Cholesteric flexoelectric domains

In both the cases considered, an optical contrast of the patterns observed in isotropic liquids is very small. Certainly, the anisotropy of Uquid crystals brings new features in. For instance, the anisotropy of (helectric or diamagnetic susceptibility causes the Fredericks transition in nematics and wave like instabilities in cholesterics (see next Section), and the flexoelectric polarizaticm results in the field-controllable domain patterns. In turn, the anisotropy of electric conductivity is responsible for instability in the form of rolls to be discussed below. All these instabilities are not observed in the isotropic liquids and have an electric field threshold controlled by the corresponding parameters of anisotropy. In addition, due to the optical anisotropy, the contrast of the patterns that are driven by isotropic mechanisms , i.e. only indirectly dependent on anisotropy parameters, increases dramatically. Thanks to this, one can easily study specific features and mechanisms of different instability modes, both isotropic and anisotropic. The characteristic pattern formation is a special branch of physics dealing with a nonlinear response of dissipative media to external fields, and liquid crystals are suitable model objects for investigation of the relevant phenomena [39]. 

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... 

For the zero zone with the directors at opposite boundaries parallel to each other (no twist) and zero dielectric anisotropy, both the threshold voltage and the wavevector can be calculated analytically as a function of the cholesteric pitch, despite the completely unwound state of the helix. The sign and amplitude of the angle of the field-induced domain rotation (at threshold) depends on the handedness and the pitch of the helix and the sign of the difference in the flexoelectric coefficients e = 11- 33 ... 

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