Nanometer-Sized Water Bridge and Pull-Off Force in AFM at Different Relative Humidities: Reproducibility Measurement and Model Based on Surface Tension Change.

This article deals with the analysis of the relationship between the pull-off force measured by atomic force microscopy and the dimensions of water bridge condensed between a hydrophilic silicon oxide tip and a silicon oxide surface under ambient conditions. Our experiments have shown that the pull-off force increases linearly with the radius of the tip and nonmonotonically with the relative humidity (RH). The latter dependence generally consists of an initial constant part changing to a convex-concave-like increase of the pull-off force and finally followed by a concave-like decrease of this force. The reproducibility tests have demonstrated that the precision limits have to be taken into account for comparing these measurements carried out under atmospheric conditions. The results were fitted by a classical thermodynamic model based on water-bridge envelope calculations using the numerical solution of the Kelvin equation in the form of axisymmetric differential equations and consequent calculation of adhesive forces. To describe the measured data more precisely, a decrease of the water surface tension for low RH was incorporated into the calculation. Such a decrease can be expected as a consequence of the high surface curvature in the nanometer-sized water bridge between the tip and the surface.