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where F is the force needed to shift a body with the area A with the velocity v over a viscous layer with a thickness d. For displays, the kinematic viscosity
(2.14)
is used, where d is the density of the viscous material. As for most LC materials, d is around 1 Ns2/mm4; the values for ηd and η do not differ much. The viscosity depends upon the orientation of the directors. For a random orientation, the bulk or turbid kinematic viscosity is given in Table 2.1. The rotational viscosity is measured according to Figure 2.6, where the vector of the rotation is perpendicular to the director. Values for dynamic rotational viscosities of LCs are 0.02 Pas to about 0.5 Pas. This viscosity is important for the movement of the director in an electric field.
The elastic constants belong to restoring torques if the field of directors is deformed. The three deformations from the equilibrium are splay, twist and bend, with the elastic constants K11, K22 and K33, as shown in Figure 2.7. The dimension is a force. The values are very small in the range of 10 × 10−2N. These elastic forces determine the equilibrium in the presence of electric and magnetic fields.
A large variety of chemical compounds exhibit the properties of liquid crystals. The basic structure with rings, linking groups and terminal groups is shown in Figure 2.8. Rings can be cyclohexyl, pyridine, dioxane, phenylcyclohexane or phenyldioxane. Fluorinated compounds have a high specific resistance ρ = 5 × 1015 Ω cm. The characteristic temperatures of LC compounds can be shifted by additive ingredients. By this means, Merck’s nematic compounds reached the wide temperature range of operation, from −40 °C to 120 °C, which is very suitable for automotive application. In Table 2.2 properties of LC materials with this wide temperature range are listed.
Figure 2.6 The rotational viscosity for rotation of a molecule perpendicular to the director
Figure 2.7 Equilibrium configuration; the elastic deformations splay (a), twist (b) and bend (c)
Figure 2.8 The basic structure of a calamitic LC molecule
2.2 The Operation of a Twisted Nematic LCD
The liquid crystals used are calamitic and thermotropic in the nematic phase. The operation of this most widely applied LCD will be phenomenologically described in order to give an overview over the entire flat panel display system, including the addressing scheme (Demus et al., 1998a; Kaneko, 1987; Lueder, 1998a). This alleviates the more analytical and detailed treatments that follow.
2.2.1 The electro-optical effects in transmissive twisted nematic LC cells
Figure 2.9 depicts the top view of a display panel with the conducting rows and columns terminating in the contact pads. The rectangular pixels can only be electrically addressed from those contact pads.
A colour VGA display, as used in laptops, has 480 rows and 3 × 320 columns forming triple dots for the three colours red, green and blue. An NTSC TV display has 484 rows and 3 × 450 columns corresponding to 653 400 pixels, whereas an HDTV display has 1080 × 3 × 1920 = 7320 800 pixels. For more standardized formats, see the table in Appendix 1.
Table 2.2 Properties of nematic LC materials with a wide temperature range
| MLC-1380000 | MLC-13800100 | MLC-1390000 | MLC-13900100 | |
|---|---|---|---|---|
| Transition temp, smectic-nematic | < −40°C | < −40°C | < −40°C | < −40°C |
| Clearing pt Tc | 110 °C | 111°C | 110.5 °C | |
| Rotational viscosity, 20 °C | 228 mPas | 151 mPas | 235 mPas | 167 mPas |
| Δε 1 kHz 20 °C | + 8.9 | + 5.0 | + 8.3 | ++ 5.2 |
| n0= n┴ | 1.4720 | 1.4832 | 1.4816 | 1.4906 |
| ne= n|| | 1.5622 | 1.5735 | 1.5888 | 1.5987 |
| Δn | + 0.0902 | +0.0903 | 0.1073 | + 0.1081 |
Figure 2.9 Top view of the rows, columns, pixels and contact pads of a display panel
Figure 2.10 shows a pixel of a transmissive twisted nematic LC cell with no voltage applied. The white backlight/passes the polarizer a. The light leaves it linearly polarized in the direction of the lines in the polarizer, and passes the glass substrate b, the transparent electrode c out of Indium-Tin-Oxide (ITO) and the transparent orientation layer g. This layer, made of an organic material such as polyimide, 100 nm thick, is rubbed to generate
