Structure of the Smectic C Phase

In the smectic C phase the constituent molecules are arranged in diffuse layers 

The molecules within the layers are locally hexagonally close-packed with respect to the director of the phase however, this ordering is only short range, extending over distances of approximately 1.5 nm. Over large distances, therefore, the molecules are randomly packed, and in any one domain the molecules are tilted roughly in the same direction in and between the layers (see Fig. 11). Thus, the tilt orientational ordering between successive layers is preserved 

A sub-phase of the smectic C phase also exists which is called (for the moment) the alternating smectic C (SmCai,) phase [55-57]. This phase was originally discovered by Levelut et al. [55] and given the code letter smectic O. However, the chiral version of this phase was labelled as being an antiferroelectric smectic C phase by Fuku-da [58], and it is this descriptor that is in current, general use. Consequently, the achiral modification of the antiferroelectric phase requires a matching code letter, and therefore, for the present we have opted to use smectic C i, as this term best describes the structure of the phase in relation to the antiferroelectric label. 

The in-plane ordering of the molecules is thought to be identical to that of the smectic C phase. The major difference between the alternating C and normal smectic C phases resides in the relationship between the tilt directions in successive layers. In the alternating tilt phase the tilt direction is rotated by 180° on passing from one layer to the next [56]. Thus the tilt direction appears to flip from one layer to the next, thereby producing a zig zag layered structuring. Consequently, the director of the phase is effectively normal to the layer planes, as shown in Fig. 12. However, there appear to 

In addition to the alternating smectic C sub-phase, other sub-phases of the smectic C phase can be found for systems where the molecules carry terminal polar groups (e.g. cyano) [3]. These sub-phases are identical to those of the smectic A phase, except for the fact that the molecules are tilted with respect to the layer planes. Thus, the smectic Cj, C2, Cd and C phases are the direct analogues of the A, A2, Ad and A phases respectively [59, 60]. The sub-phases of smectic C can therefore be described in exactly the same way  

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As mentioned earlier, the helical structure of the smectic C phase should be untwisted by an electric or magnetic field, or suppressed by a surface effect, to observe ferroelectric properties of the phase. In the first publication on ferroelectric liquid crystals [5] an approach to nontwisted ferroelectric LC materials was suggested. By mixing two individual ferroelectric liquid crystals having opposite signs of P but different absolute values, one can compensate the helical twisting without zeroing the polarization. That has been done for low-molar-mass liquid crystals... 

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]. 

In addition to the homopolyesters 80a-i, 81a-i and 82a-i, three classes of co PEIs were studied 83a-g [24], 84a-d and 85a-f [84]. The combination of two different alkane spacers did not significantly change the properties of the co PEIs 83a-d, when compared to 82i. However, when the difference on their length increased, a destabilization of the smectic layer-structures became evident, with the consequence that a nematic phase was formed on top of the smectic-C phase... 

In the helical structure, the optical ellipsoid of the smectic C phase rotates together with the tilt plane. Like in cholesterics, we can imagine that helical turns form a stuck of equidistant quasi-layers that results in optical Bragg reflections in the visible range. Therefore, like cholesterics, smectic C liquid crystals are onedimensional photonic crystals. However, in the case of SmC, the distance between the reflecting layers is equal to the full pitch Pq and not to the half-pitch as in cholesterics, because at each half-pitch the molecules in the SmC are tilted in opposite directions. Hence, we have a situation physically different from that in cholesterics. 

Monoclinic and triclinic crystals have the lowest number of symmetry elements, and the smectic C phase also has a monoclinic symmetry. Therefore, the symmetry of alignment layers with monoclinic and triclinic crystal structures resembles the symmetry of the smectic C phase. It is plausible to think that the epitaxial growth of a smectic C liquid crystal proceeds most smoothly on alignment layers which resemble their crystallographic structures [12,13]. 

Essentially, the structural features described above apply to both non-chiral and chiral compounds. However, the presence of chiral molecules in smectic- and C phases results in additional properties and structures not present in phases of nonchiral substances. These are the ferroelectric properties and the electroclinic effect, which will be discussed in detail in Sections 8.3 and 8.4, and the helical structure in the smectic-C phase. 

The molecular theory of Van der Meer and Vertogen is based on a specific molecular model that is not in contradiction with experiment. At the same time Barbero and Durand [89] have shown that the molecular tilt is an intrinsic property of any layered quadrupolar structure. This idea has been used by Poniwierski and Sluckin in their model [84] that presents a rather general mechanism for the stabilization of the smectic C phase. It is interesting to note that the mathematical form of the interaction potential in the Poniwierski-Sluckin theory is similar to the potential (Eq. 85). The energy of electrostatic interaction between two axial quadrupoles, employed in [84], can be written as... 

There are a variety of ways in which the space or environmental symmetry and asymmetry can be expressed in liquid crystals, with the most commonly discussed system being that of the chiral smectic C phase. Thus, for the purposes of describing space symmetry in liquid crystals, the structure and symmetry properties of the smectic C phase will be described in the following sections [5, 6]. 

Figure 6. Comparison of the local structures of the smectic C and the ferroelectric smectic C phases.

On a macroscopic scale, the spontaneous polarization vector in the optically active phase spirals about an axis perpendicular to the smectic layers (Fig. 20), and sums to zero. This macroscopic cancellation of the polarization vectors can be avoided if the helical structure is unwound by surface forces, by an applied field, or by pitch compensation with an oppositely handed dopant. The surface stabilized ferroelectric liquid crystal display utilizes this structure and uses coupling between the electric field and the spontaneous polarization of the smectic C phase. The device uses a smectic C liquid crystal material in the so-called bookshelf structure shown in Fig. 21a. This device structure was fabricated by shearing thin (about 2 i,m) layers of liquid crystal in the... 

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