Liquid crystal display panels subjected to tactile force will show ripple propagation on screens. Tactile forces change tilt angles of liquid crystal molecules and alter optical transmission so as to generate ripple on screens. Based on the Ericksen-Leslie theory, this study investigates ripple propagation by dealing with tilt angles of liquid crystal molecules. Tactile force effects are taken into account to derive the molecule equation of motion for liquid crystals. Analytical results show that viscosity, tactile force, the thickness of cell gap, and Leslie viscosity coefficient lead to tilt angle variation. Tilt angle variations of PAA liquid crystal molecules are sensitive to tactile force magnitudes, while those of 5CB and MBBA with larger viscosity are not. Analytical derivation is validated by numerical results.
Many physical phenomena exhibited by the nematic phase liquid crystals (LC), such as unusual flow properties or the LC response to electric and magnetic fields, can be studied by treating LC as a continuous medium. Ericksen and Leslie [
Brochard et al. [
Liquid crystal display panels subjected to tactile force will show ripple propagation on screens. Tactile forces change tilt angles of liquid crystal molecules and alter optical transmission so as to generate ripple on screens. Based on the Ericksen-Leslie theory, this paper aims to develop LC dynamics subject to tactile force. Tactile force effects are taken into account to derive the molecule director equation of motion for liquid crystals. A theoretical model is thus proposed to analyze the tilt angle of nematic liquid crystals subject to tactile forces.
Figure
Homeotropic alignment LC layer sandwiched between parallel substrates, where
Based on separation of variables, assume
In Case 2, which happens when the tactile force is negligible, the solution for
The above derivation is based on 1D LC model. Further, this study intends to use (
Directors of LC molecules with homeotropic alignment are changed by Poiseuille flow.
The molecule ignores the moment of inertia; that is,
Shear rate
The LC sample is homeotropic alignment, and we have the boundary conditions
The shearing velocity belongs to Poiseuille flow [
According to the above assumptions, (
On boundary
Consider the following.
On boundary
Subject to both electric field of 8.9 V and tactile force, simulation results for Case 1 are depicted in Figures
Comparison of molecule tilt angles between cell gap thicknesses of (a) 3
Comparison of molecule tilt angles between cell gap thicknesses of (a) 3
Comparison of molecule tilt angles among cell gap thicknesses of (a) 3
Comparison of molecule tilt angles with different LC materials (a) 5CB, (b) MBBA, and (c) PAA when a tactile force is applied to LCD screen.
Tilt angle variations are shown under different voltages in Figure
Comparison of molecule tilt angles between cell gap thicknesses of 3
Comparison of molecule tilt angles between cell gap thicknesses of 3
Based on (
(a) Comparison of molecule tilt angles depicted in 3
(a) Comparison of molecule tilt angles depicted in 4
(a) Comparison of molecule tilt angles depicted in 5
(a) Comparison of molecule tilt angles depicted in 3
(a) Comparison of molecule tilt angles depicted in 4
(a) Comparison of molecule tilt angles depicted in 5
(a) Comparison of molecule tilt angles depicted in 3
(a) Comparison of molecule tilt angles depicted in 4
(a) Comparison of molecule tilt angles depicted in 5
The Ericksen-Leslie theory deals with the dynamics of nematic liquid crystals. Based on the Ericksen-Leslie theory, this paper contributes to LC dynamics subject to tactile force. LC molecule tilt leads to a change in the optical intensity transmitted through a liquid crystal cell. LCD panels subject to tactile force will show ripple-like propagation on screens. The present results show that the viscosity, tactile force, thickness of cell gap, and Leslie viscosity coefficient are the factors of tilt angle variation. Tilt angle variations of PAA liquid crystal molecules are sensitive to tactile force magnitudes, while those of 5CB and MBBA with larger viscosity are not. Analytical derivation has been carried out in this study and analytical results have been validated by numerical results.
This work was supported by Chi Mei Optoelectronics Corp. and Innolux Display Corp. in Taiwan.