Twist fluctuations and rotational diffusion of the director near hedgehog defects in nematic droplets

When strong homeotropic boundary conditions are set at the interface of emulsion droplets containing nematic liquid crystal (NLC), the spherical confinement combined with the system bulk elasticity is known to produce a point-like defect called a radial hedgehog with topological charge +1. However, this configuration is not necessarily the ground state. For favorable ratios of the elastic constants, a twist perturbation has been observed near the defect. Here we report experimental observation and quantification of twist fluctuations in emulsion droplets of the NLC 5CB. These fluctuations can be understood as a new kind of rotational diffusion corresponding to a collective motion of the whole system. To explain this phenomenon, we build a model for the nematic director that accounts quantitatively for the origin of our experimental observations and also provides insight about the physical properties of the defect. The model offers a more complete understanding of the transition between pure radial and twisted configurations in spherically confined NLC, and it could useful for future investigation of trapped colloidal particles in nematic hosts.