Determination of mechanical properties of materials in terms of models of interaction between afm probe and sample surfac

The atomic force microscope (AFM) is widely used in characterizing the relief of the examined material and its nanoscale mechanical properties, which can differ strongly from its macroscale characteristics. The AFM uses a probe mounted on a spring cantilever beam (cantilever) to scan a sample surface. Scanning is done by approaching and retracting the probe at different points of the material surface. Force -versus-distance curves typically show the cantilever deflection with respect to the vertical displacement of its rigidly fastened probe. The analysis of the AFM force-distance curve makes it possible to determine the mechanical properties of materials. However, in order to get reliable information, the appropriate contact interaction models need to be used. With these models, one can evaluate forces that affect the motion of an AFM probe and correctly interpret the experimental data. This paper presents a review of the literature relevant to key models describing the interaction of the AFM probe with the sample surface and aimed at determining such local mechanical properties of materials as elastic modulus, surface energy and dissipative characteristics. The mechanical effect of the probe on the sample is modeled using two approaches: 1) modeling a microscope probe as a mass-spring system, 2) continuum representation of a microscope probe by a beam with distributed mass. Static contact and dynamic interactions between the probe and the sample surface (Herz, Deryagin-Muller-Toporov, Johnson-Kendall-Roberts models) are examined. Application of numerical methods such as the finite element method and the methods of molecular dynamics is considered for modeling contact interaction problems. Distinguishing features of the examined models and the range of their applicability are discussed.