Miscibility dome

When the stable boundaries of an equilibrium phase diagram are extended as, for example, in Figure 11.14, regions of metastability are shown. In eutectic systems (Fig. 11.14fl), metastable equilibria of the solvus lines usually form a liquid miscibility dome. On the other hand, as illustrated in Figure 11.14/7, metastable extensions of... 

Figure 11.14. Metastable extensions of equilibrium-phase boundaries. Solvus line extensions usually form a liquid miscibility dome. Extensions of incongruently melting compounds form a congruent melting point and extensions of congruently melting compounds often form eutectics with non-neighboring phases.

Around the stoichiometric concentration, miscibility of the mixture is sufficiently improved for the usual UCST miscibility dome to split into two gaps, each having a critical point (white circle). The intersections (black circles) between the MST and the SP lines are the Lifshitz point. As expected, the miscibility of the blend is improved with an increase in the association energy. 

The miscibility loop [38-42] has one upper critical solution temperature (UCST) at its top and one lower critical solution temperature (LCST) at its bottom. The miscibility dome has an ordinary UCST. As the molecular weight is increased, the LCST of the loop and the UCST of the dome come closer. Figure 6.9(b) shows how the miscibility loop and dome merge. At a certain value of n (1670 for the parameters given in this figure) the LCST and UCST merge into a higher-order critical point, which... 

Figure 6.13(a) draws the spinodal curves for different cooperative parameters a with other parameters fixed. The bottom part of the miscibility square becomes flatter with decreasing a. In the calculation, the usual miscibility domes with UCST appear at low temperatures, but these are not observable in the experiments because the water freezes. For polymer concentrations higher than (/>=0.5, our theoretical description becomes poor because of the depletion of water molecules the number of water molecules becomes insufficient to cover the polymers. 

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. 

Fink synthesized a series of siUcone-based surfactants [39] and used these to examine the emulsion polymerization of vinyl pyrrolidone (VP) in CO2. These monomers are liquids under ambient conditions, and hence phase behavior in CO2 was measured to determine under what conditions one could operate in an emulsion polymerization mode (Fig. 7.7). As is the case with NVF, the phase behavior of 1-vinyl-2-pyrrolidone offers the possibility for distinct polymerization regimes. Above pressures of ca. 28 MPa at 338 K, VP is miscible with carbon dioxide in all proportions. Below 28 MPa, VP and CO2 will either phase split into monomer-rich and C02-rich phases, or exist as a single phase, depending upon the initial VP concentration and system pressure. Consequently, a polymerization can be conducted initially in the single phase regime above 28 MPa, leading to a purely dispersion mechanism, or initially within the two-phase dome in P-x space, leading to an inverse emulsion polymerization. Finally, a polymerization can be conducted where pressure and composition are chosen to initially... 

Any composition at a given temperature represented by points on the left of the curve AC or the right of the curve CB consists of only one layer. All compositions between pure water and point A yield a solution of phenol in water. Within the dome shaped area ACB, the system is heterogenous and two liquid phases exist, while in the area outside the dome only a single liquid layer, i.e., a homogeneous system exists. The upper critical solution temperature may, therefore be defined as the temperature above which the two partially miscible liquids become miscible in all proportions. For phenol-water system the temperature is 339 K. 

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