Among all possible shapes of a volume V, a sphere has the smallest surface area A. Therefore, liquid droplets are spherical, minimizing their interfacial energy gA for a given interfacial tension g. We demonstrate¹ that liquid oil droplets in water, stabilized by a common surfactant, adopt icosahedral and other faceted shapes, tunable by temperature T, above the bulk melting point of the oil T_m. Although emulsions have been studied for centuries, no faceted droplets have ever been detected.

We attribute the observed transition from a spherical to an icosahedral shape to the interplay between g and the elastic properties of the interfacial monomolecular layer, which in these systems crystallizes at T>T_m. We propose a simple theoretical model, which reproduces the observed transition, emphasizing the role of topological lattice defects in this system.

In addition to faceting, we observe a wide range of other unexpected phenomena, such as a spontaneous splitting of liquid droplets and tail growth. The common physical mechanism, responsible for all these effects will be demonstrated¹.

These phenomena allow deeper insights into the fundamentals of molecular elasticity to be gained, opening new horizons for a wide range of technologies, from self-assembly of complex shapes to new delivery strategies in bio-medicine.

[1] S. Guttman, Z. Sapir, M. Schultz, A. V. Butenko, B. M. Ocko, M. Deutsch, and E. Sloutskin, PNAS (under revision, 2015)