Generalized van der Waals theory for phase behavior of two-dimensional nematic liquid crystals: Phase ordering and the equation of state.

Liquid crystalline ordering of anisotropic particles in two dimensions is important in many physical and biological systems and their phase behavior is still a topic of interest. A generalized van der Waals theory is formulated, accounting for repulsive excluded volume and attractive van der Waals and Maier-Saupe interactions, for rectangles confined to two dimensions. The phase ordering transitions and equation of state are analyzed as a function of the model parameters (aspect ratioL/B and isotropic and anisotropic interaction parameters χ and ν). Different phase transitions are observed: continuous isotropic-nematic (high L/B and ν), first-order isotropic-nematic (intermediate L/B and small ν), and continuous isotropic-tetratic (small L/B and ν) followed by a continuous tetratic-nematic transition at higher densities. Increasing L/B decreases the pressure, and this effect is more pronounced in the nematic than in the isotropic phase. Increasing both interaction parameters decreases pressure and can lead to phase separation.