Modelling and Nanoscale Force Spectroscopy of Frequency Modulation Atomic Force Microscopy

Amir Farokh Payam

doi:10.1016/j.apm.2019.10.051

Modelling and Nanoscale Force Spectroscopy of Frequency Modulation Atomic Force Microscopy

Amir Farokh Payam

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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Abstract

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 language	English
Pages (from-to)	544-554
Number of pages	11
Journal	Applied Mathematical Modelling
Volume	79
Early online date	31 Oct 2019
DOIs	https://doi.org/10.1016/j.apm.2019.10.051
Publication status	Published (in print/issue) - 1 Mar 2020

Keywords

Amplitude
Dissipation
Frequency modulation AFM
Phase
Slow time varying function
Virial

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10.1016/j.apm.2019.10.051

Accepted_AMM AFPAuthor Accepted Manuscript, 887 KB

Cite this

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title = "Modelling and Nanoscale Force Spectroscopy of Frequency Modulation Atomic Force Microscopy",

abstract = "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.",

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T1 - Modelling and Nanoscale Force Spectroscopy of Frequency Modulation Atomic Force Microscopy

AU - Farokh Payam, Amir

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

AB - 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.

KW - Amplitude

KW - Dissipation

KW - Frequency modulation AFM

KW - Phase

KW - Slow time varying function

KW - Virial

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U2 - 10.1016/j.apm.2019.10.051

DO - 10.1016/j.apm.2019.10.051

M3 - Article

SN - 0307-904X

VL - 79

SP - 544

EP - 554

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

ER -

Modelling and Nanoscale Force Spectroscopy of Frequency Modulation Atomic Force Microscopy

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