Implementation of $Q$-Tensor Model in Three-Dimensional Finite Element Method Simulator

概要

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In this paper, we report the first successful implementation, to the best of our knowledge of a $Q$-tensor model in a full three-dimensional (3-D) finite element method (FEM) simulator. Our FEM simulation code is based on the Landau–de Gennes $Q$-tensor model as well as the models of Dickmann and Nakagawa. The Oseen–Frank free-energy representation was formulated into a 3-D FEM code wherein tensor-order parameters as well as scalar-order parameters were employed for handling the defects and topological transitions such as splay-to-bend transition for the optically compensated bend (OCB) mode. The accuracy of our FEM simulator was verified using our simulation results with Mori's simulation data for the OCB mode. Splay-to-bend transition voltage was calculated to be 4 V according to the $Q$-tensor-model-based simulation while the conventional vector-model-based FEM solver showed 8 V. Our comparative study revealed that the vector model overestimates splay-to-bend voltage for the OCB mode.
Published by the Japan Society of Applied Physics through the Institute of Pure and Applied Physicsの論文
2008-07-25