Director rotation

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

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... 

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

Mesophase with a helicoidal supramolecular structure of blocks of molecules with a local smectic C structure. The layer normal to the blocks rotates on a cone to create a helix-like director in the smectic C. The blocks are separated by plane boundaries perpendicular to the helical axis. At the boundary, the smectic order disappears but the nematic order is maintained. In the blocks the director rotates from one boundary to the other to allow the rotation of the blocks without any discontinuity in the thermomolecular orientation. 

Molecular alignment for which the director rotates in a helical fashion when passing between two substrate surfaces having molecules in uniform planar alignments. 

The product s0r yields the angle by which the director turns on a closed curve around the disclination center. If a complete circuit is made around the center of an 5 = I/2 disclination, the director rotates by 71. For 5 = 1 a similar circuit yields a total director rotation of 2ti. So, 5 = I/2 defines a 7r-line disclination and 5 = 1 defines a 27r-Iine disclination. 

Liquid crystals may have line defects called disclinations. The name comes from discontinuity and inclination. The director rotates about a line normal to the disclination. The strength of a disclination, S, is defined by... 

In cholesterics, the structure is similar to nematics, but the director rotates in a corkscrewlike fashion along n. Electric-field-induced transitions between the cholesteric and nematic phases are used in the dye phase change display discussed below. 

Molecules that contain a chiral center can form chiral liquid crystalline phases, where the orientation direction rotates in a helical fashion as one moves along the helical axis, which is perpendicular to the locally preferred direction of orientation. Both nematic and smectic phases can be chiral. In a chiral nematic phase, also known as a cholesteric, as one moves along the helical axis, the director rotates sinusoidally (see Fig. 10-31. Thus, if z is... 

If A < 1, Eq. (10-4) has no solutions in the shearing plane. This means that the director rotates endlessly in the deformation plane. The period of this rotation—that is, the time it takes to rotate through an angle of tt, is... 

Note that the director rotation rate is proportional to the shear rate y. Hence, the period of the stress oscillations is equal to the period P for rotation of the director through an angle of 7T, given by Eq. (10-6) ... 

As the director rotates, the shearing stress shows periodic maxima and minima. After solving Eq. (10-29) for the strain-dependent director angle 9 y), the strain-dependent viscosity afy is given by (Gu and Jamieson 1994)... 

If a homeotropically aligned tumbling nematic is sheared at small Er = yxVh/K, then the director at the midplane of the sample rotates modestly toward the flow direction, until it reaches a steady state where the viscous forces driving the director rotation are balanced by the Frank stresses (see Fig. 10-16 at Er 1). As Er increases in small increments, so that a steady state is attained between each increment in Er, the steady-state director at the midplane is rotated to a greater and greater extent (see Fig. 10-16 at Er 10). 

When the molecules that form a liquid-crystalline phase are chiral, the structure of these mesophases can have an additional property. In the chiral nematic phase (N ) the director precesses about an axis perpendicular to the director and describes in this way a helix (Figure 2.7). The pitch of a chiral nematic phase is the distance along the helix over which the director rotates over 360°. The chiral nematic phase is sometimes... 

It was shown in the previous chapter that CP light induces quasiperiodic director rotation (QPR) if the incident intensity exceeds the one for OFT by about 40% (no backflow). This is already in a higher region of intensities than that considered in [49]. So the question was what happens if one mismatches shghtly from the CP case at higher intensities It became clear [50] that a full numerical analysis is needed to capture the QPR for the elliptic case, because... 

Thus the director rotates about Oz with an angular velocity [Pg.263]

We assume that the director is strongly anchored at the substrates. Therefore in the absence of deformation = Oq, while in the deformed (flexed) state the director rotates with the substrates ... 

Unoriented poly (p-hydroxybenzoic acid-co-2,6-hydroxynaphthoic acid) exhibited smoothly wandering director fields in three dimensions. Alignment with a 1.1 T magnetic field for 30 min at 300 C transformed this structure to domains with an anisotropic shape within which the polymer was highly oriented, and the global order parameter amounted to 0.85 [110]. Boundaries were of the splay-bend type and involved a 180 director rotation. At lower field strengths, the domains were less... 

Kent Display is a pioneer of cholesteric liquid crystal displays (ChLCDs) in which the director of the liquid crystal twists around a helical axis [3]. The remarkable property is that the cholesteric material reflects light of certain wavelengths depending on the pitch over which the director rotates. When an electric held is applied. 

The cholesteric phase is similar to that of the nematic phase on a local scale. As in the nematic phase, the molecules can be described by a director. However, the director in the cholesteric phase is twisted about an axis normal to the molecular orientation, following a helical path (Figure 1.3). The distance over which the molecular director rotates by 2tt along the helix axis is defined as the length of the cholesteric helix pitch, P. The twist is right-handed or left-handed depending on the molecular conformation. Iridescent colors are characteristic of cholesteric phases [1,2]. 

Because of the dielectric anisotropy property of LCs, the LC molecules can align either parallel or perpendicular to the electric field, theoretically, according to their values of dielectric anisotropy [44]. However, under certain conditions, the uniform director reorientation in an a-c electric field is unfavorable the domain structure corresponding to a minimum free energy is formed. The domain patterns can be classified into two main types orientational domains with pure director rotation without fluid motion and the electrohydrodynamic domains caused by the combined effects of the periodic director reorientation and regular vortices of material moving [44]. This kind of movement of LC materials is called hydrodynamic flow, mainly resulting from the effects of conductivity anisotropy of LC molecules and ionic electric current. 

The dissipation related to the pure director rotation has to be taken into account when writing the conservation energy equation. In addition, the heat transfer becomes anisotropic and the thermal conductivity is described by two coefficients K and Kj. ... 

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