Modeling and Analysis of the Capillary Force for Interactions of Different Tip/Substrate in AFM Based on the Energy Method

This paper presents a simple and robust model to describe the wet adhesion of the AFM tip and substrate joined by a liquid bridge. The effects of contact angles, wetting circle radius, the volume of a liquid bridge, the gap between the AFM tip and substrate, environmental humidity, and tip geometry on the capillary force are studied. To model capillary forces, while a circular approximation for the meniscus of the bridge is assumed, the combination of the capillary adhesion due to the pressure difference across the free surface and the vertical component of the surface tension forces acting tangentially to the interface along the contact line is utilized. Finally, the validity of the proposed theoretical model is verified using numerical analysis and available experimental measurements. The results of this study can provide a basis to model the hydrophobic and hydrophilic tip/surfaces and study their effect on adhesion force between the AFM tip and the substrate.