Nanoparticles adsorbed at the interface of nematic liquid crystals are known to form ordered structures whose morphology depends on the orientation of the underlying nematic field. The origin of such structures is believed to result from an interplay between the liquid crystal orientation at the particles' surface, the orientation at the liquid crystal's air interface, and the bulk elasticity of the underlying liquid crystal. In this work, we consider nanoparticle assembly at the interface of nematic droplets. We present a systematic study of the free energy of nanoparticleladen droplets in terms of experiments and a Landau-de Gennes formalism. The results of that study indicate that, even for conditions under which particles interact only weakly at flat interfaces, particles aggregate at the poles of bipolar droplets and assemble into robust, quantized arrangements that can be mapped onto hexagonal lattices. The contributions of elasticity and interfacial energy corresponding to different arrangements are used to explain the resulting morphologies, and the predictions of the model are shown to be consistent with experimental observations. The findings presented here suggest that particle-laden liquid crystal droplets could provide a unique and versatile route toward building blocks for hierarchical materials assembly.growing body of theoretical and experimental work has sought to direct the assembly of molecules and nanoparticles at interfaces by exploiting the elastic forces that arise in liquid crystals (LCs) (1-5). Nematic LCs possess orientational order along a unit vector, the so-called nematic director. They also exhibit defects-regions of low order whose morphology and position depends on a delicate balance between elastic, enthalpic, and interfacial contributions to the free energy. The orientation of nematic LCs and any corresponding defects can be perturbed by introducing particles. The symmetry and structure of the director field around a particle also depends on the interaction between the LC and the particle, often referred to as anchoring. Particles with perpendicular (homeotropic) anchoring induce either dipolar or quadrupolar symmetry in the LC, leading to formation of point defects or Saturn-ring defects, respectively (6). Particles with planar anchoring induce quadrupolar symmetry, which is accompanied by two surface defects, generally referred to as boojums (6). Distortions of the nematic field cost elastic energy and therefore give rise to anisotropic, long-range interactions between particles. Indeed, particles in nematic LCs aggregate and "bind," thereby minimizing the volume of defects and the large free energy that is associated with their elastic strain. Equilibrium particle arrangements in nematic LCs depend strongly on the topology of the underlying defects. Homeotropic particles with point, dipolar defects form chains along the nematic director, whereas quadrupolar, Saturn-ring defects form kinked chains that are perpendicular to the nematic director (7). Particles with planar anchor...