Modelling and Nanoscale Force Spectroscopy of Frequency Modulation Atomic Force Microscopy

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In this paper, a simulation model for frequency modulation atomic force microscopy (FM-AFM) operating in constant amplitude dynamic mode is presented. The model is based on the slow time varying function theory. The mathematical principles to derive the dynamical equations for the amplitude and phase of the FM-AFM cantilever-tip motion are explained and the stability and performance of its closed-loop controller to keep the amplitude at constant value and phase at 90° is analysed. Then, the performance of the theoretical model is supported by comparison of numerical simulations and experiments. Furthermore, the transient behaviour of amplitude, phase and frequency shift of FM-AFM is investigated and the effect of controller gains on the transient motion is analysed. Finally, the derived FM-AFM model is used to simulate the single molecule/nanoscale force spectroscopy and study the effect of sample viscosity, stiffness and Hamaker constant on the response of FM-AFM.

Original languageEnglish
Pages (from-to)544-554
Number of pages11
JournalApplied Mathematical Modelling
Early online date31 Oct 2019
Publication statusPublished (in print/issue) - 1 Mar 2020


  • Amplitude
  • Dissipation
  • Frequency modulation AFM
  • Phase
  • Slow time varying function
  • Virial


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