Chiral: axis nematic

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. 

Chira.lNema.tlc, If the molecules of a Hquid crystal are opticaHy active (chiral), then the nematic phase is not formed. Instead of the director being locaHy constant as is the case for nematics, the director rotates in heHcal fashion throughout the sample. This chiral nematic phase is shown in Figure 7, where it can be seen that within any plane perpendicular to the heHcal axis the order is nematic-like. In other words, as in a nematic there is only orientational order in chiral nematic Hquid crystals, and no positional order. Keep in mind, however, that there are no planes of any sort in a chiral nematic Hquid crystal, since the director rotates continuously about the heHcal axis. The pitch of the helix formed by the director, ie, the distance it takes for the... 

Fig. 7. The chiral nematic Hquid crystal stmcture. The director (arrow) traces out a heHcal path within the medium. Siace the rotation of the director is continuous, the figure does not mean to imply the existence of layers perpendicular to the heHcal axis.

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

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. 

Mesophase with a helicoidal superstructure of the director, formed by chiral, calamitic or discotic molecules or by doping a uniaxial nematic host with chiral guest molecules in which the local director n precesses around a single axis. 

Note 1 Locally, a chiral nematic mesophase is similar to a uniaxial nematic, except for the precession of the director n about the axis, Z. 

A cholesteric, or chiral nematic (N ) phase. This is a positionally disordered fluid in which the constituent molecules align on average their axes along a common direction called the nematic director. Being the DNA helices chiral, the orientational order develops an additional macro-helical superstructure with the twist axis perpendicular to the local director. The phase thus consists of local nematic layers continuously twisted with respect to each other, with periodicity p/2 (where p is the cholesteric pitch see Fig. 8a) [27,28]. For 150-bp helices, the N phase appears at a concentration around 150 mg/mL in 100 mM monovalent salt conditions. This LC phase is easily observed in polarized optical microscopy. Since the N pitch extends to tens of micrometers (that is, across... 

Recently, the importance of the structure of chiral metal complexes on the handedness of the mesophases induced in a nematic LC was exemplified [114]. The chiral metal complexes 10 and 11—in which the alkyl substituents are aligned almost perpendicularly to the C2 axis in the former and parallel in the latter—show very different induction phenomena. Not only are the induced helicities in the nematic LC of opposite sense for the two compounds, but the helical twisting power of 10 is much higher than that of 11. The reason for these differences is the way in which the molecules are incorporated into the host nematic phase and exert their force upon it to create the twist between the layers. 

Twisting a nematic structure around an axis perpendicular to the average orientation of the preferred molecular axes, one arrives at the molecular arrangement commonly called cholesteric (Kelker and Hatz, 1980). The twisted nematic phase is optically uniaxial, however with the axis perpendicular to the (rotating) director. Such a mesophase combines the basic properties of nematics with the implications of chirality The structure itself is chiral and as a consequence, a non-identical mirror image exists as it is shown schematically in Fig. 4.6-7. Besides the order parameters mentioned before, the essential characteristics of a cholesteric mesophase are the pitch, i.e., the period of the helical structure as measured along the twist axis, and its handedness, i.e., whether the phase is twisted clockwise or anticlockwise. 

Molecules that contain a chiral center can form chiral liquid crystalline phases, where the orientation direction rotates in a helical fashion as one moves along the helical axis, which is perpendicular to the locally preferred direction of orientation. Both nematic and smectic phases can be chiral. In a chiral nematic phase, also known as a cholesteric, as one moves along the helical axis, the director rotates sinusoidally (see Fig. 10-31. Thus, if z is... 

Liquid crystalline (LC) solutions of cellulose derivatives form chiral nematic (cholesteric) phases. Chiral nematic phases are formed when optically active molecules are incorporated into the nematic state. A fingerprint texture is generally observed under crossed polarizers for chiral nematic liquid crystals when the axis of the helicoidal structure is perpendicular to the incident light (Fig. 2). 

When the molecules that form a liquid-crystalline phase are chiral, the structure of these mesophases can have an additional property. In the chiral nematic phase (N ) the director precesses about an axis perpendicular to the director and describes in this way a helix (Figure 2.7). The pitch of a chiral nematic phase is the distance along the helix over which the director rotates over 360°. The chiral nematic phase is sometimes... 

As this compound was one of the higher homologues in the series, and because we knew that the earlier homologues did not exhibit a chiral nematic phase, it was clear that the new phase also could not be a chiral nematic phase. In addition, it was clear from the formation of the defect structures seen in the microscope that the phase first formed from the isotropic liquid possessed a helix, see Plate 1, which had its heli-axis at right angles to the heli-axis in the lower temperature chiral ferroelectric smectic phase. This simple observation meant that if the phase was a lamellar smectic phase then the helix would have to be formed, inconceivably, in a direction parallel to the layers. Synthesis of the achiral variant confirmed that the phase formed first on cooling from the isotropic liquid was indeed a smectic A phase, and thus we immediately knew that we had found a smectic A phase where the helical macro structure formed in the planes of the layers, and thus the helix must... 

Looking back, the earliest written report concerning the possibility of having a smectic phase with twisted layers comes from the work of Wolfgang Ullrich Muller at the Technischen Universitat Berlin in 1974 [40], In his thesis entitled Verhalten cholesterischer Mesophasen unter dem Einfluss von Phasenum-wandlungen , Muller examined the mesophase behavior at the chiral nematic to smectic transition for various mixtures of cholesteryl oleoyl carbonate (COG), 5, and cholesteryl chloride (CC), 6. Muller came to the conclusion from his work that the smectic phase must have a helical structure and that the heli-axis must lie in the plane of the layers, and the structure must also have... 

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