Dielectric Instability of Cholesterics

In this chapter we consider the most characteristic phenomena related to the electric field interaction with chiral, quasi-layered structure of cholesteric liquid crystals. 

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W. Helfrich, Electrohydrodynamic and Dielectric Instabilities of Cholesteric Liquid Crystals, J. Chem. Rhys. 55, p. 839 (1971). 

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

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 6.9. Optical appearance of the square grid dielectric instability in a cholesteric liquid crystal (the grid has dimensions of 80 x 80 fim). 

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. 

For further discussion of the physics of the dielectric and electrohydrodynamic instabilities in cholesteric liquid crystal, see Pikin [79]. The features of the electrohydrodynamic behavior of polymer lyotropic cholesterics were recently studied in [80]. 

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. 

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. 

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. 

Helfrich [49] was first to propose electro-hydrodynamic instability in cholesterics with negative dielectric anisotropy. Harault [56], combining Helfrich theory with time-dependent formalism, calculated a voltage frequency relationship similar to that observed for Williams domains. The existence of conduction and dielectric regimes was experimentally verified. The domain periodicity is proportional to wherepo... 

Let both the helical axis and the electric field are parallel to the normal z of a cholesteric liquid crystal layer of thickness d and >0. In the case of a very weak field the elastic forces tend to preserve the original stack-like arrangement of the cholesteric quasi-layers as shown in Fig. 12.15a. On the contrary, in a very strong field, the dielectric torque causes the local directors to be parallel to the cell normal, as shown in Fig. 12.15c. At intermediate fields, due to competition of the elastic and electric forces an undulation pattern appears pictured in Fig. 12.15b. Such a structure has two wavevectors, one along the z-axis (nld) and the other along the arbitrary direction x within the xy-plane. The periodicity of the director pattern results in periodicity in the distribution of the refractive index. Hence, a diffraction grating forms. Let us find a threshold field for this instability. 

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, the result obtained is the same— the appearance of a two-dimensional periodic pattern for the distribution of the director. 

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