Analytical description for the chiral nematic state in terms of molecular parameters

Abstract

An analytical description for helical twisting in chiral liquid crystals is derived, which explores the correlation between the macroscopic properties of a liquid crystal and the parameters of single molecules. This theory is based on a simple model of a spiral-like rigid molecules that possess a limited number of parameters, each having transparent geometrical meaning. Expressions for the macroscopic helical pitch in the chiral nematic phase and the nematic order parameters were obtained in terms of molecular parameters. The theory explains the experimentally observed helical sense inversions induced by a change of temperature or mutual concentration of components in mixtures. It is also shown that the helical sense inversion may be observed in the process of denaturation of polypeptides. Different reasons for helical sense inversions were identified, such as competition between the dispersion attraction and the steric repulsion, distinct mechanisms of the steric packing for different kinds of molecules, and biaxiality of molecules.