Uniaxial nematics

The term nematic is derived from the Greek word nema , a thread, and refers to the presence of a large number of apparent threads in relatively thick samples. Stirring a nematic leads to a pronounced increase in their number. When the motion stops, many of them disappear and other progressively stabilize. In uniaxial nematies, the threads are of two types either thin or thick, clearly distinguishable, both directly observable in light microscopy (Fig. 6). 

II Defects and Textures in Nematic Main-Chain Liquid Crystalline Polymers 

A half-integral line of any strength can be continuously deformed into the half-integral line of opposite strength as illustrated in [19]. So it is with integral lines. 

The threaded texture changes to the Schlieren texture when the lines are all perpendicular to the sample boundaries. This texture observed between crossed polarizers displays dark brushes (also called black 

It should be noted that twist lines are visible in threaded textures while wedge lines are observed in Schlieren textures. The continuous transformation of a wedge S line into a wedge -S line involves the passage through an intermediate twist 5 line [19]. 

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Luckhurst G R, Zannoni C, Nordic P L and Segre U 1975 A molecular field theory for uniaxial nematic... 

The above spectral densities can be modified for the occurence of chain flexibility, and for the director being oriented at dLD w.r.t. the external BQ field in the L frame. For CD bonds located in the flexible chain, the effect of DF is reduced due to an additional averaging of the time dependent factor (/f g) by conformational transitions in the chain. Consequently, the spectral densities given in Eqs. (60)-(62) are modified by replacing Soc%0(Pm,q) by the segmental order parameter YCD of the C-D bond at a particular carbon site on the chain.146,147 As observed experimentally,148,149 the spectral densities in a flexible chain show a SqD dependence when DF dominate the relaxation rates. The general expression of Jm(co 0LD) due to DF in uniaxial nematic phases is given by... 

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

Note 5 From a crystallographic point of view, the uniaxial nematic structure is characterised by the symbol Dooh in the Schoenflies notation (Wmm in the International System). 

Note 6 Since the majority of nematic phases are uniaxial, if no indication is given, a nematic phase is assumed to be uniaxial but, when there is the possibility of a biaxial as well a uniaxial nematic, a uniaxial phase should be denoted as N . 

Note 2 In uniaxial nematics, formed by compounds consisting of either rod-like or disclike molecules, the mean direction of the effective molecular symmetry axis coincides with the director. 

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. 

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. 

In the spirit of our model, two order parameters play a role the nematic tensorial order parameter Q,j and the smectic A complex order parameter practical reason we use the director fl and the modulus sW in the uniaxial nematic case... 

Figure I Schematic representation of an example of hierarchical self-assembly at microscopic, mesoscopic, and macroscopic levels. At the microscopic level, molecules assemble into supramolecular polymer-like assemblies. This involves conformational changes to the monomer units that themselves are complex molecules. The polymers assemble into bundles at mesoscopic levels that under appropriate conditions spontaneously align macroscopically along some preferred direction to form a uniaxial nematic liquid-crystalline phase (after Aggeli et al., 2001).

The order parameters S for all three molecular axes or alternatively, the combination S plus D describe on the level of the first relevant polynomial term the orientational distribution of a rigid, non-cylindrical molecule in the uniaxial nematic phase. Additional order parameters come into play for biaxial phases (Straley, 1974). A concise overview on the concepts from statistical mechanics relevant to order parameters was given by Zannoni (1979). 

In the simplest liquid-crystalline phase, namely the uniaxial nematic, there is at rest a special direction designated by a unit vector n called the director (see Fig. 10-2). In the plane transverse to the director, the fluid is isotropic. The most common nematics are composed of oblong molecules that tend to point in a common direction, which defines the director orientation. Oblate, or disc-like, molecules can also form uniaxial nematics for these discotic nematics, the director is defined by the average orientation of the short axis of the molecule. Lath-like molecules or micelles (shaped like rectangular slabs), in which all three dimensions of the molecule are significantly different from each other, can form biaxial nematics (Praefcke et al. 1991 Chandrasekhar 1992 Fialtkowski 1997). A biaxial... 

The degree of orientational order in a uniaxial nematic is given by the order parameter S, defined by Eq. (2-3). S is zero in the isotropic state, and it approaches unity for hypothetically perfect molecular alignment (i.e., all molecules pointing in the same direction). In single-component small-molecule nematics, such as MBBA, S varies with temperature from 5 0.3 at Tni, the nematic-isotropic transition temperature, to S 0.7 or so at lower... 

Although uniaxial nematics possess rotational symmetry about the nematic axis, the molecules composing them are usually not axisymmetric (Emsley et al. 1981 Running et al. 1986), but the axial asymmetry of the molecules is averaged out by the rotations of the molecules about their backbones. In some nematics, however, molecular interactions... 

According to the competition of all the interactions in the side chain nematic polymers, there are three uniaxial nematic phases Ni, Nn, Nm- The three phases, each having a special conformation, may transform each other when the free energies are equal. These phases are shown in Figure 2.26 with the director pointing upward. 

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... 

In the uniaxial nematic case, = 22-If the molecule is flexible more parameters are required to define the degree of alignment of its different parts.However, in a large part of the discussion that follows on the theory of the nematic state we shall ignore all these details and assume the molecules to be cylindrically symmetric rods. 

As observed earlier, the assumption that the molecule is cylindrically symmetric is clearly not valid for real systems, and consequently the use of a single order parameter is not adequate. Most molecules are lath-shaped and have a biaxial character. Therefore two order parameters are required to describe the uniaxial nematic phase composed of biaxial molecules. If are the principal axes of the molecule (C defining the molecular long axis), it is necessary to introduce an additional order parameter... 

Fig. 6.6.3. Raw microdensitometer scans of the X-ray intensity plotted against diffracting angle (20) for magnetically aligned nematic samples (a) the uniaxial nematic phase of 80CB at 77 °C (b) the biaxial nematic phase of complex A at 168.5 C, (i) meridional scan (parallel to H), (ii) equatorial scan (perpendicular to H). M represents the diffraction peaks from the mylar film which covered the windows of the sample holder and heater assembly. ...

Fig. 6.6.4. Schematic diagram of the molecular order in (a) the uniaxial nematic phase and (b) the biaxial nematic phase.

According to this model, the free energy expansion, in the case of uniaxial nematic order and incompressible strain of the sam-... 

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