cells can phenomenologically be explained by the fact that half of the molecules are already rotated in the direction imposed by the field, horizontally for Δε < 0 and vertically for Δε > 0. The decay time Td is derived in Saito and Yamamoto (1978) as
(3.106)
Figure 3.25 Normalized rise time Tm versus normalized voltage Vn with the ratio K of elastic constants as parameter (a) for p-type and (b) n-type nematic LCs
which is independent of the applied voltage V and of Δε, and has the same factor outside the magnitude sign as Tr in Equation (3.103). For Θd = Θ0 = π/2 we obtain Td of the Fréedericksz cell as
(3.107)
and for Θd = Θ0 = 0 Td of the DAP cell as
(3.108)
whereas the decay time for the HAN cell is obtained by putting Θd = π/2 and Θ0 = 0, yielding
(3.109)
A comparison between the HAN cell and the Fréedericksz cell which is valid for p-type nematic LCs reveals for the same cell-thickness
Figure 3.26 The ratio Tdn in Equation (3.110) versus K for a p-type nematic LC
For K > 0 the decay time of the HAN cell is shorter, and for − 1 < K< 0 longer than that of the Freedericksz cell, whereas they are equal for K= 0 reached by K11 = K33. Comparing the HAN cell to the DAP cell, which applies for n-type nematic LCs, yields for the same cell thickness
In contrast to the Fréedericksz cell, the decay time of the HAN cell for K > 0 is longer, and for − 1 < K < 0 shorter than that of the DAP cell. Again, for K = 0 the two decay times become equal.
The ratios Tdn in Equations (3.110) and (3.111) are plotted in Figures 3.26 and 3.27 versus K with Θd and Θ0 as parameters. For the p-type nematic in Figure 3.26, Tdn decreases, and for n-type nematics in Figure 3.27 it increases with increasing K. For p-type nematics and for K > 0 the Fréedericksz cell exhibits the longest decay time, whereas for the n-type nematics and for K > 0 the DAP cell has the shortest decay time. The reflective version of the Fréedericksz and the DAP cell with cell gap d/2 have rise times and decay times four times smaller than their transmissive counterparts because of the proportionality to d2. The reflective HAN cell requires the same thickness d as the transmissive Freedericksz and DAP cells, and hence does not share the enhancement of switching speed of the other reflective cells.
Figure 3.27 The ratio Tdn in Equation (3.111) versus K for an n-type nematic LC
3.2.9 Fast blue phase liquid crystals
The blue phase of liquid crystals is isotropic with Δn = 0 as shown in Figure 3.28(a) (Yang et al., 2009). If a voltage V is applied between the two electrodes, the in-plane electric field E parallel to the surface of the substrates switches the LC molecules into a position tending to align parallel to E, which represents an anisotropic state with Δn ≠ 0. This is depicted in Figure 3.28(b). The transition from the isotropic to the anisotropic phase induced by E is called the Kerr effect governed by
(3.112)
where K is the Kerr constant ranging from 10−13 m/V2 to 10−8m/V2 (Kikuchi et al., 2007).
Liquid crystals exhibiting the Kerr effect are nematics or fluorinated nematics and a photo initiator monomer which are stabilized by a polymeric chiral dopant, such as ZLI-4572 by Merck (Kikuchi et al., 2009). This LC mixture is designated the polymer stabilized isotropic (PSI) mode. The cell is filled with this material at 100 °C, is UV cured and then cooled down at a rate of 1 °C/min. The LC mixture has the large Kerr constant of 10−8 m/V2. Figure 3.29 depicts a phase diagram with the two parameters, the weight fraction of the chiral dopant and the temperature. The blue phases occur in the areas designated by BP I and BP II. Below a weight fraction of 0.05 no blue phases occur. Without the chiral dopant the blue phases occurred only in a very narrow temperature range. The isotropic blue phase shows up just above the nematic- isotropic transition temperature.
The remarkable fact is the very short transition time between the two phases, which is in the range of 300 μs and below. This opens up the prospect of a very fast LC cell. In addition this cell needs neither alignment layers nor electrodes on the upper substrate, as is shown in Figures 3.28 (a) and (b).
