Helix lattice

Figure 5.11 contains a selection of projections of rational helices that correspond to the indicated screw axes. If there is no equivalent screw axis indicated, it does not exist in space-lattice symmetry. The helix lattice generates the complete molecule starting with the first motif, but one must specify whether the helix rotation is left- or right-handed. While the screw axis 3j corresponds to aright-handed 3/1 helix, the 32 screw axis generates a left-handed 3/1 helix, but every second lattice point is generated... 

It is of interest to note that one may change the translation lattice of Fig. 5.3 by replacing the translation lattice vector c with the molecular helix lattice, keeping the translation symmetries a and This would lead to a match of the molecular helix symmetry with the crystal symmetry and even for irrational helices, a crystal stracture symmetry would be recognized. In fact, a whole set of new lattices can be generated replacing all three translation symmetry operations by helix symmetry operations [5]. Since a 1 1/1 hehx has a translational symmetry, this new space lattice description with helices would contain the traditional crystallography as a special case. 

A simple model for a parallel p helix lattice protein... 

Micellar structure has been a subject of much discussion [104]. Early proposals for spherical [159] and lamellar [160] micelles may both have merit. A schematic of a spherical micelle and a unilamellar vesicle is shown in Fig. Xni-11. In addition to the most common spherical micelles, scattering and microscopy experiments have shown the existence of rodlike [161, 162], disklike [163], threadlike [132] and even quadmple-helix [164] structures. Lattice models (see Fig. XIII-12) by Leermakers and Scheutjens have confirmed and characterized the properties of spherical and membrane like micelles [165]. Similar analyses exist for micelles formed by diblock copolymers in a selective solvent [166]. Other shapes proposed include ellipsoidal [167] and a sphere-to-cylinder transition [168]. Fluorescence depolarization and NMR studies both point to a rather fluid micellar core consistent with the disorder implied by Fig. Xm-12. 

The many commercially attractive properties of acetal resins are due in large part to the inherent high crystallinity of the base polymers. Values reported for percentage crystallinity (x ray, density) range from 60 to 77%. The lower values are typical of copolymer. Poly oxymethylene most commonly crystallizes in a hexagonal unit cell (9) with the polymer chains in a 9/5 helix (10,11). An orthorhombic unit cell has also been reported (9). The oxyethylene units in copolymers of trioxane and ethylene oxide can be incorporated in the crystal lattice (12). The nominal value of the melting point of homopolymer is 175°C, that of the copolymer is 165°C. Other thermal properties, which depend substantially on the crystallization or melting of the polymer, are Hsted in Table 1. See also reference 13. 

Fig. 21.—Structure of the 6-fold anhydrous curdlan III (19) helix, (a) Stereo view of a full turn of the parallel triple helix. The three strands are distinguished by thin bonds, open bonds, and filled bonds, respectively. In addition to intrachain hydrogen bonds, the triplex shows a triad of 2-OH - 0-2 interchain hydrogen bonds around the helix axis (vertical line) at intervals of 2.94 A. (b) A c-axis projection of the unit cell contents illustrates how the 6-0H - 0-4 hydrogen bonds between triple helices stabilize the crystalline lattice.

The poly(5-fnethyl-l, 4-hexadiene) fiber pattern (Figure 6) gave an identity period of 6.3 A, indicating a 3 isotactic helix structure. The X-ray diffraction pattern was not very sharp, which may be due to the difficulty of the side chain with a double bond to fit in a crystalline lattice. The crystallinity was determined to be 15% using the Hermans and Weidinger method (27). A Chloroform-soluble fraction free from catalyst residues showed no improvement in the sharpness of the X-ray diffraction pattern. These data show that the configuration of the 1,2-polymerization units in the homopolymer of 5-methyl-1,4-hexadiene is isotactic. 

The unit cell is tetragonal, with a symmetry approximating P2i2 2i. The cell dimensions are a = b= 18.87 A (1.887 nm) and c = 7.99 A (799 pm). The helix diameter is 13.3 A (1.33 nm). One ethylenediamine molecule for every two D-glucose residues is indicated. The location of the ethylenediamine molecule in the lattice was discussed. The structure is almost identical to that of the amy-lose-dimethyl sulfoxide complex. 

Figure 3.44. Views, according to Fredrickson et al. (2004a, b), of the Ru2Sn3 structure type, an example of the chimney-ladder Nowotny phases. On the left, a lateral view of the Ru helix (black balls) and of the Sn helix (white balls). The periods of the two helices (cn and cm) are given together with the lattice parameter c.

The structures of both the 5-methyl and 5-bromo derivatives of d(OOTAOG) are similar to each other and likewise similar to the structure of (dC-dG) as well as (m dC-dG). They form a double helix with six base pairs and stack together to form an essentially continuous Z-mA double helix running along the axis of the unit cell. The crystal of the methylated hexamer diffracts to a resolution of 1.2 A, and the bromlnated derivative to 1.5 A. Both crystals form an Isomorphous lattice with that of the (dC-dG)j. Thus it is not surprising that the gross form of Z-UtA is the same whether it is made of OG base pairs or AT base pairs. 

Isotactic PP, which is a commercial variety of PP, exists as a helix instead of an extended planar conformation in order to relieve the strain and thus attain a state of low free energy. Such helical conformations are actually rodlike and thus pack parallel to other rods in the crystal lattice. 

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