Nonlinear modeling of nanoscale interaction forces between atomic force microscope and carbon nanotubes

Abstract

This paper introduces a non-linear non-classical model of nanoscale interaction forces between atomic force microscope and carbon nanotubes in a manipulation process. To accurately model the 3D manipulation process, Prandtl-Tomlinson friction model and the Hertz, JKR, and Lundberg contact mechanics theories were employed, taking into account the CNT geometry and manipulation conditions. The applied forces exerted by both the substrate and the probe on the CNT were extracted. The dynamic characteristics of the nanorods and nanotubes were investigated by employing the non-linear modified couple stress Timoshenko beam. Additionally, the cantilever was modeled using the Mindlin plate theory. The findings showed a good agreement between the experimental data of multi-walled carbon nanotube with a diameter of 100 nm, and the theoretical simulations. In addition to critical force and time, CNT bending results were presented using various Timoshenko theories. In order to validate the results of the maximum bending, the outcomes derived from the computational modeling of a polystyrene nanorod using the Euler-Bernoulli and Timoshenko theories were juxtaposed with the existing classical bending outcomes. Finally, the effects of the size parameter were investigated in non-classical polystyrene models. The findings indicated that considering the size effects is important; For instance, the variance between classical and non-classical models can exceed 57% for l/D = 0.5.