Multiscale modelling of an Atomic Force Microscope for the study of nanoscale contacts

The Atomic Force Microscope (AFM) off ers advantages in studying the surface interactions at nanoscale. However, quantitative measurements in friction mode are not easy to obtain due to the sensitivity of the AFM in regards to external factors. The modelling of nanoscale contacts is an active area of research but the size of typical models is not easily applicable to micro-mechanical devices.This work attempts to bring closer simulations and experiments of contact at nanoscale by modelling the Atomic Force Microscope. It is an ideal system to model, on which nanoscale contact theories can be explored and new techniques can be developed. The laser based measurement chain, used in many AFMs, is modelled through the coupling of the Finite Element Method and ray tracing. A fi rst order approximation of the system is proposed and used to assess the resilience of the popular`Wedge method' in regards to force-based crosstalks. Quantitative diff erences between continuum and discrete models of contact are studied. It is shown that these models do not predict equivalent interaction forces for realistic atomic densities. Since the discrete description is best suited to model the contact at the tip end, a multiscale scheme is proposed to model the AFM cantilever through the coupling of FEM and Molecular Dynamics. The resulting approximation lies between continuum contact theories and fully atomistic models. The Virtual AFM is capable of representing adhesion, stick slips phenomenon and provides a framework where the system, calibration methods and contact models can be systematically evaluated.