Computer Simulation of Band Texture Formation in Liquid Crystalline Polymer

The relationship between the vector version and tensor version of Frank distortion energy for the liquid crystal was established, through which the relationship between the Frank elastic constants and the expansion coefficients of spatial derivatives for the orientational order parameter Sij of liquid crystalline polymer was obtained. Ginzberg-Landau equation for the orientational order parameter Sij was numerically solved by using the cell dynamical system, which involves a free energy functional containing Landau-de Gennes orientational free energy, Maier-Saupe anisotropic interaction free energy and Frank distortion free energy. Incase of the splay elastic constant being much lager than the bend elastic constant, the evolution process of band textures in liquid crystalline polymer during the shear relaxation and its small angle light scattering patterns were simulated. The influence of preshear rate on the band forming and band structure was investigated. It was found that the formation of longitudinal band textures is due to the much rapider longitudinal splay relaxation than the latitudinal bend relaxation, and the induced times of band forming and the characteristic length of band structure decrease with the increasing of preshear rate, which is consistent with the experimental results.