Three-component mixtures types

Figure 1.5 shows mainly physically valuable types of three-component azeotropic mixtures deduced by Gurikov (1958) by means of systematic apphcation of Eq. (1.12). In Fig. 1.5, one and the same structure cover a certain type of mixture and an antipodal type in which stable nodes are replaced by unstable ones and vice versa (i.e., the direction of residue curves is opposite). Besides that, the separatrixes are shown by the straight lines. Let s note that the later classifications of three-component mixture types (Matsuyama Nishimura, 1977 Doherty Caldarola, 1985) contain considerably greater number of types, but many of these types are not different in principle because these classifications assume light, medium, and heavy volatile components to be the fixed vertexes of the concentration triangle. 

Most LB-forming amphiphiles have hydrophobic tails, leaving a very hydrophobic surface. In order to introduce polarity to the final surface, one needs to incorporate bipolar components that would not normally form LB films on their own. Berg and co-workers have partly surmounted this problem with two- and three-component mixtures of fatty acids, amines, and bipolar alcohols [175, 176]. Interestingly, the type of deposition depends on the contact angle of the substrate, and, thus, when relatively polar monolayers are formed, they are deposited as Z-type multilayers. Phase-separated LB films of hydrocarbon-fluorocarbon mixtures provide selective adsorption sites for macromolecules, due to the formation of a step site at the domain boundary [177]. 

This type of chromatographic development will only be briefly described as it is rarely used and probably is of academic interest only. This method of development can only be effectively employed in a column distribution system. The sample is fed continuously onto the column, usually as a dilute solution in the mobile phase. This is in contrast to displacement development and elution development, where discrete samples are placed on the system and the separation is subsequently processed. Frontal analysis only separates part of the first compound in a relatively pure state, each subsequent component being mixed with those previously eluted. Consider a three component mixture, containing solutes (A), (B) and (C) as a dilute solution in the mobile phase that is fed continuously onto a column. The first component to elute, (A), will be that solute held least strongly in the stationary phase. Then the... 

A number of fused thiopyranopyrazolopyrimidines with potential as potassium channel openers have been prepared by a three-component Hantzsch-type reaction between a ketone, an aldehyde, and an aminopyrazole. These reactions give a mixture of isomers, with and without ring junction heteroatoms (Equation 49) <2002BML1481> among the compounds of particular interest are those in which the ketone is a derivative of thiopyran or its A,A-dioxide. 

The pH can also determine the type or composition of the coacervates formed from a three-component mixture, such as gum arabic, gelatin, and yeast nucleic acid, for example. In such a coacervate, at pH 3.36, the drops consist mainly of gum arabic and gelatin at pH 3.48, of gelatin, gum arabic, and nucleic acid at pH 3.8, of gelatin and nucleic acid. 

A convenient notation for classifying mixtures employed in liquid-liquid extraction is C/, where C is the number of components and the number of partially miscible pairs. Mixtures 3/1, 3/2, and 3/3 are called Type I, Type II, and Type III by some authors. A typical 3/1 three-component mixture with only one partially miscible pair is furfural-ethylene glycol-water, as shown in Fig. 3.10, where the partially miscible pair is furfural-water. In practice, furfural is used as a solvent to remove the solute, ethylene g yco, from water the furfural-rich phase is called the extract, and the water-rich phase the raffinate. Nomenclature for extraction, leaching, absorption, and adsorption always poses a problem because, unlike distillation, concentrations are expressed in many different ways mole, volume, or mass fractions mass or mole ratios and special solvent-free designations. In this chapter, we will use V to represent the extract phase and L the raffinate phase, and y and x to represent solute concentration in these phases, respectively. The use of V and L does not imply that the extract phase in extraction is conceptually analogous to the vapor phase in distillation indeed the reverse is more correct for many purposes. 

Three-component mixtures represent the simplest type of multicomponent mixtures. The majority of multicomponent mixture peculiarities become apparent in three-component mixtures. This is why the three-component mixtures are best studied. Liquid-vapor equilibrium in the concentration triangle C3 is represented by a vector connecting a point of hquid composition with a point of equilibrium vapor composition x y. This vector is called a liquid-vapor tie-line. The opposite vector y X (vapor-liquid) is called a vapor-liquid tie-line. The tie-hnes field in the concentration triangle characterizes phase equihbrium in each of its points. 

Figure 1.4. Types of stationary points of three-component mixtures (a) one-component stable node, (b) one-component unstable node, (c) one-component saddle, (d) two-component stable node, (e) two-component unstable node, (f) two-component saddle, (g) three-component stable node, (h) three-component unstable node, and (i) three-component saddle. Arrows, direction of residium curves.

The first topological equation that connects a possible number of stationary points of various types for three-component mixtures (N, node S, saddle upper index is the number of components in a stationary point) was deduced (Gurikov, 1958) ... 

The structure of residue curve bundles of four-component mixtures is significantly more complex and diverse than that of three-component mixtures. This is due to the fact that each four-component mixture consists of four three-component constituents. Therefore, the number of types of four-component mixtures is enormous. In addition to that, four-component mixtures can have four-component node and saddle azeotropes. In contrast to three-component mixtures, the enormous... 

Figme 1.13. Some types of liquid-liquid phase diagrams for three-component mixtures. Region of three liquid phases Reg is shaded. Thin line, tie-line liquid-liquid cr, critical points. 

Division of main types of three-component mixtures phase diagrams according to classification of Gurikov (1958) into product triangles is given in Fig. 3.16. Each type pertains to two different antipodal phase diagrams, which differ from each other by direction of all the bonds and replacement of stable nodes by unstable ones and vice versa. This flgure can serve as the basis for determination of feasible sharp and semisharp sphts of various azeotropic mixtures at any feed composition. 

Diagrams of reversible distillation of various types of three-component mixtures can be obtained in various ways with the help of the model of phase equilibrium describing these types of mixtures. It is possible to calculate the trajectory consequently for each chosen product point using Eq. (4.6) (4.13) and increasing step... 

It is obvious that for the separation of three-component mixtures by means of extractive distillation, the mixtures of the type 4a (according to the classification given by Gurikov) that are widespread in practice are of the biggest interest. For these mixtures, according to Fig. 4.21, one can get pure component 1 as top product and zeotropic mixture 2,3 as bottom product. One can get the same result for the mixtures of type 4b. 

We examine the most typical splits and separation sequences for various types of three-component mixtures (Fig. 6.16 shows examples of heteroazeotropic distillation Fig. 6.17 shows examples of heteroextractive distillation). 

The last step towards the three-component Ugi-type coupling envisaged in the ret-rosynthesis is described below. The, commercial amine 27 was oxidized to imine 26 (94% ee) by MAO-N, as previously described [20], which was then combined with 25 and 28 give the advanced intermediate 40. Finally, cleavage of the acetate followed by Dess-Martin oxidation gave Telaprevir (24) as a 83 13 4 mixture of diastere-omers, with one minor diastereomer derived from the incomplete stereoinduction of the Ugi-type 3CR and the other from the minor enantiomer of imine 26. Flash chromatography allowed straightforward separation of the diastereomers to afford pure Telaprevir (24) in 80% yield over the last two steps (Scheme 15.11). 

In both pure benzene and pure DMBD, just one radical is observed via TF- SR, with narrow lines (2,q <0.5 ps i). However, in binary mixtures of the compounds or in three-component mixtures with cyclohexane, the cyclohexadienyl lines broaden with increasing DMBD concentration while the line width of the allyl-type radical remains narrow. This obviously indicates a reaction of the cyclohexadienyl radical with DMBD. From the variation of line... 

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 order to optimize the formulation, a different experimental design was used. Based on the results of the first design, the particular molecular weight of SiUMA was chosen which seemed to have the best chance of giving the desired balance of properties. Further, it had been established that Variable II (and not Variable III) was preferable for further work. With these variable types (i.e., not involving a component amount) eliminated, the problem was reduced to a "constrained mixture deslgn"(12,13) involving three components SiUMA-18, Variable I, and Variable II. 

So far, only those domino Knoevenagel/hetero-Diels-Alder reactions have been discussed where the cycloaddition takes place at an intramolecular mode however, the reaction can also be performed as a three-component transformation by applying an intermolecular Diels-Alder reaction. In this process again as the first step a Knoevenagel reaction of an aldehyde or a ketone with a 1,3-dicarbonyl compound occurs. However, the second step is now an intermolecular hetero-Diels-Alder reaction of the formed 1 -oxa-1,3 -butadiene with a dienophile in the reaction mixture. The scope of this type of reaction, and especially the possibility of obtaining highly diversified molecules, is even higher than in the case of the two-component transformation. The stereoselectivity of the cycloaddition step is found to be less pronounced, however. 

Therefore we tried to obtain EG-AC-TiC>2 composites using the procedure similar to that elaborated for production of EG-AC composites. The only difference here from the scheme described above is the preparation of initial mixture for now containing three components residual graphite hydrosulfate, sucrose and anatase-type Ti02 (Aldrich). 

If the bed material is a mixture of different particle types, abrasion of one component can be reduced by the decrease of its surface in relation to the entire material surface in the bed (cf. Sec. 2). A potential field of application is the coal combustion process with the three components coal, ash and limestone. 

All process oils used by the rubber industry are in practice mixtures of all classes of the three components, the mixtures deriving their classification from the preponderance of the main constituent type. 

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