Determinate and stochastic orientation dynamics of nematic liquid crystals in the cross electric fields with frequencies up to the megahertz range

Abstract

A theoretical and experimental description is given of the director orientation dynamics in nematic liquid crystals placed in variable electric fields comprising several components and having different directions (crossed fields) and frequencies up to 5 MHz. The calculations show that the system of interest is a physical object governed by non‐linear dynamics. Depending on numerical values of governing parameters, the following director state regimes are obtained: stationary, periodic, quasi‐periodic (multi‐modal), and stochastic strange‐attractor‐type. In the calculations, all the states are obtained by solving a determinate system of two time‐dependent first order non‐linear equations, ignoring the electrohydrodynamic effect. Preliminary verification is performed, and qualitative agreement with the mathematical model under consideration is obtained in the range of frequencies (approximately 100 Hz and higher) that allows electrical conductivity to be ignored. The influence of 2D and 3D rotating electric fields with one frequency, and two‐ or three‐component fields with different frequencies, in the interval from 10 Hz to 5 MHz on the orientation of a nematic liquid crystal is considered.