Helical structures

Due to chiral intermolecular interaction the overall multi-layered structure of smectic C becomes twisted, like in cholesterics. The twist angle of the tilt plane is 

In the helical structure, the optical ellipsoid of the smectic C phase rotates together with the tilt plane. Like in cholesterics, we can imagine that helical turns form a stuck of equidistant quasi-layers that results in optical Bragg reflections in the visible range. Therefore, like cholesterics, smectic C liquid crystals are onedimensional photonic crystals. However, in the case of SmC, the distance between the reflecting layers is equal to the full pitch Pq and not to the half-pitch as in cholesterics, because at each half-pitch the molecules in the SmC are tilted in opposite directions. Hence, we have a situation physically different from that in cholesterics. 

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Qualitatively similar results were obtained in preliminary calculations of several (Ala)io and (Aib)io helical structures in water. 

Table 2. Geometric description of MD average helical structures...

Amorphous or "plastic" sulfur is obtained by fast cooling of the crystalline form. X-ray studies indicate that amorphous sulfur may have a helical structure with eight atoms per spiral. Crystalline sulfur seems to be made of rings, each containing eight sulfur atoms, which fit together to give a normal X-ray pattern. 

A helical structure for DNA strands had been suggested in 1949 by Sven Furberg in his Ph D dissertation at the University of London... 

Hydrogen bonding stabilizes some protein molecules in helical forms, and disulfide cross-links stabilize some protein molecules in globular forms. We shall consider helical structures in Sec. 1.11 and shall learn more about ellipsoidal globular proteins in the chapters concerned with the solution properties of polymers, especially Chap. 9. Both secondary and tertiary levels of structure are also influenced by the distribution of polar and nonpolar amino acid molecules relative to the aqueous environment of the protein molecules. Nonpolar amino acids are designated in Table 1.3. 

R = -CH2CH(CH3)2, there occurs a modest deviation from a strict 0°-120° alternation which characterizes the trans-gauche sequence. This produces a helical structure with seven repeat units occurring in two turns. Even bulkier substituents, for example, o-methyl phenyl, produce still more open helices... 

Poly(7-benzyl-L-glutamate) is known to possess a helical structure in certain solvents. As part of an investigationf of this molecule, a fractionated sample was examined in chloroform (CHCI3) and chloroform saturated ( 0.5%) with dimethyl formamide (DMF). The following results were obtained ... 

RNA structures, compared to the helical motifs that dominate DNA, are quite diverse, assuming various loop conformations in addition to helical structures. This diversity allows RNA molecules to assume a wide variety of tertiary structures with many biological functions beyond the storage and propagation of the genetic code. Examples include transfer RNA, which is involved in the translation of mRNA into proteins, the RNA components of ribosomes, the translation machinery, and catalytic RNA molecules. In addition, it is now known that secondary and tertiary elements of mRNA can act to regulate the translation of its own primary sequence. Such diversity makes RNA a prime area for the study of structure-function relationships to which computational approaches can make a significant contribution. 

The polypeptide chain of the 92 N-terminal residues is folded into five a helices connected by loop regions (Figure 8.6). Again the helices are not packed against each other in the usual way for a-helical structures. Instead, a helices 2 and 3, residues 33-52, form a helix-turn-helix motif with a very similar structure to that found in Cro. 

They started from the sequence of a domain, Bl, from an IgG-binding protein called Protein G. This domain of 56 amino acid residues folds into a four-stranded p sheet and one a helix (Figure 17.16). Their aim was to convert this structure into an all a-helical structure similar to that of Rop (see Chapter 3). Each subunit of Rop is 63 amino acids long and folds into two a helices connected by a short loop. The last seven residues are unstructured and were not considered in the design procedure. Two subunits of Rop form a four-helix bundle (Figure 17.16). 

The properties of optimized helical structures, which were derived from torus C54D and Cs7a, >yps (A), (proposed by Dunlap) and torus C ,o> Dpe (B), (proposed by us) by molecular dynamics were compared. (see Figs. 9 (a) and 10). (Although the torus Cs7f, is thermodynamically stable, helix 57 was found to be thermodynamically unstable 14]. Hereafter, we use helix C to denote a helix consisting of one torus (C ) in one pitch. 

From elongated tori, such as type (C), type (D), and type (E), helical structures are derived. For example, from the type (C) elongated torus of mentioned in 3.2.2, helix C756 (/t = 6, /t2 = 3, L = 1) and... 

Fig. 12. Elongated helical structures (a) helix C75, and (b) helix C2if,ci.

C.-H. Kiang e o/.[33] reported that the singlelayered coiled lubes were obtained by co-vaporizing cobalt with carbon in an arc fullerene generator. A single-layered helical structure with radii of curvature as small as 20 nm was seen. These helically coiled forms lend to bundle together. In the soot obtained with sulfur-containing anodes, they also found the 1.3-nm diameter lube coil around the 3.6 nm tube (see Fig. 14). This kind of structure was theoretically proposed in ref. [14]. 

The tubes (a, a) and (a, 0) are generated from hexagons with 0 = jt/6 and 0, respectively. These tubes become non-helical and are called, respectively, armchair and zigzag structures. Other condition (0 < 0 < Jt/6) generates the tube (a, b) of helical structures (see Fig. 2). 

Armchair structure Zigzag structure Helical structure All other tubes ... 

Electronic structures of SWCNT have been reviewed. It has been shown that armchair-structural tubes (a, a) could probably remain metallic after energetical stabilisation in connection with the metal-insulator transition but that zigzag (3a, 0) and helical-structural tubes (a, b) would change into semiconductive even if the condition 2a + b = 3N s satisfied. There would not be so much difference in the electronic structures between MWCNT and SWCNT and these can be regarded electronically similar at least in the zeroth order approximation. Doping to CNT with either Lewis acid or base would newly cause intriguing electronic properties including superconductivity. 

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