Comparisons between the Vector and Tensor Approaches for the 3-Dimensional Director Simulation of Liquid Crystal Displays

In this paper, we investigated dynamic behaviors of liquid crystal director profiles by simulating two different modeling equations based on vectorial and tensorial approaches. By performing 3-dimensional simulation for a unit pixel, we found that the simulation results from the each of modeling equations lead to different motional behaviors of liquid crystal directors around the disclination line. This is due to the fact that the vectorial approach has a physically meaningless sign of liquid crystal director ${\overline{n}}$. Consequently, it is clarified that the tensorial approach gives more realistic behaviors for the rotation of the directors around the disclination line when the voltages were removed since it maintains nematic symmetry that gives an equivalence of ${\overline{n}}$ and its opposite - ${\overline{n}}$.