Phase Diagrams of Enantiomer Systems

We call enantiomer systems mixtures containing the two mirror-image d and l components in any ratio, either without solvent (binary (d, l) mixtures), or in the presence of a solvent (ternary (d, l, E) mixtures). Depending on the nature of the crystal phases which may coexist with the liquid (melt or solution), three categories of enantiomer systems have been identified.

In the first category, which represents 5-10% of cases, the enantiomers crystallize separately from one another (homochiral crystallization, spontaneous resolution). A solid (d, l) system then consists of a mechanical mixture of d and l crystals in a ratio corresponding to their respective mole fractions (x; 1 — x). The melting point phase diagram shows a simple eutectic at x = 0.5 (racemate composition). Such a (d, l) system is said to be a conglomerate of enantiomers (Figure 1A). In a conglomerate, the racemate has a melting point about 30 K lower than those of its pure enantiomers. Its solid-state infrared spectrum is identical with the solid-state spectrum of a pure enan-tiomer, because the infrared spectrometer does not make a difference between right- and left-handed crystals. Since most binary mixtures of enantiomers

->

P

N R

<-

N

E R

<-

-1-

-1-1-1-1-1-1-1-

- mole fraction of d

- mole fraction of d

Figure 1 Binary melting point phase diagram for enantiomer systems. (A) Conglomerate; (b) racemic compound with Tr < Ta, eutectic at x = 0.3 and 0.7; (c) racemic compound with Tr > Ta, eutectic at x = 0.1 and 0.9. On recrystallization, a solid mixture M in which the mole fraction of the major enantiomer (here d) is 0.8 (enantiomeric excess ee = 60%) can give this enantiomer in pure form in cases (A) and (B), the maximum yield being given by the ratio NA/EA; in case (C) only the racemic compound can be obtained (see text).

behave ideally in the liquid state, the liquidus curves of a conglomerate phase diagram can generally be accurately calculated by means of the Schroder-van Laar equation, where TA and AHa are the temperature and enthalpy of fusion, respectively, of a pure enantiomer, and R is the gas constant. This equation gives the melting temperature T of a mixture in which x represents the mole fraction of the major enantiomer:

AHw 1

In the second, main category of enantiomer systems, representing 90-95% of cases, the d and l enan-tiomers crystallize together to form an ordered 1:1 compound, called a racemic compound (heterochiral crystallization). Typical binary phase diagrams corresponding to this case are shown Figure 1(B) and (C). The melting point TR of the racemic compound can be either lower or higher than that of the pure enan-tiomers (however, on average, the difference between TR and TA rarely exceeds +20 K). The solid-state infrared spectrum of a racemic compound is different from that of a pure enantiomer. This is a simple way of distinguishing between a racemic compound and a conglomerate (in addition to the melting point criterion). In such systems, a partially resolved solid consists of a mechanical mixture of two crystal phases, the racemic compound, in amount r = 2( 1 — x), and the enantiomer in excess, in amount ee = 2x—1. In Figure 1(B) and (C) the liquidus curves for the enantiomer branches are calculated by means of the Schroder-van Laar equation, while the racemic compound branch is calculated by a similar equation first given by Prigogine and Defay, where TR and Ahr are the temperature and enthalpy of fusion, respectively, of the racemic compound:

In the last category of enantiomer systems, called pseudoracemates, there is almost no chiral discrimination between the d and l species which co-crystallize more or less at random within the same lattice to form a solid solution. In a pseudoracemate, a partially resolved sample consists of a single crystal containing the d and l enantiomers in a ratio (x; 1 — x). Such systems are, fortunately, not common. They may occur with rod-shaped or quasi-spherical molecules (e.g. camphor). They do not lend themselves easily to separation by crystallization techniques, and for this reason they will no longer be considered here.

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