Biaxial nematic phase, multiphase critical point, and reentry transition in binary liquid crystal mixtures

A model considering both short-range and long-range interactions for liquid crystals mixtures of rod-like and plate-like molecules is presented in this paper. The model is treated in the framework of a mean field, van der Waals-type theory. The relationship of the model to a Landau-type treatment is discussed in an Appendix. It can be shown for this model that a multiphase critical point exists between the isotropic, rod nematic, plate nematic, and biaxial nematic phases. This point can be located from a set of analytic equations. The fluctuations and the magnetically induced birefringence around this point are calculated. The model predicts the phase diagrams of binary liquid crystal mixtures both with and without reentry transition. The reentrant phase transitions from the biaxial to the uniaxial nematic phase and from the uniaxial nematic to the isotropic phase have not received prior theoretical attention but have been demonstrated in recent experiments.