Uniform Smectic

This is a chiral smectic A with symmetry Dqo. Its properties are similar to those of the achiral SmA. However, close to the transition to the smectic C phase, the chiral smectic A phase shows interesting pretransitional phenomena in the dielectric and electrooptical effects (the so-caUed soft dielectric mode and electroclinic effect). They will be discussed in Chapter 13. 

---

Quite recently, Finkelmann and co-work-ers [232, 233] showed that an appropriate mechanical deformation of an SmC elastomer 50 yields a permanent macroscopically uniform orientation. This process also unwinds the helicoidal superstructure, and accordingly, frequency doubling is observed where the intensity of the SHG is directly related to the perfection of the uniform smectic layer orientation. The 22 < 23= 34 coefficients for a highly oriented sample were reported to be 0.1 pm/V and 0.15 pm/V, respectively. Taking into account that only 50% of the mesogenic units in the LC elastomer are active groups, these values are of the same order as those reported for low molar mass LCs containing similar chromophores [222]. 

It is very instructive to consider a behaviour of the smectic layers attached to a corrugated surface. This would explain why the uniform smectic phase is much more transparent than the nematic phase. The geometry is shown in Fig. 8.25a. A solid substrate is assumed to have a (Mie-dimensional cosine-form relief ... 

The results of an investigation of the electric-field-induced transition between these two phases is shown in Fig. 9 [56]. At any given temperature the short pitch helix of TGBA is unwound by the field and either a uniform smectic C structure (I) or a modulated one in the form of stripes (II) or parquet (III) appears. The slope of the boundary between the TGBA and SmC phases can be explained by the Clausius-Clapey-ron equation (Eq. (9)) where, in this case, AP=Es(C ) as Ps(TGBA)=0. Note that the transition temperature from TGBA to the isotropic phase is, in fact, field independent due to the much higher enthalpy of that transition. 

Note 2 For a smectic mesophase, the term monodomain also implies a uniform arrangement of the smectic layers. 

Note 1 In the equation for g, the term go is usually equal to zero because the undistorted state of nematics is the state of uniform alignment. However, for chiral nematics, a nonzero value of go allows for the intrinsic twist in the structure. In order to describe g for smectic phases, an additional term must be added, due to the partially solid-like character of the smectic state and arising from positional molecular deformations. 

Early work predicted smectic (or lamellar) ordering in rod-coil copolymers (Semenov 1991 Semenov and Vasilenko 1986). In liquid crystals, a smectic A phase is a lamellar phase where the molecules are, on average, parallel to the layer normal. In a smectic C phase, the molecules are tilted with respect to this direction. The imbalance in interfacial area per chain for a rod or coil can lead to tilting of chains to maintain uniform density. Semenov (1991) constructed a phase diagram for rod-coil copolymers in which second-order phase transitions... 

The Oseen theory embraces smectic mesophases, but is not really required for this case. The interpretation of the equilibrium structures assumed by smectic substances under a particular system of external influences may be carried out by essentially geometric arguments alone. The structures are conditioned by the existence of layers of uniform thickness, which may be freely curved, but in ways which do not require a breach of the layering in regions of greater extension than lines. These conditions automatically require the layers to be Dupin cyclides and the singular lines to be focal conics. Nothing, essentially, has been added... 

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. 

In the b orientation in Fig. 10-28b, uniform shear tends to rotate the layers and change their spacing. Since the layer spacing is a solid-like property of the smectic phase, shearing in this orientation should produce a solid-like material response, at least for shearing stresses... 

Figure 10.29 Response of an aligned smectic to layer dilation, (a) Initial equilibrium sample, (b) For a very small dilation Sh < Ink, the layer spacing simply increases, (c) A uniform rotation of the layers decreases the spacing toward that of equilibrium, but doesn t satisfy the boundary conditions, (d) Hence, the sample undergoes an mdulational instability, which also narrows the layer spacing while satisfying homeotropic boundary conditions, (e) For a large enough dilation, the undulation instability leads to formation of parabolic focal conic defects. (From Rosenblatt et al. 1977, with permission from EDP Sciences.)...

The synthesis described in this paper renders possible the preparation of block copolymers of uniform molecular weight composed of amorphous and LC side chain blocks. Beside the specific cholesterol mesogen introduced by carbonate linkages leading to a smectic system other mesogens with various spacer lengths can be introduced, e.g. by esterification. 

Fig. 14 Image of smectic blue phase based on uniform layer spacing of the Schwartz P surface [38]...

Almost all the smectic phases, in which the molecules are arranged in layers and are tilted with respect to the layers, have counterpart chiral phases. The most important one of this class is the chiral smectic C phase — Sc phase. In these chiral liquid crystal phases, the molecules are tilted at a constant angle with respect to the layer normal but the tilt azimuthal rotates uniformly along the chiral axis and forms a helical structure. 

Fig. 6. However, these two structures are incompatible with one another and cannot co-exist and the molecules still fill space uniformly without forming defects. The matter is resolved by the formation of a periodic ordering of screw dislocations which enables a quasi-helical structure to co-exist with a layered structure. This is achieved by having small blocks/sheets of molecules, which have a local smectic structure, being rotated with respect to one another by a set of screw dislocations, thereby forming a helical structure [15]. As the macroscopic helix is formed with the aid of screw dislocations, the dislocations themselves must be periodic. It is predicted that rows of screw dislocations in the lattice will form grain boundaries in the phase, see Fig. 7, and hence this structurally frustrated phase, which was theoretically predicted by Renn and Lubensky [15], was called the twist grain boundary (TGB).

---