V-shaped Molecules Of Liquid Crystal Phase Transition Theory

In nematic liquid crystal , the anisotropy of the molecular shape leads to phase transitions from isotropic phase to nematic, from unixial nematic to biaxial nematic. When the molecular shape has cylindrical symmetry , system only occurs uniaxial nematic phase. When the molecular has no cylindrical symmetry, molecular interactions make molecules orient along two perpendicular directions, so a biaxial nematic phase occurs in the system.In order to investigate analytically the phase transitions and Landau point temperatures as functions of molecular structure parameter in non-symmetric V-type, symmetric V-type molecule systems, compare the phase transitions in the V-type and Y-type molecule sytem, and obtain the optimal molecular structure for generating biaxial phase, we, in this paper, abstract a V-shaped biaxial liquid crystal molecule found in recent experiments into two linked rod-like arms with the interarm angleα. The interaction energy of the molecule is obtained by the superposition of all rod-to-rod interactions.Using mean field theory and numerical calculations, the phase diagrams in the plane of reduced temperature and molecular structure parameter are obtained. Relationship between reduced temperature and molecular structure at the Landau point where system directly goes from isotropic to biaxial phase is discussed. Furthermore, we extend this V-shaped molecule model to the Y-shaped molecule model and discuss the corresponding Landau point temperature. Results show that among the Y-shaped, nonsymmetric V-shaped, symmetric V-shaped liquid crystal molecular systems, the Y-shaped has the highest Landau point temperature, the nonsymmetric V-shaped has the lower, the symmetric V-shaped has the lowest Landau point temperature. These suggest that the Y-shaped system is easier than the symmetric V-shaped system, while the symmetric V-shaped is in turn easier than the nonsymmetric V-shaped to enter into biaxial phase.