Chaos

The speed limiting phenomenon in dynamic atomic force microscopy

Journal article (2017)

Authors

A. Keyvani Janbahan Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering , TNO
F. Alijani Dynamics of Micro and Nano Systems - Mechanical, Maritime and Materials Engineering
H. Sadeghian TNO, Eindhoven University of Technology
J.F.L. Goosen Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
A. van Keulen Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
Research Group
Computational Design and Mechanics (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2017 A. Keyvani Janbahan, F. Alijani, Hamed Sadeghian, Klara Maturova, J.F.L. Goosen, A. van Keulen
DOI: https://doi.org/10.1063/1.5000130
Atomic force microscopy Control theory Chaotic systems Phase space methods Attractors
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Published Date

2017

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Precision and Microsystems Engineering

Research Group

Computational Design and Mechanics

Abstract

This paper investigates the closed-loop dynamics of the Tapping Mode Atomic Force Microscopy using a new mathematical model based on the averaging method in Cartesian coordinates. Experimental and numerical observations show that the emergence of chaos in conventional tapping mode AFM strictly limits the imaging speed. We show that, if the controller of AFM is tuned to be faster than a certain threshold, the closed-loop system exhibits a chaotic behavior. The presence of chaos in the closed-loop dynamics is confirmed via bifurcation diagrams, Poincaré sections, and Lyapunov exponents. Unlike the previously detected chaos due to attractive forces in the AFM, which can be circumvented via simple changes in operation parameters, this newly identified chaos is seemingly inevitable and imposes an upper limit for the closed-loop bandwidth of the AFM.

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