Modelling of interaction between the atomic force microscope probe with a polymer surface with account of van der Waals forces and surface tension

The paper presents results of computer simulation of the probe contact mode atomic force microscope (AFM) in interaction with the surface of a nonlinear elastic polymer material. The modeling took into account not only the forces of mechanical response to indentation of the probe into the polymer, but also such important factors as to the nanoscale surface tension forces associated with the curvature of the sample surface and intermolecular interactions of the van der Waals forces. The corresponding contact boundary-value problem is solved numerically to determine the force of the nonlinear elastic response. Comparison of the results for the nonlinear case with a classical solution of the Hertz problem for linearly elastic medium held. For the intermolecular and surface forces, the analytical formulas relating the strength of the interaction with the geometry of the probe and the distance between its apex and the sample surface.