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Generalized Hertz model for bimodal nanomechanical mapping.

Aleksander Labuda1, Marta Kocuń1, Waiman Meinhold1

  • 1Asylum Research, an Oxford Instruments company, Santa Barbara, CA, 93117, USA.

Beilstein Journal of Nanotechnology
|August 23, 2016
PubMed
Summary

Bimodal atomic force microscopy simultaneously drives a cantilever at two resonant modes. This technique extracts quantitative nanomechanical properties, revealing tip-sample interactions and tip geometry on surfaces like polystyrene.

Keywords:
bimodal atomic force microscopybimodal spectroscopycontact mechanicsmultifrequencynanomechanical mappingnanomechanics

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Area of Science:

  • Atomic Force Microscopy
  • Nanomechanics
  • Surface Science

Background:

  • Bimodal atomic force microscopy (AFM) utilizes simultaneous excitation of two cantilever eigenmodes.
  • This dual-resonance excitation allows for the measurement of multiple parameters.
  • These parameters are crucial for obtaining quantitative nanomechanical information from sample surfaces.

Purpose of the Study:

  • To present a generalized theoretical framework for extracting nanomechanical sample properties using bimodal AFM.
  • To demonstrate the experimental equivalence of amplitude, phase, and frequency modulation modes for measuring cantilever parameters.
  • To extend contact mechanics theory to power-law tip shapes for analyzing experimental data.

Main Methods:

  • Simultaneous excitation of the first eigenmode at large amplitude and a higher eigenmode at small amplitude.
  • Application of Hertzian contact mechanics theory, extended for power-law tip geometries.
  • Measurement and analysis of four independent observables sensitive to tip-sample interactions.

Main Results:

  • Demonstrated a generalized theoretical framework for bimodal AFM nanomechanical measurements.
  • Confirmed the experimental equivalence of amplitude, phase, and frequency modulation techniques.
  • Successfully extracted the shape and size of an AFM tip interacting with a polystyrene surface.

Conclusions:

  • Bimodal AFM, driven at two eigenmodes, provides a robust method for quantitative nanomechanical analysis.
  • The presented theoretical framework and experimental approach enable precise characterization of tip-sample interactions.
  • This study successfully determined AFM tip geometry by analyzing interactions with a model polystyrene surface.