Dynamic Simulation of Nanoscale Particle Motion Driven by Atomic Force Microscope Probe in Nanomanipulation Applications

The Atomic Force Microscope (AFM) is a versatile nanorobotic platform for imaging and controlled manipulation of nanoscale objects. This paper presents a dynamic simulation of a spherical gold nanoparticle pushed by an AFM probe on a silicon oxide substrate. Contact deformation and adhesion are governed by the Johnson-Kendall-Roberts (JKR) model, while friction follows a modified Coulomb law with an interfacial shear strength of 28 MPa. A two-phase algorithm captures the manipulation process. During the sticking phase, the lateral cantilever force increases until reaching the sliding or rolling threshold. In the slipping phase, transient particle motion is solved by integrating Newton’s second law using an adaptive Runge-Kutta integrator, modeling the cantilever as a linear spring. Although the particle’s inertial time scale is negligible compared to the pushing time, leading to quasi-static mean motion, the full dynamic solution captures nanoscale stick-slip cycles. The lateral force oscillates between the static friction threshold and a lower kinetic boundary governed by a kinetic-to-static friction ratio of 0.89, producing approximately 50-nanometer slip events lasting under a microsecond. For the baseline case, sliding initiates at 0.213 seconds with a critical force of 0.647 micro-Newtons, preceding rolling by 0.107 seconds. Across examined material configurations, sliding consistently precedes rolling, with the rolling-to-sliding force ratio ranging from 1.24 to 1.37. Validated against analytical solutions, these parametric findings regarding particle radius, tip radius, and contact angle provide robust guidelines for optimizing AFM nano-manipulation protocols.