Crystallization symmetry breaking

Another example of symmetry breaking is provided by the crystal structure of form III of iP4MP. Electron diffraction patterns of the square single crystals of form III have indicated that chains in fourfold helical conformation... 

So far we have considered the formation of tubules in systems of fixed molecular chirality. It is also possible that tubules might form out of membranes that undergo a chiral symmetry-breaking transition, in which they spontaneously break reflection symmetry and select a handedness, even if they are composed of achiral molecules. This symmetry breaking has been seen in bent-core liquid crystals which spontaneously form a liquid conglomerate composed of macroscopic chiral domains of either handedness.194 This topic is extensively discussed in Walba s chapter elsewhere in this volume. Some indications of this effect have also been seen in experiments on self-assembled aggregates.195,196... 

Spontaneous Reflection Symmetry Breaking in Liquid Crystals... 

The author was supported by the Ferroelectric Liquid Crystal Materials Research Center (National Science Foundation MRSEC award No. DMR-9809555) during the writing of this chapter. The author thanks Professors Tom Lubensky, Leo Radzihovsky, and Joseph Gal for helpful discussions around the issue of terminology for reflection symmetry breaking, and especially Professor Noel Clark for his help on this and many other banana-phase issues. The author also thanks Dr. Renfan Shao for the photomicrographs shown in Figures 8.32 and 8.33. 

This volume of Topics in Stereochemistry could not be complete without hearing about ferroelectric liquid crystals, where chirality is the essential element behind the wide interest in this mesogenic state. In Chapter 8, Walba, a pioneering contributor to this area, provides a historical overview of the earlier key developments in this field and leads us to the discovery of the unique banana phases. This discussion is followed by a view of the most recent results, which involve, among others, the directed design of chiral ferroelectric banana phases, which display spontaneous polar symmetry breaking in a smectic liquid crystal. 

Rg. 11.2 Single crystals of morphologically enantiomeric quartz. Note the mirror symmetry of the facets on the respective crystals. Unlike amino acids, the component silicon dioxide molecules have no chirality. The spontaneous resolution of quartz into crystals of opposite morphological handedness is an example of local symmetry breaking in the environment. 

In 1969 Calvin [64] proposed a scheme for autocatalytic symmetry breaking, which he called stereospecific autocatalysis . Calvin s mechanism has been validated experimentally in the context of the total spontaneous resolution during the crystallization of racemic mixtures. During crystallization, crystals of one enantiomer may spontaneously separate, leaving the other enantiomer in solution. If the possibility of the equilibration of the enantiomers in solution exists and if the enantiomer in solution can convert rapidly to the enantiomer that is crystallizing before crystallization is complete, then the entire racemate may deposit as a single enantiomer. At least half a dozen examples of Calvin s stereospecific autocatalysis involving such... 

SRURC is such an interesting example of the facile formation of chiral induction from racemic mixtures in the absence of any external symmetry-breaking agent that it deserves special attention. One of the best studied examples is the crystallization of bromofluoro-l,4-benzodiazepinooxazole (Fig. 11.3), which possesses a single asymmetric carbon atom at C14 and a potentially asymmetric bridgehead nitrogen atom at N4. 

One other reason why many chemists and biologists are skeptical about parity violation and other subtle physical effects, is that the breaking of symmetry can be realized rather simply in the chemistry laboratory. According to Meir Lahav, one of the best known researchers in the field, breaking of symmetry is not the problem. He means by that, that the problem is rather the propagation and amplification of chirality. In sidebox 3.3 he summarizes some of the main concepts in particular, he considers crystals as agents of symmetry breaking (Weissbruch et al, 2003). 

Crystals as agents for symmetry breaking and survival of homochirality in prebiotic chemistry... 

Crystallization and reactivity in two-dimensional (2D) and 3D crystals provide a simple route for mirror-symmetry breaking. Of particular importance are the processes of the self assembly of non-chiral molecules or a racemate that undergo fast racemization prior to crystallization, into a single crystal or small number of enantiomorphous crystals of the same handedness. Such spontaneous asymmetric transformation processes are particularly efficient in systems where the nucleation of the crystals is a slow event in comparison to the sequential step of crystal growth (Havinga, 1954 Penzien and Schmidt, 1969 Kirstein et al, 2000 Ribo et al 2001 Lauceri et al, 2002 De Feyter et al, 2001). The chiral crystals of quartz, which are composed from non-chiral Si02 molecules is an exemplary system that displays such phenomenon. 

Kondepudi, D. K., Kaufman, R., and Singh, N. (1990). Chiral symmetry breaking in sodium chlorate crystallization. Science, 250, 975. 

In this section some examples for spontaneous magnetovolume effects in cubic Gd based compounds will be presented. As will be discussed in section 5, in cubic systems also distortions of the crystal symmetry have been observed. In all cases of our knowledge these distortions are, however, very small compared to strains which conserve the crystal symmetry and which will be the main topic of the rest of this chapter. The symmetry breaking effects are so small that they probably can only be observed in the highly symmetric cubic systems, where the detection of such distortions is easier. 

What is not shown in the tables, are spontaneous distortions of the crystal symmetry, which are usually very small (i.e. < 10-4) and have only been observed in cubic systems, where the detection of symmetry distortions is easier. To our knowledge the largest symmetry breaking effect has been observed for cubic GdZn by Rouchy et al. (1981), namely a tetragonal distortion of (A///)ooi -3.7 x 10-4 (see section 5). 

Vaupotic N, Copic M (2005) Polarization modulation instability in liquid crystals with spontaneous chiral symmetry breaking. Phys Rev E 72 031701-1-031701-4... 

Walba DM, Korblova E, Huang C-C, Shao R, Nakata M, Clark NA (2006) Reflection symmetry breaking in achiral rod-shaped smectic liquid crystals J Am Chem Soc 128 5318-5319... 

Prasang C, Whitwood AC, Bruce DW (2008) Spontaneous symmetry-breaking in halogen-bonded, bent-core liquid crystals observation of a chemically driven Iso-N-N phase sequence. Chem Commun 2008 2137-2139... 

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