Miscibility in the solid state

In the systems described so far, only pure solids have been involved. Many solids are capable of dissolving other materials to form solid solutions. Copper and nickel, for example, are soluble in each other in all proportions in the solid state. The phase diagram for the copper-nickel system is shown in Fig. 15.16. 

The upper curve in Fig. 15.16 is the liquidus curve the lower curve, the solidus curve. If a system represented by point a is cooled to b, a solid solution of composition c appears. At point d the system consists of liquid of composition b in equilibrium with solid solution of composition c. The interpretation of the diagram is similar to the interpretation of the liquid-vapor diagrams in Section 14.6. An experimental difficulty arises in working with this type of system. Suppose the system were chilled quickly from a to e. If the system managed to stay in equilibrium, then the last vestige of liquid b would be in contact with a 

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M. Amadori studied fused mixtures of sodium fluoride and carbonate no compound is formed, and the salts are not miscible in the solid state. There is a eutectic at 690° and 39 mols. per cent, sodium fluoride. Similar results obtain with sodium chloride and carbonate. There is an eutectic at 636° and 59 mols. per cent, of sodium chloride. Similarly, with potassium fluoride and carbonate, there is with a eutectic at 636° and 65 mols. per cent, of potassium chloride. With the system potassium fluoride and carbonate there is a eutectic at 688° with nearly 46 mols. per cent, of potassium fluoride, and another eutectic at 682° with 62 mols. per cent, of potassium fluoride there is a slight rise in the m.p. between the two eutectics, corresponding with the formation of potassium fluorocarbonate, KF.K2C03. 

The general case of two compounds forming a continuous series of solid solutions may now be considered. The components are completely miscible in the solid state and also in the liquid state. Three different types of curves are known. The most important is that in which the freezing points (or melting points) of all mixtures lie between the freezing points (or melting points) of the pure components. The equilibrium diagram is shown in Fig. 1,16, 1. The liquidus curve portrays the composition of the liquid phase in equilibrium with solid, the composition of... 

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

Solid solutions can be classified by two methods. According to the extent of miscibility of the two components, they may be classified as continuous or discontinuous. In continuous solid solutions, the two components are miscible in the solid state in all proportions. Typical phase diagrams of continuous and discontinuous solid solutions are shown in Figs. 2 and 3, respectively. Discontinuous solid solutions exist at extremes of composition. In general, some solid-state solubility can be expected for all two-component systems. 

Solid solutions The drug and the carrier are miscible in the solid state. Polyvinylpyrrolidones (PVP) with different molecular weights dissolve drug substances such as diazepam through hydrophobic interactions. The disparition of the DSC peak of the drug substance demonstrates the formation of the solid solution. 

The situation is again changed if the two substances A and B are miscible in the solid state. For equilibrium at constant pressure we now have... 

The relations between solid and liquid to which these principles lead are shown in Figs. 4 and 5. In Fig. 4 a is the melting-point of pure A, b that of pure B. If there is no miscibility in the solid state, the composition of solid must correspond either to A or to B, except at the eutectic, where it can correspond to any proportion of the two sohd phases. Thus composition of sohd foUows the line axyb. That of hquid foUows acb. 

The conditions governing miscibility in the solid state are fairly well understood. The atoms and molecules which enter into the mixed lattice must not differ by more than a limited margin in size. Furthermore, the detailed study of alloys has revealed that the possible solid phases are determined by certain definite electron ratios, and that in fact the structure is mainly governed by the concentration of valency electrons. 

Fig. 10 Thermodynamic and kinetic basis for solute depletion in the case of a binary alloy consisting of solvent A and solute B. (a) Binary equilibrium phase diagram with complete miscibility in the liquid state, partial miscibility in the solid state given by existence of a terminal solid solution. Cs is the composition along the solvus line. is the overall composition of the alloy, (b) Time-temperature-transformation diagram for precipitation of in an a matrix for the alloy shown in (a) with overall composition,...

Knoester etal (1972) examined the 15 binary systems which can be formed by these glycerides. Most of these diagrams are of the eutectic type with ideal miscibility in the melt and no or very low miscibility in the crystalline state. In systems with an asymmetric triglyceride, however, there is a considerable degree of miscibility in the solid state, and values of the mutual solubilities are given in Table 8.27. It was also found in this work that differences in polymorphic form have no effect on the mutual solubility. 

Type III MiscibiUty in the liquid state, partial miscibility in the solid state, melting point diagram shows eutectic point and mixed crystal region. 

Such is not the case in blends of two liquid crystal polymers or LCP s that were first extensively studied by DeMeuse and Jaffe. In their initial study (DeMeuse and Jaffe 1988), they examined blends of LCP s that contain copolymers of p-hydroxybenzoic acid (HBA) and 6-hydroxy-2-naphthoic acid (HNA) of different copolymer ratios. It was surmised that miscibility in the melt state depended on the difference in copolymer ratios between the two component polymers. However, miscibility in the solid state seemed to be present for all blends that were studied. This is an interesting contrast to the systems previously mentioned because there is no obvious enthalpic interaction that is occurring between the two blend components. 

Components A and B in Figure 17.12, on the other hand, behave differently. Liquid A and liquid B still mix to form a homogeneous solution, but when solid A and solid B are mixed together, they dissolve into one another to a limited extent. Salt will dissolve into water, but not without limit - it will dissolve only until the water becomes saturated. Similarly, solid B will dissolve into solid A, but not without limit. It dissolves into A until A is saturated with B, and at the same time A dissolves into B until B is saturated with A. The saturation limits of each component in the other is shown by a line called the solvus. The existence of a solvus shows that A and B exhibit limited miscibility in the solid state. They exhibit complete miscibility in the liquid state. Miscibility does not really mean mixability, although they sound similar. MixabiUty, if it is a word, just means things can be mixed together - mutual dissolution is not implied. Miscibility means the ability to dissolve into something else. 

A simple eutectic mixture consists of two compounds that are completely miscible in the liquid state (melt) but only show limited miscibility in the solid state. At a specific composition (E in Fig. 2.1), the two components crystallize simultaneously when the temperature is reduced (Fig. 2.1). If mixtures with different compositions to the eutectic composition of A and B are cooled, one component will start to crystallize before the other, which initially leads to a mixture of pure solid compound and liquid. Therefore, a true eutectic only exists for a defined composition of A and B. The microstructure of a eutectic mixture is different from the microstructure of either components, and this property may be used to differentiate the eutectic mixture from other forms of crystalline mixtures. A theoretical method to determine the eutectic composition of a binary mixture and the temperature at which it crystallizes has been suggested by Karunakaran (1981). 

Successive purification steps using the solid phases separated after each step lead to a stepwise purification, a process called fractional crystallization. It differs from simple repeated recrystallization in fractional crystallization procedures, both the crystals obtained and the mother liquor are repeatedly fractionated. Usually two or more compounds shall be separated with the objective of isolating each as pure substance. In case that the target compound and the impurity form solid solutions, elaborate fractionation schemes may be necessary to finally provide pure substances. The procedure is best illustrated by means of the binary phase diagram. Figure 7.3 shows the phase diagram of a model system exhibiting full miscibility in the solid state. 

A phase diagram showing complete miscibility in the solid state is known, for example, for the binary systems of phenanthrene and anthracene or naphthalene and /3-naphthol. 

Figure 7.3 Phase diagram of a target compound (P) and an impurity (Imp), a system characterized by full miscibility in the solid state. Thus, P and Imp form a so-called continuous series of mixed crystals covering the entire concentration range in the phase...

When lattice integration due to a partial or complete miscibility in the solid state is the dominant mechanism of impurity incorporation, the impurity content in the crystalline product increases with the yield. This can be easily verified on the basis of the phase diagram (Figure 7.5a). Assuming equilibrium conditions (i.e., slow crystallization), the concentration of the impurity incorporated in the target compound steadily increases with progressing crystallization (arrow at the solidus line) and reaches a maximum value close to the eutectic temperature. Simultaneously, the... 

If PAANa and POE were miscible, single ion conduction would be possible because anions would be fixed to the polymer matrix. Since PAANa and POE, however, were not miscible in the solid state, acrylic acid moieties were introduced to PAANa for the purpose of the partial complexation through hydrogen bonding. In the experiment, the glass transition temperature and ionic conductivity were studied for PAANa-PAA-POE composite films having different neutralization of PAA and different incorporation of POE. 

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