Molecular Chirality and Chiral Parameters

Details Molecular Chirality and Chiral Parameters Molecular Chirality and Chiral Parameters

1999-01-18

arxiv.org/abs/cond-mat/9901174v2

Rev. Mod. Phys. 71 (1999) 1745

Physics

Condensed Matter

Statistical Mechanics

14 pages, 7 included eps figures, RevTeX with rmp macros

Scientific paper

10.1103/RevModPhys.71.1745

The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. We show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations but changing sign under improper rotations) and must involve three-point correlations which only come into play when the molecule has at least four atoms. In general, a molecule is characterized by an infinite set of chiral parameters. We illustrate the fact that these parameters can have differing signs and can vanish at different points as a molecule is continuously deformed into its mirror image. From this it is concluded that handedness is not an absolute concept but depends on the property being observed. Within a simplified model of classical interactions, we identify the chiral parameter of the constituent molecules which determines the macroscopic pitch of cholesterics.

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