Dynamic Behavior of Nanoparticles in Pushing Based on V-Shape Cantilevered AFM

In this paper, pushing of nanoparticles based on V-shape cantilevered (VC) AFM is modeled and effect of VC on pushing critical force and time is investigated. Simulation algorithm is analogous to our prior work for a rectangular cantilevered (RC) AFM. Dynamic equations are developed based on the free body diagram of pushing. Substrate moves in constant speed and tip force FT increases until overcome to adhesion of particle/substrate. The proposed model includes both adhesion and normal friction forces. Pull-off forces are modeled using the JKR contact model. Cantilever forces are modeled using equations by Butt, Sader, and Neumeister for normal stiffness, and equations by Hazel, and Neumeister for torsional stiffness, and finally the lateral stiffness by Sader and Green. Results show error of various stiffness equations in comparison with Neumeister's equations which are known as the most accurate ones. Also in this paper condition in pushing with VC AFM, sliding occur before rolling similar to RC AFM based pushing and particle start to motion sooner with a lower pushing force.

Keywords:

AFM , V-shape , Pushing , Nanoparticles , Dynamic