We report on the formation of organized assemblies of 1 μm-in-diameter colloids (polystyrene (PS)) at the poles of water-dispersed droplets (diameters 7 - 20 μm) of nematic liquid crystal (LC). For 4-cyano-4′-pentylbiphenyl droplets decorated with two to five PS colloids, we found 32 distinct arrangements of the colloids to form at the boojums of bipolar droplet configurations. Significantly, all but one of these configurations (a ring comprised of five PS colloids) could be mapped onto a local (non-close packed) hexagonal lattice. To provide insight into the origin of the hexagonal lattice, we investigated planar aqueous—LC interfaces, and found that organized assemblies of PS colloids did not form at these interfaces. Experiments involving the addition of salts revealed that a repulsive interaction of electrostatic origin prevented formation of assemblies at planar interfaces, and that regions of high splay near the poles of the LC droplets generated cohesive interactions between colloids that could overcome the repulsion. Support for this interpretation was obtained from a model that included (i) a long-range attraction between adsorbed colloids and the boojum due to the increasing rate of strain (splay) of LC near the boojum (splay attraction), (ii) an attractive inter-colloid interaction that reflects the quadrupolar symmetry of the strain in the LC around the colloids, and (iii) electrostatic repulsion between colloids. The model predicts that electrostatic repulsion between colloids can lead to a ∼1,000 kBT energy barrier at planar interfaces of LC films, and that the repulsive interaction can be overcome by splay attraction of the colloids to the boojums of the LC droplets. Overall, the results reported in this paper advance our understanding of the directed assembly of colloids at interfaces of LC droplets.
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