A new model for contact interaction between an atomic force microscope probe and a sample

Polymer nanocomposites have found increasing use in various industries. The mechanical properties of these materials and their operational characteristics are directly dependent on the material structure at the nanoscale. In this context, investigation of filler-matrix interactions and their contribution to generation of the macroscopic properties of the material is the problem of current interest. An atomic force microscope (AFM) opened new possibilities for studying not only the structure of the material at the nanoscale and its local mechanical properties as well. The AFM images the topography of a sample surface by scanning the cantilever over the sample and yields a relationship between the applied load and the penetration depth. An understanding of this relationship requires special mathematical contact interaction models. The most common models for this purpose are the Derjaguin-Muller-Toporov (DMT) and Johnson-Kendall-Roberts (JKR) models. In both models the Hertz solution is used as a basis for the elastic component of contact interaction. However, in contrast to the Hertz model, they are able to take into account intermolecular interaction energy: the DMT model - out of the contact region, and the JKR model - within the contact region. A specific feature of the DMT model is that it does not allow one to evaluate how the probe moving away from the sample surface drags the material. The JKR model makes it possible to approximate experimental data in both cases, i.e., when the cantilever approaches and retracts the sample surface. However, it neglects the stiffness of the AFM cantilever, which should affect the accuracy of the calculation results. In the present paper, a new model for contact interaction between the AFM cantilever and the sample made of soft material is proposed. It takes into account the specific features of the elastic behavior of a cantilever by analyzing the value of probe lifting due to surface forces and by considering the probe as a rotational paraboloid. © 2015 by Begell House, Inc.