Twisted nematic cell

In Fig. 3 we show a planar cell containing nematic liquid crystal, two of whose bounding walls are rubbed or otherwise treated so that the directors near the walls are pinned in the directions shown. Since the 

From this representation of the director field, it is easily calculated that V h(f) = 0 and V X h(r) = (dS(x)/dx)[sin0j + cosOk], where we use ij,k to denote the unit vectors in the x,y,z directions, respectively. Using Eqs. [6] and [7], we obtain 

The Kquid crystal director is described by the polar angle 0 and the aziniuthal angle (p. Both angles are a function of z. The components of the director n are given by 

We consider the case where the anchoring is finitely strong and the boundary conditions are 

Using Euler-Lagrange method to minimize the total free energy, 

When the applied field is slightly above the threshold, G is very small, and we have the approximations sin0f 0 and cos0 l. Keeping only first-order terms, Equation (5.51) becomes - dflScp = if22 = 0, whose solution is 

Because of the boundary condition given in Equation (5.46), the solution is 

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Figure 8.11 Illustration of Mauguin twisted nematic cell, reported in 1911. Substrates are thin mica plates, which are uniaxial with their optic axis parallel to plane of plates. Apparently, uniaxial crystal stmcture of mica produces strong azimuthal anchoring of nematic LCs of Lehmann, such that director is parallel (or perpendicular) to optic axis of mica sheets at both surfaces. Mauguin showed that method of Poincard could be used to explain optics of system if it was assumed that LC sample created layer of material with uniformly rotating optic axis in twisted cells.

Time required for the light intensity viewed through crossed polarizers to increase to 90% of the final value from the off-state to the on-state of an electro-optical twisted-nematic cell. 

Time required by an electro-optical twisted-nematic cell for a light-intensity change from 90% to 10 % of the maximum intensity on going from the on-state to the off-state. 

Figure 7.34 The twisted nematic cell in the absence of field (left) and in the field (right). (After Raynes, 1983.)...

Fig. 13 Schematic representation of the orientation-dependent elastic torque on a nickel nanowire with longitudinal anchoring in 5CB (a) in equilibrium, and (b) in the presence of a magnetic field, (c) Levitation of the nanowire in a twisted nematic cell [446]. (Copyright 2004, American Association for the Advancement of Science)...

Figure 13.22 Operation of a twisted nematic cell. In the absence of an applied electric field, the twisted nematic rotates the plane of polarised light from one side of the cell to the other allowing light to pass through. An applied potential renders it opaque.

Fig. 4.2 Structure of the different layers of an LC display shown in cross-section of a single pixel (twisted nematic cell).

Figure 1.19. The twisted nematic cell. The twist angle 6 = 7t/2 and the two polars make an angle = 0 or tt/2.

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. ... 

Ferroelectric liquid crystals (FLC) are of great interest due to their fast electro-optical response which is about 1,000 times faster than conventional twisted nematic cells [131]. The geometry used is called a surface stabilized FLC cell which utilizes a very thin gap (=2 pm) to unwind the FLC supramolecular pitch (=1-2 pm) since the bulk FLC materials do not show macroscopic polarization. This very thin gap, however, leads to difficulties in manufacturing large panels and very poor shock resistance. Researchers have proposed the concept of microphase stabilized FLC [79,109, 130] using FLC-coil diblock copolymers for electro-optical applications as shown in Fig. 15. This concept takes advantage of ferroelectric liquid crystallinity and block copolymer microphase separation since the block... 

Fig. 7.9. Tapping mode images of 80 nm polyimide films, rubbed using AFM. (a) scan force 0.2 x 10 N. (b) scan force 0.8x10 N. (c) scan force 1.5 x 10 N. Optical micrograph of twisted nematic cells, formed by AFM patterned substrate.

Fig. 2.4. A transverse electric field, indicated by the arrow pointed towards the right at the top of the figiu-e, tilts the apolar director as shown by double headed arrows in a specific direction due to the flexoelectric effect on a 90° twisted nematic cell. The tilting direction reverses if the field direction is reversed. The transmitted intensity mesisured with a polarized light beam traversing the cell vertically as indicated by the dashed line will be identical in the two cases. On the other hand, with an oblique beam, the transmitted intensities for the two tilted director structures will be different, and can be used to me siu-e the flexocoefficient (adapted from Kischfai et cU. ).

Electro-Optical Effects in Twisted Nematic Cells. 224... 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

Another example is a twist nematic cell with a planar orientation of the director at both boundaries 9 = ti/2 differing by their azimuth, cp = 0 and Jt/2. In such cells, the areas with the director twist in the bulk by angle -rjt/2 and —Jt/2 have the same... 

Figure 5.20 Representation of the twisted-nematic cell. In the absence of an applied field (a), light passes through and the display looks transparent to the observer. When a voltage is applied (b), light is unable to pass through and the cell is darkened.

Consider a 90° twisted nematic cell sandwiched between two polarizers. Use Equation (3.45) to calculate and plot the transmittance as a function of u = 2AnhlA in the following case. The polarizers are parallel to each other and the transmission axis of the polarizer at the entrance plane is parallel to the liquid crystal director. 

A. Lien, The general and simplified Jones matrix representations for the high pretilt twisted nematic cell,... 

Figure 7.4 The polar and azimuthal angles of the liquid crystal director as functions of z in the 90° twisted nematic cell under various applied voltages.

Figure 7.5 The polar angle at the middle plane vs. the applied voltage in twisted nematic cells with the twist angles 0°, 45°, 90°, 135°, 180°, 225°, and 270°.

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