Based on the V-shaped molecule of biaxial nematic liquid crystal
a model of symmetric Y-shaped molecule is developed. In this model the Y-shaped molecule is abstracted to three linked rod-like arms. Using a simple biaxial molecular interaction model in nematic liquid crystal
the interaction energy between two molecules is obtained by the superposition of all rod-to-rod interactions. With the mean field approximation
the free energy of the system is derived and the result shows that the free energy is the function of order parameters. The relationship between the Y-shaped molecule and its ability to form a biaxial nematic phase is established. And phase transitions from isotropic to uniaxial nematic (NI phase transition) and from uniaxial to biaxial nematic(IB phase transition) are obtained.
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references
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