Smectic tilt angle

In an interesting application, the long-chain substituted 4- -hexoxybenzylidene-4 -iodoaniline (HBIA), 5 has been incorporated in the liquid-crystal phase of 4- -hexoxy-benzylidene-4 -propylaniline (HBPA, 6)13. The intensity pattern of the Mossbauer spectrum allowed the orientation of the molecule to be estimated, showing that the smectic tilt angle was 50°. 

A degree of polymerization of about ten was determined by end-group analysis via H-NMR. Glass transitions were found to occur below room temperature. In each case, the material was smectic at 80 The polymers exhibited a broad enantiotropic phase range. A uniaxial teflon monolayer gave well-aligned parallel samples which were used to determine the smectic tilt angle as a function of temperature. The materials were well-behaved... 

Smectic elastomers, due to their layered structure, exhibit distinct anisotropic mechanical properties and mechanical deformation processes that are parallel or perpendicular to the normal orientation of the smectic layer. Such elastomers are important due to their optical and ferroelectric properties. Networks with a macroscopic uniformly ordered direction and a conical distribution of the smectic layer normal with respect to the normal smetic direction are mechanically deformed by uniaxial and shear deformations. Under uniaxial deformations two processes were observed [53] parallel to the direction of the mechanical field directly couples to the smectic tilt angle and perpendicular to the director while a reorientation process takes place. This process is reversible for shear deformation perpendicular and irreversible by applying the shear force parallel to the smetic direction. This is illustrated in Fig. 2.14. 

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]. 

Figure 86. The dependence of the errors in the tensor components e, and 3 calculated by the short pitch method when the smectic tilt angle 6 approaches 45 °. The input value is assumed to be measured with a 2% error (from Buivydas [155]).

Figure 90. Surface-stabilized configuration with less than optimum efficiency, switchable between two symmetric states with low optical contrast. The surface pretilt angle has been chosen equal to the smectic tilt angle 0in this example. For a strong boundary condition with zero pretilt, a different extreme limiting condition with approaching zero at the boundary is also conceivable, without any essential difference in the performance of the cell.

The inequality (6.35) 1 was first derived by Carlsson et al [32] for the special case when the smectic tilt angle 0 is assumed small (see the small angle approximations... 

One final set of properties for the elastic constants is worth noting. As the smectic tilt angle 6 tends to zero the elastic energy ought to converge to that for the SmA phase, given by [110, 258]... 

Recall that 0 is the constant smectic tilt angle. These results were stated by Kedney and Stewart [140] in terms of the electric energy simply replace by o a and H by E in the above expressions. The elastic constants Ki can of course be replaced by the equivalent Orsay constants if desired using the relations (6.25). 

Figure 6.8 A magnetic field H is applied across a sample of depth d of SmC liquid crystal in the bookshelf geometry, as shown. For simplicity, the director is assumed to be strongly anchored at the surfaces in such a way that 0(0) = 0(d) = 0 where 0(z) is the orientation angle of the c-director defined by (6.120)2 this indicates that the director makes an in-plane surface twist angle j3 = 0 to the x-axis at the boundaries, equivalent to the constant smectic tilt angle. Other values for are feasible see page 279. (a) When H < where He is the F eedericksz threshold defined by (6.143), only 0 = 0 is available and the director alignment is uniformly constant across the sample, (b) There is a Freedericksz transition at H = He and for H > He the c-director reorients within the 2/2 -plane, as shown schematically.

Notice, from the lists in equations (6.219) to (6.222), that rji only contains isotropic and smectic A-like viscosities, while 772 only consists of viscosities which are nematiclike or are involved with the coupling of the a and c vectors. Further, for a sample of SmC where the smectic tilt angle 0 can be considered small, we observe from the expressions in equations (6.223) to (6.226) that 7/1 is independent of whereas 772 may be approximated by... 

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. 

Fig. 10. The chiral smectic Chquid crystal stmcture. The director, n, rotates about the normal to the smectic layers, keeping the tilt angle. A, constant.

The compounds crystallise in noncentrosymmetric space groups namely PI, P2i, C2, and P2i2i2i (but with priority of P2i) due to the chirality of the molecules. Most of the compounds have a tilted layer structure in the crystalline state. The tilt angle of the long molecular axes with respect to the layer normal in the crystal phase of the compounds is also presented in Table 18. Some compounds show larger tilt angles in the crystalline state than in the smectic phase. In the following only the crystal structures of some selected chiral liquid crystals will be discussed. 

The layer spacing for smectic Ad and Cd phases significantly exceeds the molecular length (d/L = 1.35-1.65) and increases as the Ad<= Cd transition is approached from above. However, the temperature variations of the layer spacing in the Cd phase are very small in comparison to the classical smectic A-smectic C transition (Fig. 14). This unique behaviour results from the fact that both the tilt angles for different molecular moieties and the relative... 

Let us first consider the case where the preferred orientation of the polar director is perpendicular to the tilt plane (K > 0). The spatial variation of the layer normal and the nematic and polar directors is shown in Fig. 12. We see that regions of favorable splay (called blocks or layer fragments in Sect. 2) are intersected by regions of unfavorable splay (defects, walls). In the region of favorable splay the smectic layer is flat. In the defects regions the tilt angle decreases to reduce energy... 

As mentioned in Sect. 2.1, we consider a shear induced smectic C like situation (but with a small tilt angle, i.e., a weak biaxiality). We neglect this weak biaxiality in the viscosity tensor and use it in the uniaxial formulation given above (with the director h as the preferred direction). This assumption is justified by the fact that the results presented in this chapter do not change significantly if we use p instead of h in the viscosity tensor. 

Equation (39) shows that nematic degrees of freedom couple to simple shear, but not the smectic degrees of freedom the modulus of the nematic order parameter has a non-vanishing spatially homogeneous correction (see (39)), whereas the smectic order parameter stays unchanged. The reason for this difference lies in the fact that J3 and /3 include h and p, respectively, which coupled differently to the flow field (see (22) and (23)). Equation (38) gives a well defined relation between the shear rate y and the director tilt angle 9o, which we will use to eliminate y from our further calculations. To lowest order 0O depends linearly on y ... 

In the previous sections we have shown that the inclusion of the director of the underlying nematic order in the description of a smectic A like system leads to some important new features. In general, the behavior of the director under external fields differs from the behavior of the layer normal. In this chapter we have only discussed the effect of a velocity gradient, but the effects presented here seem to be of a more general nature and can also be applied to other fields. The key results of our theoretical treatment are a tilt of the director, which is proportional to the shear rate, and an undulation instability which sets in above a threshold value of the tilt angle (or equivalently the shear rate). 

C - nematic mesophase sequence, and in the case of n=12 the tilt angle of the smectic C phases decreased with temperature, resulting in the formation of an additional smectic A phase [73]. The phase transitions of these polymers are given in Table 13. WAXD studies of poly-(XX-n), n=2-7 confirmed that these polymers had a nematic phase. Some additional structural features in the X-ray pattern were interpreted as smectic C fluctuations. Poly-(XX-8), however, showed a smectic C mesophase similar to those of poly-(XX-n), n=9-12 [74]. 

Cholesteric liquid crystals are similar to smectic liquid crystals in that mesogenic molecules form layers. However, in the latter case molecules lie in two-dimensional layers with the long axes parallel to one another and perpendicular or at a uniform tilt angle to the plane of the layer. In the former molecules lie in a layer with one-dimensional nematic order and the direction of orientation of the molecules rotates by a small constant angle from one layer to the next. The displacement occurs about an axis of torsion, Z, which is normal to the planes. The distance between the two layers with molecular orientation differing by 360° is called the cholesteric pitch or simply the pitch. This model for the supermolecular structure in cholesteric liquid crystals was proposed by de Vries in 1951 long after cholesteric liquid crystals had been discovered. All of the optical features of the cholesteric liquid crystals can be explained with the structure proposed by de Vries and are described below. 

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