Uniaxial nematic mesophase

Note 1 See Fig. 1 for an illustration of the molecular organization in a uniaxial nematic mesophase. 

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. 

Mesophase with a helicoidal superstructure of the director, formed by chiral, calamitic or discotic molecules or by doping a uniaxial nematic host with chiral guest molecules in which the local director n precesses around a single axis. 

Note 1 Locally, a chiral nematic mesophase is similar to a uniaxial nematic, except for the precession of the director n about the axis, Z. 

In an anisotropic medium such as a nematic mesophase or a uniaxially stretched medium film, /(0) is given by... 

Proton, deuteron and carbon spin relaxation measurements of liquid crystals have provided detailed information about the molecular motions of such anisotropic liquids (anisotropic rotation and translation diffusion of individual molecules), and about a peculiar feature of liquid crystalline phases, namely collective molecular reorientations or order fluctuations. Spin relaxation in liquid crystalline mesophases has challenged NMR groups since the early 1970s, shortly after the publication of theoretical predictions that order fluctuations of the director (OFD, OF), i.e. thermal excitations of the long-range orientational molecular alignment (director), may play an important unusual role in nuclear spin relaxation of ordered liquids. Unique to these materials, which are composed of rod-like or disc-like (i.e. strongly anisotropic molecules), it was predicted that such thermal fluctuations of the director should, at the frequencies of these fluctuation modes, produce rather peculiar Ti(p) dispersion profiles. For example in the case of uniaxial nematic... 

For the purpose of this article, we focus our attention on the nematic mesophase smectic orders are more crystal-like and thus are beyond our scope. Typical nematic liquid crystals are characterized by a uniaxial order, though imperfect, along the preferred axis of the domain. No such long-range order exists in directions transverse to the domain axis. In most examples, low molar mass (monomer) liquid crystals carry flexible tails. Conformational ordering of these tails in the mesophase has been extensively studied in relation to the odd-even character of the phase behavior with the number of constituent atoms of the pendant chain. Various statistical models and theories have been presented [52-57]. In most cases, however, the ordering of the tail is relatively weak [58,59]. 

Essentially all of the techniques developed to characterize MLCs can be applied to PLCs with the realization that phenomena that are dependent on reorientation processes in the liquid crystal must be considered on considerably longer time scales in a PLC. Underlying most of the physical measurements performed on liquid crystals is the relationship between the observed anisotropic properties of the mesophase and orientational order of the mesogen. For uniaxial nematic phases and idealized low molar mass mesogens (cylindrical molecules), this relationship is embodied in the following equation ... 

As a result of the chain structure of the macromolecules, they may exhibit not only uniaxial order observed in the nematic mesophase but also the orientational polar order. The physical value directly characterizing the orientational polar order in a chain molecule is its dipole moment. If the monomer unit exhibits a dipole moment directed along the chain, then the molecule as a whole in a given conformation is characterized by the dipole moment y ... 

For uniaxial liquid crystals like nematic mesophases, and lamellar and hexagonal amphiphilic phases, the system is cylindrically symmetric with respect to an axis called the director. It is convenient to perform the transformation from the molecular coordinate system to the laboratory system via the director coordinate system (D). For a sample which is macroscopically aligned so that the director has the same direction throughout the sample we then have... 

Figure 1.8(a) shows a typical columnar mesophase, consisting of liquidlike columns of molecules arranged in the hexagonal lattice. This mesophase can be referred to as a unidimensional liquid and as a two-dimensional solid. The point group symmetry is Dqyi- Disc-like molecules can also form the nematic mesophase [22] shown in Fig. 1.8(b). As a rule, such a phase is optically uniaxial and negative. The optical axis coincides with the director L. 

The molecular theory is similar to Cauchy s description of the elastic theory of solids [1] and utilizes additive local molecular pair interactions to describe elasticity. The latter approach was taken by Oseen [2], who was the first to establish an elastic theory of anisotropic fluids. Oseen assumed short-range intermolecular forces to be the reason for the elastic properties, and he derived eight elastic constants in the expression for the elastic free energy density of uniaxial nematic phases. Finally, he retained only five of them, which enter the Euler-Lagrange equations describing equilibrium deformation states of the nematic mesophase, and omitted the other three. 

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. 

Twisting a nematic structure around an axis perpendicular to the average orientation of the preferred molecular axes, one arrives at the molecular arrangement commonly called cholesteric (Kelker and Hatz, 1980). The twisted nematic phase is optically uniaxial, however with the axis perpendicular to the (rotating) director. Such a mesophase combines the basic properties of nematics with the implications of chirality The structure itself is chiral and as a consequence, a non-identical mirror image exists as it is shown schematically in Fig. 4.6-7. Besides the order parameters mentioned before, the essential characteristics of a cholesteric mesophase are the pitch, i.e., the period of the helical structure as measured along the twist axis, and its handedness, i.e., whether the phase is twisted clockwise or anticlockwise. 

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]. 

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