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

Abstract

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.

Synthesis of Raspberry-like Nanoparticles via Surface Grafting of Positively Charged Polyelectrolyte Brushes: Colloidal Stability and Surface Properties

“…The higher adhesion is expected as the presence of humidity results in attractive capillary forces between the tip and the dry sample, which is independent of the tip−sample intrinsic interactions. 63 The smooth surface of the pristine PS core shown previously in the SEM images (Figure 1) results in low roughness values (1.5 and 1.8 nm when dry and in DI water, respectively). Raspberry-like globules are observed for the brush-bearing NPs in both dry and DI water, which is consistent with the SEM images and consistent with a collapsed, "mushroom-like" brush structure.…”

Salicylhydroxamic Acid as a Novel Switchable Adhesive Molecule

“…This indicates that the capillary effect is not a factor in our adhesion testing. Additionally, we estimated the capillary force (0.894 mN from eq S1) 49 to be negligible when compared to the F max values (>20 mN).…”

Modulation of the Capillary Force Profile at the Solid–Solid Interface through Topographical Modifications

“…Furthermore, the modeling approach developed in this study was also verified with the experimentally validated model of Payam. 20 They determined capillary forces acting between a spherical AFM probe (with radius 30 nm) and a planar substrate at different separation distances. The contact angles were taken as θ 1 = 60°and θ 2 = 30°at a relative humidity of 95%.…”

“…The formation of liquid menisci between the adhering bodies was simulated. There are generally two approaches, molecular − and macroscopic − based, adopted in the literature to model the liquid meniscus formed between solid interfaces for the computation of capillary forces. Cheng et al used molecular dynamics simulation and demonstrated that the macroscopic method predicted the formation of liquid meniscus and capillary forces very accurately for the height of a liquid bridge as small as 2 molecular diameters (∼1 nm).…”

“…The macroscopic method is useful in predicting capillary forces between large-scale solid interfaces as well. Several scientific studies are available on the modeling of capillary forces among solid bodies using the macroscopic method, − and the model’s predictions were verified by the experimentally measured data obtained from atomic force microscopy (AFM) . The prediction of capillary forces at solid–solid interfaces will assist in optimizing surface modifications to augment or mitigate capillary condensation.…”