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.

本文针对负介电与导电各向异性的向列相液晶（nematic liquid crystals）在施加交变电场（alternating electric field）时产生的实验观测到的三维类粒子波展开建模研究。该液晶被限制在与外加电场垂直的两平板间的薄区域内，由于介质的负各向异性，其水平均匀排列的指向矢场（director field）原本处于平衡态，但该平衡态对扰动不稳定——这些扰动表现为受限的子弹状指向矢畸变，以数百微米每秒的速度在样品中往复传播。实验研究证实，挠曲电效应（flexoelectricity）在类孤子行为（soliton-like behaviour）的产生过程中发挥关键作用。我们构建了考虑各向异性介电、导电、挠曲电、弹性与粘性力的变分模型（variational model），并对均匀对齐的平衡态开展稳定性分析，以此确定类孤子扰动的临界波数、尺度、相移与传播速度。结果表明，模型预测值与实验测量值吻合极佳。本研究对首次在挠曲电液晶（flexoelectric liquid crystals）中报道的三维类孤子不稳定性进行建模与分析，为其作为新型纳米传输器件（nanotransport device）的潜在应用指明了方向。