  Molecular dynamics simulations are used to study the capillary adhesion from
a nonvolatile liquid meniscus between a spherical tip and a flat substrate. The
atomic structure of the tip, the tip radius, the contact angles of the liquid
on the two surfaces, and the volume of the liquid bridge are varied. The
capillary force between the tip and substrate is calculated as a function of
their separation h. The force agrees with continuum predictions for h down to ~
5 to 10nm. At smaller h, the force tends to be less attractive than predicted
and has strong oscillations. This oscillatory component of the capillary force
is completely missed in the continuum theory, which only includes contributions
from the surface tension around the circumference of the meniscus and the
pressure difference over the cross section of the meniscus. The oscillation is
found to be due to molecular layering of the liquid confined in the narrow gap
between the tip and substrate. This effect is most pronounced for large tip
radii and/or smooth surfaces. The other two components considered by the
continuum theory are also identified. The surface tension term, as well as the
meniscus shape, is accurately described by the continuum prediction for h down
to ~ 1nm, but the capillary pressure term is always more positive than the
corresponding continuum result. This shift in the capillary pressure reduces
the average adhesion by a factor as large as 2 from its continuum value and is
found to be due to an anisotropy in the pressure tensor. The cross-sectional
component is consistent with the capillary pressure predicted by the continuum
theory (i.e., the Young-Laplace equation), but the normal pressure that
determines the capillary force is always more positive than the continuum
counterpart.
