rel="nofollow" href="#ulink_e8cb0983-067e-5b6e-bd86-47fa9322b7f9">(4.67)
For
Equations (4.66) and (4.67) yield
(4.69)
and
Osx′ reaches its maximum
(4.71)
for
If the axis x′ of the analyser is at an angle ψ = −α to the x-axis, the maximum intensity
(4.73)
with the first realizable value for v = 2. For β = 3(π/2), we obtain the values
(4.74)
From Equation (4.64), we calculate the thickness
For λ = 550 nm, β = 3(π/2),
The intensity passing the analyser at an angle ψ describes the normally white state, with the maximum for ψ = −α. If a high enough field is applied, the linear polarized light reaches the analyser at the angle α, resulting (according to Figure 4.5) in a component
For α = π/4, and hence ψ = −α = π/4, we obtain Ea = 0 independent of λ. This normally white state exhibits an excellent black state, and works with crossed polarizers.
For the optimum ψ = −α and the normally black state, the analyser has to be placed, due to Equation (4.70), in the y′ -direction, which is for ψ = −α = −π/4 parallel to the polarizer. In this case, however, Osy holds only for one wavelength in Equation (4.75). The white state after a field has been applied fully passes the analyser.
As the normally white state exhibits a black independent of wavelength, it is the preferred mode of operation.
If the large thickness of an STN cell is decreased, the transmission falls below optimum and some luminance is sacrificed, but a wider viewing angle is obtained. The reason for this will be explained in the chapter on compensation foils later.
The larger twist angle β in supertwist nematic LCDs has a pronounced effect on the transmitted luminance versus voltage curve in Figure 4.6 by rendering the transition from the white state to the black state much steeper. As will be explained in Chapter 12, this enhanced steepness is required for addressing an STN cell with a larger number of lines without losing too much contrast. The increase in steepness with increased β is now explained phenomenologically. In the transition from, let’s say, the white state to the black state, the LC molecules have to be tilted by a torque stemming from the applied electrical field. They finally end up parallel to the field. A smaller torque is needed if the molecules exhibit a larger twist angle from layer to layer as the restoring force by the vertically neighbouring molecules becomes weaker. Hence, a smaller voltage is required to achieve the tilt angles.
Figure 4.6 Transmitted luminance and midlayer tilt versus the voltage across an STN cell with a twist of β = 240°, an off-voltage of 2.58V and an on-voltage of 2.75V for addressing 240 lines (Reproduced from Scheffer and Nehring, 1998 with permission of Annual Reviews.)
A calculation of this effect is based on fluid mechanics and liquid crystal continuum equations (Degen, 1980), where the mechanical parameters K11, K22 and K33, the dielectric constants ε┴ and ε||, the pretilt angle at the orientation layers and, of course, the twist angle β and d/p play a role. The calculations are similar to the electro-optical investigations of TN cells in Section 4.1, because propagation matrices based on the mechanical properties are established for a sequence of twisted layers, and are finally multiplied.
Figure 2.12 shows that the tilt of the molecules is larger in the midlayer due to the restoring forces of the molecules anchored on top of the orientation layer. Figure 4.7 depicts the midlayer tilt versus the voltage VLC across the cell with twist angles β as a parameter. The larger is β, the greater is the slope of the curves. For β = 3π/2(270°) the curve rises perpendicularly in the centre portion. For β greater than 270° the curves become double-valued, causing bistability and hysteresis. Therefore, the twist must not exceed 270°. STN cells use twists between 180° and 270°, where 240° is often encountered