions of diffusion amorphization (e.g., au-rum and lanthanum [8], nickel and zirconium [9]), a metastable amorphous phase, which is absent in an equilibrium state diagram, appears first. In multicomponent systems with two-phase zones, the problem of evolutionary path choice becomes even more complicated [10-16]. Therefore, the formulation of a heuristic principle of choice forecasting the evolutionary path based on a general thermodynamic bacl ound would be very important. 

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