Chirality, definition helical

Because the sense, or sign, of chiral asymmetry in the forward-backward electron scattering asymmetry depends on the helicity of the photon and of the molecule, it is essential that these variables are properly specified in any study to permit meaningful comparisons to be made. Discussing and comparing quantitative asymmetry factors, y [Eq. (8)] and dichroism [Eq. (9)] likewise requires agreement on the convention adopted in the definition of these terms. 

A quantitative study of the cholesteric induction and of the chiral transfer from dopant to phase requires the definition of the helical twisting power 3. This quantity expresses the ability of a chiral dopant to twist a nematic phase and can be numerically expressed in Eq. (2) where p is the cholesteric pitch, c the dopant molar fraction, and r its enantiomeric excess its sign is taken to be positive or negative for right-handed (P), or left-handed (M) cholesterics, respectively. This relation holds for molar fractions <0.01-0.05 ... 

FIGURE 5.11 Supramolecular, helical architecture and definition of pitch length p of chiral nematic liquid crystals. 

A helical unit is inherently chiral. Its chirality sense or helicity can assume two values that correspond to the sign of the torsional angle. Although the definition of the sign is arbitrary (sec Section 1.1.1.). a universal scientific convention2 is followed (Klyne Prelog convention) ... 

Bridged binuclear, trinuclear and tetranuclear chelated octahedral structures were examined by Schaffer,17 who used the skew line helical definition for the chirality symbols A and A. The configurational isomers for a tetrakisbidentate, edge-fused-bis-octahedral structure are AA, AA, AA, and AA. 

Up to this point, our description has been general it applies to crystals of rhenium chloride as accurately as to crystals of the ribosome. In addition to the translational symmetry (periodicity) that is inherent in the definition of a crystal, other symmetry can occur, but the kinds that can occur are restricted to crystals of biological macromolecules. Because the molecules are chiral, the symmetry operations in crystals must not change the handedness of the molecule, and so mirror planes, inversions, and glide planes (sliding mirror planes) do not occur. This leaves only rotations and screws (helical-type symmetry, sliding rotations). 

Recent studies of molecular chirality in which precise new definitions are used, such as chiropticity and stereogenicity , specifying chirality and topicity, give rise to some optimism also in the field of helical structures... 

Finally, there is a pressing need for more-detailed information on the molecular fine-structure, or conformation, of polysaccharides in solution. The potential of small-angle x-ray diffraction for distinguishing between a random coil and a broken or partial helix in solution has been established. A better definition of the helical conformation of dissolved polysaccharides, which, because of basic chemical asymmetry, have a favored chirality ( handedness ), is awaited. This area of x-ray study is only beginning to be developed. ... 

Whyte [2-37] extended the definition of chirality as follows Three-dimensional forms (point arrangements, structures, displacements, and other processes) which possess non-superposable mirror images are called chiral . A chiral process consists of successive states, all of which are chiral. The two main classes of chiral forms are screws and skews. Screws may be conical or cylindrical and are ordered with respect to a line. Examples of the latter are the left-handed and right-handed helices in Figure 2-50. The skews, on the other hand, are ordered around their center. Examples are chiral molecules having point-group symmetry. 

Snatzke G (1991) Helicity of molecules different definitions and application to circular dichroism. In Janos-check R (ed.) Chirality - From Weak Bosons to the oc-Helix, pp. 59-85. Berlin Springer. 

In the nematic phase the typical temperature dependence of dielectric constants and e are given in Fig. 2.4. Similar temperature curves are observed in the chiral nematic phase. The only difference comes from a specific definition of the main dielectric constants in the chiral nematic phase the components e h and e h are taken into consideration, denoting the dielectric properties parallel and perpendicular to the helical axis... 

Figure 11. Definitions of helical twist direction in chiral nematic phases.

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