Capillary condensation under atomic-scale confinement

Abstract

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 [1][2][3][4] . The century-old Kelvin equation 5 is commonly used to describe condensation phenomena and shown to hold well for liquid menisci with diameters as small as several nm [1][2][3][4][6][7][8][9][10][11][12][13][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 . 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 Å 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 (graphite) ones. We show that this agreement is somewhat fortuitous and can be attributed to elastic deformation of capillary walls [23][24][25] , which suppresses giant oscillatory behavior expected due to commensurability between atomic-scale confinement and water molecules 20,21 . Our work provides a much-needed basis for understanding of capillary effects at the smallest possible scale important in many realistic situations.The Kelvin equation predicts that capillaries become spontaneously filled with water at the relative humidity RHK = exp (-2σ/kBTdρN)where σ ≈ 73 mJ m -2 is the surface tension of water at room temperature T, ρN ≈ 3.3×10 28 m -3 is the number density of water, kB is the Boltzmann constant, and d is the diameter of the meniscus curvature. For a two-dimensional (2D) confinement created by parallel walls separated by a distance h, d = h/cos(θ) where θ is the contact angle of water on the walls' material. For capillary condensation to occur at relative humidity (RH) considerably below 100%, equation 1 dictates that d must be comparable to 2σ/kBTρN ≈ 1.1 nm. For example, under typical ambient RH of 40-50%, water is expected to condense in slits with h < 1.5 nm and cylindrical pores with diameters < 3 nm, if θ is close to zero. Even stronger confinement is required for capillaries involving less hydrophilic materials. So far, a broad consensus has been reached that the Kelvin equation remains accurate for menisci with d ≥ 8 nm [1][2][3][4][6][7][8][9][10][11] and can also describe condensation phenomena in hydrophilic pores as small as 4 nm in diameter 12-14 . To achieve agreement with the experiments at this scale, the Kelvin equation is usually modified to account for so-called wetting films that are adsorbed on...

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