Smectic phase symmetry

NMR is not the best method to identify thennotropic phases, because the spectmm is not directly related to the symmetry of the mesophase, and transitions between different smectic phases or between a smectic phase and the nematic phase do not usually lead to significant changes in the NMR spectmm [ ]. However, the nematic-isotropic transition is usually obvious from the discontinuous decrease in orientational order. NMR can, however,... 

As for crystals, tire elasticity of smectic and columnar phases is analysed in tenns of displacements of tire lattice witli respect to the undistorted state, described by tire field u(r). This represents tire distortion of tire layers in a smectic phase and, tluis, u(r) is a one-dimensional vector (conventionally defined along z), whereas tire columnar phase is two dimensional, so tliat u(r) is also. The symmetry of a smectic A phase leads to an elastic free energy density of tire fonn [86]... 

Moreover, the new smectic phases with the broken head-to-tail inversion symmetry (of the type of A, A2, A, etc.) and the re-entrant effects (i.e. the reentrance of the less ordered phase at temperatures below those of a more ordered phase) were found among strongly asymmetric mesogens [11-13, 30] (Fig. 2). These observations indicate that with asymmetric molecules, dipolar and steric interactions are important for the liquid crystalline behaviour. 

In this section we will discuss in some detail the application of X-ray diffraction and IR dichroism for the structure determination and identification of diverse LC phases. The general feature, revealed by X-ray diffraction (XRD), of all smectic phases is the set of sharp (OOn) Bragg peaks due to the periodicity of the layers [43]. The in-plane order is determined from the half-width of the inplane (hkO) peaks and varies from 2 to 3 intermolecular distances in smectics A and C to 6-30 intermolecular distances in the hexatic phase, which is characterized by six-fold symmetry in location of the in-plane diffuse maxima. The lamellar crystalline phases (smectics B, E, G, I) possess sharp in-plane diffraction peaks, indicating long-range periodicity within the layers. 

A number of experiments performed since the late 1970s [11-13, 301 found a variety of smectic phases with a broken head-to-tail symmetry among mesogens possessing strongly polar cyano or nitro terminal groups (Fig. 6). 

The smectic phases Ai, A2 and A have the same macroscopic symmetry, differing from each other in the wavelength of spacing. Hence it is possible to go from Ai to Aa or from Aa to A2 by varying only the layer periodicity in a continuous or discontinuous way(with the jump in the layer spacing d). Smectic-smectic transition lines of first order may terminate at a critical point, where the differences between the periodicities of the smectic A phases vanish, providing a continuous evolution from an Aa to bilayer A2 phase [12]. 

We note that the bilayer smectic phase which may be formed in main-chain polymers with two odd numbered spacers of different length (Fig. 7), should also be polar even in an achiral system [68]. This bilayer structure belongs to the same polar symmetry group mm2 as the chevron structure depicted in Fig. 17b, and macroscopic polarization might exist in the tilt direction of molecules in the layer. From this point of view, the formation of two-dimensional structure of the type shown in Fig. 7, where the polarization directions in neighbouring areas have opposite signs, is a unique example of a two dimensional antiferroelectric structure. 

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

The structure of the B6 phase is also illustrated in Figure 8.17. This achiral, orthogonal smectic phase is one of the class of intercalated smectics wherein the layer spacing is actually about half the molecular length. This phase, which has full translational symmetry within the layers, has the same symmetry (D2h), and the same basic structure as the all-anticlinic SmCA phase. Intercalated SmCA phases of this type were first described in pioneering work of Watanabe in main-chain polyesters.37... 

Figure 8.20 Structure and phase sequence of prototypical bent-core mesogen NOBOW (8) are given, along with space-filling model showing one of many conformational minima obtained using MOPAC with AMI force field. With observation by Tokyo Tech group of polar EO switching for B2 smectic phases formed by mesogens of this type, banana LC field was bom. Achiral, polar C2v layer structure, with formation of macroscopic spontaneous helix in polarization field (and concomitant chiral symmetry breaking), was proposed to account for observed EO behavior.

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. 

Soft non-spherical potentials are one step towards a more realistic model. Luckhurst et al. [413] have used a potential having the prolate spheroidal symmetry discussed above but which is based on the well known Lennard-Jones or twelve-six potential. This involves an attractive 1/r6 potential based on London forces and a repulsive 1/r12 potential. Once again it is possible to predict the existence of a smectic phase. 

The free energy density terms introduced so far are all used in the description of the smectic phases made by rod-like molecules, the electrostatic term (6) being characteristic for the ferroelectric liquid crystals made of chiral rod-like molecules. To describe phases made by bent-core molecules one has to add symmetry allowed terms which include the divergence of the polar director (polarization splay) and coupling of the polar director to the nematic director and the smectic layer normal ... 

Thermotropic liquid crystals can then be furflier subdivided into high molecular mass, main and side-chain polymers [10] and low molecular mass, the latter class of compounds being one of the areas of this review. The phases exhibited by the low molecular mass molecules are then properly described with reference to the symmetry and/or supramolecular geometry of the phases, which are briefly introduced here and are discussed in more detail further below. Thus, the most disordered mesophase is the nematic (N), which is found for calamitic molecules (N), discoidal molecules (Nq) and columnar aggregates (Nc), among others. The more ordered lamellar or smectic phases (S) [11, 12] are commonly shown by calamitic molecules, and there exists a variety of such phases distinguished by a subscripted letter (e. g. Sa, Sb)- Columnar phases (often, if incorrectly, referred to as discotic phases) may be formed from stacks of disc-like molecules, or from... 

The local symmetry of smectic A phase is the same as that of the nematics, be., its point group is D h, while the symmetry of the smectic C phase is ( b/, (a ( 2 symmetry axis plus a reflection plane perpendicular to the axis). In addition, both smectic phases exhibit a one-dimension translational order. Owing to the difference in symmetry, the smectic phases show different optical properties. The smectic A phase is optically uniaxial, but the smectic C phase is optically biaxial. 

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