Deciphering the defect structures around nanoparticle shells self-assembled in nematic droplets using Jones matrix calculations

Nematic liquid crystal droplets are being investigated as a means to create self-assembled shells of quantum dot nanoparticles.1 A rich variety of possible structures is suggested both by experiments using polarized optical microscopy and by numerical modeling, but it is challenging to compare the two. Although some liquid crystal droplets display the well-known ‘Maltese cross’, the structure of the nematic director and topological defects near the self-assembling shell breaks rotational symmetry in a manner not yet well understood. Here we explore one way to characterize the director fields under spherical confinement using Jones matrix calculations. Starting with simulated director fields, we compute the predicted intensity of transmitted light that a nematic director field would show under polarized optical microscopy. This approach will enable us to compare predicted director fields with experimental observations of various assembly outcomes, providing a link between experimental data and theoretical models for controlled self-assembly in liquid crystal droplets.