Dynamic Modeling of Nanoparticle Pushing Based on V-Shape Cantilevered AFM

Abstract

In this paper, dynamics of pushing process based on V-shape cantilevered atomic force microscopy (VSC-AFM) is studied and the effect of VSC-AFM on required force and time of nanoparticle manipulation is discussed. The VSC is proved to be the most popular design, and the present model offers a more accurate estimation of nanoparticle displacement in pushing based on VSC-AFM. The proposed model takes both adhesion and normal friction forces into account. Pull-off forces are modeled using the Johnson–Kendall–Roberts model. Cantilever forces are modeled using various proposed stiffness models including Butt, Sader, and Neumeister and Ducker (ND) equations for normal stiffness Kz, and Hazel, ND equations for torsional stiffness Kθ, and lateral stiffness Ky by Sader et al. Results of simulations show that the assumption of parallel beam approximation theory is not accurate enough and therefore, it is not suitable for estimation of VSC stiffness in manipulation purposes. Moreover, in nanoparticle pushing based on VSC-AFM, the required pushing force is decreased in comparison with the obtained values based on rectangular cantilevered AFM (RC-AFM). The nanoparticle begins to move very soon with a VSC-AFM in comparison with a practically similar RC-AFM. Furthermore, as a comparison between torsional stiffness equations, ND and Hazel equations are examined. It is observed that Hazel equation are overestimated the torsional stiffness in comparison with ND.