Double twist

Fig. 16a-c. The model proposed for blue phase II showing a,b the director arrangement within a double twist cylinder c the packing of these cylinders along three orthogonal axes... 

Fig. 4. Illustrating a cubic lattice formed by double-twist cylinders as a possible model of a...

Experimental evidence was reported for the existence of various additional phases a pre-cholesteric order in the form of a network of double-twisted cylinders, analogous to the thermotropic blue phases [27], a hexatic phase that replaces the hexagonal columnar in very long DNA fragments [31], and a structure with orthorhombic symmetry appearing in the transition to crystalline order [27]. 

A massive polymer molecule that contains all the genetic information of the cell. It has a complicated structure containing many thousands of smaller units of amino acids, proteins, bases and sugars. It forms a double-twisted helix string-like molecule. The strands are held in position by cross links of hydrogen bonds from matching pairs of base materials on opposite chains. 

Rzepa, H. S. Lemniscular hexaphyrins as examples of aromatic and antiaromatic double-twist Mobius molecules, Org. Lett. 2008,10, 949-952. 

Rzepa, H. S. A double-twist Mobius-aromatic conformation of [14]annulene, Org. Lett. 2005, 7, 4637-4639. 

The most favourable relative configuration of identical chiral molecules is that where all neighbouring molecules are twisted relative to each other. This is achieved by a "double-twist" stacking, illustrated in Fig. 4.32. In three-dimensional euclidean space, this double-twist caimot be realised throughout space some "disclination" singularities must occur [61]. How then can this double twist be most closely approached A simple model, involving nothing more than potatoes, and oven and matches, is useful. The lower-... 

This (local) double twist configuration clearly involves a hyperbolic deformation of the imaginary layers. In contrast to the hyperbolic layers found in bicontinuous bilayer lyotropic mesophases, the molecules within these chiral thermotropic mesophases are oriented parallel to the layers, to achieve nonzero average twist. The magnitude of this twist is deternuned by the direction along which the molecules lie (relative to the principal directions on the surface), and a function of the local curvatures of the layers (K1-K2), cf. eq. 1.4. Just as the molecular shape of (achiral) surfactant molecules determines the membrane curvatures, the chirality of these molecules induces a preferred curvature-orientation relation, via the geodesic torsion of the layer. 

Figure 4.32 The ideal (left-handed) double-twist configuration of neighbouring molecules about a central chiral molecule. For simplicity, a square arrangement of molecules is assumed in practice, the array is more likely to be hexagonal.

Hgure 4.33 Representation of the local structure of some chiral mesophases on heating. The matches describe the relative orientations of chiral molecules in space. As the temperature is raised, the system transforms from a crystalline phase (left) to a cholesteric phase (centre) characterised by a single twist, to a double-twist blue" phase (right). 

The twist of yam plays an important role and low twist appears to be essential for maximum increase in strength. Grey yam with soft doubling twist gives stronger yam. 

Keywords Blue phase Frustration Double twist Electrooptic effect Photonic crystal... 

Fig. 2 Frustration in twisted arrangements, a In the case of simple twists, arrangements from Points A and B, which are separated, do not result in inconsistency, b Double twists result in inconsistency...

Fig. 3 Comparison of simple-twist and double-twist arrangements...

Fig. 4 Model of molecule arrangements within a double-twisted cylinder...

Fig. 5 Structures of Blue Phases I and II. The rods in (a) and (c) represent double-twist cylinder. The black lines in (b) and (d) represent disclination lines...

Researchers have confirmed the existence of BP III, the structure of which is predicted to be more amorphous with the short-distance order of double twist alone. However, further details of this phase have yet to be cleared. 

A screw dislocation is similar in structure to that of a double twist cylinder which is the basis for the formation of Blue Phases [24], The equivalent of the... 

Fig. 31. Structure of a double twist cylinder (the molecules are shown as rods)...

Fig. 32a-f. Various models for the filamentary texture of TGBA phases. The molecules are shown as short lines, or nails when they are tilted out of the page. In each case the filaments are shown looking down the axis of the double twist cylinder (after Gilli and Kamaye [43])... 

Fig. 4.33 Double-twist cylinder (a) and the structure of the body-centered cubic phase BPl (b) and simple cubic phase BPII (c), both consisted of double-twist cylinders (adapted from [22])...

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