(499e) Topological Dereliction in Liquid Crystal-Mediated Nanoparticle Assembly

Nematic liquid crystals (LCs) exhibit orientational order that can be manipulated through external stimuli. Particularly, a LC confined in a droplet and subject to tangential molecular orientation at the surface develops two antipodal defects, regions of low order, with high elastic energy. These defects attract nanoparticles in order to alleviate nematic distortions, and thereby offer precise control over their self-assembly. As the number of particles increases so does the multitude of possible configurations that are metastable states. This work is a computational exploration of the delicate interplay between LC-mediated forces and entropic frustration of nanoparticle assembly on the surface of a droplet. The material is described with the tensorial order parameter Q in the Landau-de Gennes formalism, and a novel relaxation technique involves a Ginzburg-Landau minimization of the order field along a Metropolis sampling algorithm of the nanoparticle packing. Particles that induce perpendicular LC alignment are shown to reduce the global free energy by ∼1000k_BT when adsorbed at the defects. Through this sampling technique, we demonstrate that the free energy landscape bifurcates for systems with more than 5 nanoparticles, in which a variety of geometrical arrays are observed. The kinetically trapped states are further studied with a toy model that unveils the glassy dynamics occurring at the poles. These results explain previous experimental observations in micron-sized LC droplets, and the new computational method offer the possibility of studying kinetically trapped states at the continuum scale.