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 a 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. We measure the director fluctuations about this state and compare them to the predictions of a theoretically calculated normal mode analysis. Three distortion modes are evident experimentally using two different optical microscopy techniques. Using polarizing microscopy, we observe the motion of the two extinction axis and identify two angular diffusions: a fast one, following the angle the axes make in respect to each other, and a slow one, tracking the angle they make in respect to the polarizers’ orientations. In bright field, we are also able to measure the translational motion of the hedgehog. Analysis of these distortion modes indicates the possibility of an instability toward a twisted hedgehog configuration in droplets of the NLC 5CB.