Molecular Chirality and Chiral Parameters

Chirality permeates the entire fabric of the biological world. Indeed, life as we know it could not exist without chirality. The function of fundamental components of the cell, like actin, myosin, proteins, and lipids, relies upon their being chiral. The handedness of a molecule can affect its odor, potency, and toxicity. Thus the synthesis of a single enantiomer of a compound is crucial for the delivery of safe and effective pharmaceuticals and food additives. Microscopic chiral constituents have a profound effect on the macroscopic structures they form, striking examples of which are common in liquid crystals (de Gennes and Prost, 1993). The simplest liquid crystalline phase is the nematic phase, characterized by long-range uniaxial orientational order of anisotropic molecules called nematogens as shown in Fig. 1a. The centers of mass of the constituent molecules are distributed homogeneously as in as isotropic fluid, but one of their anisotropy axes aligns, on average, along a common unit vector n called the director. Strongly biaxial molecules (Fig. 2) can in principle condense into a biaxial rather than a uniaxial nematic phase with long-range biaxial orientational order (de Gennes and Prost, 1993). In this phase, one molecular axis aligns along n, and a second orthogonal axis aligns on average along a second vector e perpendicular to n as shown schematically in Fig. 1b. Biaxial molecules can also condense into a uniaxial nematic phase with short-ranged biaxial correlations rather than long-range biaxial order as depicted in Fig. 1c.