Cholesteric liquid crystal pitch dependence

In main chain cholesteric liquid crystalline polymers, the mesogenic groups and flexible spacers are linked alternatively. The flexible units contain asymmetrical carbon atoms which enable the polymers to possess chirality and thus form cholesteric liquid crystals. By varying the ratio of chiral to non-chiral parts, the cholesteric temperature range and pitch can be changed. The cholesteric range depends on the mol fraction of the polymers. A typical main chain cholesteric liquid crystalline polymer is shown in Figure 6.27. 

Kent Display is a pioneer of cholesteric liquid crystal displays (ChLCDs) in which the director of the liquid crystal twists around a helical axis [3]. The remarkable property is that the cholesteric material reflects light of certain wavelengths depending on the pitch over which the director rotates. When an electric held is applied. 

Cholesteric liquid crystal (ChLC)-driven electronic paper has been investigated mainly by Kent Display [2], Since ChLCs are chiral molecules, the particular color of light depends on the pitch denoted as P, where the pitch is the distance along the helical axis for ChLC to twist 360 and is determined by the amotmt and type of chiral additive within the liquid crystal mixture. ChLCDs are driven by switching the different textures of the ChLC electrically [1, 3], as shown in Fig. 4. 

Depending on its chemical stmcture, the pitch of a cholesteric liquid crystal could take any value in the region from a few tenths of a micron to infinitely long. The periodicity of a cholesteric liquid crystal with the pitch Pg is PJ2, because n and - n are equivalent. Cholesteric liquid crystals are also called chiral nematic liquid crystals and denoted as N. Nematic liquid crystals can be considered as a special case of cholesteric liquid crystals with an infinitely long pitch. 

Cell thickness-dependence of the reflection of a cholesteric liquid crystal in the planar state. The pitch of the liquid crystal is P = 350 nm. The refractive indices of the liquid crystal are tig = 1 -7 and = 1.5. The liquid crystal is sandwiched between two glass plates with the refractive index = 1.6. The incident light is circularly polarized with the same helical handedness as the liquid crystal. Neglect the reflection from the glass-air interface. Use two methods to calculate the reflection spectrum of the liquid crystal with the following cell thicknesses P, 2P, 5P and lOP. The first method is the Berreman 4x4 method and the second method is using Equation (2.186). Compare the results from the two methods. 

The action of the field on a planar texture of a cholesteric liquid crystal for cell thickness, comparable to the pitch and with rigid anchoring of the liquid crystal molecules to the surface, does not cause the two-dimensional deformations discussed. In this case, one-dimensional periodic patterns are observed [19, 24], with the orientation of the domains depending on the number of half-turns of the helix contained within the cell thickness. The phenomenon of one-dimensional, instead of two-dimensional, deformations... 

FIGURE 6.19. Dependence of the threshold voltage of an electrohydrodynamic instabihty of a cholesteric liquid crystal on cell thickness (hehcal pitch Po = 115 /mi). The solid lines indicate the experimental results. The dashed line shows the calculated values according to an equation similar to (6.38) without allowance for oscillations in the helical pitch [17]. 

As the intermolecular dispersion forces that maintain the molecules in the cholesteric structure are relatively small, a low additional amount of energy suffices to change the helix pitch. The pitch depends particularly on temperature. In some cases the dependence is so pronounced that typically a temperature rise of less than 3°C is adequate to change the color of reflected light from red over the entire visible spectrum to blue. The use of cholesteric liquid crystals in thermographic applications is based on this property (see also first part of this book). 

Cholesteric liquid crystals are also nematic, only difference is that their different layers of molecules have helical orientations. The pitch is dependent on temperature. It may also be called as chiral nematic. The nematic liquid crystals may also be made up of Disc -shaped molecules instead of cylindrical rod-shaped molecules. 

The theory for the threshold of the instability in cells with thicknesses considerably exceeding the equilibrium pitch (1>Pq) has been considered by analogy with the case of dielectric instability [121, 266], but with allowance being made for the additional, destabilizing term in the free energy which is caused by the space charge. The frequency dependence of the threshold field for <0 has been shown to be similar to that caleulated for nematics. For a cholesteric liquid crystal with >0 the presence of electrical conductivity is revealed by a lowering of the threshold of the instability at low frequencies. 

A twist angle 0>9O° can be achieved by doping the nematic liquid crystal mixture with a cholesteric liquid crystal. For a cell with zero pretilt the twist angle

cell-thickness d to the pitch p of the doped liquid-crystal mixture ... 

The flow properties of cholesteric liquid crystals are surprisingly different from those of the nematics. The most important difference is that, in some directions (along the helical axis), the viscosity measured in Poiseuille flow geometries (see Appendix B) is about six orders of magnitude larger than in the isotropic phase, or in the cholesteric phase when the flow direction is perpendicular to the helix axis. In this latter case, the viscosity is similar to that of nematics, although the behavior is somewhat non-Newtonian above a pitch-dependent threshold shear rate. It was found that the shear rate above which the fluid becomes non-Newtonian is inversely proportional to the square of the pitch. The apparent viscosities as the function of shear rate of materials with different pitch values are shown in Figure 4.6. 

In many cases, the pitch of the cholesteric helix is dependent on the temperature to a significant degree. For most cholesteric liquid crystals, the... 

Thermotropic cholesterics have several practical applications, some of which are very widespread. Most of the liquid crystal displays produced use either the twisted nematic (see Figure 7.3) or the supertwisted nematic electrooptical effects.6 The liquid crystal materials used in these cells contain a chiral component (effectively a cholesteric phase) which determines the twisting direction. Cholesteric LCs can also be used for storage displays utilizing the dynamic scattering mode.7 Short-pitch cholesterics with temperature-dependent selective reflection in the visible region show different colors at different temperatures and are used for popular digital thermometers.8... 

The temperature dependence of the cholesteric pitch in the polypeptide liquid crystals has been investigated in various solvents. The pitch P is related to the twisting angle (p between neighboring molecules separated by a distance d along the axis of torsion as follows. 

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