The Helical Smectic C State

The helical smectic C state has the point symmetry (< 22), illustrated in Fig. 19, which does not permit a polar vector. It is therefore neither pyroelectric nor ferroelectric. Nor can it, of course, be piezoelectric, which is also easily realized after a glance at Fig. 14 if we apply a pressure or tension vertically, i.e. across the smectic layers (only in this direction can the liquid crystal sustain a strain), we may influence the pitch of the helix but no macroscopic po-... 

Figure 19. The point symmetry of the helical smectic C state is ) (o<>22) illustrated by a twisted cylinder. The principal rotation axis is along the smectic layer normal and there are an infinite number of twofold rotation axes perpendicular to this axis, one of them illustrated to the right. The symmetry does not allow pyroelectricity.

Figure 51. (a) In the helical smectic C state the constant tilt 0 changes its azimuthal direction such that

linear function in the coordinate z along the layer normal, (b) The c director is a two component vector (c , Cy) of magnitude sin 0, which is the projection of n on the smectic layer plane, (c) P makes a right angle with the tilt direction. The P direction here corresponds to a material with Pq>0-... 

In the helical smectic C case, again with (p z) = qz, the director components were stated in Eq. (141)... 

A helical director field also occurs in the chiral smectic-C phase and those smectic phases where the director is tilted with respect to the layer normal (Figure 1.13(c)). In these cases, the pitch axis is parallel to the layer normal and the director inclined with respect to the pitch axis. Very complicated defect structures can occur in the temperature range between the cholesteric (or isotropic) phase and a smectic phase. The incompatibility between a cholesteric-like helical director field (with the director perpendicular to the pitch axis) and a smectic layer structure (with the layer normal parallel or almost parallel to the director) leads to the appearance of grain boundaries which in turn consist of a regular lattice of screw dislocations. The resulting structures of twist grain boundary phases are currently extensively studied. The state of the art in this topical field is summarized in Chapter 10. 

X-ray measurements on LC elastomers have shown [6-8] that the reversible transition between a chiral smectic C phase with and without a helical superstructure can be induced mechanically. The helix untwisted state corresponds in this case to a polar ferroelectric monodomain. The piezoelectricity arising from this deformation of the helical superstructure (which does not require a complete untwisting) has been demonstrated [9] for polymers cross-linked by polymerization of pendant acrylate groups (Figure 15). 

Figure 14. Idealized presentation of the orientation process, which leads to piezoelectricity in chiral smectic C elastomers (only the mesogens are shown) [28], P macroscopic polarization). The deformed states with a partially unwound helix (left and right) are prepared from the ground state with a helical superstructure (middle) by mechanical forces. 0 and direction of the spontaneous polarization in and out of the plane of drawing, respectively.

More recently, it has been theoretically predicted by Brand [81] that elastomeric networks that have chiral nematic or smectic C mesophases should have piezoelectric properties. The non-centro-symmetric material responds to the deformation via a piezoelectric response. Following this prediction, both Finkelmann and Zental have reported the observation of piezoelectricity. In one case, a nematic network was converted to the cholesteric form with the addition of CB15, 2 -(2-methylbutyl)biphenyl-4-carbonitrile [82]. By producing a monodomain, it is possible to measure the electro-mechanical or piezoelectric response. Compression leads to a piezoelectric coefficient parallel to the helical axis. Elongation leads to the perpendicular piezoelectric response. As another example, a network with a chiral smectic C phase that possesses ferroelectric properties can also act as a piezoelectric element [83]. Larger values of this response might be observed if crosslinked in the Sc state. 

We can answer the last question if consider a constraction of the so-called surface stabilised ferroelectric liquid crystal cell or simply SSFLC ceU [9]. Such SSFLC cell is only few micrometers thin and, due to anchoring of the director at the surfaces, the intrinsic helical stmcture of the SmC is unwound by boundaries but a high value of the spontaneous polarisation is conserved. The cell is con-stracted in a way to realise two stable states of the smectic C liquid crystal using its interaction with the surfaces of electrodes, see Fig. 13.6a. First of all, in the SSFLC cell, the so-called bookshelf geometry is assumed the smectic layers are vertical (like books) with their normal h parallel the z-axis. Then the director is free to rotate along the conical surface about the h axis as shown in Fig. 13.6b (Goldstone mode). It is important that, to have a bistability, the director should be properly... 

The deformed helical ferroelectric (DHF) effect. If the voltage applied to the smectic C phase is lower than the untwisting field value, the helix is not completely suppressed but only distorted (Fig. 14). For a square voltage, there will be an alternation between two deformed helical states, and optically it appears as switching of the refractive index ellipsoid [6,121). In contrast to ferroelectric switching, the response time for the DHF effect is independent of... 

The helical structure which can develop in thick cells of chiral smectic C phases having planar surface alignment conditions can be used to obtain measurements of the components of the dielectric permittivity tensor [29], but the technique is restricted to chiral smectic phases. Measurements are made (see Fig. 9) of the homeotropic state, as above, and additionally the helical state (Fig. 12), and the uniformly-tilted state ob-... 

Figure 16. Elastic unwinding, by the surfaces, of the helical twist in the bookshelf geometry of smectic C. The helical bulk state is incompatible with the surface conditions and therefore can never appear in sufficiently thin cells. The surface acts as an external symmetry breaking agent, reducing the degeneracy of the bulk to only two selected states. In the most attractive case these are symmetric, which also leads to a symmetric bistability of the device. The two memorized director states, and 2 n 2 in the case of a...

As already pointed out, one condition for achieving the fast bistable switching and all the additional characteristic properties is to get rid of the antiferroelectric helix (to use the expression employed in the 1980 paper [93]). Therefore, achieving the same properties by adding appropriate chiral dopants to the smectic C could be imagined, in order to untwist the helical structure but, as the same time, keeping a residual polarization. This is illustrated by the structure to the left in Fig. 22. However, such a hypothetical bulk structure is not stable in the chiral case. It would transform to a twisted state where the twist does not take place from layer to layer, but in the layers, in order to cancel the macroscopic polarization. For this reason, surface-stabilization requires not only that dsample thickness is sufficiently small to prevent the ap-... 

Equation (378) reveals that the helical state of the smectic C is effectively uniaxial, if the pitch is sufficiently short to al-... 

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