Cholesteric layer

As already indicated briefly in 3.5.8 the effect of elastic anisotropy has some interesting implications for cholesterics, especially for long-pitched structures. We have seen that disclination pairs in nematics have angular forces in the presence of elastic anisotropy. For all practical purposes, the solutions that were obtained for nematics will hold good for each nematiclike cholesteric layer, except that the layers now twist continuously in the... 

Figure 11 shows the dependence of the critical unwinding voltage Vf on the cell thickness-to-pitch ratio for a cholesteric layer with perpendicular boundary orientation. For these measurements two reusable cells, having thicknesses of 7.8 and 10.9 ym, were filled with various mixtures of the nematic liquid crystal RO-TN-103 and the chiral substance CB 15.We used the Cano wedge technique to determine the pitch of the mixtures and found the simple inverse relationship... 

In addition to band-edge lasing, defect mode lasing is possible [97]. A defect in the photonic structure creates fine bands of allowed transmissions inside the photonic band gap. A defect may result from an isotropic or anisotropic layer between adjacent cholesteric layers, but also from phase shifts [106], particle stabilized defects [107], deformation of the cholesteric helix [108] or local polymerization [109]. The threshold of such defect modes are low and can be as low as a few nanojoules per pulse [110]. 

The other flexoelectric structure can arise in a very thin planar cholesteric layer at a certain set of material parameters. The instabihty occurs in the form of spiral domains [89] whose handedness depends on the sign of an electric field. While the threshold voltage for the hnear domains discussed above slightly depends on cell thickness, Uth 27rRT/ eii - 633 , the threshold for the spiral domains is proportional to thickness... 

Liquid crystals may be nematic, smectic, or cholesteric, depending on the type of ordering the molecules can adopt. Nematic liquid crystals contain order in only one dimension (parallel moleoiles), smectic liquid crystals contain order in two dimensions (parallel molecules in parallel layers), and cholesteric liquid crystals contain layers that are rotated with respea to one another. Within each cholesteric layer, the molecules are parallel. 

When the deviations of layers from the flat geometry are substantial, the deformations are more appropriately characterized by the principal curvatures a = jR and elastic free energy density can be cast in the form... 

When the cholesteric layers are tilted with respect to the bounding plate, the disclinations might occur to match the twisted structure in the bulk with an (usually unidirectional or conical) orientational field of anchoring forces [47]-[49]. Here again, the / dislocations split into X and r pairs. The X lines... 

Figure 5.15. Cholesteric textures in spherical droplets with tangential director anchoring at the boundary. Top A monopole configuration with a point defect N =l in the field / of normals to the cholesteric layers and an attached nonsingular line k — 1, stable when R/p 1 (microphotograph in crossed polarizers). Bottom A boojum configuration with an isolated k — 2 surface point defect at R/p 1 (no crossed polarizers). The insert shows the director field at the surface of the droplet.

The SMLC cholesterics most frequently present polygonal textures with domains of a negative Gaussian curvature. In these domains the focal conditions are not exaetly satisfied [91], and unlike the situation in smectics, the cholesteric layers might deviate from the exact geometry of Dupin cyclides... 

The anchoring term is caused by tilting the cholesteric layers at the boundaries. The tilt angle increases from 0 outside the streak to max = arctan at the vertical middle plane of the streak, see Figure 5.21(b) = lajh is the width of the streak renormalized by the cell thickness h. The anchoring penalty increases when 2a increases (since max increases) this increase can be avoided if the oily streak simply elongates, preserving max = const. 

Sinusoidal undulations of the optical axis, thin cholesteric layers between columnar domains, and nested-arc textures are all strong indications of a helical structure (Figures 11.18 and 11.19). The nested-arc texture shows the structure of the tilt grain boundary phase particularly well. 

Such oriented cholesteric layers have been used for circular dichroism studies (Section 3). 

It is well known that transitions between cis- and trans-azobenzene can be induced photochemically [145] by excitation with appropriate wavelength (cf Fig. 20). Accordingly, colored pictures may be produced in a reversible way on cholesteric layers [143]. In the same way as azobenzene, the derivatives of azoxy-benzene undergo cis-trans (or trans cis) isomerization upon excitation and induce different color changes in cholesteric phases. 

When the cholesteric pitch is less than 0.5 pm, the parallel profiles of the cholesteric layers cannot be resolved in light microscopy, but the straight or bent segments due to... 

---