Dispiration

The local translational and orientational order of atoms or molecules in a sample may be destroyed by singular points, lines or walls. The discontinuities associated with the translational order are the dislocations while the defects associated with the orientational order are the disclinations. Another kind of defect, dispirations, are related to the singularities of the chiral symmetry of a medium. The dislocations were observed long after the research on them began. The dislocations in crystals have been extensively studied because of the requirement in industry for high strength materials. On the contrary, the first disclination in liquid crystals was observed as early as when the liquid crystal was discovered in 1888, but the theoretical treatment on disclinations was quite a recent endeavor. 

It is named the wedge dispiration, designated as (b,—b/p). Similarly, an edge dislocation of the Burger vector b must be accompanied by a partial twist disclination, designated as the twist dispiration (b,b/p). 

Fig. 2.23 Disclinations, among aligned molecules in a chain-folded crystal lamella (a) a twist disclination that can be a part of a dispiration loop (b) a fold-over of two neighboring molecules and (c) a wedge disclination (from Li and Gilman (1970) courtesy of the American Institute of Physics).

Finally, for the kinetics of lamella thickening it is essential to know the lattice resistance to the motion of dispiration loops. This has been estimated by Reneker and Mazur (1983) to be describable by a diffusion constant 1 x 10 cm /s at 343 K. They consider that dispiration loops are likely to have a thermal equilibrium concentration of roughly one defect per molecule stem in a lamella, or a linear concentration of roughly 10 m ... 

Reneker, D. H. and Mazur, J. (1983) Dispirations, disclinations, dislocations, and chain twists in polyethylene crystals, Polymer, 24, 1387-1400. 

Th-cycle is just an example of several possible hierarchical tetrahedral systems built on biological principles. Twist-boat associated with the ciystal stmctures of water (hexagonal and cubic ice) can be obtained by a simple dispiration transformation. Enthalpy of ice-th-cycle transition is negligible and caused by H-bonds distortion. This fact consistent with the enthalpy of transition ice-lh - liquid water [25],... 

Finally, a rotation of 180° can be combined with a translational defect of c/2 to achieve crystalline register above and below the defect. Such combination of disclination and dislocation is call a disfMration. The nomenclature of chain dislocation, disclination and dispiration was developed by Reneker and Maair [14]. 

Figure 9.9. Model structure of the two-brush defect i.e., dispiration, a combined defect of a wedge disclination and a screw dislocation.

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