Threshold cholesteric nematic transition

Finally, it should be noted that if the field is initially applied parallel to the helical axis, the cholesteric helix would usually rotate at H < He SO as to make the field perpendicular to the helical axis. Therefore, the geometry shown in Fig. 10 is always the situation seen experimentally just before the field strength reaches the cholesteric-nematic transition threshold. 

It is interesting to note that this threshold field is lower than that for a conical distortion or that for cholesteric-nematic (unwinding) transition. For a conical distortion, the theory is closely similar to that discussed in 3.4.2 and has been treated by Leslie the critical field is given by... 

The elastic coefficient K22 could be measured according to (2.34) either from the threshold of the twist distortion of the homogeneous alignment induced by a magnetic field, or from the threshold of the initially twisted director alignment [58]. It is also possible to measure the unwinding voltage t unw of the cholesteric to nematic transition... 

In Section 9.2.1 of this Chapter we discussed field-induced changes in the microstructure of liquid crystals. However, field-induced unwinding of the cholesteric (macroscopic) helix (see Section 9.3.2.3 of this Chapter) shows that the transition from a twisted to a uniform nematic may also be considered as a phase transition. In the latter case the field energy term competes with a rather small elastic energy proportional to nematic-like elastic moduli and the squared wave vector of the helical superstructure Kq As the pitch of the helix p = lKlq is large, the field threshold for the transition is very low. On the other hand, between the two extreme cases (a microstructure with a molecular characteristic dimension and a... 

Greubel has recently analyzed the cholesteric-to-nematic transition for an applied voltage. With perpendicular alignment of the liquid crystal molecules at the cell surfaces, he found that the field transition for the cholesteric-to-nematic transition was higher than the opposite nematic-to-cholesteric transition. With one mixture, the ratio of field thresholds was approximately 2.5. This work points out the importance of the proper surface orientation and cell cleanliness in achieving the best bistability. 

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]. 

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