Microcantilever chaotic motion suppression in tapping mode atomic force microscope

The tapping mode is one of the mostly employed techniques in atomic force microscopy due to its accurate imaging quality for a wide variety of surfaces. However, chaotic microcantilever motion impairs the obtention of accurate images from the sample surfaces. In order to investigate the problem the tapping mode atomic force microscope is modeled and chaotic motion is identified for a wide range of the parameter's values. Additionally, attempting to prevent the chaotic motion, two control techniques are implemented: the optimal linear feedback control and the time-delayed feedback control. The simulation results show the feasibility of the techniques for chaos control in the atomic force microscopy.

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Numerical Exploratory Analysis of Dynamics and Control of an Atomic Force Microscopy in Tapping Mode with Fractional Order

Shock and Vibration ◽

10.1155/2020/4048307 ◽

2020 ◽

Vol 2020 ◽

pp. 1-18

Author(s):

Mauricio A. Ribeiro ◽

Jose M. Balthazar ◽

Wagner B. Lenz ◽

Rodrigo T. Rocha ◽

Angelo M. Tusset

Keyword(s):

Mathematical Model ◽

Atomic Force Microscopy ◽

Feedback Control ◽

Fractional Order ◽

Delayed Feedback Control ◽

Linear Feedback ◽

Tapping Mode ◽

Force Microscopy ◽

Control Techniques ◽

Atomic Force

In this paper, we investigate the mechanism of atomic force microscopy in tapping mode (AFM-TM) under the Casimir and van der Waals (VdW) forces. The dynamic behavior of the system is analyzed through a nonlinear dimensionless mathematical model. Numerical tools as Poincaré maps, Lyapunov exponents, and bifurcation diagrams are accounted for the analysis of the system. With that, the regions in which the system presents chaotic and periodic behaviors are obtained and investigated. Moreover, the fractional calculus is introduced into the mathematical model, employing the Riemann-Liouville kernel discretization in the viscoelastic term of the system. The 0-1 test is implemented to analyze the new dynamics of the system, allowing the identification of the chaotic and periodic regimes of the AFM system. The dynamic results of the conventional (integer derivative) and fractional models reveal the need for the application of control techniques such as Optimum Linear Feedback Control (OLFC), State-Dependent Riccati Equations (SDRE) by using feedback control, and the Time-Delayed Feedback Control. The results of the control techniques are efficient with and without the fractional-order derivative.

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Time Delayed Feedback Control Applied in an Atomic Force Microscopy (AFM) Model in Fractional-Order

Journal of Vibration Engineering & Technologies ◽

10.1007/s42417-019-00166-5 ◽

2019 ◽

Vol 8 (2) ◽

pp. 327-335 ◽

Cited By ~ 3

Author(s):

Angelo M. Tusset ◽

Mauricio A. Ribeiro ◽

Wagner B. Lenz ◽

Rodrigo T. Rocha ◽

Jose M. Balthazar

Keyword(s):

Atomic Force Microscopy ◽

Feedback Control ◽

Fractional Order ◽

Delayed Feedback ◽

Delayed Feedback Control ◽

Force Microscopy ◽

Atomic Force ◽

Time Delayed Feedback

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Frequency Response of Carbon Nanotube Probes during Tapping Mode of Atomic Force Microscopy

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.378.466 ◽

2013 ◽

Vol 378 ◽

pp. 466-471

Author(s):

Po Jen Shih ◽

Shang Hao Cai

Keyword(s):

Atomic Force Microscopy ◽

Carbon Nanotube ◽

Atomic Force Microscope ◽

Frequency Response ◽

Tapping Mode ◽

Force Microscopy ◽

Frequency Responses ◽

Atomic Force ◽

Frequency Drop ◽

Atomic Force Microscope Measurement

The dynamic behaviors of carbon nanotube probes applied in Atomic Force Microscope measurement are of interest in advanced nanoscalar topography. In this paper, we developed the characteristic equations and applied the model analysis to solve the eigenvalues of the microcantilever and the carbon nanotube. The eigenvalues were then used in the tapping mode system to predict the frequency responses against the tip-sample separations. It was found that the frequency drop steeply if the separation was less than certain distances. This instability of frequency is deduced from the jump of microcantilever or the jump of the carbon nanotube. Various lengths and binding angles of the carbon nanotube were considered, and the results indicated that the binding angle dominated the frequency responses and jumps.

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Exploring the Basins of Attraction of Tapping Mode Atomic Force Microscopy With Capillary Force Interactions

Volume 11: Micro and Nano Systems, Parts A and B ◽

10.1115/imece2007-43778 ◽

2007 ◽

Cited By ~ 2

Author(s):

Nastaran Hashemi ◽

Mark Paul ◽

Harry Dankowicz

Keyword(s):

Atomic Force Microscopy ◽

Capillary Force ◽

Basins Of Attraction ◽

Large Set ◽

Tapping Mode ◽

Force Microscopy ◽

Atomic Force ◽

Wide Range ◽

Periodic Dynamics ◽

Mode Atomic Force Microscopy

We numerically explore the nonlinear dynamics of the oscillating cantilever tip in tapping mode atomic force microscopy. The cantilever dynamics are determined by complex force interactions between the sample surface and the oscillating cantilever tip which are dominated by attractive, adhesive, and repulsive contributions depending on the instantaneous position of the cantilever. We use a model proposed by Zitzler et al that includes a capillary force interaction due to the thin film of water that covers all surfaces as a result of ambient humidity. As the cantilever approaches the surface a meniscus is formed and as the cantilever retracts this water layer forms a neck and eventually breaks. This introduces hysteresis since the formation of the meniscus and the breaking of the water neck occur at different spatial locations during an oscillation of the cantilever. Using forward-time simulation with event handling techniques tailored for situations with rapid changes in force interactions we find three classes of steady-state dynamics: (i) a branch of solutions with periodic dynamics and large amplitude of oscillation; (ii) a branch of solutions with periodic dynamics and small amplitude of oscillation; (iii) windows of irregular aperiodic dynamics. We quantify the global basins of attraction for these solutions by performing a large set of numerical simulations over a wide range of initial conditions. Our findings provide a useful framework for further studies interested in controlling these dynamics.

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