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

Abstract

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.