Optical Fluctuation of Texture in Nematic Liquid Crystal Droplets

We report the observation of texture of a nematic liquid crystal droplet using a high-speed camera mounted on a polarizing optical microscope. The dark crossed texture obtained by the polarizing optical microscope of a nematic liquid crystal droplet has texture wobbles, which are related to the director field fluctuation excited by thermal energy. We confirm relaxation and oscillation modes. An exact solution of the director fluctuation modes with one-constant approximation and an external electric field is proposed. The theoretical predictions of the relaxation time match with our experimental results when varying the temperature, droplet size, and electric field. Relaxation time was insensitive to the temperature, increased with radius of droplet and slightly decreased with electric field. Several oscillation modes, which have no specific trend, were also found. The external electric field freezes the oscillation modes.