Three-dimensional soliton-like distortions in flexoelectric nematic liquid crystals: modelling and linear analysis

This article models experimentally observed three-dimensional particle-like waves that develop in nematic liquid crystals, with negative dielectric and conductive anisotropy, when subject to an applied alternating electric field. The liquid crystal is confined in a thin region between two plates, perpendicular to the applied field. The horizontal, uniformly aligned director field is at equilibrium due to the negative anisotropy of the media. However, such a state is unstable to perturbations that manifest themselves as confined, bullet-like, director distortions travelling up and down the sample at a speed of several hundred microns per second. It is experimentally predicted that flexoelectricity plays a key role in generating the soliton-like behaviour. We develop a variational model that accounts for ansiostropic dielectric, conductive, flexolectric, elastic and viscous forces. We perform a stability analysis of the uniformly aligned equilibrium state to determine the threshold wave numbers, size, phase-shift and speed of the soliton-like disturbance. We show that the model predictions are in very good agreement with the experimentally measured values. The work models and analyzes a three-dimensional soliton-like instability reported, for the first time in flexoelectric liquid crystals, pointing towards a potential application as a new type of nanotransport device.