Phase transitions and separations in a distorted liquid crystalline mixture.

A theoretical method is proposed for modelling phase transitions and phase ranges in a multi-component liquid crystalline mixture where the liquid crystal structure is distorted and defects are formed. This method employs the Maier-Saupe and Kobayashi-McMillan theories of liquid crystalline ordering and the Flory-Huggins theory of mixtures. It builds on previous work on mixed systems that can form smectic-A and nematic phases by incorporating "distortion factors" into the expression for the local free energy of the mixture, which account for the effects of a deviation of the liquid crystal structure from the uniform nematic and smectic-A states. The method allows a simple description of chiral defect phases such as the blue phase and the twist grain boundary phase. In a previous work, it was shown that a model of the blue phase along these lines could effectively explain the observed effect whereby an added guest compound can stabilize the phase by separating into the high energy defect regions of the structure. It is shown here that with the correct choice of guest material a similar effect could be observed for the twist grain boundary phase.