Modelling and Nanoscale Force Spectroscopy of Frequency Modulation Atomic Force Microscopy

Research output: Contribution to journalArticle

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 is explained and the stability and performance of its closed-loop controller to keep the amplitude at constant value and phase at 90o 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.
LanguageEnglish
JournalApplied Mathematical Modelling
Early online date31 Oct 2019
DOIs
Publication statusE-pub ahead of print - 31 Oct 2019

Fingerprint

Frequency Modulation
Atomic Force Microscopy
Frequency modulation
Spectroscopy
Atomic force microscopy
Modeling
Controller
Controllers
Transient Behavior
Motion
Cantilever
Theoretical Model
Closed-loop
Stiffness
Time-varying
Viscosity
Simulation Model
Numerical Experiment
Numerical Simulation
Molecules

Cite this

@article{75299f69e5614c8b98ab352d7f753ba8,
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 is explained and the stability and performance of its closed-loop controller to keep the amplitude at constant value and phase at 90o 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.",
author = "{Farokh Payam}, Amir",
year = "2019",
month = "10",
day = "31",
doi = "10.1016/j.apm.2019.10.051",
language = "English",
journal = "Applied Mathematical Modelling",
issn = "0307-904X",
publisher = "Elsevier",

}

TY - JOUR

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

AU - Farokh Payam, Amir

PY - 2019/10/31

Y1 - 2019/10/31

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 is explained and the stability and performance of its closed-loop controller to keep the amplitude at constant value and phase at 90o 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 is explained and the stability and performance of its closed-loop controller to keep the amplitude at constant value and phase at 90o 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.

U2 - 10.1016/j.apm.2019.10.051

DO - 10.1016/j.apm.2019.10.051

M3 - Article

JO - Applied Mathematical Modelling

T2 - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

ER -