Frequency-dependent nanomechanical profiling for medical diagnosis

• Santiago D. Solares and
• Alexander X. Cartagena-Rivera

Beilstein J. Nanotechnol. 2022, 13, 1483–1489, doi:10.3762/bjnano.13.122

• piezoelectrically actuated membrane equipped with a mechanical response sensing mechanism [31][32]. Illustration of a 2D adherent cell indented by a micrometer-sized spherical AFM probe, as well as storage and loss modulus calculated from the parameterized Generalized Maxwell model for 2D adherent normal and

Interaction between honeybee mandibles and propolis

• Leonie Saccardi,
• Franz Brümmer,
• Jonas Schiebl,
• Oliver Schwarz,
• Alexander Kovalev and
• Stanislav Gorb

Beilstein J. Nanotechnol. 2022, 13, 958–974, doi:10.3762/bjnano.13.84

• properties of propolis, a generalized Maxwell model was used [31]. The viscosity of the sample was estimated from experimental force curves using the following equation [32][33]: where d is the displacement, t is the time under load, E∞/E1/E2 and η1/η2 are the Young’s moduli and viscosities of the static and

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

• help inform dynamic AFM characterization. Keywords: dynamic atomic force microscopy; Generalized Maxwell model; loss modulus; storage modulus; viscoelasticity; Introduction There have been significant methodology developments since the introduction of atomic force microscopy (AFM) in the mid-1980s [1

• correspondence principle, was introduced by Efremov et al. [34], which they applied to living cells. In contrast to the discrete nature of the Generalized Maxwell model, which allows the use of arbitrary parameters at different time scales modeled by different spring–damper combinations, they focused primarily

• viscoelastic harmonic functions as a function of frequency in the range of frequencies involved in the experiment. For example, for the Generalized Maxwell model, which this paper focuses on, the storage shear modulus, G′, which accounts for the elastic behavior of the material under harmonic excitation, is

Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy

• Miead Nikfarjam,
• Enrique A. López-Guerra,
• Santiago D. Solares and
• Babak Eslami

Beilstein J. Nanotechnol. 2018, 9, 1116–1122, doi:10.3762/bjnano.9.103

• Laplace transformed stress is regarded as the excitation and the transformed strain as the response. Numerical simulations corresponding to a parabolic AFM tip tapping on a polyisobutylene surface, described as a viscoelastic material containing multiple characteristic times using the generalized Maxwell

• model with the parameters of Table 1. The results show: (a) the peak tip–sample interaction force, and (b) the maximum indentation depth, with respect to amplitude setpoint ratio for AM-AFM using the first eigenmode (red line), AM-AFM using the second eigenmode (blue line), and bimodal AFM using the

Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times

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

Beilstein J. Nanotechnol. 2017, 8, 2230–2244, doi:10.3762/bjnano.8.223

• ) is physically represented in Figure 1 for the case of a Generalized Maxwell model with an arbitrary number of characteristic times. The load in Equation 1 may also be written in the time domain as a convolution of the relaxation modulus (G(t)) with the time derivative of the displacement: where the

• obtain: Now, turning our attention to the second part of the excitation in Equation 18 and applying transformation we obtain: Inserting Equation 26 into Equation 1 and using the relaxance of the Generalized Maxwell model in Figure 1 (see Equation S2 in Supporting Information File 1) leads to

• : Retransforming Equation 27 gives: The term in brackets is the stress–relaxation function (stress response to a unit step strain [8]) shifted by the time t′, (G(t − t′)). For further details on the stress relaxation of the Generalized Maxwell model see Equation S5 in Supporting Information File 1. Combining