Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

A simple and efficient quasi 3-dimensional viscoelastic model and software for simulation of tapping-mode atomic force microscopy

Journal Article · · Beilstein Journal of Nanotechnology
DOI:https://doi.org/10.3762/bjnano.6.229· OSTI ID:1240994
 [1]
  1. George Washington Univ., Washington, DC (United States); George Washington University

This study introduces a quasi-3-dimensional (Q3D) viscoelastic model and software tool for use in atomic force microscopy (AFM) simulations. The model is based on a 2-dimensional array of standard linear solid (SLS) model elements. The well-known 1-dimensional SLS model is a textbook example in viscoelastic theory but is relatively new in AFM simulation. It is the simplest model that offers a qualitatively correct description of the most fundamental viscoelastic behaviors, namely stress relaxation and creep. However, this simple model does not reflect the correct curvature in the repulsive portion of the force curve, so its application in the quantitative interpretation of AFM experiments is relatively limited. In the proposed Q3D model the use of an array of SLS elements leads to force curves that have the typical upward curvature in the repulsive region, while still offering a very low computational cost. Furthermore, the use of a multidimensional model allows for the study of AFM tips having non-ideal geometries, which can be extremely useful in practice. Examples of typical force curves are provided for single- and multifrequency tappingmode imaging, for both of which the force curves exhibit the expected features. Lastly, a software tool to simulate amplitude and phase spectroscopy curves is provided, which can be easily modified to implement other controls schemes in order to aid in the interpretation of AFM experiments.

Research Organization:
George Washington Univ., Washington, DC (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
SC0011912
OSTI ID:
1240994
Journal Information:
Beilstein Journal of Nanotechnology, Journal Name: Beilstein Journal of Nanotechnology Vol. 6; ISSN BJNEAH; ISSN 2190-4286
Publisher:
Beilstein InstituteCopyright Statement
Country of Publication:
United States
Language:
English

References (20)

Dynamic atomic force microscopy methods journal September 2002
Viscoelastic Property Mapping with Contact Resonance Force Microscopy journal December 2011
Visualizing the Subsurface of Soft Matter: Simultaneous Topographical Imaging, Depth Modulation, and Compositional Mapping with Triple Frequency Atomic Force Microscopy journal October 2013
Fast nanomechanical spectroscopy of soft matter journal January 2014
An atomic force microscope tip designed to measure time-varying nanomechanical forces journal July 2007
The emergence of multifrequency force microscopy journal April 2012
Nanoscale mechanics by tomographic contact resonance atomic force microscopy journal January 2014
Bimodal frequency-modulated atomic force microscopy with small cantilevers journal January 2015
Vibrations of free and surface‐coupled atomic force microscope cantilevers: Theory and experiment journal September 1996
Energy dissipation in tapping-mode atomic force microscopy journal May 1998
Compositional mapping of surfaces in atomic force microscopy by excitation of the second normal mode of the microcantilever journal January 2004
Inverting dynamic force microscopy: From signals to time-resolved interaction forces journal June 2002
Measuring phase shifts and energy dissipation with amplitude modulation atomic force microscopy journal March 2006
Numerical analysis of dynamic force spectroscopy using the torsional harmonic cantilever journal January 2010
Nanoscale mapping of contact stiffness and damping by contact resonance atomic force microscopy journal May 2012
The role of nonlinear dynamics in quantitative atomic force microscopy journal June 2012
Reconstruction of tip-surface interactions with multimodal intermodulation atomic force microscopy journal September 2013
Towards 4-dimensional atomic force spectroscopy using the spectral inversion method journal January 2013
Probing viscoelastic surfaces with bimodal tapping-mode atomic force microscopy: Underlying physics and observables for a standard linear solid model journal January 2014
Modeling viscoelasticity through spring–dashpot models in intermittent-contact atomic force microscopy journal January 2014

Cited By (3)

Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times journal January 2017
Calculation of standard viscoelastic responses with multiple retardation times through analysis of static force spectroscopy AFM data journal March 2017
Transverse viscoelastic properties of pulp fibers investigated with an atomic force microscopy method journal May 2019