Tip-sample interaction force modeling for AFM simulation, control design, and material property measurement

Tip-sample interaction force is the key feature measured and manipulated by Atomic Force Microscopy (AFM). It is the main reason why this interaction must be the major component of quasistatic and dynamic controls used in AFM instrumentation. Many dynamic control models are available for AFM but only few explicitly contain the tip-sample forces. One of them is based on asymptotic dynamics using Krylov-Bogoliubov-Mitropolsky (KBM) averaging. In the latter the tip-sample forces acting on approach and retraction are considered. Conservative Hertz model was applied in the first AFM simulations with KMB averaging. This simple and useful model does not cover many aspects of AFM tip-sample interactions (adhesion, energy dissipation, etc.) vital for accurate control of the instrument. The purpose of this paper is to provide adequate interaction force models for AFM control system and illustrate specific features, such as jumping between amplitude branches, adhesive avalanche, etc. These features are routinely observed in AFM experiments but mostly discarded in the control system. We suggest a hybrid model for the control system design to account for these phenomena. The model is based on matching the Maugis´s JKR-DMT transition that describes elasto-adhesive interaction after geometrical contact (penetration) and the Integrated Lennard-Jones model with adhesive avalanche that describes the molecular level interaction before the contact. Matching parameters can be calculated based on the assumption that both curves describe the same physical interactions and must match smoothly at the common point of geometrical contact. Hybrid model algorithms are developed that can be used in AFM real-time adaptive control systems with parameter estimation.