Regions in the phase diagram

Of course, LC is not often carried out with neat mobile-phase fluids. As we blend solvents we must pay attention to the phase behavior of the mixtures we produce. This adds complexity to the picture, but the same basic concepts still hold we need to define the region in the phase diagram where we have continuous behavior and only one fluid state. For a two-component mixture, the complete phase diagram requires three dimensions, as shown in Figure 7.2. This figure represents a Type I mixture, meaning the two components are miscible as liquids. There are numerous other mixture types (21), many with miscibility gaps between the components, but for our purposes the Type I mixture is Sufficient. 

In the dynamic Monte Carlo simulations described earlier, we used a crystalline template to suppress supercooling (Sect. A.3). If this template is not present, there will be a kinetic interplay between polymer crystallization and liquid-liquid demixing during simulations of a cooling run. In this context, it is of particular interest to know how the crystallization process is affected by the vicinity of a region in the phase diagram where liquid-liquid demixing can occur. 

Prepare 6-10 reservoirs with a solutions containing precipitant concentration that would result In producing a clear drop If crystallization drops were set up and left to Incubate under these conditions. Determine these concentrations from the region In the phase diagram that Is just under the supersolublllty curve (Fig. 3.3). 

In the case of vinyl chloride polymerisation in polyfbutyl acrylate) these materials are completely miscible but a two phase region exists within the phase diagram as shown in Fig. 4 Polymerisation from A to B produces a homogeneous blend whereas from E to F produces a two phase structure. Composition B can be reswollen to C with vinyl chloride which can then be polymerised to D to producea homogeneous blend. This route avoids the two phase region in the phase diagram and in principle all compositions of polymer blend can be prepared in a series of steps. 

The middle diagram of Figure 11 illustrates phase behavior that may be more desirable for some applications. In this case the presence of a lamellar liquid crystal region in the phase diagram, although it will not be revealed by experiments confined to low surfactant concentrations, may be exploitable for the formation of very stable dispersions (82). 

Even a small deviation of / from zero results in a considerable bfoadening of the heterophase region in the phase diagram. This calculation was made by Miller et al. for f = 0.1. It turned out that for x = 100, the concentration vf shifts from 0.08 to 0.165 (volume fractions). Werbowyi and Gray extended these calculations to / = 0.2, 0.4, and 0.5. As is shown in Fig. 6, the values of vj in this case are equal to 0.4, 0.65, and 0.8 respectively. 

The common structure models for Iniim symmetry are shown in Figure 8.28. Among the well known lyotropic liquid-crystal mesophases, these are at least two mesostructures with Im3m symmetry one locates near the Ii region in the phase diagram, with a possible spherical micelle packed structure. Another one is close to the Vi region, and its most probable structure can be described by a P surface. 

The binodal separates the homogeneous (single phase) and hetero-geneous (two phase) regions in the phase diagram (see Figs 4.10 and 4.11). 

When a drying temperature is selected, the relative humidity should not be too low so as to initiate calcination, or too high so as to promote surface adsorption and capillary condensation. In addition the drying conditions of temperature and relative humidity must not affect the chemical equilibrium. However, since each calcium sulfate compound has its own stability region in the phase diagram, the drying conditions must be in a region where all the phases present in the sample remain stable. 

At higher surfactant concentrations the ratio of alcohol to surfactant molecules does not exceed 2 at the phase boundary, and it appears that the alcohols promote structural changes of the micelles, for example from spherical to rodlike or ellipsoidal structures. This structural change is dependent both on the surfactant concentration and on the amount of solute, which is apparent from the study carried out by Backlund and co-workers who mapped the whole LI-phase of the SDS-1-hexanol and C gBr-l-hexanol systems demonstrating regions in the phase diagram relating to spherical micelles, spherical swollen micelles, and rodlike micelles. 

The region in the phase diagram denoted crystals + water often contains other structures as well. For phospholipids, which are generally mixtures and are very poorly soluble in water, vesicles and liposomes , i.e., fragments of liquid crystalline phases (or possibly of a-gel), have been observed. 

The principal factor is the shape of the two-phase liquid-vapor region in the phase diagram (usually a temperature-composition diagram). The closer the liquid and vapor lines are to each other, the more theoretical plates needed. See Figure 6.15 of the text, But the presence of an azeotrope could prevent the desired degree of separation from being achieved. Incomplete miscibility of the components at specific concentrations could also affect the number of plates required... 

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