Exploring the basins of attraction of tapping mode atomic force microscopy with capillary force interactions

Nastaran Hashemi, Mark Paul, Harry Dankowicz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationProceedings of the ASME International Mechanical Engineering Congress and Exposition, IMECE 2007
Pages255-261
Number of pages7
DOIs
StatePublished - 2008
EventASME International Mechanical Engineering Congress and Exposition, IMECE 2007 - Seattle, WA, United States
Duration: Nov 11 2007Nov 15 2007

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings
Volume11 PART A

Other

OtherASME International Mechanical Engineering Congress and Exposition, IMECE 2007
CountryUnited States
CitySeattle, WA
Period11/11/0711/15/07

ASJC Scopus subject areas

  • Engineering(all)

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