Validation of Capillarity Theory at the Nanometer Scale by Atomistic Computer Simulations of Water Droplets and Bridges in Contact with Hydrophobic and Hydrophilic Surfaces

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 mu m) 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, ?. Using CT, the calculated forces indicate that gamma = 0.054 +/- 0.001 N/m(2). This is in agreement with the value ? = 0.056 +/- 0.001 N/m(2) obtained independently using the Kirkwood-Buff method, and it is consistent with values of gamma 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 self-assembly processes at interfaces. We discuss briefly this and other consequences of the present results.