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

Abstract

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.

Thickness and Structure of Adsorbed Water Layer and Effects on Adhesion and Friction at Nanoasperity Contact

“…However, when RH > 23%, an adsorbed water layer begins to form and expands from the initial liquid island to the entire graphene surface, thereby increasing the F c and F a as RH rises to~45% [88]. Several other studies demonstrated that the increase of RH above 50% may result in a decrease of F a , especially on hydrophilic surfaces (Figure 10c) [80,81,93]. Xiao and Qian [80] built a new formulation to fit this complex RH-dependent adhesion behavior and explain the observed decrease in F a at high RH.…”

“…Chen et al [4] measured the F a on a hydrophobic H-terminated Si surface (water contact angle~83 • ) and found that the force decreases substantially as the test environment transits from humid air to liquid water. During this process, A Hamaker is reduced by 80% [80,85,93]. On a hydrophobic Si surface, water adsorption is very weak (Figure 5d), so F c is negligible and F vdW decreases, leading to a considerable decrease of F a .…”

“…The variations in adhesion as a function of surface wettability obey the model in Equation 3. Many research groups have shown the possibility of controlling interfacial adhesion by adjusting the wettability of a surface [91][92][93]. As shown in Figure 12, upon either nor p-type doping with subsurface polyelectrolytes, graphene surfaces become more hydrophilic [59], water adsorption is enhanced, and F a (i.e., the pull-off force) increases significantly.…”

“…A significant decrease in Fc at high RHs is a consequence of a marked decrease in the Laplace pressure relative to the size of the water bridge, which is considered to play a dominant role in the drop in Fa with RH in many studies [15]. Bartosík et al [93] investigated the Fa between a The schematic shown in Figure 10 reveals that the adhesion behavior strongly depends on RH. However, the contribution of this factor to adhesion is not considered in Equation (3).…”

A Model for the Characterization of the Polarizability of Thin Films Independently of the Thickness of the Film

“…This distance is the jump-to-contact distance D jtc and it will be determined by the mechanical instability of the cantilever when the electrostatic force is applied. If the cantilever is considered a harmonic oscillator, D jtc can be obtained from K=dF elec /dD where K is the spring constant and F elec the electrostatic force) It may also be produced by the formation of a water bridge between tip and sample 23 . The error increases when h increases and  decreases and it vanishes when h→0 and →∞.…”