Aerosol-OT
reverse micelles represent a chemical construct where
surfactant molecules self-assemble to stabilize water nanodroplets
1–10 nm in diameter. Although commonly assumed to adopt a spherical
shape, all-atom molecular dynamics simulations and some experimental
studies predict a nonspherical shape. If these aggregates are not
spherical, then what shape do they take? Because the tools needed
to evaluate the shape of something that lacks regular structure, order,
or symmetry are not well developed, we present a set of three intuitive
metricscoordinate-pair eccentricity, convexity, and the curvature
distributionthat estimate the shape of an amorphous object,
and we demonstrate their use on a simulated aerosol-OT reverse micelle.
These metrics are all well-established methods and principles in mathematics,
and each provides unique information about the shape. Together, these
metrics provide intuitive descriptions of amorphous shapes, facilitate
ways to quantify those shapes, and follow their changes over time.