Elastic Rectangular Plate Attached To The Liquid Crystal Molecules Bond System Biaxial Nematic Phase Transition

The phase transitions of molecular system consisted by rectangular plates connected by flexible chain are studied in this paper. We consider two kinds of molecular model.(1) A molecular system consisted by double rectangular plates is considered. Based on a simple interaction energy between molecules and the approximation of mean-field theory, as the interaction strength of flexible chain increases, four kinds of phase diagrams in the plane of molecular structure and temperature are obtained.In the first kind (where the interaction strength is the smallest) there is only one Landau point that allows system directly transit from isotropic phase to biaxial phase.In the second kind Landau point spreads to a Landau curve. The region of positive uniaxial phase increases and that of negative uniaxial phase decreases.In the phase diagram, a first order transition from uniaxial phase to biaxial phase appears. In the third kind Landau point also spreads to a Landau curve, but the region of negative uniaxial phase disappears.In the fourth kind (the interaction strength of flexible chain is the largest), the range of Landau curve becomes narrower. The above phase diagrams show that the phase transition types, appearance and the range of Laudau curve depend on the size of the flexible chain.(2) The second model is a molecular system consisted by a rectangular plate and a stick. Based on a simple interaction energy between molecules and the approximation of mean-field theory, four kinds of phase diagrams in the plane of temperature and molecular structure are obtained. In the first kind (where the interaction strength is to make two sticks parallel) there is only one Landau point that allows system directly transit from isotropic phase to biaxial phase.In the second kind Landau point moves to the right, and the region of positive uniaxial phase increases and that of negative uniaxial phase disappears.In the third kind (where the interaction strength is to make two sticks vertical), Landau point spreads to a Landau curve. The system can enter to the biaxial phase at high temperature easily. In the fourth kind (where the interaction strength is to make three sticks vertical), Landau curve becomes Landau point. The above phase diagrams show that the phase transition type, appearance and the range of Laudau curve depend on the molecular structure and the flexible chain.