Nematic mesophase biaxial

Note 3 In lyotropic systems, biaxial nematic mesophases have been identified from the biaxial symmetry of their tensorial properties. 

Note 2 Short board-like shaped molecules usually form biaxial nematic mesophases. It is recommended that the use of the term disordered sanidic mesophases for such mesophases be discontinued (see Definition 3.3.1, Note 5). 

There exists a more complicated situation for boardshaped molecules. The mesophase composed of board-shaped molecules is characterized by long-range ordering of both the longer and the shorter molecular axes. In this case, a biaxial nematic mesophase is realized (Table 2). 

In biaxial nematic mesophases, the rotational symmetry of the phase around its director n is broken. It is commonly understood that the term biaxial nematic refers to an orthorhombic nematic phase. With respect... 

Here the first term suppresses local density fluctuations [73,74] and the rest is an analog of the Ginzburg-Landau free energy associated with the instantaneous tensorial fields Q and B. Phenomenological parameters V,]i and A entering this functional are normally chosen such that the thermodynamic state of interest, e.g., a biaxial-nematic mesophase, is reproduced. In this respect, mean-field estimates can help to limit the physically adequate parameter ranges. Positive isothermal compressibility, for example, requires k >V + Ji + A [64]. 

Note 1 See Fig. 16 for an illustration of the molecular arrangement in a Nb mesophase. Note 2 From a crystallographic point of view, the biaxial nematic structure is characterised by the symbol D2h in the Schoenflies notation (2 m, m in International System). 

Note 5 A biaxial nematic has the same structure as a disordered sanidic mesophase (see Definition 3.4, Note 2) it is recommended that the latter name be discontinued and the name biaxial nematic be used. 

Note 1 See 3.1.1 for the definition of a uniaxial nematic mesophase, 5.8.1 for the definition of uniaxial mesophase anisotropy, and Definitions 3.3 and 5.8.2 relating to biaxial mesophases. 

Molecules which combine the features of the rod and the disc may be expected to form new types of mesophases. An example is the biaxial nematic phase reported in thermotropic systems (see 6.6). Malthete et a/. have prepared an interesting series of mesogens shaped like stick insects called phasmids (fig. 6.1.5(n)). Some of them form columnar mesophases the structure proposed for the hexagonal phase is shown schematically in fig. 6.1.5( >). 

There is also a group of the so-called lyotropic nematics. They are intermediate between the isotropic micellar phase and structured (lamellar or hexagonal) phases and can be formed by both discotic and calamitic molecules. The lyotropic nematics can be aligned by an electric or magnetic field and show Schlieren texture as thermotropic nematics. The building blocks of these mesophases are vesicles or similar mesoscopic objects. From the symmetry point of view the nematic phases can be uniaxial or biaxial, as shown in Fig. 4.22. In fact, the biaxial nematics have been found unequivocally only in the lyotropic systems [13]. 

The mesophases differ from each other regarding the positional order of the molecules (Fig. l). In the nematic phase there is no long range positional order at all just as in isotropic liquids. Nematics are normally uniaxial, however biaxial nematics were discovered very recently. In the smectic phases the centre of masses of the molecules are concentrated in layers forming a one-dimensional density wave. In the smectic A and C phases there is no long-range positional order within the layers. The smectic A phase is uniaxial, the director (n) is parallel with the layer normal, 1. In the C phase the director is tilted with respect to the layer normal. This phase is biaxial although the deviation from uniaxiality is usually small. There are further smectic phases in which the molecules form two-dimensional lattices within the layers (ordered smectic phases). The difference between ordered... 

As mentioned in Section 3.1, phase biaxiality may be described by a set of microscopic order parameters when the mesogen is a rigid uniaxial particle, where a and (5 refer to the space-fixed axes x y z). Biaxial nematics [3.31], some smectic phases, like smectic C, and certain discotic phases [3.32] exhibit phase biaxiality. The order parameters 5, , and 5, , are different in these phases. NMR may be used to detect phase biaxiality through measurement of a non-zero motionally induced asymmetry parameter in nuclear spin interactions such as dipole-dipole and electric quadrupole interactions. To see how exists in biaxial mesophases, the previous discussion on motional averaging of spin Hamiltonian is gen-... 

Note 3 The tensorial properties of a biaxial mesophase have biaxial symmetry unlike the uniaxial symmetries of, for example, the nematic and smectic A mesophases. 

A variety of systems exhibit liquid crystalline properties and a rich variety of phases that have been investigated by NMR have been reported. Particularly, molecules exhibiting unusual topologies different from the usual rod like structure such as bent-core or hockey stick-shape have been of significant interest. The biaxial nature of some of these systems has also attracted much attention. Here, reports of studies on the above systems as well as studies on molecules exhibiting nematic, smectic, columnar or lyotropic mesophases and the study of orientational order in such systems have been included. 

The orthogonal arrangement of the disc-like molecules in the columns of and D id phases makes these phases uniaxial, while the tilted phases (Drd and Doh.d and Dt) are optically biaxial. There are two additional columnar phases labeled as and that have not yet been classified. The columnar phases were discovered before the observation of a nematic phase for disc-like molecules. Both chiral nematic phases and the re-entrant behavior have now been observed in discotics. The phase diagram and molecular structure of a typical discotic liquid crystal are shown in Fig. 1.11. Finally, it is noted that another classification scheme for the discotic mesophases has been used [1.26], which is based on the notation used for the conventional smectics. 

Intermicellar forces are generally of a repulsive nature (i.e., charged amphiphiles) and a reduction of such repulsion accompanies the transformation from spherical to cylindrical micelles. Further increase of concentration results in the formation of linear assemblies and liquid crystalline lyotropic mesophases (cf. Section ni.B). Not only nematic (Nc and Nd from rodlike or disklike shapes, respectively), hexagonal, and smectic phases, but also biaxial (mixtures of Nc and Nd) and complex cubic phases (bicontinuous networks or plastic crystals)... 

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