A new method for obtaining model-free viscoelastic material properties from atomic force microscopy experiments using discrete integral transform techniques

• Berkin Uluutku,
• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2021, 12, 1063–1077, doi:10.3762/bjnano.12.79

• robustly than analyses in the time domain, especially when specific features are expected in the plots of the viscoelastic functions. For example, the fact that in the Kelvin–Voigt model, non-zero-centered peaks are not expected in the storage compliance (see Figure 11) could be used to discriminate noise

Correction: Extracting viscoelastic material parameters using an atomic force microscope and static force spectroscopy

• Cameron H. Parvini,
• M. A. S. R. Saadi and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2021, 12, 137–138, doi:10.3762/bjnano.12.10

• microscopy (AFM); creep; force mapping; indentation; Kelvin–Voigt; static force spectroscopy (SFS); viscoelasticity; In the “Useful Viscoelastic Quantities” section of the original publication, it is stated that the storage modulus (E′) and storage compliance (J′) are inverses of one another (Equation 10

Extracting viscoelastic material parameters using an atomic force microscope and static force spectroscopy

• Cameron H. Parvini,
• M. A. S. R. Saadi and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 922–937, doi:10.3762/bjnano.11.77

• microscopy (AFM); creep; force mapping; indentation; Kelvin–Voigt; static force spectroscopy (SFS); viscoelasticity; Introduction Modern AFM applications commonly involve testing samples that are soft, biological, or polymeric in nature. Understanding the dissipative nature of these materials at the

• here and that of Lopez et al., the generalized Kelvin–Voigt model has been selected for analysis. The retardance is usually found by taking the derivative of the compliance of a model [17]: Several new parameters have been introduced. The first is the “glassy compliance” (Jg), representing the elastic

• providing a close approximation of the experimental data in panel (a). The loss angle variances shown in panel (d) are driven by significant changes in the storage compliance, shown in panel (b). Summary of viscoelastic models and the corresponding applications [14][15][22]. Generalized Kelvin–Voigt

Nanoscale spatial mapping of mechanical properties through dynamic atomic force microscopy

• Zahra Abooalizadeh,
• Leszek Josef Sudak and
• Philip Egberts

Beilstein J. Nanotechnol. 2019, 10, 1332–1347, doi:10.3762/bjnano.10.132

• and elastic aspects of the contact when examining the data collected without using a relative calibration procedure. We modeled the contact with a highly sophisticated model where the Kelvin–Voigt model can represent the boundary conditions at the tip–sample contact. Thus, the cantilever spring is in

• series with the contact elements, which are two Kelvin–Voigt linear elements with a spring, accounting for the contact stiffness and a dash pot describing the contact damping. Figure 9 illustrates two elements of a spring and a dash pot in parallel, defining the contact at the tip of the cantilever and

• uncovered and covered HOPG step edges. The calibration sample was a polycrystalline Nb glass, which also has very little viscoelasticity, similar to the HOPG sample. As indicated in Figure 10, the calculated elastic modulus using the Kelvin–Voigt model resulted in an elastic modulus of about 2 GPa for the

High-stress study of bioinspired multifunctional PEDOT:PSS/nanoclay nanocomposites using AFM, SEM and numerical simulation

• Alfredo J. Diaz,
• Hanaul Noh,
• Tobias Meier and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2017, 8, 2069–2082, doi:10.3762/bjnano.8.207

• ). Using the Euler–Bernoulli beam model interacting with a Kelvin–Voigt spring-dashpot element at the tip–sample junction, decoupling of the conservative and dissipative interactions of the tip–sample junction is possible [73]. In CRFM-DART, the amplitude and phase of the cantilever response are monitored

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

• contact-resonance AFM (CR-AFM) methods (including dual-amplitude resonance tracking, DART) [2][3][4][5][6], the surface is treated using a linear Kelvin–Voigt model, which consists of a linear spring in parallel with a linear damper. Linear models are used in this case because the oscillation amplitude of

• behaviors, namely creep and stress relaxation [13][14][18][25]. There exist simpler models [13], such as the Maxwell model by itself (described above) and the Kelvin–Voigt model, which consists of a linear spring in parallel with a linear damper (this model is used in CR-AFM [3]). However, in the former

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

• –sample interaction when a 1D model is used, unless the user explicitly programs geometric effects into the model, for example through the use of nonlinear springs [11]. In CR-AFM and DART [3][4][5] surface viscoelasticity is generally interpreted in terms of the Kelvin–Voigt model, consisting of a linear

Capillary and van der Waals interactions on CaF₂ crystals from amplitude modulation AFM force reconstruction profiles under ambient conditions

• Annalisa Calò,
• Oriol Vidal Robles,
• Sergio Santos and
• Albert Verdaguer

Beilstein J. Nanotechnol. 2015, 6, 809–819, doi:10.3762/bjnano.6.84

• range has been modeled with the Kelvin–Voigt model as [27][34][35]: where η is the viscosity in Pascal·second, a0 is an intermolecular distance [14][27] and δ is the tip–sample deformation, i.e., δ = a0 − d. In this work η = 50 Pa·s throughout. In the short range the standard Derjaguin–Muller–Toporov

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

• 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

• that although a Linear Maxwell arm might appear to be too simplistic, there may be samples whose recovery is so slow that their response could be approximately mimicked by this model [26]. Linear Kelvin–Voigt model Another simple model comprised by a spring and a dashpot in parallel is known as the

• Linear Kelvin–Voigt model (Figure 2a). This model is known for successfully describing creep compliance, but failing to describe stress relaxation. The surface lacks a spring that is able to accommodate the immediate force applied to it. Instead, the only spring in the model does not have an immediate

• discontinuous increment of the force occurs at the moment when the probe encounters the surface. Figure 2c shows the creep experiment on a Linear Kelvin–Voigt surface. In the inset of the figure, force and surface position are plotted as a function of the time. In this experiment a downward force of 35 nN is

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

• observables and calculated quantities from the AFM measurement (frequency, phase, amplitude, quality factor, etc.) to the surface properties. In contact resonance typically the Kelvin–Voigt model [40] is used, which consists of a linear spring in parallel with a damper (dashpot). It is incorporated into the

• relaxation and creep compliance. The simplest model that meets these conditions is the standard linear solid (SLS), which combines the Kelvin–Voigt and Maxwell models as illustrated in Figure 1a. Figure 1b illustrates typical tip–sample force trajectories during intermittent-contact AFM single- and dual-mode

Frequency, amplitude, and phase measurements in contact resonance atomic force microscopies

• Gheorghe Stan and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 278–288, doi:10.3762/bjnano.5.30

• with a dashpot (Kelvin–Voigt model) and no lateral contact coupling was considered; vertical and lateral refer here to the normal and parallel directions to the sample surface, respectively. The Euler–Bernoulli equation of motion for damped flexural vibrations of a cantilever beam in air is where the

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

• folding/unfolding. For example, it should be possible to develop methods for fitting experimental data to increasingly elaborate viscoelastic models that go beyond the Kelvin–Voigt model used in the current state of the art in contact-resonance AFM [15][16]. In particular, the Kelvin–Voigt model is not

• and Kelvin–Voigt models. In the SLS configuration a Maxwell element is connected in parallel with a second spring (this setup is also known as the Zener model). The SLS approximation provides the simplest form of a linear viscoelastic approximation that can reproduce both stress relaxation and creep