Mathematical Model of the Tapping Mode Atomic Force Microscopy in the Study of Subsurface Structures of Filled Elastomers
摘要
The purpose of the work was to substantiate the methodology for constructing the subsurface layer structure of the material under study. The method is suitable for studying soft filled materials. This method consists in constructing a three-dimensional image of a rigid filler structure hiding under the surface using a phase portrait and a relief map of the sample surface. The model considers the AFM cantilever as a spring pendulum with given parameters (stiffness and resonant frequency) and calculated ones (effective mass and internal viscosity). The parameters of the numerical model describe the real experimental setup. The behavior of the material is described by an elastic model, the dissipation is given by the forces of adhesion that draw the probe into the material after contact with its surface. For a given material and experimental parameters, the obtained phase shift map is interpreted as the result of the influence of rigid objects located at a certain depth. The values of these depths are converted into the relief of hidden subsurface structures.