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

Modeling viscoelasticity through spring–dashpot models in intermittent-contact atomic force microscopy

Journal Article · · Beilstein Journal of Nanotechnology
DOI:https://doi.org/10.3762/bjnano.5.224· OSTI ID:1628613
 [1];  [2]
  1. Univ. of Maryland, College Park, MD (United States). Dept. of Mechanical Engineering; DOE/OSTI
  2. Univ. of Maryland, College Park, MD (United States). Dept. of Mechanical Engineering

We examine different approaches to model viscoelasticity within atomic force microscopy (AFM) simulation. Our study ranges from very simple linear spring–dashpot models to more sophisticated nonlinear systems that are able to reproduce fundamental properties of viscoelastic surfaces, including creep, stress relaxation and the presence of multiple relaxation times. Some of the models examined have been previously used in AFM simulation, but their applicability to different situations has not yet been examined in detail. The behavior of each model is analyzed here in terms of force–distance curves, dissipated energy and any inherent unphysical artifacts. We focus in this paper on single-eigenmode tip–sample impacts, but the models and results can also be useful in the context of multifrequency AFM, in which the tip trajectories are very complex and there is a wider range of sample deformation frequencies (descriptions of tip–sample model behaviors in the context of multifrequency AFM require detailed studies and are beyond the scope of this work).

Research Organization:
Univ. of Maryland, College Park, MD (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
OSTI ID:
1628613
Journal Information:
Beilstein Journal of Nanotechnology, Journal Name: Beilstein Journal of Nanotechnology Vol. 5; ISSN BJNEAH; ISSN 2190-4286
Publisher:
Beilstein InstituteCopyright Statement
Country of Publication:
United States
Language:
English

References (35)

Effect of contact deformations on the adhesion of particles journal November 1975
Dynamic atomic force microscopy methods journal September 2002
How to measure energy dissipation in dynamic mode atomic force microscopy journal February 1999
Amplitude curves and operating regimes in dynamic atomic force microscopy journal February 2000
Biaxial elastic–viscoplastic behavior of Nafion membranes journal January 2011
Determination and simulation of nanoscale energy dissipation processes in amplitude modulation AFM journal May 2010
Probing of Polymer Surfaces in the Viscoelastic Regime journal February 2014
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
Effects of elastic and inelastic interactions on phase contrast images in tapping-mode scanning force microscopy journal October 1997
Energy dissipation in tapping-mode atomic force microscopy journal May 1998
Relationship between phase shift and energy dissipation in tapping-mode scanning force microscopy journal November 1998
Contact-resonance atomic force microscopy for viscoelasticity journal January 2008
Relationship between Q-factor and sample damping for contact resonance atomic force microscope measurement of viscoelastic properties journal June 2011
Mapping of conservative and dissipative interactions in bimodal atomic force microscopy using open-loop and phase-locked-loop control of the higher eigenmode journal August 2011
Loss tangent imaging: Theory and simulations of repulsive-mode tapping atomic force microscopy journal February 2012
Selection of higher eigenmode amplitude based on dissipated power and virial contrast in bimodal atomic force microscopy journal September 2014
Frequency response of higher cantilever eigenmodes in bimodal and trimodal tapping mode atomic force microscopy journal November 2010
Measuring the loss tangent of polymer materials with atomic force microscopy based methods journal March 2014
Measuring phase shifts and energy dissipation with amplitude modulation atomic force microscopy journal March 2006
The band excitation method in scanning probe microscopy for rapid mapping of energy dissipation on the nanoscale journal September 2007
Dual-frequency resonance-tracking atomic force microscopy journal October 2007
Characterization of surface stiffness and probe–sample dissipation using the band excitation method of atomic force microscopy: a numerical analysis journal December 2011
Conservative and dissipative tip-sample interaction forces probed with dynamic AFM journal October 1999
Attractive and repulsive tip-sample interaction regimes in tapping-mode atomic force microscopy journal August 1999
Dynamics of a vibrating tip near or in intermittent contact with a surface journal May 2000
Tip-surface forces, amplitude, and energy dissipation in amplitude-modulation (tapping mode) force microscopy journal October 2001
Unifying theory of tapping-mode atomic-force microscopy journal July 2002
Velocity dependence of energy dissipation in dynamic force microscopy: Hysteresis versus viscous damping journal July 2005
Atomic Force Microscope journal March 1986
General Theory of Microscopic Dynamical Response in Surface Probe Microscopy: From Imaging to Dissipation journal November 2004
Identification of Nanoscale Dissipation Processes by Dynamic Atomic Force Microscopy journal July 2006
Effect of Microscopic Nonconservative Process on Noncontact Atomic Force Microscopy journal December 2000
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

Cited By (10)

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions journal January 2016
High-stress study of bioinspired multifunctional PEDOT:PSS/nanoclay nanocomposites using AFM, SEM and numerical simulation journal January 2017
Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times journal January 2017
Advanced atomic force microscopy techniques III text January 2016
A 2D finite element model for shear wave propagation in biological soft tissues: Application to magnetic resonance elastography
  • Bilasse, M.; Chatelin, S.; Altmeyer, G.
  • International Journal for Numerical Methods in Biomedical Engineering, Vol. 34, Issue 8 https://doi.org/10.1002/cnm.3102
journal May 2018
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
Theory of Single-Impact Atomic Force Spectroscopy in liquids with material contrast journal May 2018
Determination of the viscoelastic properties of a single cell cultured on a rigid support by force microscopy journal January 2018
Mechanical stability of the cell nucleus – roles played by the cytoskeleton in nuclear deformation and strain recovery journal May 2018