Formation and annihilation of electrically driven defects in nematic liquid crystals with negative dielectric anisotropy

Orientationally ordered liquid crystals (LCs) exhibit remarkable physical anisotropy and responsiveness to external fields, which give rise to distinguished physical effects and have led to the emergence of a new generation of electric-optical applications. The LCs are also renowned for their abundance of phases and topological defects, which are of significance in studying both fundamental science and practical technology. One simple approach to generating umbilic defects involves applying an electric field to a homeotropically aligned nematic LC with negative dielectric anisotropy <inline-formula><tex-math id="M8">\begin{document}$\Delta \varepsilon $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M8.png"/></alternatives></inline-formula>. However, the influence of material properties and external conditions on the dynamic process of nematic LC defects remains unclear. Here, we select seven kinds of nematic LCs with negative dielectrically anisotropy, ranging from –1.1 to –11.5, to explore the dynamics of electric-field-induced umbilics. By using a linearly increasing electric field parallel to the molecular orientation of LC, we systematically investigate the effects of material property (dielectric anisotropy) and external conditions (temperature and electric field parameters) on the formation and annihilation of umbilic defects. The experimental results show that the dynamic process of forming the umbilic defects in nematic LCs is independent of dielectric anisotropy, temperature, and electric field frequency, but follows the Kibble-Zurek mechanism, in which the density of generated umbilic defects exhibits a power-law scaling with the change of the electric field ramp rate, with a scaling exponent of approximately <inline-formula><tex-math id="M9">\begin{document}$1/2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M9.png"/></alternatives></inline-formula>. Interestingly, a stronger dielectric anisotropy leads to a higher density of umbilic defects. Additionally, a change in temperature has a significant influence on the density of umbilic defects , in which higher temperature leads to greater defect density under the same external electric field conditions. Furthermore, the annihilation rate of umbilic defects is closely related to the material properties and the ramp of the applied electric field. Specifically, the annihilation rate of umbilic defects becomes faster when dielectric anisotropy is stronger or the electric field ramp is larger. This study provides valuable insights into the relationship between the formation and annihilation of defects, material properties, and external conditions in nematic LCs with dielectrically negative anisotropy, contributing to our comprehensive understanding of the dynamic process of topological defects in soft matter.