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Research Papers

Utilizing Off-Resonance and Dual-Frequency Excitation to Distinguish Attractive and Repulsive Surface Forces in Atomic Force Microscopy

[+] Author and Article Information
Andrew J. Dick1

Department of Mechanical Engineering and Materials Science, Rice University, 6100 Main Street, Houston, TX 77005-1892andrew.j.dick@rice.edu

Santiago D. Solares

Department of Mechanical Engineering, 2181 Glenn L. Martin Hall, University of Maryland, College Park, MD 20742ssolares@umd.edu

1

Corresponding author.

J. Comput. Nonlinear Dynam 6(3), 031005 (Dec 16, 2010) (12 pages) doi:10.1115/1.4002341 History: Received July 03, 2009; Revised January 10, 2010; Published December 16, 2010; Online December 16, 2010

A beam model is developed and discretized to study the dynamic behavior of the cantilever probe of an atomic force microscope. Atomic interaction force models are used with a multimode approximation in order to simulate the probe’s response. The system is excited at two-and-a-half times the fundamental frequency and with a dual-frequency signal consisting of the AFM probe’s fundamental frequency and two-and-a-half times the fundamental frequency. A qualitative change in the response in the form of period doubling is observed for the harmonic off-resonance excitation when significantly influenced by repulsive surface forces. Through the use of dual-frequency excitation, standard response characteristics are maintained, while the inclusion of the off-resonance frequency component results in an identifiable qualitative change in the response. By monitoring specific frequency components, the influence of attractive and repulsive surface forces may be distinguished. This information could then be used to distinguish between imaging regimes when bistability occurs or to operate at the separation distance between surface force regimes to minimize force levels.

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Figures

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Figure 1

(a) Atomic force curve for interaction between a multiwall carbon nanotube tip and a single biomolecule modeled with Eqs. 4,5. (b) Simulated phase portraits of dynamic responses to excitation at the fundamental frequency for three different separation distance values.

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Figure 2

(a) Simulated bifurcation diagram of the dynamic responses to excitation at the fundamental frequency. The separation distance is the control parameter. (b) Bifurcation diagram produced using AUTO bifurcation and continuation software for excitation at the fundamental frequency. The separation distance is the control parameter.

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Figure 3

Simulated phase portraits of dynamic responses to excitation at two- and-a-half times the fundamental frequency for (a) a macroscale test apparatus and (b) a microscale AFM cantilever probe

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Figure 4

Frequency spectrum corresponding to dynamic responses of simulated AFM probe excited at two-and-a-half times the fundamental frequency for (a) inactive conditions and (b) active conditions. (c) Simulated bifurcation diagram of the dynamic response to excitation at two-and-a-half times the fundamental frequency. The insert contains an enlarged plot of the upper branch for the smaller separation distance values. The separation distance is the control parameter.

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Figure 5

(a) Maximum tip-sample interaction force values calculated from the results of the AUTO analysis that were used to produce the bifurcation diagram. (b) Maximum tip-sample interaction force values for the separation distance ranges and response conditions presented in Fig. 4 for excitation at two-and-a-half times the fundamental frequency.

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Figure 6

Bifurcation diagram for simulations performed with dual-frequency excitation with the second component set for (a) 1% of the free response amplitude of the first frequency component and (b) one-tenth of a percent of the free response amplitude of the first frequency component. (c) Maximum steady-state tip-sample interaction force versus separation distance for harmonic excitation (solid curve), dual-frequency excitation with the second component equal to 1% of the free response amplitude (dashed curve), and dual-frequency excitation with the second component with one-tenth of a percent free response amplitude (dotted curve).

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Figure 7

Spectral component magnitude versus separation distance at (a) the fundamental frequency, (b) two-and-a-half times the fundamental frequency, (c) one-half of the fundamental frequency, and (d) two times the fundamental frequency for dual-frequency excitation with the second frequency component with 1% free response amplitude of the primary frequency component. Simulated steady-state response of cantilever probe for (e) no significant surface forces, (f) significant influence of only attractive surface forces, and (g) significant influence of surface forces including repulsive forces.

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Figure 8

Force time series corresponding to steady-state response of cantilever probe for (a) no significant surface forces, (b) significant influence of only attractive surface forces, and (c) significant influence of surface forces including repulsive forces. Note that the force units for the three subplots differ. Spectral information corresponding to steady-state response of cantilever probe for (d) no significant surface forces, (e) significant influence of only attractive surface forces, and (f) significant influence of surface forces including repulsive forces.

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Figure 9

Atomic force curve for interaction between mica and a probe tip modeled with Eqs. 7,8

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