Capillary condensation under atomic-scale confinement

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 used by microelectronics, pharmaceutical, food and other industries ^1–4. The century-old Kelvin equation ⁵ is frequently used to describe condensation phenomena and has been shown to hold well for liquid menisci with diameters as small as several nanometres ^1–4,6–14. For even smaller capillaries that are involved in condensation under ambient humidity and so of particular practical interest, the Kelvin equation is expected to break down because the required confinement becomes comparable to the size of water molecules ^1–22. Here we use van der Waals assembly of two-dimensional crystals to create atomic-scale capillaries and study condensation within them. Our smallest capillaries are less than four ångströms in height and can accommodate just a monolayer of water. Surprisingly, even at this scale, we find that the macroscopic Kelvin equation using the characteristics of bulk water describes the condensation transition accurately in strongly hydrophilic (mica) capillaries and remains qualitatively valid for weakly hydrophilic (graphite) ones. We show that this agreement is fortuitous and can be attributed to elastic deformation of capillary walls ^23–25, which suppresses the giant oscillatory behaviour expected from the commensurability between the atomic-scale capillaries and water molecules ^20,21. Our work provides a basis for an improved understanding of capillary effects at the smallest scale possible, which is important in many realistic situations.