Capillarity is the study of interfaces between two immiscible liquids or between a liquid and a vapor. The theory of capillarity was created in the early 1800s, and it is applicable to mesoscopic and macroscopic (>1 μm) systems. In general, macroscopic theories are expected to fail at the <10 nm scales where molecular details may become relevant. In this work, we show that, surprisingly, capillarity theory (CT) provides satisfactory predictions at 2−10 nm scales. Specifically, we perform atomistic molecular dynamics (MD) simulations of water droplets and capillary bridges of different symmetry in contact with various surfaces. The underlying structure of the surfaces corresponds to hydroxilated (crystalline) silica which is modified to cover a wide range of hydrophobicity/hydrophilicity. In agreement with CT, it is found that water contact angle is independent of the droplet/bridge geometry and depends only on the hydrophobicity/hydrophilicity of the surface employed. In addition, CT provides the correct droplet/bridge profile for all (hydrophobic/hydrophilic) surfaces considered. Remarkably, CT works even for the very small droplets/bridges studied, for which the smallest dimension is ≈2 nm. It follows that the concepts of surface tension and contact angle are indeed meaningful at 2−10 nm scales even when, macroscopically, such concepts are not justified. In order to confirm the self-consistency of CT at 2−10 nm scales, we also calculate the capillary forces between different surfaces induced by water capillary bridges. These forces depend on the liquid−vapor surface tension of water, γ. Using CT, the calculated forces indicate that γ = 0.054 ± 0.001 N/m 2 . This is in agreement with the value γ = 0.056 ± 0.001 N/m 2 obtained independently using the Kirkwood−Buff method, and it is consistent with values of γ reported in the literature for the present water model. Confirming the validity of CT at 2−10 nm scales has relevant implications in scientific applications, such as in our understanding of selfassembly processes at interfaces. We discuss briefly this and other consequences of the present results.

We perform molecular dynamics (MD) simulations of water capillary bridges formed between parallel walls. The underlying structure of the walls corresponds to hydroxilated (crystalline) β-cristobalite, modified to cover a wide range of hydrophobicity/hydrophilicity. The capillary bridges are stretched during the MD simulations, from wall–wall separation h = 5 nm up to h ≈ 7.5 nm, until they become unstable and break. During the stretching process, we calculate the profiles of capillary bridges as well as the force and pressure induced on the walls, among other properties. We find that, for all walls separations and surface hydrophobicity/hydrophilicity considered, the results from MD simulations are in excellent agreement with the predictions from capillarity theory (CT). In addition, we find that CT is able to predict very closely the limit of stability of the capillary bridges, i.e., the value of h at which the bridges break. We also confirm that CT predicts correctly the relationship between the surface hydrophobicity/hydrophilicity and the resulting droplets of the capillary bridge rupture. Depending on the contact angle of water with the corresponding surface, the rupture of the capillary bridges results in (i) a single droplet attached to one of the walls, (ii) two identical, or (iii) two different droplets, one attached to each wall. This work expands upon a previous study of nanoscale droplets and (stable) capillary bridges where CT was validated at the nanoscale using MD simulations. The validation of CT at such small scales is remarkable, since CT is a macroscopic theory that is expected to fail at <10 nm scales, where molecular details may become relevant. In particular, we find that CT works for capillary bridges that are ≈2-nm thick, comparable to the thickness of the water–vapor interface.

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We perform molecular dynamics (MD) simulations of nanoscale water capillary bridges (WCBs) expanding between two parallel walls and determine the smallest separation between the walls above which the capillarity theory (CT) remains valid. We consider silica-based walls with tuned surface partial charges that expand from hydrophobic to hydrophilic. We find that the CT is valid (i.e., it predicts successfully the WCB geometry and forces induced on the walls) for, approximately, wall separations h ≥ h 0 = 3.0 nm for all surfaces considered. At these separations, the CT holds without including any line tension and the results are robust relative to the method employed to obtain the WCB profile from MD simulations. At approximately 2.0 nm ≤ h < h 0 , the contact angle of water θ varies with h, suggesting that at such wall separations the CT requires the inclusion of a line tension τ. However, we find that the specific behavior of θ(h) and the associated value of τ are inherently dependent on the method employed to calculate the WCB profile from MD simulations. Interestingly, the forces induced by the WCBs on the walls obey the prediction of the CT without the need to include a line tension for approximately h ≥ 2.5 nm for all surfaces considered. Our results are interpreted in terms of the rearrangement of water molecules within the WCBs and show that the CT breaks down at h < h 0 because its assumptions, that the WCB is a bulklike water volume confined by solid−liquid and liquid−vapor interfaces, do not hold.