Intermodal coupling spectroscopy of mechanical modes in microcantilevers

• Ioan Ignat,
• Bernhard Schuster,
• Jonas Hafner,
• MinHee Kwon,
• Daniel Platz and
• Ulrich Schmid

Beilstein J. Nanotechnol. 2023, 14, 123–132, doi:10.3762/bjnano.14.13

• Q-factor of the fundamental mode. Intermodal coupling requires a strong drive tone, referred to as a pump, at either the frequency difference between or the sum of two cantilever eigenmodes of interest. Using the difference, also known as a red sideband or anti-Stokes pump, leads to sideband cooling

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

• performed with different types of cantilevers (short high-frequency cantilevers as well as traditional cantilevers) and with different methods, involving wide frequency ranges and different cantilever eigenmodes. In general, this is routinely done without considering the types of viscoelastic behavior

• dimensionality reduction (MDR) [51]. The four coupled equations (three cantilever eigenmodes and the viscoelastic model relaxation and force calculation) were integrated numerically. The simulation procedures have been discussed in detail in previous publications and their supporting information files [14][33

Artifacts in time-resolved Kelvin probe force microscopy

• Sascha Sadewasser,
• Nicoleta Nicoara and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2018, 9, 1272–1281, doi:10.3762/bjnano.9.119

• cantilever eigenmodes, namely at 500 Hz and at 1428 Hz. We speculate that these deviations are due to possible capacitive cross talk between the ac voltage and the piezo cables or the photodetector. We can disregard these deviations since they are not related to the cantilever eigenmodes and have a different

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

• versatility of the instrument, it has been proposed to use higher cantilever eigenmodes, either by themselves in single-eigenmode imaging [6][7][8][9] or within multifrequency techniques [10]. For example, in the original multifrequency AFM method, introduced by Garcia and coworkers and known as bimodal AFM

• environments, which we have not considered in this study, but where many soft samples are imaged. Some of these effects include mass loading of the cantilever, excitation of higher cantilever eigenmodes, and the inability to accurately track the tip motion for piezoelectrically excited cantilevers [31][32][33

A robust AFM-based method for locally measuring the elasticity of samples

• Alexandre Bubendorf,
• Stefan Walheim,
• Thomas Schimmel and
• Ernst Meyer

Beilstein J. Nanotechnol. 2018, 9, 1–10, doi:10.3762/bjnano.9.1

• excitation of two cantilever eigenmodes [17][18][19][20][21], are performed in non-dry air, the instability of the tip–sample distance feedback loop, due to the use of the frequency shift as control parameter, makes the application of the method difficult if not impossible. However, despite these

High-frequency multimodal atomic force microscopy

• Adrian P. Nievergelt,
• Jonathan D. Adams,
• Pascal D. Odermatt and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2014, 5, 2459–2467, doi:10.3762/bjnano.5.255

• photothermal tune shows nearly no variation. In particular, the second resonance excitation (Figure 3a) increases by 50% to 100% under piezo excitation, but by only 3% under photothermal excitation. We measured the ability of our system to drive and detect multiple cantilever eigenmodes at the corresponding

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

• et al. by using T-shaped cantilevers [26] uses the spectral response of one of the cantilever eigenmodes (the first torsional mode in the method of Sahin et al.) to invert the force curve without making any assumptions about the tip–sample contact model. The method has been demonstrated extensively

•  9 shows the behavior of the normalized second mode amplitude (A2/A2-free, Figure 9a) and phase (Figure 9b) for AM-OL spectroscopy curves simulated with parameters similar to those of Figure 7, for different values of A2, including the full dynamics of the first three cantilever eigenmodes. As the

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

• multimodal tapping-mode atomic force microscopy driving more than three cantilever eigenmodes. We present tetramodal (4-eigenmode) imaging experiments conducted on a thin polytetrafluoroethylene (PTFE) film and computational simulations of pentamodal (5-eigenmode) cantilever dynamics and spectroscopy

• driven simultaneously or sequentially at more than one frequency [1]. Often these frequencies correspond to different cantilever eigenmodes [2][3][4][5][6][7][8][9][10][11][12], but there are also methods involving single-eigenmode multi-frequency excitation [13][14][15] and spectral inversion methods in

• , as in previously validated bimodal and trimodal methods [2][3][4][5][6][7][8][9]. Although the dynamics of multimodal tapping-mode AFM can be quite complex, we find that imaging can be remarkably stable and that the cantilever eigenmodes, in general, exhibit the predicted behavior [20]. We focus our

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

• controlling indentation for a given cantilever, one should choose for this purpose the highest available eigenmode, which has the highest dynamic force constant and thus the largest product kAo for a given value of Ao (the dynamic force constants of the cantilever eigenmodes increase with the square of their

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

• total-force test appears to be satisfactory, the more stringent energy balance test singles out a discrepancy. The reason of the discrepancy in the energy balance is attributed to a different degree of interaction of the higher cantilever eigenmodes with the surface forces. It is well known that a force

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

• that have been developed for operation in air environments, which assume a nearly-equilibrated eigenmode oscillation where all cycles are sinusoidal and similar in phase and amplitude [33][34]. Due to the short equilibration times in liquids, in bimodal operation the response of the cantilever

• eigenmodes exhibits a distinct transient and a relaxed contribution. The relaxed contribution is equal to the eigenmode’s response in the absence of the sample. The transient contribution is a result of the forces that take place during each impact. The ability of these forces to modify the response of each

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

• technique. Specifically, we analyzed the response variables for the two configurations currently in use (UAFM and AFAM), and restricted our analysis to the first two cantilever eigenmodes. Similarities and notable differences were observed in the signals and calculated variables (frequency, amplitude and

Multiple regimes of operation in bimodal AFM: understanding the energy of cantilever eigenmodes

• Daniel Kiracofe,
• Arvind Raman and
• Dalia Yablon

Beilstein J. Nanotechnol. 2013, 4, 385–393, doi:10.3762/bjnano.4.45

• . Keywords: atomic force microscopy; bimodal AFM; cantilever eigenmodes; polymer characterization; Introduction Atomic force microscopy (AFM) has arisen as one of the key tools for characterization of morphology and surface properties of materials (e.g., polymer blends and composites) at the micro

• Dirac delta, respectively. The hydrodynamic forces are converted into an effective modal viscosity and added mass [23], and then the equation is discretized in the basis of cantilever eigenmodes by Galerkin’s method following [24]. The method is to write w as where ψi(x) is the ith eigenmode shape and