Enhanced feedback performance in off-resonance AFM modes through pulse train sampling

• Mustafa Kangül,
• Navid Asmari,
• Santiago H. Andany,
• Marcos Penedo and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2024, 15, 134–143, doi:10.3762/bjnano.15.13

• contrast mapping of the sample in real time. However, the topography feedback error should be minimized to reduce the effect of sample topography on the mechanical property measurements. For example, the dissipated energy on the sample, simply the integral of the area between the approach and the retract

Alteration of nanomechanical properties of pancreatic cancer cells through anticancer drug treatment revealed by atomic force microscopy

• Xiaoteng Liang,
• Shuai Liu,
• Xiuchao Wang,
• Dan Xia and
• Qiang Li

Beilstein J. Nanotechnol. 2021, 12, 1372–1379, doi:10.3762/bjnano.12.101

• mechanical energy during each trace–retrace cycle. The hysteresis in the force–distance curves between different types of cells indicates the energy dissipation. The dissipated energy can be calculated by the following formula, where W is the total amount of energy dissipation, and its value in the force

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

• can be helpful when describing the relationship between external loads and the viscoelastic response, especially when the excitations are periodic. Within the context of AFM, both the storage modulus and the loss modulus are critical to evaluating the dissipated energy during tapping-mode analysis [24

Effective sensor properties and sensitivity considerations of a dynamic co-resonantly coupled cantilever sensor

• Julia Körner

Beilstein J. Nanotechnol. 2018, 9, 2546–2560, doi:10.3762/bjnano.9.237

• good estimate for the effective spring constants of the coupled system. Effective quality factor The quality factor can either be defined as the ratio of total energy to dissipated energy per oscillation period [34] or as the bandwidth of the resonance curve. In the latter case, the bandwidth is given

• co-resonantly coupled system, the definition based on energy dissipation will be used, hence: with Ea,b denoting the total energy stored in the system and ΔEa,b the dissipated energy per oscillation period. Please note that the absolute value for the dissipated energy (often considered with a

• negative sign) is used as only the relation between total and dissipated energy is relevant for the quality factor. Based on the coupled harmonic oscillator representation, the total energy of the system can be approximated by the potential energy given by [37]: depending on the spring constants k1,2 and

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

• discussed later. Last, the ratio between dissipated energy and virial, in this case, is related to the loss tangent (tan θ(ω)): where θ(ω) – the loss angle – describes the phase lag (or lead) of the response of a viscoelastic material to a harmonic excitation in the steady state, and its value spans from

• simple DMA case, where both force and displacement oscillate harmonically (Equation 3 and Equation 5). The calculation of dissipated energy in tapping-mode AFM is well established for high quality factor (high-Q) environments [16][17], and has been successfully performed regardless of the source of

• dissipation in the tip–sample interaction [34][40][41]. However, it is well known that varying the dynamic AFM parameters (e.g., excitation frequency, tapping amplitude) can significantly alter the calculated values of dissipated energy when imaging viscoelastic polymers [35]. This clearly represents a

Velocity dependence of sliding friction on a crystalline surface

• Christian Apostoli,
• Giovanni Giusti,
• Jacopo Ciccoianni,
• Gabriele Riva,
• Rosario Capozza,
• Rosalie Laure Woulaché,
• Andrea Vanossi,
• Emanuele Panizon and
• Nicola Manini

Beilstein J. Nanotechnol. 2017, 8, 2186–2199, doi:10.3762/bjnano.8.218

• practical MD simulation cell, the dissipated energy accumulates in the phonons in the simulated sample, leading to a progressive overheating. Therefore this simulation procedure cannot address a steady sliding regime, but can at most identify the leading instabilities occurring and the most strongly coupled

Coupled molecular and cantilever dynamics model for frequency-modulated atomic force microscopy

• Michael Klocke and
• Dietrich E. Wolf

Beilstein J. Nanotechnol. 2016, 7, 708–720, doi:10.3762/bjnano.7.63

• presence or absence of adhesion hysteresis, if the dissipated energy is not replenished fast enough [14], or the effects of lateral tip displacements on the frequency shift [15] and on the cantilever damping [7]. In all these models, adhesion hysteresis can only be incorporated a priori, e.g., by using

• case: First, one can avoid the numerical integration of a force hysteresis, so that one gets numerically more accurate values for the dissipated energy. Second, in order to distinguish the two damping mechanisms in a system coupled to a thermostat, one would have to check, if the force hysteresis

• shift is commonly used instead of Δf in order to minimize the dependence on system parameters such as fz or kz. This is helpful in the simulation context, because molecular dynamics simulations are only feasible with exaggerated frequencies fz [32]). As in Figure 4, the dissipated energy ΔE fluctuates

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

• a consequence of the fact that the deformation area is larger when in-plane surface effects are included. This leads to the recruitment of a larger number of SLS elements in the subsurface, thus leading to a larger total dissipated energy. While the explanation is simple, this observation has very

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

• contamination. In these crystals we unambiguously identified fingerprints of capillary interactions, i.e., their onset and distance dependencies, from force curves on top of the water patches and from the simultaneous observation of both the corresponding dissipated energy, calculated according to the Cleveland

• avoided [41][42]. Discussion The different dynamic interactions in the two situations depicted in Figure 2a and Figure 2b is corroborated by the analysis of the normalized dissipated energy and phase difference evolutions vs dmin in the long range (see also Equation 4 and Equation 5 of the Experimental

• –sample separation is decreased were employed to reconstruct the tip–sample force [27]. In this work raw (solid circles in grey) and smooth (continuous line in blue) data are reported for the reconstructed force curves [53]. The dissipated energy (Ediss) and ΔΦ were also calculated for each APD curve vs

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

• instantaneous deflection and tip–surface force, velocity, virial, dissipated energy, sample deformation and peak force as a function of time or distance. The simulator includes a variety of interactions and contact mechanics models to describe AFM experiments including: van der Waals, Hertz, DMT, JKR, bottom

Mechanical properties of MDCK II cells exposed to gold nanorods

• Anna Pietuch,
• Bastian Rouven Brückner,
• David Schneider,
• Marco Tarantola,
• Christina Rosman,
• Carsten Sönnichsen and
• Andreas Janshoff

Beilstein J. Nanotechnol. 2015, 6, 223–231, doi:10.3762/bjnano.6.21

• simultaneously the resonance frequency and dissipated energy of the quartz crystal covered with cells and reveals information about the viscoelastic properties of these cells as well as the distance from the quartz surface [24]. In the work presented here we investigated the influence of gold nanoparticles on

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

• –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). Keywords: atomic force microscopy; creep; dissipated energy; multifrequency; stress relaxation; tapping mode; viscoelasticity

Dissipation signals due to lateral tip oscillations in FM-AFM

• Michael Klocke and
• Dietrich E. Wolf

Beilstein J. Nanotechnol. 2014, 5, 2048–2057, doi:10.3762/bjnano.5.213

• happens. The energy difference is dissipated. This mechanism has been found in various systems [6][7][8]. The ultimate goal would be to extract valuable information about the surface from the rate of the dissipated energy, e.g., the identification of functional groups within molecules [9]. Unfortunately

• -dissipated energy? The mechanical damping of the normal oscillation mode can be measured directly. It is a common assumption, that the lateral and bending modes of the cantilever are decoupled, but this only holds as long as there are no asymmetries in the mass distribution of the cantilever [21]. We will

• an excitation of the lateral degree of freedom becomes impossible. For finite γ, energy can be transferred into the lateral degree of freedom, but this energy could partly also be transferred back into the normal degree of freedom. The dissipated energy per normal cycle is just given by the viscous

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

• impacts. As A2 increases, the dissipation loops are dominated more and more by the frequency of the second eigenmode and the average level of dissipation drops (Figure 5b). The irregularity of the impacts is easily noticeable in the irregular oscillation of the dissipated energy for successive impacts

• compares the trends in dissipated energy as a function of A2 for the three cases analyzed in Figures 5–7. It shows that the trend for the real case lies in between the results of the prescribed trajectories with constant penetration and the prescribed trajectories of additive penetration for the two

• results, the behavior of the dissipated energy and the tip–sample forces is extremely complex and cannot be predicted a priori. In addition, the observables that are available during an AFM experiment can be quite sensitive to the imaging conditions, depending on the imaging mode used. For example, Figure

Energy dissipation in multifrequency atomic force microscopy

• Valentina Pukhova,
• Francesco Banfi and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2014, 5, 494–500, doi:10.3762/bjnano.5.57

• /bjnano.5.57 Abstract The instantaneous displacement, velocity and acceleration of a cantilever tip impacting onto a graphite surface are reconstructed. The total dissipated energy and the dissipated energy per cycle of each excited flexural mode during the tip interaction is retrieved. The tip dynamics

• variation of energy () and integrated dissipation () for both modes, as reported in Table 3. Having a general consistence regarding the energy conservation, we can correctly estimate the dissipated energy per cycle in each eigenmode, which is obtained as the difference between the maximum elastic energy

• instantaneous deflection (z), force (F) and velocity (v) as a function of time in various 3D representations and a comprehensive representation of the phase-space of the motion. The spiraling trajectories are connected to and are a visual representation of the dissipated energy. Figure 3A is a representation of

Energy-related nanomaterials

• Paul Ziemann and
• Alexei R. Khokhlov

Beilstein J. Nanotechnol. 2013, 4, 678–679, doi:10.3762/bjnano.4.76

• enter both experimental and theoretical simulation routes towards materials optimization. Another materials property worth of being optimized is friction, which, when trying to walk or drive on icy streets is highly welcome, but in many cases is a source of dissipated energy. The friction of an object

Mapping of plasmonic resonances in nanotriangles

• Simon Dickreuter,
• Julia Gleixner,
• Andreas Kolloch,
• Johannes Boneberg,
• Elke Scheer and
• Paul Leiderer

Beilstein J. Nanotechnol. 2013, 4, 588–602, doi:10.3762/bjnano.4.66

• the same parameters, describing a continuous gold film. This results in a factor, which depicts the local enhancement of the dissipated energy, as it is caused by the triangle. As before, the values were averaged over the triangle height. Figure 6c displays the electrical field vectors at 10 nm height

Selective surface modification of lithographic silicon oxide nanostructures by organofunctional silanes

• Thomas Baumgärtel,
• Christian von Borczyskowski and
• Harald Graaf

Beilstein J. Nanotechnol. 2013, 4, 218–226, doi:10.3762/bjnano.4.22

• amplitude–phase–distance curves [40]. From such experiments, the dissipated energy of the AFM tip oscillation can be calculated, which depends on the local elastic and therefore structural surface properties of the substrate. The surface coverage of the relatively rigid silicon oxide with “softer” organic

A measurement of the hysteresis loop in force-spectroscopy curves using a tuning-fork atomic force microscope

• Manfred Lange,
• Dennis van Vörden and
• Rolf Möller

Beilstein J. Nanotechnol. 2012, 3, 207–212, doi:10.3762/bjnano.3.23

• this process to the energy associated with the making and breaking of the bond between the PTCDA molecule and the surface, which is given by the area of the hysteresis loop [5][6]. The dissipated energy of this process was determined to be approximately 0.57 eV, which is of the order of the energy of a

• observed in the force–distance curve. Conclusion We have resolved the hysteresis loop in force-spectroscopy measurements induced by the bond formation and breakage between a PTCDA molecule at the tip of an NC-AFM probe and PTCDA molecules of the sample surface. The dissipated energy of this process is

Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus

• Elena T. Herruzo and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2012, 3, 198–206, doi:10.3762/bjnano.3.22

• are larger that the characteristic length of scale of the interaction force. Results and Discussion Frequency shift of the second mode in bimodal AFM The problem of a cantilever vibrating under bimodal excitation can be studied by means of the averaged quantities of the dissipated energy and the

Molecular-resolution imaging of pentacene on KCl(001)

• Julia L. Neff,
• Jan Götzen,
• Enhui Li,
• Michael Marz and
• Regina Hoffmann-Vogel

Beilstein J. Nanotechnol. 2012, 3, 186–191, doi:10.3762/bjnano.3.20

• the molecules on the surface. Another possibility is that the line defect results from a twinned growth. The line defect also has a profound effect on the energy dissipation (Figure 2b). The dissipated energy per oscillation cycle can be estimated by Ediss ≈ E0(Aexc − Aexc,0)/Aexc,0 with E0 = πkA2/Q

Effect of the tip state during qPlus noncontact atomic force microscopy of Si(100) at 5 K: Probing the probe

• Adam Sweetman,
• Sam Jarvis,
• Rosanna Danza and
• Philip Moriarty

Beilstein J. Nanotechnol. 2012, 3, 25–32, doi:10.3762/bjnano.3.3

• a valuable resource for theoreticians working on the development of realistic tip structures for NC-AFM simulations. Force spectroscopy measurements show that the tip termination critically affects both the short-range force and dissipated energy. Keywords: force spectroscopy; image contrast

Manipulation of gold colloidal nanoparticles with atomic force microscopy in dynamic mode: influence of particle–substrate chemistry and morphology, and of operating conditions

• Samer Darwich,
• Karine Mougin,
• Akshata Rao,
• Enrico Gnecco,
• Shrisudersan Jayaraman and
• Hamidou Haidara

Beilstein J. Nanotechnol. 2011, 2, 85–98, doi:10.3762/bjnano.2.10

• cantilever oscillations with respect to the external periodic excitation can be used to estimate the dissipated energy during manipulation. This method was recently used by Ritter and coworkers to manipulate antimony particles on a graphite surface in air [17][18]. Paollicelli et al. manipulated gold

• particles (at least 10) were moved under similar conditions. Our results in Figure 10 show that for both nanoparticle sizes (35 and 60 nm), the dissipated power during the tip–particle contact depends on the chemical nature of the substrate. The magnitude of the dissipated energy gradually and significantly

The description of friction of silicon MEMS with surface roughness: virtues and limitations of a stochastic Prandtl–Tomlinson model and the simulation of vibration-induced friction reduction

• W. Merlijn van Spengen,
• Viviane Turq and
• Joost W. M. Frenken

Beilstein J. Nanotechnol. 2010, 1, 163–171, doi:10.3762/bjnano.1.20

• lateral force only when sliding in two directions takes place (Figure 3). From this dissipated energy, we calculated the average friction force such as plotted in the succeeding graphs, by dividing this energy by the distance slid. In the measurements used for this paper, we systematically varied the