Multi-scale modeling of an atomic force microscope tip for the study of frictional properties and oscillation behavior

Abstract

In this paper, the vibrational behavior of the atomic force microscope (AFM) on a graphene sheet sample was analyzed using a multi-scale model. The cantilever and silicone tip base were simulated using continuum mechanics and finite element modeling, while the tip apex was modeled using Tersoff potential and structural mechanics modeling. The modified Morse potential was used to model the single-layer graphene, and the Lennard-jones potential was employed as nonlinear springs to model the interactions between the graphene layers and the tip-sample. In addition, the contact behavior between the tip and graphene was investigated by measuring the friction force during the movement of the tip on the graphene sheet, and the results were compared to those obtained from a molecular dynamics simulation and an experimental test. The friction force between the tip and graphene increased by enhancing the tip radius and the contact surface between the tip and the sample. With the initial distance displacement of the tip from the sample, two curves of the tip oscillation amplitude variations and the tip oscillation and excitation vibration phase shift were plotted. In conclusion, the results of the present multi-scale model are compared with those of the MD simulation and demonstrate the strong correlation between the proposed model and the MD model.