Right-handed cholesteric liquid crystal

In Fig. 7 the optical rotatory dispersion (ORD) as well as the circular dichroism (CD) is shown for the right-handed cholesteric liquid crystal. A right-handed helical structure reflects right circularly polarized light and it shows positive optical rotation on the short wavelength side of the reflection band. 

Fig. 7. Optical properties of right-handed cholesteric liquid crystals...

We showed in last section that in a uniform anisotropic medium, for each propagation direction, there are two eigenmodes which are linearly polarized. The polarization state of the eigenmodes is invariant in space. In this section, we discuss the propagation of light in a special case of a non-uniform anisotropic medium a cholesteric liquid crystal which locally is optically uniaxial, but the optic axis twists uniformly in space [6,7]. Choose the z axis of the lab frame to be parallel to the helical axis of the cholesteric liquid crystal. The pitch P of the liquid crystal is the distance over which the liquid crystal director twists In. The components of the liquid crystal director of a right-handed cholesteric liquid crystal q > 0) are given by... 

In general, cholesteric liquid crystals are found in optically active (chiral) mesogenic materials. Nematic liquid crystals containing optically active compounds show cholesteric liquid crystalline behavior. Mixtures of right-handed and left-handed cholesteric liquid crystals at an adequate proportion give nematic liquid crystals. From these results cholesteric liquid crystals are sometimes classified into nematic liquid crystals as twisted nematics . On the other hand, cholesteric liquid crystals form batonnet and terrace-like droplets on cooling from isotropic liquids. These behaviors are characteristic of smectic liquid crystals. Furthermore, cholesteric liquid crystals correspond to optically negative mono-axial crystals, different from nematic... 

In Fig. 23 the relationship between B/kg and XA/D are shown for the polypeptide liquid crystals in various solvents. Following Eq. (25), the compensation temperature is determined by the ratio (fi/kg)/(lA/D) at a constant polymer concentration. The solid and broken lines shown in Fig. 23 correspond to the theoretical values calculated for Tjj = 25 °C and 80 °C, respectively. The solvents located above and below the solid line support the right-handed and left-handed cholesteric liquid crystals, at 25 °C, respectively. The situation is the same for the broken line at 80 °C. The solvents located between the two straight lines invert the cholesteric sense from right-handed to left-handed in the range of measurements. 

The recent studies on the structure and properties of polypeptide liquid crystals, which are formed in solution as well as in the solid state, are reviewed in this article. Especially the cholesteric pitch and the cholesteric sense (right-handed or left-handed), which are characteristic factors of cholesteric liquid crystals, are discussed in detail in relation to the effects of temperature, concentration, and solvent. Further cholesteric liquid crystalline structure retained in cast fdms and thermotropic mesomorphic state in some copolypeptides are also discussed. 

Cholesteric liquid crystals are similar to nematic phases except that the molecular orientation between one layer and the next shows a progressive helical order. This helical structure arises from the chiral properties of the constituent molecules. Chiral molecules differ from their mirror image and have a left- or right-hand sense and are called enantiomorphic. The director is not fixed in space and rotates throughout the sample as shown in Figure 3.3. 

Cholesteric liquid crystals (CLCs) can also be used to make reflective polarizers. CLCs reflect circularly polarized hght with the same handedness as the helical stmcture of the liquid crystal. An unpolarized incident hght can be decomposed into a left-handed circular polarized hght and a right-handed circular polarized hght. One component is reflected and the other component is transmitted. The reflected hght is reflected toward the CLC polarizer by a back mirror and its handedness is converted to the opposite handedness and thus it passes the CLC polarizer. The transmitted circular polarized hght is converted into hnear polarization by a quarter waveplate. 

In the beetle Chrysina gloriosa, left-handed green colour reflection is observed from the exoskeleton, but without colour variation, and patterns are structurally and optically analogous to the focal conic domains formed spontaneously on the free surface of a cholesteric liquid crystal. More sophisticated helicoidal structures can be found in Plusiotis resplendens. The latter species is capable of reflecting both left and right circularly polarised light. In contrast to Pallia condensate, the right-handed circular... 

K. Kato, K. Tanaka, S. Tsuru, and S. Sakai, Characteristics of right- and left-handed polymer-dispersed cholesteric liquid crystal, Jpn. J. Appl. Phys. 33, 4946-4949 (1994). 

Five separate additive terms can be identified in the right-hand side of Eq. (2) these will be referred to as terms I to V in the discussion below. Terms I and III represent the energy due to the splay and bend deformations discussed earlier. As the magnitude of the director deformation increases, both of these terms grow monotonically, but term I rises more quickly immediately above the threshold. Term II represents the twist elastic energy. Both (j) and P are included in this term to allow for deviation of the rate of twist away from that due to the natural helical structure of a cholesteric liquid crystal. The final term V is the dielectric energy. 

Positive values of P correspond to right-handed cholesterics, while negative values correspond to left-handed cholesterics the magnitude varies between 1 and about 100 depending on solute structure and the nematic liquid crystal employed for the analysis [341]. The values of P are highest when the stuctures of the solvent and solute are similar, and the central cores of the nematic solvent molecules are conformationally mobile (see [341]) and references cited therein). 

The cholesteric liquid crystal state consists of either all left-handed helices or all right-handed helices. The physical difference between these two states is manifested in their optical activities. See, for example, H. de Vries, Rotatory Power and Other Optical Properties of Certain Liquid Crystals, Acta. Cryst, 4, p. 219(1951). 

A similar thermally-induced inversion of the cholesteric sense was observed for the PBLG liquid crystal in benzyl alcohol. In this solution, a gel-like opaque phase coexists with the cholesteric phase at lower temperatures. The opaque phase disappears around 70 °C, where endothermic peaks are observed in the differential scanning calorimetry curve. The value of S below 70 °C remains constant, and then changes with temperature above 70 °C. The compensation occurs at about 103 °C, and the transition from biphasic phase to the isotropic phase is observed above 150 °C in this case. The results are summarized in Fig. 12, where the reciprocal of the half-pitch is plotted against temperature. The sign of 1/S is taken as positive when the cholesteric sense is the right-handed. 

Let the cholesteric film be bounded between the planes z = 0 and z = h, and let there be a temperature gradient along the screw axis z. The components of the director in a right-handed cartesian coordinate system are cos0(z, ), sin0(z, ),0. We assume that there are no heat sources within the liquid crystal, no external body forces and that the velocity vector is zero. Hence T = T(z),ff = G, = rfy = Wy = 0. Thus from (4.3.4)... 

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