Structural stability of nematic liquid crystal droplets in the light of the catastrophe theory

Dynamical systems and defects in liquid crystals (LCs) are described using topological methods. Meanwhile, the director field distribution in LC droplets is affected by many bulk and surface factors that are difficult to take into account in the topological analysis. Therefore, the structural instability of a LC droplet formed in a magnetic field has been investigated by us in the framework of the catastrophe theory. The effect of temperature on the control parameters of the cusp catastrophe, which leads to the transition from a bipolar structure with extended poles to the homogeneous or radial configuration, has been estimated. It has been established from the potential curves that the transition is induced by the variation in the LC director orientation between the potential minima related to the LC polymer anchoring energy and magnetic field. The interplay of the cusp catastrophe control parameters and anchoring parameters has been elucidated.