A biaxial nematic liquid crystal composed of matchbox-symmetric molecules

By means of Monte Carlo simulations in the isothermal-isobaric ensemble, we investigate the structure and phase behaviour of a thermotropic liquid crystal composed of matchbox-symmetric (or board-like) molecules. Besides the isotropic phase the liquid crystal exhibits also uniaxial and biaxial nematic phases. The interaction potential is derived through an expansion in terms of Stone's rotational invariants [A. J. Stone, Mol. Phys. 78, 241-256 (1978).] that can be reexpressed in terms of Cartesian tensors. This latter formulation is particularly well suited for computer simulations. We analyse the orientation distribution function which allows us to distinguish between intrinsic and extrinsic biaxiality. In addition, we study the orientation-dependent correlation functions. In the limit of large intermolecular separations, the value of the orientation correlation function corresponds to the uniaxial and biaxial order parameters which are coupled in a complex fashion.