On the frequency dependence of viscoelastic material characterization with intermittent-contact dynamic atomic force microscopy: avoiding mischaracterization across large frequency ranges

• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 1409–1418, doi:10.3762/bjnano.11.125

• on the standard-linear-solid model and on power-law rheological models, which can be thought of as infinite collections of spring–damper combinations that form a continuous relaxation spectrum governed by a power-law. In both approaches, from the constants of the model one can easily obtain the

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

• Santiago D. Solares

Beilstein J. Nanotechnol. 2016, 7, 554–571, doi:10.3762/bjnano.7.49

• AFM simulation. A multifrequency AFM simulation tool based on the above sample model is provided as supporting information. Keywords: atomic force microscopy; modeling; polymers; simulation; spectroscopy; standard linear solid; surface elasticity; surface energy; viscoelasticity; Introduction The

• and interpretation of AFM experiments. The work departs from a previously introduced quasi-three-dimensional (Q3D) implementation of the standard linear solid (SLS) model for representing viscoelastic surfaces [13][14][22][23][24] and considers the enhancement of the model through the incorporation of

• , which can cause the material properties to vary with time and location within the sample. This paper, therefore, offers only a glimpse into the research gaps that exist in the treatment of sample material properties within AFM simulation. Viscoelasticity and the standard linear solid The standard linear

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

• Santiago D. Solares

Beilstein J. Nanotechnol. 2015, 6, 2233–2241, doi:10.3762/bjnano.6.229

• . 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

• modified to implement other controls schemes in order to aid in the interpretation of AFM experiments. Keywords: atomic force microscopy (AFM); modeling; multifrequency; multimodal; polymers; simulation; spectroscopy; standard linear solid; tapping-mode AFM; viscoelasticity; Introduction The

• studies we have used the 1D standard linear solid (SLS) model, which is a well-known textbook problem in viscoelasticity. The model is illustrated in Figure 1a and consists of a linear spring (k1) in parallel with a ‘Maxwell arm,’ which in turn consists of a linear spring (k2) in series with a linear

Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments

• Horacio V. Guzman,
• Pablo D. Garcia and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2015, 6, 369–379, doi:10.3762/bjnano.6.36

• effect cone correction, linear viscoelastic forces or the standard linear solid viscoelastic model. We have compared two numerical integration methods to select the one that offers optimal accuracy and speed. The graphical user interface has been designed to facilitate the navigation of non-experts in

• Paulo [51] combines the relationship between the stress and strain given by the Kelvin–Voigt model and the sample deformation given by Hertz contact mechanics as where η is the viscosity coefficient. Standard linear solid viscoelastic model (SLS) The SLS model is considered to represent the time

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

• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 2149–2163, doi:10.3762/bjnano.5.224

• relaxation, creep or multiple relaxation times, which are very distinct features in materials that exhibit rate-dependent behaviors, such as polymers [22]. A recent attempt has been made to model viscoelastic samples in AFM by using a standard linear solid (SLS) model (which is also discussed below) in order

• customarily used in contact-mode methods [28][29], for which there is no transition between contact and noncontact regimes as in tapping mode, so the sudden force artifact discussed above does not occur. Standard Linear Solid (SLS) model The SLS model is recognized as being the simplest one that is able to

• dissipation for models that accommodate initial response through springs (e.g., standard linear solid and Linear Maxwell) and those that do not (e.g., Linear Kelvin–Voigt and standard linear fluid) is fundamentally different. The latter ones experience immediate viscous dissipation whenever there is a surface

Probing viscoelastic surfaces with bimodal tapping-mode atomic force microscopy: Underlying physics and observables for a standard linear solid model

• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 1649–1663, doi:10.3762/bjnano.5.176

• single-mode and bimodal atomic force microscopy (AFM) with particular focus on the viscoelastic interactions occurring during tip–sample impact. The surface is modeled by using a standard linear solid model, which is the simplest system that can reproduce creep compliance and stress relaxation, which are

• ; frequency modulation; multi-frequency atomic force microscopy; viscoelasticity; standard linear solid; Introduction Atomic force microscopy (AFM) has developed considerably since its introduction in the mid-1980s, and today constitutes one of the most powerful and versatile tools in nanotechnology [1][2][3

• applicable and useful for certain types of samples [9]. The purpose of this paper is to explore computationally the expected physics and the response of the observables for a viscoelastic contact model that exhibits both creep compliance and stress relaxation. Thus, the standard linear solid model (SLS [10

Multi-frequency tapping-mode atomic force microscopy beyond three eigenmodes in ambient air

• Santiago D. Solares,
• Sangmin An and
• Christian J. Long

Beilstein J. Nanotechnol. 2014, 5, 1637–1648, doi:10.3762/bjnano.5.175

• repulsive tip–sample forces were accounted for through a standard linear solid (SLS) model [9] which exhibits both stress relaxation and creep (see Figure 10 and notice the variety of force and surface trajectories for the single and multiple impacts observed in multimodal tapping-mode imaging [20]). Long

• for different free amplitudes and sample parameters; (f) second eigenmode spectra for different free amplitudes. The surface properties were accounted for through a standard linear solid model (see methods section) with K0 = 7.5 N/m, Kinf = 7.5 N/m and Cd = 1 × 10−5 N·s/m for the “soft” sample and K0

• similar to one another as eigenmode spacing increases). The sample and cantilever parameters are the same as for Figure 2. (a) Standard linear solid (SLS) model [9]; (b) illustration of the force trajectory for a single tip–sample impact along with the relaxation trajectory of the surface (notice how the

Trade-offs in sensitivity and sampling depth in bimodal atomic force microscopy and comparison to the trimodal case

• Babak Eslami,
• Daniel Ebeling and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 1144–1151, doi:10.3762/bjnano.5.125

• imaging conditions lead to more or less sensitive phase response for a given type of sample. Figure 5a shows an illustration of the (simulated) phase behavior for the standard linear solid model used here (see section Methods for further details). Clearly the phase response as a function of the cantilever

• of each eigenmode’s frequency to the fundamental frequency), ω is the excitation frequency, and τ is the nominal period of one oscillation. The amplitude and phase were calculated, respectively, as: The repulsive tip–sample forces were accounted for through a standard linear solid (SLS) model [9

Challenges and complexities of multifrequency atomic force microscopy in liquid environments

• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 298–307, doi:10.3762/bjnano.5.33

• N/m, Q1 = 3, Q2 = 6, Afree = 15 nm, and Asetpoint = 70% (a and b only). The sample was modeled as a standard linear solid (see methods section) with Ko = 3.5 N/m, Kinf = 3.5 N/m and Cd = 1 × 10−5 Ns/m. Illustration of eigenmode perturbation for two different cases. The results are color coded for

• natural frequency (see discussion in the text). (a) Standard linear solid model; (b) illustration of tip–sample impact force trajectory and surface recovery for a bimodal imaging case. Acknowledgements The author gratefully acknowledges support from the U.S. Department of Energy, through award

• linear solid (SLS) model (Figure 11) [11][40], but Hertzian contacts [41] were also used in some cases. Long-range attractive interactions were included but for liquid environment simulations were assumed to be screened down to ≈10% of their typical value in air for a tip radius of curvature of 10 nm and

Towards 4-dimensional atomic force spectroscopy using the spectral inversion method

• Jeffrey C. Williams and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2013, 4, 87–93, doi:10.3762/bjnano.4.10

• coefficient that decayed exponentially with the tip position [14] (see equations and further details in [11]). We also conducted simulations in which the conservative and dissipative interactions were accounted for through the standard linear solid model (see Figure 3 and the next section), in combination

• well suited to study stress relaxation. (While this paper is not intended to be a study of surface viscoelasticity, we briefly illustrate the use of slightly more elaborate surface models.) Instead, one could, for example, use the standard linear solid (SLS) model, which is a combination of the Maxwell

• different incoming and outgoing velocity. (a) Schematic of a torsional harmonic cantilever interacting with a surface modeled as a standard linear solid (Ko and Kinf represent linear springs and cd represents a linear damper); (b) collection of force curves acquired for different values of the amplitude