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

• resonance angular frequency, kT the torsional force constant, which has been linearized in the vertical direction, and QT is the torsional quality factor. As the cantilever base is oscillated in the vertical direction by the piezo shaker, the fundamental flexural eigenmode is excited such that the tip

Interpreting motion and force for narrow-band intermodulation atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 45–56, doi:10.3762/bjnano.4.5

• Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip–surface force by measurement of the mixing of multiple modes in a frequency comb. A high-quality factor cantilever resonance and a suitable drive comb will result in tip motion described by a

• , providing deeper insight into the tip–surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface. Keywords: atomic force microscopy; AFM; frequency combs; force spectroscopy; high-quality-factor resonators; intermodulation; multifrequency

• flexural eigenmode of the cantilever. The high-quality factor of the resonance ensures that the responding motion of the tip is approximately sinusoidal in time, with the same frequency as the drive signal [11][12]. Such periodic motion is best analyzed in the frequency or Fourier domain, where the motion

Characterization of the mechanical properties of qPlus sensors

• Jan Berger,
• Martin Švec,
• Martin Müller,
• Martin Ledinský,
• Antonín Fejfar,
• Pavel Jelínek and
• Zsolt Majzik

Beilstein J. Nanotechnol. 2013, 4, 1–9, doi:10.3762/bjnano.4.1

• based on thermal-noise analysis. However, we performed our calibration procedure at RT, where the thermal excitation is much larger and the quality factor of the tuning fork is also significantly lower (in our case Q ≈ 1500–4500). Thus the tuning fork is less responsive to mechanical vibration, although

• information about mechanical properties of sensors such as the resonant frequency, quality factor and stiffness. We also discussed a fast and cost-effective way to perform the added-mass method under ambient conditions. This method is based on adding small pieces of tungsten wire whose mass was determined

Pure hydrogen low-temperature plasma exposure of HOPG and graphene: Graphane formation?

• Baran Eren,
• Dorothée Hug,
• Laurent Marot,
• Rémy Pawlak,
• Marcin Kisiel,
• Roland Steiner,
• Dominik M. Zumbühl and
• Ernst Meyer

Beilstein J. Nanotechnol. 2012, 3, 852–859, doi:10.3762/bjnano.3.96

• fundamental frequency, spring constant, and quality factor of the cantilever were equal to f0 = 142 kHz, k = 20 N/m, Q = 300, respectively. We avoided performing electron microscopy on the HOPG samples because the electron beam energy could ionize H2O and NH3 adsorbents and cause additional effects [43]. XPS

Spring constant of a tuning-fork sensor for dynamic force microscopy

• Dennis van Vörden,
• Manfred Lange,
• Merlin Schmuck,
• Nico Schmidt and
• Rolf Möller

Beilstein J. Nanotechnol. 2012, 3, 809–816, doi:10.3762/bjnano.3.90

• attached to the support. This is due to the area connecting the two prongs, which is deformed during the oscillation. This is not only important for the spring constant but also for the dissipation of the TF. Dynamic measurements have shown that applying glue to that area will reduce the quality factor of

Mapping mechanical properties of organic thin films by force-modulation microscopy in aqueous media

• Jianming Zhang,
• Zehra Parlak,
• Carleen M. Bowers,
• Terrence Oas and
• Stefan Zauscher

Beilstein J. Nanotechnol. 2012, 3, 464–474, doi:10.3762/bjnano.3.53

• ]. However, the quality factor of these modes decreases significantly in solution and makes it difficult to interpret cantilever vibrations around contact resonance modes. A proper probe for FMM imaging in liquid should have a high resonance frequency to simplify data analysis and at the same time it should

Drive-amplitude-modulation atomic force microscopy: From vacuum to liquids

• Miriam Jaafar,
• David Martínez-Martín,
• Mariano Cuenca,
• John Melcher,
• Arvind Raman and
• Julio Gómez-Herrero

Beilstein J. Nanotechnol. 2012, 3, 336–344, doi:10.3762/bjnano.3.38

• high quality factor Q of the cantilevers in vacuum, which present a settling time given by τcl= Q/(πf0). Frequency-modulation AFM (FM-AFM, also known as noncontact AFM) [9] is the classical alternative to AM allowing atomic resolution in UHV chambers [10] at higher scanning rates. FM-AFM has recently

• by using a conventional combination of a dry mechanical pump plus a turbopump. In order to avoid vibrations from the turbopump affecting the measurements, the microscope head is suspended by three viton cords. The quality factor of the cantilevers saturates at pressures below 10−3 mbar, and hence the

Graphite, graphene on SiC, and graphene nanoribbons: Calculated images with a numerical FM-AFM

• Fabien Castanié,
• Laurent Nony,
• Sébastien Gauthier and
• Xavier Bouju

Beilstein J. Nanotechnol. 2012, 3, 301–311, doi:10.3762/bjnano.3.34

• and the frequency setpoint. This regulation yields the sample topography. Each block was transposed into a numerical program and included in a general code written in Fortran 90 language. Just a few parameters are needed as input for the oscillator: stiffness constant k, quality factor Q, resonance

Wavelet cross-correlation and phase analysis of a free cantilever subjected to band excitation

• Francesco Banfi and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2012, 3, 294–300, doi:10.3762/bjnano.3.33

• frequency of f0 = ω0/(2π) = 1 MHz, a quality factor Q = 4 and an excitation driving frequency that linearly sweeps the frequency interval 0.1f0 < Δf < 0.9f0 in 50 μs (chirped driver). The driving function is f(t) = zdcos(νd(t)t), where zd is the driving amplitude and νd(t) the driving frequency that is

• signals must have amplitudes exceeding that of the thermal noise, because averaging is limited or absent. In this case, the choice of the excitation amplitude depends on the type of cantilever, on its quality factor and on the parameters to be measured. We anticipated that only extremely low amplitude

• frequency is linearly swept in the interval 0.1f0 < Δf < 0.9f0 over 50 μs, where f0 = ω0/(2π) = 1 MHz is the resonant frequency of the oscillator. The quality factor is Q = 4 and the initial conditions are 10 nm amplitude and zero velocity. Wavelet cross-correlation between the chirped driver and the

Pulse-response measurement of frequency-resolved water dynamics on a hydrophilic surface using a Q-damped atomic force microscopy cantilever

• Masami Kageshima

Beilstein J. Nanotechnol. 2012, 3, 260–266, doi:10.3762/bjnano.3.29

• stiffness was determined and is attributed to the reported solidification of the hydration layers. Keywords: atomic force microscopy; hydration; pulse-response; quality-factor control; viscoelasticity; Introduction Liquid solvation is a phenomenon common to a large variety of liquid–solid interfaces [1

• of quality-factor-control (Q-control) [29] is employed. The device for magnetic driving of the cantilever consists of two sections; a Q-control circuit for suppression of resonant ringing and a wide-band electromagnet driver, as shown in Figure 1. The Q-control section has an op-amp differentiator

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

• regime due to its large spring constant of about 9000 N/m, preventing a jump to contact. This offers the advantage that in this regime the measurements are more sensitive to short-range forces and dissipation processes. The resonance frequency and quality factor of the tuning fork at 77 K temperature and

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

• obtained from Equation 6 with the results estimated from the half-derivative of the force (Equation 16) for a Lennard-Jones force and for the force appearing in the DMT model [49]. The force constant, resonant frequency and quality factor of the first and second flexural modes of the cantilever are

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

• [36]. In this formula, Aexc,0 describes the excitation amplitude of the free cantilever and Aexc the excitation amplitude in the presence of the sample surface. A denotes the oscillation amplitude and Q the quality factor of the free cantilever. On the undisturbed part of the surface (marked with ‘A

qPlus magnetic force microscopy in frequency-modulation mode with millihertz resolution

• Maximilian Schneiderbauer,
• Daniel Wastl and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2012, 3, 174–178, doi:10.3762/bjnano.3.18

• noise Here A is the cantilever amplitude, f0 the undisturbed resonance frequency of the cantilever, k the spring constant, Q the quality factor of the oscillation, nq the deflection-noise density, B the bandwidth of the measurement, kB the Boltzmann constant and T the temperature. In each term, the

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

• amplitude of a piezo-element coupled to the cantilever, f0, k and Q are the resonance frequency, the spring constant and the quality factor of the free cantilever, respectively, and is the phase shift caused by the interaction between the tip and the underlying particles or surface. The calculation of the

• Equation 1 [36]. UHV measurements The images in UHV were acquired with a custom built AFM available at the University of Basel [21]. The base pressure was below 10−9 mbar. Due to the high quality factor in UHV, the out-of-contact-resonance frequency shift was used as the imaging parameter instead of the

Tip-sample interactions on graphite studied using the wavelet transform

• Giovanna Malegori and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2010, 1, 172–181, doi:10.3762/bjnano.1.21

• cantilever vibrating near a resonance can be well approximated by a simple harmonic oscillator model, described by three independent parameters, resonance frequency, ω0, amplitude at resonance, A0, and quality factor, Q. A shift in ω0 is related primarily to the tip-surface force gradient, A0 to the driving

• the thermal regime since we are dealing with small oscillations (less than 0.2 nm) [9]. If the frequency shift is proportional to the interaction elastic constant [1]. From the same PSD, besides the force gradient, it is possible to measure the quality factor Q of the mode, that is determined by

• the relative width of the resonance peaks corresponding to the oscillation eigenmodes of the cantilever (Q = Δω/ω0). Q is usually dependent on the distance from the surface. Since the quality factor Q is connected to dissipation, important informations on the tip-sample energy exchange can be