Chirality of crystals

Systematic studies of topochemical reactions of organic solids have led to the possibility of asymmetric synthesis via reactions in chiral crystals. (A chiral crystal is one whose symmetry elements do not interrelate enantiomers.) (Green et al, 1979 Addadi et al, 1980). This essentially involves two steps (i) synthesis of achiral molecules that crystallize in chiral structures with suitable packing and orientation of reactive groups and (ii) performing a topochemical reaction such that chirality of crystals is transferred to products. The first step is essentially a part of the more general problem of crystal engineering. An example of such a system where almost quantitative asymmetric induction is achieved is the family of unsymmetrically substituted dienes ... 

When pyrimidine-5-carbaldehyde 11 was treated with z-Pr2Zn in the presence of powdered [CD(+)260]-crystal, (S)-pyrimidyl alkanol with 73% ee was obtained in 88% yield (Scheme 16). On the other hand, in the presence of [CD(-)260]-crystal, the opposite enantiomer (R)-12 with 89% ee was isolated in 89% yield. When the crystals, grown from the stirred methanol solution of hippuric acid using each enantiomorph of hippuric acid as the seed crystal, were used in asymmetric autocatalysis, the same correlation between the chirality of crystal and the product 12 was observed with excellent reproducibility. It should be noted that nearly enantiopure (S)- and (K)-pyrimidyl alkanols 12 with > 99.5% ee were obtained by consecutive asymmetric autocatalysis [64], In this system, after the enantiomorphs of the crystal induced the chirality of an external organic compound, the subsequent asymmetric autocatalysis gave a greater amount of enantiomerically amplified product. 

As already mentioned, mixing can also have a significant effect on competing autocatalytic reactions as observed in the distribution of chirality of crystals in the experiments of Kondepudi et al. (1990). This was reproduced in a numerical model by Metcalfe and Ottino (1994) in a system of two competing autocatalytic reactions, of the... 

The discovery of the handedness, or chirality, of crystals and then of molecules led the symmetry concept nearer to the real chemical laboratory. It was still, however, not the chemist, in the classical sense of the profession, who was most concerned with symmetry, but the stereochemist, the structural chemist, the crystallographer, and the spectroscopist. Symmetry used to be considered to lose its significance as soon as molecules entered the most usual chemical change, the chemical reaction. Orbital theory and the discovery of... 

Observations on the chirality of crystals made it possible for Pasteur and others to identify dissymmetry as the true origin of optical activity. It became quickly evident that the molecular chirality associated with a given compound could be directly evident in the bulk crystallography of that compound. This in turn led to observable differences in a variety of physical properties, such as the melting point and the solubility of such species. Many chiral molecules have been observed to resolve spontaneously upon crystallization, forming enantiomorphic crystals that can be physically separated. Others can only be resolved through the formation and separation of diastereomeric species. 

One other aspect of inorganic morphology concerns the handedness of crystals. Indeed, Werner employed this in work on the chirality of crystals of K3[Rh(C204)3] ... 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

It is well known that spontaneous resolution of a racemate may occur upon crystallization if a chiral molecule crystallizes as a conglomerate. With regard to sulphoxides, this phenomenon was observed for the first time in the case of methyl p-tolyl sulphoxide269. The optical rotation of a partially resolved sulphoxide (via /J-cyclodextrin inclusion complexes) was found to increase from [a]589 = + 11.5° (e.e. 8.1%) to [a]589 = +100.8 (e.e. 71.5%) after four fractional crystallizations from light petroleum ether. Later on, few optically active ketosulphoxides of low optical purity were converted into the pure enantiomers by fractional crystallization from ethyl ether-hexane270. This resolution by crystallization was also successful for racemic benzyl p-tolyl sulphoxide and t-butyl phenyl sulphoxide271. 

The compounds crystallise in noncentrosymmetric space groups namely PI, P2i, C2, and P2i2i2i (but with priority of P2i) due to the chirality of the molecules. Most of the compounds have a tilted layer structure in the crystalline state. The tilt angle of the long molecular axes with respect to the layer normal in the crystal phase of the compounds is also presented in Table 18. Some compounds show larger tilt angles in the crystalline state than in the smectic phase. In the following only the crystal structures of some selected chiral liquid crystals will be discussed. 

Figure 2.48 Possible cooperative mechanism of crystal-crystal transition from (a) trans planar form III of sPP into (c) isochiral helical form II. Transition occurs through formation of (b) intermediate conformationally disordered modifications containing kink bands, characterized by helical sequences having same chirality (R = right-handed helix). Formation of helical sequences of opposite chirality (right- and left-handed) produces (if) steric interactions between neighboring chains.

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

A very different model of tubules with tilt variations was developed by Selinger et al.132,186 Instead of thermal fluctuations, these authors consider the possibility of systematic modulations in the molecular tilt direction. The concept of systematic modulations in tubules is motivated by modulated structures in chiral liquid crystals. Bulk chiral liquid crystals form cholesteric phases, with a helical twist in the molecular director, and thin films of chiral smectic-C liquid crystals form striped phases, with periodic arrays of defect lines.176 To determine whether tubules can form analogous structures, these authors generalize the free-energy of Eq. (5) to consider the expression... 

Reinitzer discovered liquid crystallinity in 1888 the so-called fourth state of matter.4 Liquid crystalline molecules combine the properties of mobility of liquids and orientational order of crystals. This phenomenon results from the anisotropy in the molecules from which the liquid crystals are built. Different factors may govern this anisotropy, for example, the presence of polar and apolar parts in the molecule, the fact that it contains flexible and rigid parts, or often a combination of both. Liquid crystals may be thermotropic, being a state of matter in between the solid and the liquid phase, or they may be lyotropic, that is, ordering induced by the solvent. In the latter case the solvent usually solvates a certain part of the molecule while the other part of the molecule helps induce aggregation, leading to mesoscopic assemblies. The first thermotropic mesophase discovered was a chiral nematic or cholesteric phase (N )4 named after the fact that it was observed in a cholesterol derivative. In hindsight, one can conclude that this was not the simplest mesophase possible. In fact, this mesophase is chiral, since the molecules are ordered in... 

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