Theory of polymer-dispersed cholesteric liquid crystals

A mean field theory is presented to describe cholesteric phases in mixtures of a polymer and a cholesteric liquid crystal. Taking into account an anisotropic coupling between a polymer and a liquid crystal, we examine the helical pitch, twist elastic constant, and phase separations. Analytical expressions of the helical pitch of a cholesteric phase and the twist elastic constant are derived as a function of the orientational order parameters of a polymer and a liquid crystal and two intermolecular interaction parameters. We also find isotropic-cholesteric, cholesteric-cholesteric phase separations, and polymer-induced cholesteric phase on the temperature-concentration plane. We demonstrate that an anisotropic coupling between a polymer and a liquid crystal can stabilize a cholesteric phase in the mixtures. Our theory can also apply to mixtures of a nematic liquid crystal and a chiral dopant. We discuss the helical twisting power, which depends on temperature, concentration, and orientational order parameters. It is shown that our theory can qualitatively explain experimental observations.