Grandjean planar texture

Another and more characteristic texture observable of the cholesteric phase is the Grandjean planar texture with a series of regularly spaced bands separated by sharp lines. This was observed by F. Grandjean (1921) when a wedge-shaped split between two sheets of fresh mica (or clean glass slides) was used as the cell for examination under crossed polars. Under such conditions the cholesteric phase formed on cooling a homeotropic planar texture with visible bands. 

Plate 1. The defect texture of the TGBA phase, under crossed polars, formed on coohng from the isotropic hquid (xlOO). The textures show both platelets and Grandjean planar regions (associated with a helical macrostructure)... 

More precise numerical calculations of the reduced threshold voltage (Uth/Uo) and the reduced wave vector d/2w (at the threshold) agree well with experimental data, Fig. 6.13, for the first four Grandjean zones. For thicker cells (or higher zones) formulas (6.17)-(6.21) work quite well. In [25] theoretical and experimental data have also been obtained for the planar texture with the directors at opposite boundaries at an angle 7t/2. 

Before attempting to develop any theory correlating molecular to cholesteric handedness, one must be completely sure of the experimental data. A cholesteric phase is fully described by its handedness and pitch, and often also knowledge of the pitch variations with temperature is fundamental. In particular, the determination of the handedness is quite a delicate matter. Before discussing the methods currently used to determine handedness and pitch, the principal textures of the cholesteric phase must be briefly reviewed The planar or Grandjean textures are obtained in thin cells by rubbing the cell walls (with... 

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 6.12. 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-... 

Several cases of dielectric, hydrodynamic, and flexoelectric instabilities and domain structures have been observed and extensively studied in CLCs. Their appearance depends on the initial orientation of molecules, the physical parameters of the material, and the applied electric field. In CLCs with positive dielectric anisotropy Ae > 0, an electric field applied along the helix axis of a planar (Grandjean) texture can induce a two-dimensional spatially periodic deformation which has the form of a square grid [96], The period and threshold voltage of this field-induced instability depend on the elastie constants, the dieleetric anisotropy, and the sample thickness [97],... 

Investigation of the EHD instability ( a<0) in a planar Grandjean texture [265] shows that the directions of the domains alternate with a transition from one Grandjean zone to another, while the domains... 

The second related example is the planar or Grandjean texture of the cholesteric mesophase. In the planar state, the main helix axis is perpendicular to the electrode surfaces of the cell. Consequently, the director is always oriented parallel to the surface with the orientation... 

The model presented so far is accurate, but incomplete. In actuality, the scattering texture with the helical axes parallel to the cell walls is not a stable state without an applied field. Rather, it is a metastable state that has a lifetime of from minutes to months, depending upon the surface alignment, fluid thickness, and pitch. The stable state is the planar or Grandjean texture. Kahn made the initial measurements of the various steps in the texture changes. Additional experiments with both electric and magnetic fields have added more detail to the model. 

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