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

• individuate the excited modes that contribute to the dynamics, Figure 1C. 3) Each flexural mode is schematized as a damped harmonic oscillator (DHO), whose equation of motion is where i is the mode index, zi is the oscillation amplitude, γi is the damping coefficient and the resonance frequency [15

• energy calculated by a balance of potential and kinetic energy () and by integrating the dissipative forces (). Quality factors are derived as Qi = 2 πfi/γi, where the damping coefficient γi = 2/τi, see Table 2). Finally, the elastic constant derived from the theoretical scaling (ki, see Table 1) and

Impact of thermal frequency drift on highest precision force microscopy using quartz-based force sensors at low temperatures

• Florian Pielmeier,
• Daniel Meuer,
• Daniel Schmid,
• Christoph Strunk and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2014, 5, 407–412, doi:10.3762/bjnano.5.48

• and the qPlus sensors (Figure 3a) and the LER (Figure 3b). Again, the wiggles in the curves for the qPlus sensors are caused by external excitations due to a lacking damping system. The kink around 13 K from Figure 2 shows up as a clear step. In temperature dependent measurements it might therefore be

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

• Santiago D. Solares Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA 10.3762/bjnano.5.33 Abstract This paper illustrates through numerical simulation the complexities encountered in high-damping AFM imaging, as in liquid enviroments, within the specific

• instrument that is available. Results and Discussion Amplitude and phase relaxation of driven eigenmodes Previous work by Raman and coworkers [22] demonstrated that in high-damping environments the phase contrast derives primarily from an “energy flow channel” that opens up when higher modes of the

• to lower frequencies (see Figure 10), while the frequency at which the phase is 90 degrees remains at the natural frequency. The natural frequency is the only frequency at which all the phase curves intersect for a given (ideal) cantilever driven in environments with different levels of damping (see

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

• cantilever is described by its Young’s modulus E, second moment of area of its cross section I, mass density ρ, and cross-sectional area A, and ηair characterizes the damping of the oscillations in air. The general solution of Equation 1 is in the form of y(x,t) = y(x)eiωt, with with A1, A2, A3, and A4

• the cantilever spring constant, k* the contact stiffness, γ* the contact damping constant, and the dimensionless contact damping constant. With the above specified boundary conditions the solution further simplifies to with the following constants for the two configurations: and with M± = sin αL cosh

• configuration. In the following analysis we will characterize the contact damping by the dimensionless contact damping constant p rather than the actual contact damping constant γ*. The discussion is focused on the dynamics of the cantilever in the two CR-AFM configurations only and further consideration of

The role of surface corrugation and tip oscillation in single-molecule manipulation with a non-contact atomic force microscope

• Christian Wagner,
• Norman Fournier,
• F. Stefan Tautz and
• Ruslan Temirov

Beilstein J. Nanotechnol. 2014, 5, 202–209, doi:10.3762/bjnano.5.22

• interaction is damped. We achieve this damping by letting z0 → 0. More details can be found in [24]. For simplicity it is assumed that PTCDA consists of only two types of atoms: the 26 backbone (all carbon plus the two anhydride oxygen atoms; hydrogen atom interaction is scaled by 0.25) and the four

Optical near-fields & nearfield optics

• Alfred J. Meixner and
• Paul Leiderer

Beilstein J. Nanotechnol. 2014, 5, 186–187, doi:10.3762/bjnano.5.19

• interaction of plasmonic structures with dielectric material that is doped with fluorescent molecules: when the emission line of the dye and the absorption resonance of the nanostructures coincide, the damping of the plasmons can be compensated by the gain in the dielectric material, so that laser-like

Friction behavior of a microstructured polymer surface inspired by snake skin

• Martina J. Baum,
• Lars Heepe and
• Stanislav N. Gorb

Beilstein J. Nanotechnol. 2014, 5, 83–97, doi:10.3762/bjnano.5.8

• NanoWizard® atomic force microscope (JPK Instruments), mounted on an inverted light microscope (Zeiss Axiovert 135, Carl Zeiss MicroImaging GmbH). The SIMPS were imaged by using the intermittent contact mode of the AFM. The error channel (also known as the amplitude channel) visualizes the change in damping

Exploring the retention properties of CaF₂ nanoparticles as possible additives for dental care application with tapping-mode atomic force microscope in liquid

• Matthias Wasem,
• Joachim Köser,
• Sylvia Hess,
• Enrico Gnecco and
• Ernst Meyer

Beilstein J. Nanotechnol. 2014, 5, 36–43, doi:10.3762/bjnano.5.4

• , . The first term of the dissipated power, , can be thought as the average power dissipated by the body of the cantilever (i.e., air damping or in our case damping of the cantilever motion in the liquid) and can be modeled by simple viscous damping. The second part, , corresponds to the power dissipated

Many-body effects in semiconducting single-wall silicon nanotubes

• Wei Wei and
• Timo Jacob

Beilstein J. Nanotechnol. 2014, 5, 19–25, doi:10.3762/bjnano.5.2

• damping nature, which is an indication of a strong binding between excited electrons and holes with large binding energy. In the case of (6,6) and (10,0) SiNTs, the wave functions of the first bound excitons extend far away along the tubes, similar to a nature of resonant excitons. The reduced electronic

• studied SiNTs are demonstrated in Figure 6. In agreement with the exciton wave functions shown in Figure 5, the first bound exciton of (4,4) SiNTs is mainly localized within a radius of 20 Å. In the case of (6,6) and (10,0) SiNTs, the exciton radii extend over 60 Å. However, we also can see the damping

Dye-doped spheres with plasmonic semi-shells: Lasing modes and scattering at realistic gain levels

• Nikita Arnold,
• Boyang Ding,
• Calin Hrelescu and
• Thomas A. Klar

Beilstein J. Nanotechnol. 2013, 4, 974–987, doi:10.3762/bjnano.4.110

• spectral broadening due to radiative damping. An alternative way to tune the LPR spectrally is to change the shape of the nanoparticle. First, one can relax the radial homogeneity of the nanoparticle and turn from solid nanoparticles to noble metal nanoshells [2][3]. Second, one can also relax the angular

• used for important applications such as biosensing [18], plasmon-enhanced solar cells [19][20], or as substrates for surface-enhanced Raman scattering [21][22] and coherent anti-Stokes Raman scattering [23]. A severe problem for all plasmonic applications is the damping of plasmons due to Ohmic losses

• when modeling is carried out without gain, because they are strongly damped because of the dispersion of the metal. If, however, damping is compensated by gain, the modes might become ultra-sharp and can still be overlooked if they are narrower than the frequency step used in simulations. The situation

Peak forces and lateral resolution in amplitude modulation force microscopy in liquid

• Horacio V. Guzman and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2013, 4, 852–859, doi:10.3762/bjnano.4.96

• beam under the action of external forces, where E is the Young modulus of the cantilever, I the area moment of inertia, a1 the internal damping coefficient, ρ the mass density; b, h and L are, respectively, the width, height and length of the cantilever; a0 is the hydrodynamic damping; w(x,t) is the

Dynamic nanoindentation by instrumented nanoindentation and force microscopy: a comparative review

• Sidney R. Cohen and
• Estelle Kalfon-Cohen

Beilstein J. Nanotechnol. 2013, 4, 815–833, doi:10.3762/bjnano.4.93

• temperature and frequency is embodied in the temperature–time superposition [70]. In general, increasing the temperature induces a molecular relaxation that leads to an increased phase lag between stress and strain. The loss modulus, which reflects the viscous damping of the sample, then increases with

• amplitude h0 induced by the modulated force amplitude P0 is: and the measured phase shift between the applied force and measured displacement is related to sample and instrumental parameters by: where ci, cs are the damping coefficients of the air gap in the displacement transducer and sample, respectively

• used in the equations together with effective k and c in order to avoid an overestimation of c and hence of E”. After calibration to determine m, ci, and ki, the sample-specific values for E′ and E″ can be obtained as shown in Equation 12. These equations also illustrate how the damping coefficient can

Size-dependent characteristics of electrostatically actuated fluid-conveying carbon nanotubes based on modified couple stress theory

• Mir Masoud Seyyed Fakhrabadi,
• Abbas Rastgoo and
• Mohammad Taghi Ahmadian

Beilstein J. Nanotechnol. 2013, 4, 771–780, doi:10.3762/bjnano.4.88

• knowledge, Yoon et al. were the first to study the flutter instability that results from fluid flow in CNTs [23]. They presented the natural frequencies and the damping of the CNT for various flow velocities. Their work had some shortages, which were overcome by Lin and Qiao [24]. They applied the

• changes in the stiffness and damping ratios, as will be studied in the paper. Mathematical formulae All mathematical formulae and expressions that are used in this study can be found in Supporting Information File 1. Results and Discussion The length and chirality of the CNT considered in this paper are

• the system but also influences the damping properties. In addition, the green and red curves show that if the applied voltage exceeds a maximum limit, the CNT does not move harmonically anymore. This phenomenom that is corresponded to the saddle-node bifurcation is known as dynamic pull-in and the

Ellipsometry and XPS comparative studies of thermal and plasma enhanced atomic layer deposited Al₂O₃-films

• Jörg Haeberle,
• Karsten Henkel,
• Hassan Gargouri,
• Franziska Naumann,
• Bernd Gruska,
• Michael Arens,
• Massimo Tallarida and
• Dieter Schmeißer

Beilstein J. Nanotechnol. 2013, 4, 732–742, doi:10.3762/bjnano.4.83

• , oscillator damping, and a distribution factor taking into account the influence of surrounding materials of the single oscillator. This model can be applied for all absorbing molecule groups in the Al2O3 film. In the infrared the thin native oxide film cannot be measured and was neglected. Figure 11 shows

k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy

• Martin Esmann,
• Simon F. Becker,
• Bernard B. da Cunha,
• Jens H. Brauer,
• Ralf Vogelgesang,
• Petra Groß and
• Christoph Lienau

Beilstein J. Nanotechnol. 2013, 4, 603–610, doi:10.3762/bjnano.4.67

• cover slip is mounted onto a three-axis piezoelectric stage (PI P-363.3CD). This allows us to slowly approach the sample to the taper over a distance of several hundreds of nanometers in steps of 30 pm until the tuning fork starts to be damped by tip–sample interactions. The damping occurs on a length

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

• frequency before every experiment. The effects of squeeze film damping [13] are such that the phase can change by an appreciable amount (10 degrees) when the cantilever is moved a few micrometers away from the surface. Further, piezo resonances can distort the tuning curve. For plain AM-AFM at the first

• given in [21][22]. Here we review the features relevant to the present work. The modeling starts with the Euler–Bernoulli partial differential equation for deflections of a slender, rectangular cantilever beam in a ground-fixed inertial frame, subject to a hydrodynamic damping force, a driving force

Determining cantilever stiffness from thermal noise

• Jannis Lübbe,
• Matthias Temmen,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 227–233, doi:10.3762/bjnano.4.23

• thermal excitation, namely the resulting noise power spectral density of the cantilever displacement , is the superposition of contributions from all modes and can be derived within the framework of the Nyquist theory [3]. Provided the simple harmonic oscillator model is valid, i.e., the internal damping

Bimodal atomic force microscopy driving the higher eigenmode in frequency-modulation mode: Implementation, advantages, disadvantages and comparison to the open-loop case

• Daniel Ebeling and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2013, 4, 198–207, doi:10.3762/bjnano.4.20

• of damping, which can be more significant when characterizing highly dissipative samples, the natural frequency is a well-defined condition, which allows the relatively easy implementation of amplitude control. That is, one can control the response amplitude by adjusting the drive amplitude, using a

• the dimensionless time, k is the cantilever force constant (stiffness) and Fts is the tip–sample interaction force. We have also used the approximation A ≈ A0 = F0Q/k [22], where F0 is the amplitude of the inertial excitation force, and have grouped the damping and excitation terms together in

Hydrogen-plasma-induced magnetocrystalline anisotropy ordering in self-assembled magnetic nanoparticle monolayers

• Alexander Weddemann,
• Judith Meyer,
• Anna Regtmeier,
• Irina Janzen,
• Dieter Akemeier and
• Andreas Hütten

Beilstein J. Nanotechnol. 2013, 4, 164–172, doi:10.3762/bjnano.4.16

• . A solution is obtained by consideration of its time-dependent extension [25] with γ the gyromagnetic ratio and α a dimensionless damping constant. The microscopic relaxation occurs on time scales significantly shorter than the time scales on which external fields change. Therefore, the microscopic

• dynamics are not in the scope of this work and the value of the damping parameter may be adjusted to provide a high numerical convergence rate. We chose α = 1 [26]. For the integration with respect to time, a backward differential formula of fifth order is applied. As a model system, we consider a two

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

• phenomena take place when imaging samples in high-damping (liquid) environments [18] or in multifrequency AFM characterization [19]. Illustration of the surface depression by the tip–sample impact, and successive recovery within the standard linear solid model. Z1 is the undisturbed surface position, before

Plasmonic oligomers in cylindrical vector light beams

• Mario Hentschel,
• Jens Dorfmüller,
• Harald Giessen,
• Sebastian Jäger,
• Andreas M. Kern,
• Kai Braun,
• Dai Zhang and
• Alfred J. Meixner

Beilstein J. Nanotechnol. 2013, 4, 57–65, doi:10.3762/bjnano.4.6

• are in-phase (see field distributions at spectral positions 1 and 3), exhibiting significant mode broadening due to radiative damping. It is worth mentioning that the peak position of the super-radiant mode cannot be exactly determined from the spectrum due to the presence of the resonance dip

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

• additional exponential damping, which is defined as where H = 2.96 · 10−7 J is the Hamaker constant, R = 10 nm is the tip radius, γ = 2.2 · 10−7 Ns/m is the damping constant, zγ = 1.5 nm is the damping decay length and E* = 2.0 GPa is the effective stiffness. For the numerical integration of Equation 39 we

• and A as seen in the two-dimensional color maps shown in Figure 6 for the vdW-DMT force with exponential damping used in the previous section. In order to emphasize the interaction region near the point of contact, data in the h–A plane with FI < −8 nN are masked with white. In both frequency

• cantilever dynamics due to a relatively long interaction time, or a change in the hydrodynamic damping forces due to the surrounding air close to the sample surface. One should also note that at this piezo extension the minimum oscillation amplitude begins to increase again. A possible artifact of the

Thermal noise limit for ultra-high vacuum noncontact atomic force microscopy

• Jannis Lübbe,
• Matthias Temmen,
• Sebastian Rode,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 32–44, doi:10.3762/bjnano.4.4

• suspension and eddy-current damping systems. As an additional precaution, connections between the electronics and piezos are removed during noise measurements to ensure that measurements are not affected by any spurious electrical signals exciting the cantilever. All systems investigated here are based on

Effect of spherical Au nanoparticles on nanofriction and wear reduction in dry and liquid environments

• Dave Maharaj and
• Bharat Bhushan

Beilstein J. Nanotechnol. 2012, 3, 759–772, doi:10.3762/bjnano.3.85

• drag. In experiments where electrostatic micromotors are operated in a liquid environment, there have been problems of excessive drag and damping, which limited operating speeds, due to the use of high viscosity (20–60 cSt) oils [24]. However, studies have also demonstrated that friction and wear can

Large-scale analysis of high-speed atomic force microscopy data sets using adaptive image processing

• Blake W. Erickson,
• Séverine Coquoz,
• Jonathan D. Adams,
• Daniel J. Burns and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2012, 3, 747–758, doi:10.3762/bjnano.3.84

• through either input shaping [38][39][40][41] of the drive signals or through electrical damping of the resonances [42]. For our experiments, we use a self optimizing method that determines the scanner resonances and compensates them with an input shaper [38]. Using this resonance-compensator system, the