Multi-scale analysis of AFM tip and surface interactions

Abstract

Thoroughly understanding AFM tip-surface interactions is crucial for many experimental studies and applications. It is important to realize that despite its simple appearance, the system of tip and sample surface involves multiscale interactions. In fact, the system is governed by a combination of molecular force (like the van der Waals force), its macroscopic representations (such as surface force) and gravitational force (a macroscopic force). Hence, in the system, various length scales are operative, from sub-nanoscale (at the molecular level) to the macroscopic scale. By integrating molecular forces into continuum equations, we performed a multiscale analysis and revealed the nonlocality effect between a tip and a rough solid surface and the mechanism governing liquid surface deformation and jumping. The results have several significant implications for practical applications. For instance, nonlocality may affect the measurement accuracy of surface morphology. At the critical state of liquid surface jump, the ratio of the gap between a tip and a liquid dome () over the dome height (y 0) is approximately (n − 4) (for a large tip), which depends on the power law exponent n of the molecular interaction energy. These findings demonstrate that the multiscale analysis is not only useful but also necessary in the understanding of practical phenomena involving molecular forces.

Theoretical Models for Surface Forces and Adhesion and Their Measurement Using Atomic Force Microscopy

“…, the interaction of two bodies is affected by the presence of other bodies, and a simple sum of the pair-wise interactions is usually greater than the actual force between the macro bodies [ 39 ]. The degree of non-additivity may depend on the density of the medium, i.e ., for rarefied media it is possible to assume additive forces [ 82 ]. An additive approximation based on the local geometry, material properties and structure of the tip [ 83 ] is used in many practical applications, including atomistic simulations for AFM [ 84 ], because the full tip contains billions of atoms.…”

Trans-scale mechanics: looking for the missing links between continuum and micro/nanoscopic reality

“…This means that the intermolecular power index n persists its trans-scale presentation under a micrometer tip [47,48].…”

A Thin Liquid Film and Its Effects in an Atomic Force Microscopy Measurement

“…[3,4] Hence, it is significant to fully understand the interaction between the AFM probe and sample in AFM measurement; namely, the deflection of the AFM cantilever induced by the interaction between tip and sample should truly reflect the surface topography and mechanical properties of the sample. [5] However, in ambient air, a liquid film may appear on sample surface. The film will interact with the AFM tip, and then affect the deflection of the cantilever leading to distorted force signals.…”