Nematic phase structure, defect structures

We note that earlier research focused on the similarities of defect interaction and their motion in block copolymers and thermotropic nematics or smectics [181, 182], Thermotropic liquid crystals, however, are one-component homogeneous systems and are characterized by a non-conserved orientational order parameter. In contrast, in block copolymers the local concentration difference between two components is essentially conserved. In this respect, the microphase-separated structures in block copolymers are anticipated to have close similarities to lyotropic systems, which are composed of a polar medium (water) and a non-polar medium (surfactant structure). The phases of the lyotropic systems (such as lamella, cylinder, or micellar phases) are determined by the surfactant concentration. Similarly to lyotropic phases, the morphology in block copolymers is ascertained by the volume fraction of the components and their interaction. Therefore, in lyotropic systems and in block copolymers, the dynamics and annihilation of structural defects require a change in the local concentration difference between components as well as a change in the orientational order. Consequently, if single defect transformations could be monitored in real time and space, block copolymers could be considered as suitable model systems for studying transport mechanisms and phase transitions in 2D fluid materials such as membranes [183], lyotropic liquid crystals [184], and microemulsions [185],... 

As this compound was one of the higher homologues in the series, and because we knew that the earlier homologues did not exhibit a chiral nematic phase, it was clear that the new phase also could not be a chiral nematic phase. In addition, it was clear from the formation of the defect structures seen in the microscope that the phase first formed from the isotropic liquid possessed a helix, see Plate 1, which had its heli-axis at right angles to the heli-axis in the lower temperature chiral ferroelectric smectic phase. This simple observation meant that if the phase was a lamellar smectic phase then the helix would have to be formed, inconceivably, in a direction parallel to the layers. Synthesis of the achiral variant confirmed that the phase formed first on cooling from the isotropic liquid was indeed a smectic A phase, and thus we immediately knew that we had found a smectic A phase where the helical macro structure formed in the planes of the layers, and thus the helix must... 

The chiral nematic phases can show a planar Grandjean textnre, with oily streaks caused by defects, but they can also show strong reflection colors, depending on the pitch of the helical structure within the phase. 

The effect of structural disclinations upon texture and the origins of these in local deformations of or discontinuities in the arrangement of the molecules have been studied only in the case of nematic MCLCPs. The primacy aim of this chapter is therefore to present to the reader defects and textures in nematic MCLCPs. Some of consequences of constructing a nematic phase from long... 

Textures correspond to various arrangements of defects. When the isotropic liquid is cooled, the nematic phase may appear at the deisotropization point in the form of separate small, round objects called droplets (Fig. 12). These can show extinction crosses, spiral structures, bipolar arrangements, or some other topology depending on boundary conditions. Theoretical studies based on a simple model confirm the stability of radial or bipolar orientation (Fig. 5) [22]. Considerations based on improved theoretical models yield stable twisted... 

Curvature of the layers in the smectic state is compatible with the formation of cylindrical, tore and Dupin cyclide defects. The most common defect is the Dupin cyclide and therefore is discussed in more detail. When the smectic A phase nucleates from either the Hquid or the nematic phase, it can do so with the formation of curved structures called baton-nets (see Figure 6), i.e., layers of molecules add to a... 

The zero shear viscosity of flexible linear polymers varies experimentally with and theoretically with [20]. Due to the highly restricted rotational diffusion, the viscosity of TLCPs is much more sensitive to the molecular weight than that of ordinary thermoplastics as discussed in section 3. Doi and Edwards predicted that the viscosity of rod-like polymers in semi-dilute solutions scales with A/ [see Equation (12)] [2]. Such a high power dependence of viscosity on the molecular weight has been experimentally observed both for lyotropic LCPs [14,15] and for TLCPs [16-18]. The experimental values of the exponent range from 4 to 7 depending on the chemical structure, the chain stiffness, and the domain or defect structure of the liquid crystalline solution or melt. The anisotropicity of the liquid seems to have little effect on the exponent. A slightly smaller exponent for the nematic phase than for the isotropic phase (6 in the nematic phase versus 6.5 in the isotropic... 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

This simple treatment of liquid crystalline defects is only applicable to nematics, and the detailed appearance of disclination lines will differ from the simple structures described above because of differences between the elastic constants for splay, twist and bend. In smectic phases, defects associated with positional disorder of layers will also be important, and some smectic phase defects such as edge dislocations have topologies similar to those described for crystals. The defect structures of liquid crystals contribute to the characteristic optical tex-... 

Due to the layer structure of a smectic liquid crystal, some types of deformation commonly found in the nematic phase are prohibited. Consider a defect-free SmA... 

Figure 8.14a, c shows double twist cylinders, and the bold black lines in Fig. 8.14b, d show disclinations (defect Unes). In each double twist cylinder, the molecules are radially twisted towards each other through 90°. The molecules are parallel to the cylinder axis at the cylinder center and are tilted by 45° at the outer radial periphery. In other words, the molecules twist from —45° to -t45° through the cylinder, which corresponds to a quarter pitch. The diameter of a double twist cylinder is typically about 100 nm, and a simple calculation shows that approximately 200 molecules with a diameter of 0.5 nm mildly twist against each other. The lattice constant for blue phase I corresponds to a one helical pitch, and the lattice constant for blue phase II corresponds to one half helical pitch. We generally see a very small mismatch in pitch length with that of the lower-temperature chiral nematic phase. Peculiar to soft matter, a complex hierarchical structure is formed in... 

Comparable to the nematic (N) phase of rod-like compounds the least orda ed (usually highest temperature) mesophase exhibited by disc-like molecules is also the nematic (discotic. No) phase the index D simply refers to their molecular shape. Both nematic phases are of the same symmetry and identical types of defects are seen in both cases [5] they exhibit similar fluid Schlieren textures [3,6]. However, the nematic phases of these two low-molar-mass liquid crystals are not miscible [3,6] and phase separation occurs due to fundamental differences in their molecular structures. 

Boden et al. [172] showed that a thermodynamically independent nematic mesophase exists in the cesium perfluorooctanoate (CsPFO)-water system between 37% and 87% (w/w) H2O and 11-75°C. The nematic phase is intermediate to an isotropic micellar solution at higher temperatures and a smectic lamellar mesophase at lower temperatures. The isotropic phase consists of disk-shaped micelles. The lamellar phase has been described by a structure in which continuous lamellae of the surfactant are broken by irregular water-filled defects without interlayer correlations [182]. In the nematic phase, the aggregates make the transition from discrete disks to continuous lamellae [160,182]. Both positional and oriental order increase when the temperature is lowered. The nematic phase of CsPFO-water is stable over a wide range of concentrations without needing a cosurfactant or salt as a stabilizer. The disk-shaped micelles of the nematic phase orient with their unique axis parallel to the direction of an applied magnetic field. 

---