Non-classic modeling of three-dimensional manipulation with different geometry of atomic force microscopy components: Multi-scale approach

The size effect must be considered for dynamic modeling of an AFM since the dimensions of the AFM, are in micro-scale. In this study, a three-dimensional multi-scale method based on a non-classical continuum mechanic theory is developed in order to include material length scale parameter (MLSP) in the dynamic behavior of manipulation carried out by AFM. First, the governing equations of Macro Field (MF) are derived using the modified coupled stress theory and the Kirchhoff plate model. Moreover, Nano Field (NF) is modeled using the molecular dynamics equations. The MF and the NF are then combined employing the multi-scale algorithm. Rectangular and dagger cantilevers are taken into account to obtain manipulation results. The influence of two types of tip on the manipulation results is also investigated. The obtained results show that the deformations of the AFM components in non-classic models are less than the one in the classical model. Furthermore, Root Mean Square (RMS) results for a nano-particle demonstrates that damage and deformation of the nano-particle are underestimated by the classical model. The investigations carried out in the present study show the significance of employing the non-classical theory for analyzing AFM performance, particularly for estimation of separation time span.