Abstract
Cooled oil emulsion droplets in aqueous surfactant solution have been observed to flatten into a remarkable host of polygonal shapes with straight edges and sharp corners, but different driving mechanisms - (i) a partial phase transition of the liquid bulk oil into a plastic rotator phase near the droplet interface and (ii) buckling of the interfacially frozen surfactant monolayer enabled by drastic lowering of surface tension - have been proposed. Here, combining experiment and theory, we analyse the hitherto unexplored initial stages of the evolution of these 'shape-shifting' droplets, during which a polyhedral droplet flattens into a polygonal platelet under cooling and gravity. Using reflected-light microscopy, we reveal how icosahedral droplets evolve through an intermediate octahedral stage to flatten into hexagonal platelets. This behaviour is reproduced by a theoretical model of the phase transition mechanism, but the buckling mechanism can only reproduce the flattening if surface tension decreases by several orders of magnitude during cooling so that the flattening is driven by buoyancy. The analysis thus provides further evidence that the first mechanism underlies the 'shape-shifting' phenomena.
Highlights
The culmination of the geometric preoccupations of Ancient Greece was doubtless the classification of the five platonic solids [1]
Cooled oil emulsion droplets in aqueous surfactant solution have been observed to flatten into a remarkable host of polygonal shapes with straight edges and sharp corners, but different driving mechanisms—(i) a partial phase transition of the liquid bulk oil into a plastic rotator phase near the droplet interface and (ii) buckling of the interfacially frozen surfactant monolayer enabled by a drastic lowering of surface tension—have been proposed
The elastic buckling mechanism, can only reproduce the experimental observations if surface tension decreases by at least four orders of magnitude during the cooling, so that the flattening is driven by a competition between buoyancy and elasticity
Summary
The culmination of the geometric preoccupations of Ancient Greece was doubtless the classification of the five platonic solids [1] It is topology, that dictates that one of their number, the icosahedron, should abound in nature, among the shapes of virus capsids and other biological structures [2]: Euler’s formula implies the formation of at least 12 topological defects in a hexagonal lattice on the surface of a spherical vesicle. IV show that the elastic buckling mechanism can only reproduce the observed deformations if the process is driven by the interplay of elasticity and buoyancy This requires surface tension to decrease by at least four orders of magnitude, yet the resulting estimate of the bending modulus of the droplets obtained in Sec. IV is three orders of magnitude below its experimental values. The analysis suggests that it is the formation of a rotator phase rather than elastic buckling at ultralow surface tension that drives the shape-shifting processes observed so far [5,8,9,11,18,19]
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