  Capillary condensation of water is ubiquitous in nature and technology. It
routinely occurs in granular and porous media, can strongly alter such
properties as adhesion, lubrication, friction and corrosion, and is important
in many processes employed by microelectronics, pharmaceutical, food and other
industries. The century-old Kelvin equation is commonly used to describe
condensation phenomena and shown to hold well for liquid menisci with diameters
as small as several nm. For even smaller capillaries that are involved in
condensation under ambient humidity and, hence, of particular practical
interest, the Kelvin equation is expected to break down, because the required
confinement becomes comparable to the size of water molecules. Here we take
advantage of van der Waals assembly of two-dimensional crystals to create
atomic-scale capillaries and study condensation inside. Our smallest
capillaries are less than 4 angstroms in height and can accommodate just a
monolayer of water. Surprisingly, even at this scale, the macroscopic Kelvin
equation using the characteristics of bulk water is found to describe
accurately the condensation transition in strongly hydrophilic (mica)
capillaries and remains qualitatively valid for weakly hydrophilic (graphene)
ones. We show that this agreement is somewhat fortuitous and can be attributed
to elastic deformation of capillary walls, which suppresses giant oscillatory
behavior expected due to commensurability between atomic-scale confinement and
water molecules. Our work provides a much-needed basis for understanding of
capillary effects at the smallest possible scale important in many realistic
situations.
