SmC Phase

This transition is usually second order [18,19 and 20]. The SmC phase differs from the SmA phase by a tilt of the director with respect to the layers. Thus, an appropriate order parameter contains the polar (0) and azimuthal ((]i) angles of the director ... 

A point at which nematic, SmA and SmC phases meet was demonstrated experimentally in the 1970s [95, 96]. The NAC point is an interesting example of a multicritical point because lines of continuous transition between N and... 

SmA phases, and SmA and SmC phases, meet tlie line of discontinuous transitions between tire N and SmC phase. The latter transition is first order due to fluctuations of SmC order, which are continuously degenerate, being concentrated on two rings in reciprocal space ratlier tlian two points in tire case of tire N-SmA transition [18,19 and 20], Because tire NAC point corresponds to the meeting of lines of continuous and discontinuous transitions it is an example of a Lifshitz point (a precise definition of tliis critical point is provided in [18,19 and 20]). The NAC point and associated transitions between tire tliree phases are described by tire Chen-Lubensky model [97], which is able to account for tire topology of tire experimental phase diagram. In tire vicinity of tire NAC point, universal behaviour is predicted and observed experimentally [20]. 

Fig. 2 Schematic representation of the molecular arrangement in the A nematic B smectic A (SmA) and C smectic C (SmC) phases...

Fig. 8 Optical micrograph of a a nematic phase, b a SmA phase (reproduced with kind permission of the American Chemical Society) and c a SmC phase (reproduced with kind permission of the copyright owner, D.W. Bruce)... 

Consider the graphic representation of a SmC phase shown in Figure 8.4. It is understood that there are an infinite number of smectic layers, which... 

Figure 8.4 Illustration showing layer normal (z), director (n), and other parts of the SmC structure. Twofold rotation axis of symmetry of SmC phase for singular point in center of layer is also illustrated. There is also mirror plane of symmetry parallel to plane of page, leading to C2h designation for the symmetry of phase. This phase is nonpolar and achiral.

Polar structures may have rotation symmetry and reflection symmetry. However, there can be no rotation or reflection normal to the principal rotation axis. Thus, the presence of the mirror plane normal to the C2 axis precludes any properties in the SmC requiring polar symmetry the SmC phase is nonpolar. 

Molecular chirality, however, proved an extremely powerful tool in the quest for polar LCs. In 1974 Robert Meyer presented to participants of the 5th International Liquid Crystal Conference his now famous observation that a SmC phase composed of an enantiomerically enriched compound (a chiral SmC, denoted SmC ) could possess no reflection symmetry.1 This would leave only the C2 symmetry axis for a SmC a subgroup of C. The SmC phase is therefore necessarily polar, with the polar axis along the twofold rotation axis. 

Figure 8.5 gives the structure of the molecular subject of this classic study, decyloxybenzylideneaminomethylbutylcinnamate (DOBAMBC, 2). DOBAMBC possesses the archetypal FLC molecular structural features A rigid core with two flexible tails, one of which possesses a stereogenic center. A classic theoretical treatment of the SmC phase from 1978 by Durand et al. suggested that a zigzag conformation of the LC molecules is important.9... 

On heating from a crystalline phase, DOBAMBC melts to form a SmC phase, which exists as the thermodynamic minimum structure between 76 and 95°C. At 95°C a thermotropic transition to the SmA phase occurs. Finally, the system clears to the isotropic liquid phase at 117°C. On cooling, the SmC phase supercools into the temperature range where the crystalline solid is more stable (a common occurrence). In fact, at 63°C a new smectic phase (the SmF) appears. This phase is metastable with respect to the crystalline solid such phases are termed monotropic, while thermodynamically stable phases are termed enantiotropic. The kinetic stability of monotropic LC phases is dependent upon purity of the sample and other conditions such as the cooling rate. However, the appearance of monotropic phases is typically reproducible and is often reported in the phase sequence on cooling. It is assumed that phases appearing on heating a sample are enantiotropic. 

Figure 8.6 Three-dimensional slice of C2 symmetrical SmC phase, showing tilt cone, polar axis (congruent with twofold symmetry axis), smectic layer planes, tilt plane, and polar plane.

Since P must remain normal to z and n, the polarization vector forms a helix, where P is everywhere normal to the helix axis. While locally a macroscopic dipole is present, globally this polarization averages to zero due to the presence of the SmC helix. Such a structure is sometimes termed a helical antiferroelectric. But, even with a helix of infinite pitch (i.e., no helix), which can happen in the SmC phase, bulk samples of SmC material still are not ferroelectric. A ferroelectric material must possess at least two degenerate states, or orientations of the polarization, which exist in distinct free-energy wells, and which can be interconverted by application of an electric field. In the case of a bulk SmC material with infinite pitch, all orientations of the director on the tilt cone are degenerate. In this case the polarization would simply line up parallel to an applied field oriented along any axis in the smectic layer plane, with no wells or barriers (and no hysteresis) associated with the reorientation of the polarization. While interesting, such behavior is not that of a true ferroelectric. 

Along with the prediction and discovery of a macroscopic dipole in the SmC phase and the invention of ferroelectric liquid crystals in the SSFLC system, the discovery of antiferroelectric liquid crystals stands as a key milestone in chiral smectic LC science. Antiferroelectric switching (see below) was first reported for unichiral 4-[(l-methylheptyloxy)carbonyl]phenyl-4/-octyloxy-4-biphenyl carboxylate [MHPOBC, (3)],16 with structure and phase sequence... 

In fact, as also indicated in Figure 8.12, an achiral SmC phase possesses antiparallel polarized sheets, in this case with a pitch of half the layer spacing. Photinos and Samulski have made much of this polar symmetry of the SmC phase,28 but neither the SmCA nor the SmC phases have net macroscopic polar symmetry (the SmCA is Di/, while the SmC is C21, as mentioned above), and thus neither shows properties associated with polar materials (e.g., a pyroelectric effect). 

Figure 8.12 Longitudinal sheets with antiparallel polar symmetry are illustrated for achiral SmCA and SmC phases. Since it is not possible to switch to ferroelectric state in such system upon application of electric field, these structure should not be considered antiferroelectric.

Apparently this switching mode is disfavored since, in fact, the chirality of the layers does not change upon switching to the ferroelectric state rather the layer interface clinicity changes. This occurs when the molecules in alternate layers simply precess about the tilt cone in a manner exactly analogous to antiferroelectric to ferroelectric switching in the chiral SmC phase. As shown in Figure 8.25, the ferroelectric state obtained from the ShiCsPa antiferroelectric phase is a ShiCaPf structure, an achiral macroscopic racemate with anticlinic layer interfaces. 

Chirality (or a lack of mirror symmetry) plays an important role in the LC field. Molecular chirality, due to one or more chiral carbon site(s), can lead to a reduction in the phase symmetry, and yield a large variety of novel mesophases that possess unique structures and optical properties. One important consequence of chirality is polar order when molecules contain lateral electric dipoles. Electric polarization is obtained in tilted smectic phases. The reduced symmetry in the phase yields an in-layer polarization and the tilt sense of each layer can change synclinically (chiral SmC ) or anticlinically (SmC)) to form a helical superstructure perpendicular to the layer planes. Hence helical distributions of the molecules in the superstructure can result in a ferro- (SmC ), antiferro- (SmC)), and ferri-electric phases. Other chiral subphases (e.g., Q) can also exist. In the SmC) phase, the directions of the tilt alternate from one layer to the next, and the in-plane spontaneous polarization reverses by 180° between two neighbouring layers. The structures of the C a and C phases are less certain. The ferrielectric C shows two interdigitated helices as in the SmC) phase, but here the molecules are rotated by an angle different from 180° w.r.t. the helix axis between two neighbouring layers. 

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