Nanometer-scale Bodies Mechanical Interaction Mathematical Model

Atomic force microscopy (AFM) is based on registration of the interaction of the AFM probe with the sample. A new mathematical model has been developed for the interpretation of experimental data. The relevance of the work is caused by the need to correctly account for the effects that arise in the interaction of bodies at the nanoscale under conditions of large deformations. Standard models (Deryagin-Muller-Toporov (DMT), Johnson-Kendall-Rob­erts (JKR), etc.)  represent a modification of the Hertz model, whose assumptions are not always correct for specific cases. The new model takes into account the curvilinearity of the interface between the probe and the material. Also in the process of model construction the disappearance and appearance of new nonlinear contact surfaces and the corresponding change of surface tension energy were taken into account, which plays an important role in indentation of soft materials (polymers, biological tissues). The results of testing the developed model on experimental data of nanoindentation showed its ability to describe with high accuracy the effects accompanying the contact and the indentation process: a jump-like retraction of the probe into the sample under the influence of surface effects, sticking of the probe at its removal from the sample, and the moment of probe detachment from the sample. A comparison of the obtained model with the results given by the standard DMT and JKR models was carried out. It has demonstrated the greater flexibility of the new model and its ability to describe the experimental data more accurately.