Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Instability of the Planar Cholesteric Texture

For unwinding the helical structure, Eq. (12.29) relates the threshold coherence length to a characteristic size of the system, namely, the pitch of the helix = Po/n3- [Pg.366]

In Chapter 11 we have found that, for the Frederiks transition in nematics, the threshold field coherence length is determined by the cell thickness, = din, see Eq.(11.53). Now we shall briefly discuss another type of instability with a threshold determined by the geometrical average of the two parameters mentioned [17], [Pg.367]

Let both the helical axis and the electric field are parallel to the normal z of a cholesteric liquid crystal layer of thickness d and 0. In the case of a very weak field the elastic forces tend to preserve the original stack-like arrangement of the cholesteric quasi-layers as shown in Fig. 12.15a. On the contrary, in a very strong field, the dielectric torque causes the local directors to be parallel to the cell normal, as shown in Fig. 12.15c. At intermediate fields, due to competition of the elastic and electric forces an undulation pattern appears pictured in Fig. 12.15b. Such a structure has two wavevectors, one along the z-axis (nld) and the other along the arbitrary direction x within the xy-plane. The periodicity of the director pattern results in periodicity in the distribution of the refractive index. Hence, a diffraction grating forms. Let us find a threshold field for this instability. [Pg.367]

In the absence of the field, the director components are n = (cosqoz, sinq oz, 0) and qo = 3cp/3z. For a small field perturbation, both the conical distortion appears (angle 9) and the azimuthal angle cp slightly changes. The new components of the director are  [Pg.367]

If we intend to calculate precisely the threshold field for the two-dimensional distortion we should write the Frank free energy with the director compcments (12.34) and the field term (Ea/47t)(En) and then make minimization of the free energy with respect to the two variables cp and 9 [18]. For a qualitative estimation of the threshold we prefer to follow the simple arguments by Helfrich [17]. We consider a one-dimensional (in layer plane xy) periodic distortion of a cholesteric [Pg.367]

The threshold field for the formation of periodic distortion has been calculated [22, 23] based on the expression for the free energy of a cholesteric liquid crystal [Pg.323]

The conditions of large layer thickness d Pq) and small Ae e are assumed in this equation. Also, the assumptions are made of small deviations of the axis of the cholesteric helix from the normal to the glass surfaces [Pg.323]

The maximum compression Aqm of the cholesteric planes and the maximum angle of deviation 0m of the helical axis from the normal can be related using purely geometric considerations [Pg.324]

By minimizing the elastic part of the free energy (6.14) (without the term containing the field) by a choice of a value of w satisfying the condition dqe /dw = 0, we obtain the period of the deformation [Pg.324]

When the dielectric anisotropy is not small the term Ae/dTr in (6.18) must be substituted for j (e — e )/[27r e + )]. The threshold field is independent of firequency up to the dispersion region o d of the dielectric permittivity (Chapter 2). [Pg.324]


When an electric or magnetic field is applied to a liquid crystal cell, a texture transition occurs to minimize the free energy of the system. These texture changes in cholesteric liquid crystals are physically similar to the Frederiks transition in a nematic liquid crystal and result in a significant change in the optical properties of the layer. Texture transitions have been reviewed previously [8, 9] with allowance made for the sign of the dielectric or diamagnetic anisotropy, the initial texture, and the direction of the applied field. Here, we consider only the instability of the planar cholesteric texture, which has been widely discussed in recent literature. [Pg.532]

Figure 19. Illustration of the dielectric instability of a planar cholesteric texture for 6 >0. Figure 19. Illustration of the dielectric instability of a planar cholesteric texture for 6 >0.
FIGURE 6.12. The planar Grandjean texture in an a.c. electric field [25] (cholesteric mixture with Pq = 30 /mi and Ae = +0.74, directors at opposite boundaries are parallel to the ridge of the wedge), (a) Pitch dependence on reduced cell thickness d — 2djPo (b) director distribution in different Grandjean zones and (c) thickness dependence of the dielectric instability just at the threshold voltage. [Pg.327]

A special case was considered in [21]. The dielectric instability was investigated in the hybrid [4] or so-called corkscrew texture. A wedge-form cell was prepared with the planar and homeotropic orientation of a cholesteric mixture at opposite boundaries. It was shown that the Cano-Grandjean disclinations are not observed in this case and the electrooptical response... [Pg.322]

Investigation of an electrohydrodynamic instability (Ae < 0) in a planar Grandjean texture shows [17] that, in this case also, the directions of the domains alternate with a transition from one Grandjean zone to another, while the domains are perpendicular to the director of the cholesteric liquid crystal in the middle of the layer in each case. This can be seen in Fig. 6.18. With an increase in d, one-dimensional deformations transform to a two-dimensional grid. The threshold voltages for the formation of a periodic instability and the period of the domains, in this case, oscillate with an increase in thickness (Fig. 6.19). In principle, this can be accounted for by the Helffich-Hurault theory [22, 23], developed with the approximation d Po, in the spirit of (6.20) and (6.21) where the forced pitch P is substituted for the equilibrium pitch Pq-... [Pg.336]

Figure 31. Optical patterns accompanying different EHD processes, (a) Electrolytic mode for the homeo-tropic orientation of a nematic liquid crystal, (b) Ka-pustin-Williams domains (KWD) in homogeneously oriented nematic, (c) Anisotropic EHD mode for the planar texture of a cholesteric, (d) A chevron structure due to interference of two instabilities (KWD and inertial mode). Figure 31. Optical patterns accompanying different EHD processes, (a) Electrolytic mode for the homeo-tropic orientation of a nematic liquid crystal, (b) Ka-pustin-Williams domains (KWD) in homogeneously oriented nematic, (c) Anisotropic EHD mode for the planar texture of a cholesteric, (d) A chevron structure due to interference of two instabilities (KWD and inertial mode).
The EHD behavior of cholesteric liquid crystals is very similar to that of nematics. When the anisotropy of the electrical conductivity is positive (cTa>0), the planar texture of a cholesteric liquid crystal in a field parallel to the helical axis is unstable for any sign of [263, 264]. The instability is caused by the torque induced by the electrical conductivity acting against the elastic torque of the cholesteric and, although the cause is different from the purely dielectric case (see Sec. 9.3.2.2 of this Chapter), the result obtained is the same that is, the appearance of a two-dimensional periodic pattern for the distribution of the director. [Pg.559]


See other pages where Instability of the Planar Cholesteric Texture is mentioned: [Pg.366]    [Pg.323]    [Pg.532]    [Pg.366]    [Pg.323]    [Pg.532]    [Pg.510]    [Pg.332]    [Pg.164]    [Pg.1231]    [Pg.250]    [Pg.1091]    [Pg.23]   


SEARCH



Cholesteric

Cholesterics

Instabilities planar cholesteric textures

Planar cholesteric texture

Planar texture

© 2024 chempedia.info