Crystal, defect, point twist

Zero-dimensional defects or point defects conclude the list of defect types with Fig. 5.87. Interstitial electrons, electron holes, and excitons (hole-electron combinations of increased energy) are involved in the electrical conduction mechanisms of materials, including conducting polymers. Vacancies and interstitial motifs, of major importance for the explanation of diffusivity and chemical reactivity in ionic crystals, can also be found in copolymers and on co-crystallization with small molecules. Of special importance for the crystal of linear macromolecules is, however, the chain disorder listed in Fig. 5.86 (compare also with Fig. 2.98). The ideal chain packing (a) is only rarely continued along the whole molecule (fuUy extended-chain crystals, see the example of Fig. 5.78). A most common defect is the chain fold (b). Often collected into fold surfaces, but also possible as a larger defect in the crystal interior. Twists, jogs, kinks, and ends are other polymer point defects of interest. 

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. 

The first such model put forth was the Utah twist [21], named after the institution where it was developed. It was documented through detailed molecular mechanics calculations on an array of C22H46 molecules of orthorhombic crystal structure and compared to the previously suggested models. The main reservations against the previous models, primarily from relaxation studies, were summarized as follows. Point defect mechanisms assume an equilibrium or induced number of stable defects that are thermally activated to give rise to various motions. It was shown by NMR however, that all the crystalline chains participate and not just a small number of defective segments. 

As pointed out in the previous section, there are voids between the double-twist cylindas when they are packed in 3-D space. Liquid crystal must fill the void. Because of the boundary condition imposed by the cylinders, the hquid crystal director is not uniform in this space and forms a defect... 

There are other dischnations besides axial disclinations that form in nematic liquid crystals. In axial dischnations, the rotation axis of the director in traversing a loop aroimd the disclination is parallel to the disclination. In a twist dischnation, the rotation axis is perpendicular to the disclination. Figure 2.15 shows +1/2 and +1 strength twist dischnations in which the rotation axis for the director is along the y-axis and the dischnation points along the z-axis Due to the fact that the director twists, an entirely new class of dischnations form in chiral nematic liquid crystals. Likewise, the spatial periodicity of both chiral nematic and smectic hquid crystals ahows for defects in the perio(hc stmcture in addition to defects in the director configuration. These additional defects are quite different and resemble dislocations in solids. 

The crux of the present method is how well the relaxation portion converges. Some experience has now been gained with it (11,12,13). Figure 4 shows results of calculations made in our laboratory (11,13) on the energies of three conformational defects in polyethylene crystals. These are a kin)c (15, ), a Reneker twist (Ig) and a smooth twist (12) (see Figure 1). The first two have been proposed as stable point defects cind the last one as a transition state for the motion that accomplishes... 

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