Theoretical modeling of atomic force microscopy in the study of surfaces with complex nanostructures

Standard software supplied to decrypt the atomic force scanning (AFM), based mainly on the models using a classical solution of the Hertz contact of two linearly elastic spheres (or a sphere and a flat half, if one of them has infinite radius). In most cases this is enough. However, there are situations where the Hertz solution should be used with great caution. This work is devoted to the theoretical study of these versions. The results of numerical modeling of contact interaction of the probe of an atomic force microscope and the surface with complex nanostructure are presented. Research was conducted for two types of materials: 1) anisotropic elastic medium (tooth enamel), 2) non-linear elastic finite deformable polymer. These are two classes of materials that are fundamentally different in their mechanical behavior. Respectively different theoretical models are needed for the correct interpretation of experimental data. The problem indentation an AFM probe in a transversally isotropic elastic surface is solved for the materials of the first type. Computational dependencies of reaction force in the probe on the depth of indentation and the degree of anisotropy of the material is built. Computer modeling of AFM probe contact interaction with elastomeric nano strands, which can be formed in the polymer at the crack tip, are carried out for the materials of the second type (elastomers). nanostrand is represented as a long longitudinal convexity, lying on a flat elastic surface. The problem was solved in a three-dimensional formulation.