Defect screening in faceted emulsion droplets.

Oil emulsion droplets in water have been observed to spontaneously deform into polyhedral shapes at temperatures where the surfactant interface freezes while the bulk oil and water remain liquid. The interface monolayer crystalizes into a hexagonal lattice, which is topologically constrained to accomodate a certain number of defects, namely disclinations. Additional defects, called dislocations, are also expected to be found in crystals with large number of particles. Dislocations are not only thermally induced but, more importantly, they are known to screen the large stresses around disclinations by forming chain-like structures at their vicinity. We address the problem of faceting droplets by studying the interplay between the interface geometry and the arragement of dislocations. We have found that the coupling between the distribution of crystal defects, surface curvature and entropy is key to understand the temperature and size-dependent behaviour of the shape transformations.