Symmetry chiral nematics

A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

Here, ry is the separation between the molecules resolved along the helix axis and is the angle between an appropriate molecular axis in the two chiral molecules. For this system the C axis closest to the symmetry axes of the constituent Gay-Berne molecules is used. In the chiral nematic phase G2(r ) is periodic with a periodicity equal to half the pitch of the helix. For this system, like that with a point chiral centre, the pitch of the helix is approximately twice the dimensions of the simulation box. This clearly shows the influence of the periodic boundary conditions on the structure of the phase formed [74]. As we would expect simulations using the atropisomer with the opposite helicity simply reverses the sense of the helix. 

When the mesogenic compounds are chiral (or when chiral molecules are added as dopants) chiral mesophases can be produced, characterized by helical ordering of the constituent molecules in the mesophase. The chiral nematic phase is also called cholesteric, taken from its first observation in a cholesteryl derivative more than one century ago. These chiral structures have reduced symmetry, which can lead to a variety of interesting physical properties such as thermocromism, ferroelectricity, and so on. 

In this liquid crystal phase, the molecules have non-symmetrical carbon atoms and thus lose mirror symmetry. Otherwise optically active molecules are doped into host nematogenic molecules to induce the chiral liquid crystals. The liquid crystals consisting of such molecules show a helical structure. The most important chiral liquid crystal is the cholesteric liquid crystals. As discussed in Section 1.2, the cholesteric liquid crystal was the first discovered liquid crystal and is an important member of the liquid crystal family. In some of the literature, it is denoted as the N phase, the chiral nematic liquid crystal. As a convention, the asterisk is used in the nomenclature of liquid crystals to mean the chiral phase. Cholesteric liquid crystals have beautiful and interesting optical properties, e.g., the selective reflection of circularly polarized light, significant optical rotation, circular dichroism, etc. 

When the nematic phase is composed of optically active materials (either a single component or a multicomponent mixture made up of chiral compounds or chiral compounds mixed with achiral materials), the phase itself becomes chiral and has reduced environmental space symmetry. The structure of the chiral nematic (or cholesteric) modification is one where the local molecular ordering is identical to that of the nematic phase, but in the direction normal to the director the molecules pack to form a helical macrostructure, see Fig. 5. As in the nematic phase the molecules have no long-range positional order, and no layering exists. The pitch of the helix can vary from about 0.1 x 10 m to almost infinity, and is dependent on optical purity and the degree of molecular... 

It should be noted that cholesteric liquid crystals (chiral nematics) having point group symmetry Dqo are also periodic with flie pitch considerably exceeding a molecular size. The preferable direction of the local molecular orientatiOTi, i.e. the director oriented along the Coo axis, rotates additionally through subsequent infinitesimal angles in the direction perpendicular to that axis. Hence a helical structure forms with a screw axis and continuous translation group. 

The nematic phase has point group symmetry Dooh- If we add some amount of chiral, e.g., right-handed molecules, the symmetry is reduced from Dooh to Dqo (symmetry of a twisted cylinder). Such a phase is called chiral nematic phase. Chiral molecules used as a dopant (solute) in nematic solvent considerably modify the nematic surrounding and the overall structure becomes twisted with a helical pitch Pc, incommensurate with a molecular size a, na (n is an integer) and usually Po a. Typically, a < 10 nm, Pq = 0.1-10 pm. 

If the molecules that form a hquid crystal phase are chiral (lack inversion symmetry), then chiral phases exist in place of certain non-chiral phases. In calamitic liqnid crystals, the nematic phase is replaced by the chiral nematic phase, in which the director rotates in helical fashion about an axis perpendicirlar to the director. Such a phase is illustrated in Figme 1.11. 

The chiral nematic phase has a structure that is similar to the conventional, achiral nematic phase except that the reduced symmetry of the phase causes the molecular director to be gradually rotated at a shght angle through a section of the phase structure to describe a helix (see Chapter 6). 

This chapter reviews the present understanding of blue phases. Blue phases are distinct thermodynamic phases that appear over a narrow temperature range at the helical-isotropic boundary of highly chiral liquid crystals. In the absence of electric fields, there can be three blue phases BPI and BPII, both of which have cubic symmetry and BPIII, which possesses the same symmetry as the isotropic phase. Figure 7.1 shows schematically the phases in both nonchiral and chiral nematics. For nonchiral nematics, including racemic mixtures (with equal numbers of left- and right-handed versions of the same molecule) and even weakly chiral nematics, the nematic (or weakly chiral) phase heats directly to the isotropic phase. When the chirality is high, however, as many as three blue phases may appear. 

That a liquid can have a cubic structure is truly remarkable. For a long time it was thought that a chiral nematic was just a nematic with twist, and that nothing fundamentally new was involved. As it turns out, this assumption was wrong. A nematic has orientational order, including mirror symmetry, but no positional order—it is invariant under a translation in any direction. When the nematic becomes chiral, the mirror symmetry is lost and the translational symmetry is reduced. Thus, in addition to becoming chiral, the chiral nematic also becomes spatially periodic. 

The chiral nematic phase is characterized by a helical structure, and so the electric permittivity is biaxial, with three independent components along the principal axes, which are the local director axis, the helix and a third orthogonal axis. Since the pitches of chiral nematics are usually many molecular diameters, chiral nematics are locally uniaxial, and the pitch does not affect the symmetry or the magnitude of the permittivity. 

Aspects of Molecular Symmetry for Chiral Nematic Phases.308... 

So far we have only assumed that the system is a liquid with rotational symmetry. If the molecules are nonpolar with respect to the preferentially ordered axis (n), as is empirically the case in nematic and chiral nematic phases, or if polar molecules are distributed with equal probability in each direction, then the choice of the sign of n is arbitrary. Hence we can employ the condition n=-n, i.e., transform, such that x =x, y = y, z --z, which gives... 

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