Capillary force between wetted nanometric contacts and its application to atomic force microscopy.

We extend to the case of perfect wetting the exact calculation of Orr et al. (J. Fluid. Mech. 1975, 67, 723) for a pendular ring connecting two dry surfaces. We derive an approximate analytical expression for the capillary force between two highly curved surfaces covered by a wetting liquid film. The domain of validity of this expression is assessed and extended by a custom-made numerical simulation based on the full exact mathematical description. In the case of attractive liquid-solid van der Waals interactions, the capillary force increases monotonically with decreasing vapor pressure up to several times its saturation value. This accurate description of the capillary force makes it possible to estimate the adhesion force between wet nanoparticles; it can also be used to quantitatively interpret pull-off forces measured by atomic force microscopy.