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Singular Loss of Stability Due to Hysteretic Capillary Forces in Atomic Force Microscopy

[+] Author Affiliations
Michael Katzenbach, Harry Dankowicz

University of Illinois at Urbana-Champaign, Urbana, IL

Paper No. DETC2010-28686, pp. 489-497; 9 pages
doi:10.1115/DETC2010-28686
From:
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 12th International Conference on Advanced Vehicle and Tire Technologies; 4th International Conference on Micro- and Nanosystems
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4412-0 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME

abstract

This paper considers discontinuity-induced bifurcations due to the onset and termination of hysteretic, capillary tip-sample interaction forces in a single-mechanical-mode model of intermittent-contact atomic-force microscopy. The theoretical analysis generalizes earlier results for a piecewise-linear hybrid dynamical system to establish the singular termination of branches of steady-state oscillations of the AFM cantilever at critical equilibrium separations corresponding to the grazing contact of the cantilever tip with a fluid layer deposited on the sample. It is shown that this termination is preceded by rapid changes in linearized stability characteristics with one characteristic multiplier going to plus or minus infinity in the deterministic model. The paper describes the application of a discontinuity-mapping technique that allows for unfolding the system response in the vicinity of the grazing condition and the critical equilibrium separation. Numerical simulations and results of parameter continuation are shown to closely agree with the predictions of the theoretical analysis.

Copyright © 2010 by ASME

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