Contrary to everyday
experience, where all liquid droplets assume
rounded, near-spherical shapes, the temperature-tuning of liquid droplets
to faceted polyhedral shapes and to spontaneous splitting has been
recently demonstrated in oil-in-water emulsions. However, the elucidation
of the mechanism driving these surprising effects, as well as their
many potential applications, ranging from faceted nanoparticle synthesis
through new industrial emulsification routes to controlled-release
drug delivery within the human body, have been severely hampered by
the micron-scale resolution of the light microscopy employed to date
in all in situ studies. Thus, the thickness of the interfacially frozen
crystalline monolayer, suggested to drive these effects, could not
be directly measured, and the low limit on the droplet size still
showing these effects remained unknown. In this study, we employ a
combination of super-resolution stimulated emission depletion microscopy,
cryogenic transmission and freeze-fracture electron microscopy, to
study these effects well into the nanometer length scale. We demonstrate
the occurrence of the faceting transition in droplets spanning an
incredible 12 decades in volume from nanoliters to yoctoliters and
directly visualize the interfacially frozen, few nanometer thick,
crystalline monolayer suggested to drive these effects. Furthermore,
our measurements allow placing an upper-limit estimate on the two-dimensional
Young modulus of the interfacial nanometer-thick surface crystal in
the smallest droplets, providing insights into the virtually unexplored
domain of nanoelasticity.