Chiral symmetry breaking

The second issue is how to explain the observation of both left- and right-handed helices in the phosphonate material. While Thomas et al. found both helical senses in the early stages of formation of DCggPC tubules, they found both helical senses even in the equilibrium state of the phosphonate. In the previous section, we attributed their results on tubule formation kinetics to a biased chiral symmetry-breaking in which the molecular packing has two possible states which are approximately mirror images of each other. The... 

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... 

Following the notation of Eq. (9), a general free energy for chiral symmetry -breaking in membranes can be written as... 

Here, the final three terms are a Ginzburg-Landau expansion in powers of i j. The coefficient t varies as a function of temperature and other control variables. When it decreases below a critical threshold, the system undergoes a chiral symmetry-breaking transition at which i becomes nonzero. The membrane then generates effective chiral coefficients kHp = k n>i f and kLS = which favor membrane curvature and tilt modulations, respec-... 

There are two reasons to think this situation might occur. The first reason is experimental. As discussed in Sections 2-5, in most experiments on chiral materials, tubules and helical ribbons are observed with only one sense of handedness. However, there are a few exceptions in experiments on diacetylenic phospholipids,144 diacetylenic phosphonate lipids,145 146 and bile.162 In these exceptional cases, some helices are observed with the opposite sense of handedness from the majority. In the work on diacetylenic phospholipids, the minority handedness was observed only during the kinetic process of tubule formation at high lipid concentration,144 which is a condition that should promote metastable states. Hence, these experiments may indeed show a case of biased chiral symmetry-breaking in which the molecular chirality favors a state of one handedness and disfavors a mirror image state. 

We close our theoretical discussion with the concept of biased chiral symmetry-breaking because it sums up this speculation about the interplay... 

Figure 8.20 Structure and phase sequence of prototypical bent-core mesogen NOBOW (8) are given, along with space-filling model showing one of many conformational minima obtained using MOPAC with AMI force field. With observation by Tokyo Tech group of polar EO switching for B2 smectic phases formed by mesogens of this type, banana LC field was bom. Achiral, polar C2v layer structure, with formation of macroscopic spontaneous helix in polarization field (and concomitant chiral symmetry breaking), was proposed to account for observed EO behavior.

The order parameters the diquark gap A, which can be seen as the gain in energy due to diquark condensation, and the mass gaps (pu,indicate chiral symmetry breaking. 

Chiral molecules have a nonsuperposable mirror image (see Fig. 11.1) and so possess intrinsic handedness in three-dimensional space. In a perfectly symmetric, chi-rally unbiased world, each handed version (enantiomer) must exist with an equal probability. The observed preference of one enantiomer over the other in biomolecules implies that this symmetry has been broken. The initial induction of a symmetry-breaking chiral excess is the sine qua non of eventual chiral dominance. Several mechanisms have been proposed to bring about chiral symmetry breaking. 

A process that has been studied widely in relation to phenomena such as chiral symmetry breaking, spontaneous resolution and chiral amplification is the reaction (Fig. 18) of [Co(H20)2 (OH)2Co(en)2 2](S04)2 (denoted 1) with NH4Br to give the chiral complex cA-[CoBr(NH3)(en)2]Br2 (denoted 2). This reaction is historically important, as 2 was one of the first octahedral metal complexes to be resolved into A and A stereoisomers, some years after Werner predicted that octahedral ions M(en)2XY should exist as enantiomeric pairs. 

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

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

Summary. We consider the Josephson effect in a ballistic Superconductor/ Quantum Wire/ Superconductor junction. It is shown that the interplay of chiral symmetry breaking generated by Rashba spin-orbit interaction and Zeeman splitting results in the appearance of a Josephson current even in the absence of any phase difference between the superconductors. 

The effect of chiral symmetry breaking on the physical picture described above is to additionally split the degenerate Andreev levels. A dispersion asymmetry Aa 0 lifts the left-right symmetry of electron transport through the junction and splits the doubly degenerated Andreev levels at

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Influence of Chiral Symmetry Breaking on a Critical Current... 

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