  Wettability is the affinity of a liquid for a solid surface. For energetic
reasons, macroscopic drops of liquid are nearly spherical away from interfaces
with solids, and any local deformations due to molecular-scale surface
interactions are negligible. Studies of wetting phenomena, therefore, typically
assume that a liquid on a surface adopts the shape of a spherical cap. The
degree of wettability is then captured by the contact angle where the
liquid-vapor interface meets the solid-liquid interface. As droplet volumes
shrink to the scale of attoliters, however, surface interactions become
significant, and droplets gradually assume distorted shapes that no longer
comply with our conventional, macroscopic conception of a drop. In this regime,
the contact angle becomes ambiguous, and it is unclear how to parametrize a
liquid's affinity for a surface. A scalable metric for quantifying wettability
is needed, especially given the emergence of technologies exploiting
liquid-solid interactions at the nanoscale. Here we combine nanoscale
experiments with molecular-level simulation to study the breakdown of spherical
droplet shapes at small length scales. We demonstrate how measured droplet
topographies increasingly reveal non-spherical features as volumes shrink, in
agreement with theoretical predictions. Ultimately, the nanoscale liquid
flattens out to form layer-like molecular assemblies, instead of droplets, at
the solid surface. For the lack of a consistent contact angle at small scales,
we introduce a droplet's adsorption energy density as a new metric for a
liquid's affinity for a surface. We discover that extrapolating the macroscopic
idealization of a drop to the nanoscale, though it does not geometrically
resemble a realistic droplet, can nonetheless recover its adsorption energy if
line tension is properly included.
