Ternary Phase Diagrams

For applications in which accurate quantitative data are required (e.g. optimization of large-scale recrys-tallizations), it is preferable to utilize ternary (solubility) phase diagrams (d, l, E). Solubility phase diagrams are 3D triangular prisms where each face is a binary melting point phase diagram, (d, l), (d, E) and (l, E). It is customary to convert this 3D representation into a 2D one by keeping one of the variables fixed, most often the temperature. Accordingly, a horizontal slice of the prism generates the usual triangular isotherm describing the solid-liquid phase equilibria at given T. This is illustrated in Figure 2(A), for a conglomerate. In order to facilitate the use of such triangular isotherms, it is convenient to adopt a system of cartesian axes (C, E), where C represents the concentration and E the excess of enan-tiomer, expressed in the same dimensionless unit (generally in weight %); C and E are defined as follows:

x 100

x 100

Typical ternary isotherms for a conglomerate and a racemic compound are shown in Figure 2(B) and (C), respectively. In a conglomerate the solubility of the racemate is normally twice the solubility of each

Figure 2 (A) 3D-representation of a {d, l X} system and the corresponding 2D-isotherm, for a conglomerate. The composition of a ternary system X is conveniently defined by its cartesian coordinates (C, E). Note that E/C = ee, the usual enantiomeric excess, defined as ee = (d — l)/(d + l); (B) and (C) represent ternary isotherms that correspond roughly to the binary phase diagrams (A) and (B) of Figure 1. On recrystallization, mixture Mwill only afford the major enatiomer in pure form if the composition of the ternary system is comprised between Nand P, the maximum yield being obtained for system N (see text). In diagram (C), e represents the eeof the ternary eutectic E.

Figure 2 (A) 3D-representation of a {d, l X} system and the corresponding 2D-isotherm, for a conglomerate. The composition of a ternary system X is conveniently defined by its cartesian coordinates (C, E). Note that E/C = ee, the usual enantiomeric excess, defined as ee = (d — l)/(d + l); (B) and (C) represent ternary isotherms that correspond roughly to the binary phase diagrams (A) and (B) of Figure 1. On recrystallization, mixture Mwill only afford the major enatiomer in pure form if the composition of the ternary system is comprised between Nand P, the maximum yield being obtained for system N (see text). In diagram (C), e represents the eeof the ternary eutectic E.

individual enantiomer, unless special circumstances, such as common ion effects or aggregation phenomena, decrease or increase the solubility ratio with respect to its normal value. Figure 2(B) and (C) roughly correspond to the binary phase diagrams of Figure 1(A) and (B), respectively. On recrystallization of mixture M, the major enantiomer d can be obtained between N and P, for instance from system O. However, the best yield Y in pure d will be obtained from system N, at concentration CN (in weight %):

Y NE 100

For a conglomerate the above calculated yield is the same as that derived from the binary phase diagram, Y = NE/AE. For a racemic compound, Y calculated from the ternary isotherm is usually very close to that derived from the binary phase diagram because in such systems the ee of the eutectic does not change significantly with temperature, except in the case of polymorphism or of solvation.

This is why information on the type of enantiomer system and, in particular, on the location of the eutec-tics in racemic compound phase diagrams is of great importance when the purification of partially resolved mixtures by crystallization techniques is undertaken. When the phase diagram of the considered system is not favourable (e.g. as in Figure 1C), recrys-tallization should be avoided and it may be advisable to postpone the purification to a next step, or to seek derivatives having more favourable phase diagrams. These concepts are particularly useful for the final purification of enantiomers prepared by asymmetric synthesis or chiral chromatography.

Solar Panel Basics

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