Multidimensional Director Modeling Using the Q Tensor Representation in a Liquid Crystal Cell and Its Application to the π Cell with Patterned Electrodes

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  • Mori Hiroyuki
    Ashigara Research Laboratories, Fuji Photo Film Co., Ltd., 210 Nakanuma, Minamiashigara, Kanagawa 250–0193, Japan
  • Gartland Eugene C. Jr.
    Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242, U.S.A. Liquid Crystal
  • Kelly Jach R.
    Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, Ohio 44242, U.S.A.
  • Bos Philip J.
    Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, Ohio 44242, U.S.A.

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  • Multidimensional Director Modeling Using the Q Tensor Representation in a Liquid Crystal Cell and Its Application to the .PI. Cell with Patterned Electrodes.

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To estimate numerically multidimensional director configurations in a liquid crystal cell, it is important to use the Q tensor representation of the strain free energy because it solves the problem of the difference between the directors, n and -n, in the Frank-Oseen free energy representation. In this paper, we discuss the numerical methods for calculating the multidimensional director configurations, using Berreman's Q tensor representation. Numerical issues discussed include the relaxation method for the director calculation, the liquid crystal (LC)/glass interface problem, the boundary conditions for the electric potential, and the possible ways to obtain faster convergence. We compare the calculated results obtained from the Frank-Oseen and Q tensor representations. By considering a π cell with patterned electrodes, we show the consistency of the model used with experimental observations. The calculated data explain well the position shift of the defects that appear in the test π cell.

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