Instabilities planar cholesteric textures

FIGURE 6.8. Illustration of a dielectric instability of a planar cholesteric texture when Ae > 0. 

When an electric or magnetic field is applied to a liquid crystal cell, a texture transition occurs to minimize the free energy of the system. These texture changes in cholesteric liquid crystals are physically similar to the Frederiks transition in a nematic liquid crystal and result in a significant change in the optical properties of the layer. Texture transitions have been reviewed previously [8, 9] with allowance made for the sign of the dielectric or diamagnetic anisotropy, the initial texture, and the direction of the applied field. Here, we consider only the instability of the planar cholesteric texture, which has been widely discussed in recent literature. 

FIGURE 6.12. The planar Grandjean texture in an a.c. electric field [25] (cholesteric mixture with Pq = 30 /mi and Ae = +0.74, directors at opposite boundaries are parallel to the ridge of the wedge), (a) Pitch dependence on reduced cell thickness d — 2djPo (b) director distribution in different Grandjean zones and (c) thickness dependence of the dielectric instability just at the threshold voltage. 

Investigation of an electrohydrodynamic instability (Ae < 0) in a planar Grandjean texture shows [17] that, in this case also, the directions of the domains alternate with a transition from one Grandjean zone to another, while the domains are perpendicular to the director of the cholesteric liquid crystal in the middle of the layer in each case. This can be seen in Fig. 6.18. With an increase in d, one-dimensional deformations transform to a two-dimensional grid. The threshold voltages for the formation of a periodic instability and the period of the domains, in this case, oscillate with an increase in thickness (Fig. 6.19). In principle, this can be accounted for by the Helffich-Hurault theory [22, 23], developed with the approximation d Po, in the spirit of (6.20) and (6.21) where the forced pitch P is substituted for the equilibrium pitch Pq-... 

A special case was considered in [21]. The dielectric instability was investigated in the hybrid [4] or so-called corkscrew texture. A wedge-form cell was prepared with the planar and homeotropic orientation of a cholesteric mixture at opposite boundaries. It was shown that the Cano-Grandjean disclinations are not observed in this case and the electrooptical response... 

Figure 31. Optical patterns accompanying different EHD processes, (a) Electrolytic mode for the homeo-tropic orientation of a nematic liquid crystal, (b) Ka-pustin-Williams domains (KWD) in homogeneously oriented nematic, (c) Anisotropic EHD mode for the planar texture of a cholesteric, (d) A chevron structure due to interference of two instabilities (KWD and inertial mode).

The EHD behavior of cholesteric liquid crystals is very similar to that of nematics. When the anisotropy of the electrical conductivity is positive (cTa>0), the planar texture of a cholesteric liquid crystal in a field parallel to the helical axis is unstable for any sign of [263, 264]. The instability is caused by the torque induced by the electrical conductivity acting against the elastic torque of the cholesteric and, although the cause is different from the purely dielectric case (see Sec. 9.3.2.2 of this Chapter), the result obtained is the same that is, the appearance of a two-dimensional periodic pattern for the distribution of the director. 

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