Nematic liquid crystal phase distributions/order

Figure 2.27 shows a cartoon representation of some typical scattering patterns for the smectic and nematic liquid crystal phases. The smectic phase has a layered structure with an approximately sinusoidal density distribution from layer to layer. This ID (one-dimensional) ordered structure typically produces a single scattering peak (using a high-intensity... 

Abstract The influence of randomly distributed impurities on liquid crystal (LC) orientational ordering is studied using a simple Lebwohl-Lasher t5q)e lattice model in two d=2) and three d=3) dimensions. The impurities of concentration p impose a random anisotropy field-type of disorder of strength w to the LC nematic phase. Orientational correlations can be well presented by a single coherence length for a weak enough w. We show that the Imry-Ma... 

When a nematic liquid crystal is placed in contact with another phase (solid or liquid), a surface bounding the liquid crystal is created. The presence of this surface induces a perturbation of the nematic order close to it (Fig. la). The anisotropic interactions between the molecules located right at the surface - in the surface layer - and the other phase favors certain orientations of the surface molecules. This leads to an orientational distribution of the liquid crystal molecules in the surface layer that is generally different from the bulk nematic order. The orientational order evolves from the one induced by the surface to the one in the bulk in an interfacial region of thickness which is of the order of the nematic coherence length. Just outside the interfacial re-... 

In this chapter we consider the very simplest approach to the molecular theory of liquid crystals. We shall approach the theory phenomenologically, treating the problem of the existence of the nematic phase as an order-disorder phenomenon. Using the observed symmetry of the nematic phase we shall identify an order parameter and then attempt to find an expression for the orientational potential energy of a molecule in the nematic liquid in terms of this order parameter. Such an expression is easily found in the mean field approximation. Once this is accomplished, expressions for the orientational molecular distribution function are derived and the thermodynamic functions simply calculated. The character of the transformation from nematic liquid crystal to isotropic fluid is then revealed by the theory, and the nature of the fluctuations near the transition temperature can be explored. 

The identification of the appropriate order parameter for nematic liquid crystals is aided by a consideration of the observed structure and symmetry of the phase. As in any liquid, the molecules in the nematic phase have no translational order i.e., the centers of mass of the molecules are distributed at random throughout the volume of the liquid. Experiments of many varieties, however, do demonstrate that the nematic phase differs from ordinary liquids in that it is anisotropic. The symmetry, in fact, is cylindrical that is, there exists a unique axis along which the properties of the phase display one set of values, while another set of values is exhibited in all directions perpendicular to this axis. The symmetry axis is traditionally referred to as the director . The optical properties of nematics provide an example of how the cylindrical symmetry is manifest. For light passing parallel to the director, optical isotropy is observed, while for all directions perpendicular to the director, optical birefringence is observed. Rays polarized parallel to the director have a different index of refraction from those polarized perpendicular to the director. 

Here, I introduce the phase separation of the mixed system of rodlike molecules and liquid crystal molecules. By using the orientational order parameter of the liquid crystal molecules and the rodlike molecules (Si, S2), it is possible to define four nematic phases as shown in Fig. 10.15. In particular, it is possible to define a new nematic phase that has S < 0 (a = 1,2). In the nematic phase No, rodlike molecules and liquid crystal molecules are oriented parallel to each other, and the orientational order parameter is defined as having positive value (Si > 0, S2 > 0). In the nematic phase Ni (Si >0, S2<0), the average orientation of the liquid crystal molecules describes the director and the rodlike molecules are randomly distributed in the plane perpendicular to that director. In the N2 nematic phase (Si < 0, S2 > 0), the rod-shaped molecules determine the director and the nematic liquid crystals are... 

When they are heated, mesogenic compounds do not melt directly from the highly ordered crystalline state to an isotropic liquid. They form instead, intermediate phases in which the molecules are orientated in a parallel direction and referred to as smectic (centers of the molecules organized in layers) or nematic (centers of the molecules distributed at random). Smectic and nematic mesophases are in turn divided into a variety of subgroups of thermotropic liquid crystals which will not be dealt with in detail in the present article. 

Some liquid crystals form one or more smectic phases. These display a variety of microscopic structures that are indicated by the letters A, B, C, and so forth. Figure 23.9c shows one of them, the smectic A structure the molecules continue to display net orientational ordering, but now, unlike in the nematic phase, the centers of the molecules also tend to lie in layers. Within each layer, however, these centers are distributed at random as in an ordinary liquid. TBBA enters the smectic A phase at 200°C, before undergoing transitions to two other more ordered smectic phases at lower temperatures. 

One of the most common LC phases is the nematic, where the molecules have no positional order, but they have long-range orientational order. Thus, the molecules flow and their center of mass positions are randomly distributed as in a liquid. Most nematics are uniaxial the molecules are orientationally ordered about a common axis defined as the director and represented by the unit vector n (Table 2). It is very important to stress that nematics can be easily aligned by an external magnetic or electric field. Aligned nematics have the optical properties of uniaxial crystals and this makes them extremely useful in liquid crystal display technology. 

Fig. 9 H-NMR spectrum of a conventional side-chain LCE doped with an aD2-8CB liquid crystal recorded deep in the nematic phase (a) and in the vicinity of the PN-N phase transition (b). The spectrum (a) reflects the distribution of the domain-director alignment, and (b) reflects the distribution of the local order parameter...

In general, liquid crystal molecules do not have the D200 symmetry of the uniaxial nematic phase. Since an interface acts as a field, its presence can provide polar order. Such surface polar ordering, confined to a single molecular layer, has been observed [99]. Surface SHG can also be used to probe the orientational distribution at the surface, and anchoring transitions [100]. 

NMR in Fig. 1 (top and middle). If the sample is partially ordered, like a partially aligned liquid crystal polymer, the NMR line shape reflects the orientational distribution function of the coupling tensors [28, 29]. Figure 1 (bottom) depicts the special case of a completely aligned sample. Such a sample with macroscopically uniform alignment, for nematic phases usually induced by the magnetic field, gives rise to a simple doublet. 

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