Field-Induced Director Axis Reorientation Effects

FIELD-INDUCED DIRECTOR AXIS REORIENTATION EFFECTS 

We now consider the process of director axis reorientation by an external static or low-frequency field. Optical field effects are discussed in Chapter 6. The following examples will illustrate some of the important relationships among the various torques and dynamical effects discussed in the preceding sections. We will consider the magnetic field as it does not involve complicated local field effects and other electric phenomena (e.g., conduction). The electric field counterparts of the results obtained here for the magnetic field can be simply obtained by the replacement of by AeE [cf Eq. (3.26) and (3.29)]. 

Field-Induced Reorientation without Flow Coupling  

From this and the preceding equations, the free energy [Eq. (3.4)] and elastic torque [Eq. (3.13)] are, respectively. 

The torque exerted by the external field (applied perpendicular to the initial director axis), from Equation (3.29), becomes 

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FIELD-INDUCED DIRECTOR AXIS REORIENTATION EFFECTS... 

As one can see from the preceding discussions on optical field induced director axis reorientation in hquid crystals, the torque exerted by the optical field on the director axis is basically quadratic in the field amplitude. Except for its dispersion influence on the optical dielectric constant 8(co), the frequency of the electric field is basically not involved. Furthermore, if two or more fields are acting on the director axis, the resulting torque exerted on the director axis is simply proportional to the square amplitude of the total fields. Accordingly, it is possible to enhance the optical field induced effect by application of a low-frequency ac or dc electric field, much as the optically addressed liquid crystal spatial light modulator discussed in Chapter 6. In the latter, the responsible mechanism is the photoconduction generated by the incident optical field in the semicondnctor layer adjacent to the liquid crystals. 

In general, the distortions on the electronic wave function of liquid crystal molecules caused by an applied field do not cause appreciable change to its contribution to the refractive indices (see Chapter 10). However, the orientation of the molecules can be dramatically altered by the apphed field. This process alters the overall optical properties of the medium and is the principal mechanism used in liquid-crystal-based electro-optical devices. As noted in Section 6.2.2, the electrically induced orientational refractive index changes could be Pockel or Kerr effect. In this and the next sections, we shall focus on nematic liquid crystals in which the director axis reorientation is a Kerr-like effect that is, the process is quadratic in the applied field. 

A variety of effects can occur in the TGB phases due to the influence of an electric field. The coupling between the director and the field may be due to the dielectric anisotropy Sa, or due to the dependence of the smectic tilt angle on the electric field (electroclinic effect), or due to the spontaneous polarization. In contrast to the typical behavior of smectic phases, a small electric field cannot only result in a reorientation of the director, but also in a reorientation of the smectic layers [138], Higher fields can cause a reorientation of the pitch axis, helical unwinding [139], [140], a shift of the wavelength of selective refiection [141], or field-induced phase transitions [103], [141]. 

The following example demonstrates how the viscosity coefficient Yi comes into play in field-induced reorientational effects. Consider pure twist deformation caused by an externally applied field 77 on a planar sample as depicted in Figure 3.12. Let 9 denote the angle of deformation. The director axis h is thus given by n = (cos 0, sin 0, 0). 

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