Twist external fields

In a liquid crystal most properties are best expressed relative to a director based coordinate system. This is not a problem in a macroscopic system where the director is virtually fixed. However, it can be a problem in a small system such as a simulation cell where the director is constantly diffusing on the unit sphere. Thus a director based frame is not an inertial frame. Correction terms should therefore be added to time dependent properties. Time correlation functions with slowly decaying tails might also be affected by the director reorientation. Transport coefficient obtained from them will consequently be incorrect. When NEMD-simulation algorithms are applied, the fictitious external field exerts a torque that constantly twists the director, which could make it impossible to reach a steady state. 

The liquid crystals can be deformed by applying external fields. Even a small electric or magnetic field, shear force, surface anchoring, etc., is able to make significant distortion or deformation to liquid crystals. Thus, n is actually a function of position r. According to the symmetry of liquid crystals there exist three kinds of deformations in liquid crystals splay, twist and bend deformations, shown in Figure 1.17. The short bars in the figure represent the projections of the local directors. 

This transient effect manifests itself in a direct way in the behaviour of a twisted nematic cell (see 3.4.2). When the external field (assumed to be sufficiently strong) is switched off, the light transmission shows an optical bounce effect , i.e., it does not decrease monotonically but rises again to a peak before decaying to its off value. Calculations have confirmed that the peak in transmission corresponds approximately to a perpendicular alignment of the director in the central portion of the cell. This is caused by fluid motion, which also gives rise to a reverse-twist. ... 

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. 

N.V. Madhusudana, J.F. Palierne, Ph. Martinot-Lagarde and G. Durand, Twist instability of a flexoelectric nematic domain in an external field, Phys. Rev. A 30, 2153R-2154R, (1984). doi 10.1103/PhysRevA.30.2153... 

Mathematically the molecular field vector h can be found using the Euler-Lagrange approach by a variation of the elastic and magnetic (or electric) parts of the free energy with respect to the director variable n(r) (with a constraint of = 1). For the elastic torque, in the absence of the external field, the splay, twist and bend terms of h are obtained [9] fi-om the Frank energy (8.16) ... 

As during relaxation the external field is switched off, the molecular field includes only the elastic torque. For the pure twist distortion and our geometry, the molecular field vector h is opposite to the magnetic field, i.e. directed opposite to X- axis. Its absolute value is (Section 8.3.3). The torque (n x h) is... 

In the test cells to be discussed below, the values of the helical pitch and the tunable cell thickness are close to each other (about 28 pm). Therefore, as shown in Fig. 12.17 the full pitch structure (n = 2) is the most stable n means a number of half-pitches). The elastic energy of the two states (n = 0 and n = 2) is calculated with allowance for the twist, bend and splay distortions. Solid lines in Fig. 12.18 demonstrate dependencies of the elastic energy of the two states on thickness-to-pitch ratio in the absence of an external field. In the figure, the free energy is normalized to the unit cell area and factor dlK22. It is seen that the free energy for... 

Cholesteric LCs, in which the molecules are twisted perpendicular to the helical direction, the molecular axis being parallel to the director, are used in a number of optical applications such as LC displays and electronic paper [11,12]. One of the most important properties of cholesteric LCs is that a specific wavelength can be selectively reflected by controUing the directions in which the molecules are oriented. In general, an external electric or magnetic field is used to control the cholesteric LC molecular directions, and it is important to understand the ways external fields affect the molecular arrangements and dynamics so that further developments can be made. 

Figure 5. Switching in a regular fiber array examples of director fields for different 77 a T = 1.0, R = 5a, and w = 1 yz-cioss sections through the fiber center). From left to right homogeneous (h), deformed (d), and saturated (s) structure. Anchoring easy axis is planar and z, while the external field E is directed along y. Note that the d-structure is twisted along the x-axis, while there is no twist in a simple nematic slab. This, however, does not affect the qualitative analogy of the two systems.

Both cholesteric and smectic mesophases are layered. In the former case, the periodicity arises from a natural twist to the director field, and in the latter, from a center-of-mass correlation in one dimension. There are many types of smectic phases distinguished by their symmetry and order. The set of field-induced phenomena is quite different for these two materials, owing primarily to the very different layer compressibility. That is, the cholesteric pitch can be unwound by an external field, whereas the smectic layering is typically too strong to be altered significantly. However, because of the common layered structure, there are also strong similarities. 

The optical-field-induced Freedericksz transition for a twist deformation by a normally incident laser beam in a planar-aligned nematic liquid crystal is studied. The Euler equation for the molecular director and the equations describing the evolution of the beam polarization in the birefringent medium are solved simultaneously in the small-perturbation limit. The stability of the undistorted state is investigated. An alternate series of stable and unstable bifurcations is found. This phenomenon has no analog in the Freedericksz transition induced by dc electric and magnetic external fields. 

The twisted ground state of chiral liquid crystals willingly accepts the additional deformations imposed by external fields, surface interactions, or by a tendency of molecules to form smectic layers, hexagonal order, or doubletwist arrangements. Very often such additional deformations result in topo-... 

The analog of the magnetic intensity H (produced by external currents) would be an external field coupled to the two components of curl n. A local microscopic source of bend [23] is not easy to imagine. On the other hand, chirality is naturally coupled to twist chiral mesogens develop a spontaneous twist in the nematic phase. The cholesteric is thus analogous to a normal metal in a magnetic field. 

The dynamics of the splay and bend distortions inevitably involve the flow processes coupled with the director rotation. Such a backflow effect usually renormalizes the viscosity coefficients. Only a pure twist distortion is not accompanied by the flow. In the latter case, and for the infinite anchoring energy, the equation of motion of the director (angle variation) expresses the balance between the torques due to the elastic and viscous forces and the external field (and... 

Several types of spontaneous periodic director pattern yield information about elastic coefficients. Static stripe textures, as described by Lonberg and Meyer [45], appear in polymer nematics if the twist/splay ratio below the critical value of 0.303. Calculations of director fields and the influence of elastic constants and external fields on the appearance of these periodic patterns have been performed by several authors (e.g. [49-51]). In nematic cells with different anchoring conditions at the upper and lower cell plates (hybrid cells), other types of striped texture appear these are similar in nature, but involve different director deformations and elastic coefficients. For a description of various types of static periodic texture and their relationship to elastic coefficients see, for example, Lavren-tovich and Pergamenshchik [52]. In thin hybrid aligned films, a critical thickness is observed below which the director align-... 

The configuration of molecular directors within a spherical micro-droplet depends on the boundary conditions imposed by the surrounding material, on the temperature and the elastic constants of the liquid crystal and on the strength of the external electric or magnetic fields. If the splay, twist and bend elastic constants are almost equal, the structure is, in the absence of external fields, either ... 

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