Continuous director rotation

V-shaped switching, continuous director rotation (CDR) half-V switching, and various other ways of making a SSFLC bistable cell behave V-shaped, each with its own special characteristics. "" ... 

Chira.lNema.tlc, If the molecules of a Hquid crystal are opticaHy active (chiral), then the nematic phase is not formed. Instead of the director being locaHy constant as is the case for nematics, the director rotates in heHcal fashion throughout the sample. This chiral nematic phase is shown in Figure 7, where it can be seen that within any plane perpendicular to the heHcal axis the order is nematic-like. In other words, as in a nematic there is only orientational order in chiral nematic Hquid crystals, and no positional order. Keep in mind, however, that there are no planes of any sort in a chiral nematic Hquid crystal, since the director rotates continuously about the heHcal axis. The pitch of the helix formed by the director, ie, the distance it takes for the... 

Unlike the T-deformation, the director reorientation in S- and B-effects is always accompanied by the macroscopic flow of a nematic hquid crystal (backflow) with the velocity V = (V (z),0,0), where the z eods goes perpendicular to the substrates and SB-deformations take place in the x, 2(-plane. The velocity V includes only the rr-component, because the z-component is zero according to the continuity equation (div V = 0), and the y-component vanishes due to the symmetry of the problem (Fig. 4.6). The total system of dynamic equations for V z) and the director rotation angle 6 z) gives [37-39]... 

In the nematic phase, long range order in the position of the centres of mass of the molecules is absent. The difference between a nematic and an ordinary liquid is solely the presence of the long range orientation. The cholesteric mesophase is similar to the nematic one but is characterized by the fact that the director rotates continuously to form a helical structure. 

An example of an experiment involving continuous sample rotation with synchronized data acquisition is shown in Fig. 10 [123]. A thin liquid crystal cell filled with a side chain liquid crystal polymer was continuously rotated about an axis perpendicular to the magnetic field. The director behavior was followed by deuteron NMR as well as by polarizing microscopy. The optical texture and the orientation-dependent... 

Figure 10. Convective director structures in a nematic side group polymer, (a) Schematic diagram of the experimental set-up for continuous rotation about an axis perpendicular to the magnetic field, (b) Optical texture after two hours of rotation, (c) NMR spectra obtained during one revolution after two hours, (d) Schematic diagram of convection rolls evolving due to nonlinear coupling between director rotation and viscous flow, (e) Director distribution P( P) extracted from the NMR spectra in (c). For details see [123].

Cholesteric liquid crystals are formed only from materials which are optically active. The structure is similar to that of a nematic but, instead of the molecules remaining parallel, a twist is imposed upon the structure, resulting in a helical disposition of the molecular axis, i.e. the direction of the director varies in a helical fashion around the z axis. Two layers of a cholesteric liquid crystal are shown in Fig. 8.5(c), but it must be remembered that the distribution of molecules is a continuous function of z,with the direction of the director rotating continuously as z varies. 

Fig. 7. The chiral nematic Hquid crystal stmcture. The director (arrow) traces out a heHcal path within the medium. Siace the rotation of the director is continuous, the figure does not mean to imply the existence of layers perpendicular to the heHcal axis.

On the other hand, if X is smaller than unity, the latter dominates, so that the director tumbles continuously without any steady-state orientation. The period P per rotation is given by... 

Tumbling regime At very low shear rates, the birefringence axis (or the director) of the nematic solution tumbles continuously up to a reduced shear rate T < 9.5. While the time for complete rotation stays approximately equal to that calculated from Eq. (85), the scalar order parameter S,dy) oscillates around its equilibrium value S. Maximum positive departures of S(dy) from S occur at 0 n/4 and — 3n/4, and maximum negative departures at 0 x — k/4 and — 5it/4, while the amplitude of oscillation increases with increasing T. 

If the ratio f lf2 I is greater than unity the torques induced by the symmetric and antisymmetric strain rates respectively will never cancel out and the antisymmetric pressure will never vanish. This means that the director continues rotating for ever. The liquid crystal is said to be flow unstable and complicated flow patterns arise. TTiey have been studied comprehensively both experimentally and theoretically [30]. Some nematic liquid crystals are flow stable whereas others are not. For example, 4-n-pentyl-4 -cyanobiphenyl (5CB) is flow stable whereas 4-n-octyl-4 -cyanobiphenyl (8CB) is flow unstable. The only difference between this two substances is the length of the hydrocarbon chain attached to the cyanobiphenyl skeleton. Nematic liquid crystals that are flow stable usually become flow unstable close to the nematic-smectic A transition. The reason for this is that there is an emergent layer structure in the fluid that is incommensurate with the strain rate field. 

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The simplest phase, which contains only molecular-orientational ordering, is the nematic. The term "nematic" means thread in Greek. All known nematics have one symmetry axis, called the director, n, and are optically uniaxial with a strong birefringence. The continuous rotational symmetry of the isotropic liquid phase is broken when the molecules choose a particular direction to orient along in the nematic phase. Since the nematics scatter light intensively, the nematic phase appears turbid. 

Fig. 1.2. (a) in a bulk nematic liquid crystal, the director can point in an arbitrary direction in space. This is a signature of a broken continuous rotational symmetry of the isotropic phase. The mode that restores the broken. symmetry is the Goldstone mode. It represents a homogeneous and coherent rotation of aU molecules, (b) the homogeneous surface couples to the Goldstone mode and pins the director in a certain direction in space. 

Fig. 2.2. Schematic diagram of a hybrid-aligned nematic cell. The field-free director (shown by the continuous curved line) has a splay-bend curvature distortion in the xz plane. A DC field applied along the y axis rotates the polarization and the director (shown by the curved dashed line) acquires a 4>(z) profile. (Reproduced from Dozov et al. with the permission of EDP Sciences, http //publications.edpsciences.org.)...

It should be noted that cholesteric liquid crystals (chiral nematics) having point group symmetry Dqo are also periodic with flie pitch considerably exceeding a molecular size. The preferable direction of the local molecular orientatiOTi, i.e. the director oriented along the Coo axis, rotates additionally through subsequent infinitesimal angles in the direction perpendicular to that axis. Hence a helical structure forms with a screw axis and continuous translation group. 

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