How to Characterize Amorphous Shapes: The Tale of a Reverse Micelle

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 metrics─coordinate-pair eccentricity, convexity, and the curvature distribution─that 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.