Cholesteric liquid crystal twist field

Electronic displays make use of the fact that the orientation of the molecules in liquid crystals changes in the presence of an electric field. This reorientation causes a change in their optical properties, making them opaque or transparent, and hence forming a pattern on a screen. Cholesteric liquid crystals are also of interest because the helical structure unwinds slightly as the temperature is changed. Because the twist of the helical structure affects the optical properties of the liquid crystal, these... 

If a magnetic field H is applied along the Y axis, the cholesteric liquid crystal has only the twist deformation. 

For stratified optical media (whose refractive indices are only a function of the coordinate normal to the film), Berreman introduced a 4 x 4 matrix method (now known as the Berreman 4x4 method) [14—18], in which the electric field and magnetic field (the sum of the fields of the light beam propagating in forward and backward directions) are considered. When the film is divided into slabs, the reflection at the interface between the slabs is taken into account. The Berreman 4x4 method works well for both normal and obliquely incident fight. Consider an optical film, such as a cholesteric liquid crystal in the planar texture (twisted nematic), whose dielectric tensor is only a function of the coordinate z, which is perpendicular to the film ... 

This effect has been observed experimentally in comparatively thick cells (d 50 /xm) [113]. In cells with d 20 /xm, the final twisted state (in the field) proves to be insufficiently stable and the nematic liquid crystal layer is gradually transformed into a planar structure. The addition of small quantities of cholesteric liquid crystals to the initial nematic mixture enables a stable twisted structure to be achieved with the application of a field and improves the electrooptical characteristics of the device. The electrooptical response of electrically induced twist nematic cells includes intensity oscillations observed both in the switching on and switching off regimes [114]. These oscillations take place due to the variation of birefringence, which are not important in the usual twist effect. 

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... 

A useful structural concept introduced by Kleman and FriedeF postulates a quasi-layered structure and explicitly takes into account the natural twist of the system. Concerning defects, we may think of cholesteric liquid crystals as a smectic with an in-plane nematic behavior, similar to the smectic C phase. Instead of using tire concept of a layered structure to account for the twist, we may also consider tire field of twist axis t in addition to the director field n. The two concepts are essentially equivalent, with the twist field being identical with the layer normal. The twist field accordingly suffices the condition t curti = 0, which means that in this twist field no fwist deformation is allowed. The concept of "layers" or twist-field is an approximation, which may not be valid in the core of the defects. We assume that the core structures of cholesterics (especially those with weak chirality) are similar to that of nematics. 

At this point we make a slight generalization so that the theory can be applied to cholesteric liquid crystals as well. The basic difference between cholesteric and nematic liquid crystals lies in the fact that the equilibrium state of cholesterics is characterized by a nonvanishing twist in the director field. If we denote the cholesteric helical axis as the X -axis, the equilibrium state is characterized by... 

The terminus of chirality induction is used for processes, in which the structural information of a chiral molecule is transferred to an initially achiral collective which then will form a superstructural chiral phase. One of the most prominent examples can be found in the field of liquid crystals The doping of a nematic LC phase with chiral mesogenes (dopants) can lead to a twisted, helical cholesteric phase. Noteworthy is the fact that the length scales of the chiral information that characterizes the involved species can differ by several orders of magnitude a few Angstrpms in a single chiral molecule, but the pitch of a helical cholesteric phase amounts typically a few microns. 

The subject of liquid crystals has now grown to become an exciting interdisciplinary field of research with important practical applications. This book presents a systematic and self-contained treatment of the physics of the different types of thermotropic liquid crystals - the three classical types, nematic, cholesteric and smectic, composed of rod-shaped molecules, and the newly discovered discotic type composed of disc-shaped molecules. The coverage includes a description of the structures of these four main types and their polymorphic modifications, their thermodynamical, optical and mechanical properties and their behaviour under external fields. The basic principles underlying the major applications of liquid crystals in display technology (for example, the twisted and supertwisted nematic devices, the surface stabilized ferroelectric device, etc.) and in thermography are also discussed. 

Chiral liquid crystals belong to a wide class of soft condensed phases. The director field in the ground state of chiral phases is nonuniform because molecular interactions lack inversion symmetry. Among the broad variety of spatially distorted structures the simplest one is the cholesteric phase in which the director n is twisted into a helix. The spatial scale of background deformations, e.g., the pitch p of the helix, is normally much larger than the molecular size ( > 0.1 pm) since the interactions that break the inversion symmetry are weak. 

When electric fields are applied to liquid crystals, the molecules tend to align—either parallel to the field (for Sa > 0) or perpendicular (for < 0). For the case of nematics, which already have a preferred direction, the director is simply reoriented without breaking the symmetry. However, the helical phase has two nonequivalent directions the twist axis, and the director, which rotates spatially about the twist axis. If > 0, such a helical director is clearly incompatible with a uniform field. For this case, an increasing field first distorts the helix, then stretches out the pitch, and finally causes the well-known cholesteric-nematic transition [1], If <0, the helical director is only compatible with a uniform field if the twist axis and field are parallel. 

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