Homeotropic state

Price and Wendorff31 > and Jabarin and Stein 32) analyzed the solidification of cholesteryl myristate. Under equilibrium conditions it changes at 357.2 K from the isotropic to the cholesteric mesophase and at 352.9 K to the smectic mesophase (see Sect. 5.1.1). At 346.8 K the smectic liquid crystal crystallized to the fully ordered crystal. Dilatometry resulted in Avrami exponents of 2, 2, and 4 for the respective transitions. The cholesteric liquid crystal has a second transition right after the relatively quick formation of a turbid homeotropic state from the isotropic melt. It aggregates without volume change to a spherulitic texture. This process was studied by microscopy32) between 343 and 355.2 K and revealed another nucleation controlled process with an Avrami exponent of 3. 

Figure 6. Geometry of the setup circularly polarized light incident perpendicularly on a nematic layer with the director no z (homeotropic state). The components of the director n are described in terms of the angles 0, E> (0 = 0 in the homeotropic state).

Fig. 5.10 Light-induced surface-assisted alignment change in a liquid-crystal cell. Schematic depiction of the out-of-plane change from the homeotropic state to the planar homogeneous state upon exposure to unpolarized UV light. Adapted from Ichimura [43] with permission from Springer.

Fig. 7.15. The vertically aligned nematic-hybrid aligned nematic (VAN-HAN) zenithal bistable device geometry. The homeotropic state (left) is black while the hybrid state (right) is bright.

When switching from the homeotropic to the planar state the first part of the bipolar pulse is negative. The nematic has a positive Ae and aligns with the applied field during this stage squeezing the splay and bend deformations towards the surface. This means that the homeotropic state is... 

Fig. 7.18. Scanning electron microscopy pictnres of actual surface gratings (right) and a schematic illustration of the switching between the homeotropic state C and the low-tilt (planar) state D (left). For a symmetric grating (top) the (bulk) director of the planar state is parallel to the cell plane while for a blazed grating (bottom) it is pretilted. Modified from Jones, reproduced with kind permission of the Society for Information Display.

But how to force the system relax to a particular state selected by an experimentalist Berreman and Heffner [20] suggested to exploit the backflow ejfect discussed in Section. 11.2.6. We know that, upon relaxation of the director from the field-ON quasi-homeotropic state (barrier state B) to a field-OFF state, a flow appears within the cell. The direction of the flow depends on the curvature of the director field, which is more pronounced near the electrodes. Moreover it has the opposite sign at the top and bottom electrodes, see the molecules distribution in state B in Fig. 12.17. Due to this, the close-to-electrode flows create a strong torque exerted on the director mostly in the middle of the cell that holds the director to be more or less parallel to the boundaries in favour of the n = 2) initial state in Fig. 12.17. 

Transition between the fingerprint state and homeotropic state... 

When the liquid crystal is in the focal conic state and the externally applied electric field is increased, more liquid crystal molecules are ahgned parallel to the field. The liquid crystal is gradually switched to the fingerprint state. There is no sharp boundary between the focal conic state and the fingerprint state. When the appUed field is increased further, the pitch of the hquid crystal becomes longer, as shown in Figure 10.27. When the applied field is above a threshold Ec, the helical structure is unwound [29,48], the pitch becomes infinitely long, and the liquid crystal is switched to the homeotropic state. 

Transition between the homeotropic state and the planar state... 

For the liquid crystal in the homeotropic state, when the applied field is turned down, there are two relaxation modes. One is the H-F mode in which the liquid crystal relaxes into the fingerprint state (and then to the focal conic state) as discussed in the previous section. The other is the H-P mode in which the liquid crystal relaxes into the planar state [76,77]. The rotation of the liquid crystal in the H-P mode is shown in Figure 10.28. The liquid crystal forms a conic helical... 

Relaxation from the homeotropic state to the planar state Figure 10.28 Schematic diagram showing the rotation of the hquid crystal in the H-P relaxation mode. 

Structure with the helical axis in the cell normal direction. As the relaxation takes place, the polar angle 6 increases. When the polar angle 6 is zero, the liquid crystal is in the homeotropic state. When the polar angle is mH, the liquid crystal is in the planar state. 

Because 3 > 1, the second-order derivative is negative, and therefore there is no minimum free energy state in the region O<0< nl2 therefore, there is no stable conic helical structure. The liquid crystal is either in the homeotropic state with 0 = 0 or in the planar state with 0 = nl2. In Figure 10.29 the free energy of the conic helical structure given by Equation (10.24) is plotted as a function of sin 6> at three different fields, e q = 2ln is the field at which the planar state and... 

Ec to unwind the helical structure in the fingerprint state. If the field is decreased from e q, the free energy of the planar state becomes lower than that of the homeotropic state, but the energy barrier persists. The energy barrier becomes lower with decreasing field. When the field is sufficiently low, the energy barrier decreases to zero, and the homeotropic state will become absolutely unstable. The critical field ehp = J /K i can be obtained from the equation... 

In summary, if the hquid crystal is in the homeotropic state and the applied field is reduced, there are two possible relaxation modes. If the applied field is reduced to the region liquid crystal relaxes slowly into the fingerprint state and then to the focal conic state when the apphed field is reduced further. If the applied field is reduced below Ehpy the hquid crystal relaxes quickly into the transient planar state and then to the stable planar state. In bistable Ch reflective displays, the way to switch the liquid crystal from the focal conic state to the planar state is by first applying a high field to switch it to the homeotropic state, and then turning off the field quickly to allow it to relax to the planar state. 

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