Читать книгу Liquid Crystal Displays - Ernst Lueder - Страница 30

So far we have not dealt with the time needed to switch an LC cell from the black state to the white state, or vice versa. Dynamics of a cell are based on mechanical properties of the LC material, and will be discussed in Section 3.2.8. Some information on switching speed can, however, be derived from the field of directors. That’s how a very fast switching cell, the π cell, has been found (Bos and Koehler, 1984), as will be outlined later in this chapter.

The Fréedericksz cell and the TN cell exhibit a uniform alignment of the molecules with a pretilt α in the opposite direction on the substrates, as shown in Figure 3.21(a) for the on-state of the cell. After the electric field has been switched off, the molecules relax to the off-state, resulting in a low of LC material and a tilting of the molecules. The molecules around the centre of the cell are exposed to a torque, causing aback-flow of the material and trying to rotate them through a large angle to the position in the off-state. This slows down the switching process. Figure 3.21(b) depicts the pretilt of the π cell pointing in the same direction on both substrates. In this case, the molecules in the centre of the cell experience almost no torque while they relax into the off-stage. The angles by which the relaxing molecules have to be tilted are smaller, resulting in a much higher switching speed.

The phenomenon of a ‘back-flow’ causes the ‘optical bounce’ in the electro-optical response to a rectangular voltage in Figure 3.22(a), whereas the response of the π cell in Figure 3.22(b) does not exhibit the prolonged relaxation time. In a TN cell switching off takes, as a rule, 3 to 4 ms, whereas the π cell requires only around 1 ms. However, after 1 ms the relaxation is not yet completely finished, which may not be noticeable at a high enough switching frequency. If the uncompleted relaxation is disturbing, a holding voltage of around 2 V or a polymer stabilization (Vithana and Faris, 1997) arrests the relaxation.

Figure 3.21 The pretilt angles and the relaxation to the off-state. (a) Of a TN cell; (b) of a π cell

As in the HAN cell, the optical anisotropy Δn in the π cell for V_LC = 0 changes along the z-axis, which is denoted by Δn(z). As a consequence, the optical retardation R from the input at z = 0 to the output at z = d is

Figure 3.22 The electro-optical response to a square voltage pulse. (a) Of a TN cell with a prolonged relaxation; and (b) of a π cell with a fast relaxation

(3.98)

where Δn(z) depends upon the angle Θ_e in Figure 3.21(b). We shall derive Δn(Θ_e) in Chapter 6, leading to Equation (6.29). For a π cell with crossed polarizers, the transmission T is obtained by a straightforward calculation with Jones vectors, yielding

(3.99)

A normally white cell has the first transmission maximum at (π/λ)R = (π/2), or

(3.100)

corresponding to a λ/2-plate. We introduce an effective anisotropy Δn_eff for the entire optical path in the cell, which is given by

(3.101)

providing, with Equation (3.100),

(3.102)

The term Δn_eff renders this result similar to Equation (3.97).

The wide viewing angle inherent to the π cell is discussed in Section 6.3.2.