Topological dereliction in liquid crystal-mediated nanoparticle assembly on spherical droplets

A liquid crystal droplet with planar anchoring offers precise control over the assembly of nanoparticles. The two antipodal defects are sites with high elastic energy, and adsorbed particles alleviate nematic distortions. As the number of particles increases, the multitude of possible arrangements opens the portfolio of metastable arrays. We study the interplay between LC-mediated forces and entropic frustration of nanoparticle assembly on a bipolar droplet via computational methods. The LC is described in the framework of the Landau-de Gennes formalism, and a hybrid relaxation is carried out: a Metropolis sampling algorithm explores the order tensor Q and particles location, while a Ginzburg-Landau relaxation establishes the equilibrium configuration inside the droplet. Strongly anchored homeotropic particles reduce the global free energy by ∽10³ kT when adsorbed at the defects. Through this algorithm, we find a bifurcation on the free energy surface as a function of the number of particles N. At N>5, an onset of entropic frustration aids the particle assembly resulting in kinetically trapped states. These results explain previous experimental observations in micron sized droplets. Futhermore, this algorithm can be generalized to other systems prone to free energy entrapment.