Generalized Hertz model for bimodal nanomechanical mapping

• Aleksander Labuda,
• Marta Kocuń,
• Waiman Meinhold,
• Deron Walters and
• Roger Proksch

Beilstein J. Nanotechnol. 2016, 7, 970–982, doi:10.3762/bjnano.7.89

• interaction stiffness for both resonant modes, each yielding a simple analytical expression. These two independent pieces of information are refactored to provide information about modulus and indentation depth. While the theory is generally applicable to a wide range of tip–sample interaction models, the

• theory presented in the following three sections. Methods Hertzian contact mechanics The Hertzian contact model involves the interaction stiffness kint versus indentation depth δ between a paraboloidal tip of radius R and a flat sample as where the effective Young’s modulus Eeff combines deformation of

• the Appendix (b). Importantly, it is the true contact radius rc that defines the tip–sample interaction stiffness, as derived by Oliver and Pharr [27]: Substituting in the expression for rc leads to the general form The interaction stiffness in Equation 5 is plotted for three special cases in Figure 3

Modelling of ‘sub-atomic’ contrast resulting from back-bonding on Si(111)-7×7

• Adam Sweetman,
• Samuel P. Jarvis and
• Mohammad A. Rashid

Beilstein J. Nanotechnol. 2016, 7, 937–945, doi:10.3762/bjnano.7.85

• keep the probe particle attached), and a probe particle with parameters rα = 1.66 Å and εα = 9.106 meV, and a lateral stiffness of 0.5 N/m. In the L-J model, the interaction between atoms α and β are written as: where r = |R| is the distance between atoms α and β, is the pair binding energy and rαβ

• to take the experimental images in Figure 1 was not intentionally functionalised, and, more importantly, the identity of the passivating group at the apex of the tip is not known. In the majority of the simulations performed in the previous sections, we have assumed a lateral stiffness kxy = 0.5 N/m

• , in line with previous work modelling CO terminated tips. However, a priori, we have no knowledge of the actual stiffness of our probe, and it is important to consider what a modification of the lateral stiffness may have on our simulated results. While for small modifications of kxy we find that the

Frog tongue surface microstructures: functional and evolutionary patterns

• Thomas Kleinteich and
• Stanislav N. Gorb

Beilstein J. Nanotechnol. 2016, 7, 893–903, doi:10.3762/bjnano.7.81

• of the material stiffness that were previously described for attachment structures in beetles [26][27], grasshopers [28], and geckos [29]. Here we combine scanning electron microscopy and high-resolution micro-computed tomography (micro-CT) to provide comparative accounts on the surface profiles and

• to assume that the mucus coverage on the tongue surface is more compliant than the filiform papillae themselves, which are in turn more flexible than the lacunar sub-surface layer. The muscle fibers underneath the lacunar layer supposedly have even higher stiffness than the lacunar layer. Such

Understanding interferometry for micro-cantilever displacement detection

• Alexander von Schmidsfeld,
• Tobias Nörenberg,
• Matthias Temmen and
• Michael Reichling

Beilstein J. Nanotechnol. 2016, 7, 841–851, doi:10.3762/bjnano.7.76

• can be affected by forces originating from the radiation pressure acting on the cantilever [9]. Under conditions of Fabry–Pérot interference, this yields an optical spring effect, i.e., an effective cantilever stiffness that is increased or lowered depending on the slope of the interference fringe [10

• parameters are compiled in Table 1. The fringe-dependent effective cantilever stiffness k± is determined by a method relating the intrinsic stiffness to the optical spring constant as described in detail in [8]. In a series of measurements, we determine the noise floor by measuring the displacement noise

• determining the effective modal Q-factors and effective cantilever stiffnesses (Table 1) by procedures described in [8][14][15]. The opto-mechanical effects are observable in the cantilever stiffness exhibiting the characteristic split between the fringes due to the optical spring effect of up to 4% as

High-resolution noncontact AFM and Kelvin probe force microscopy investigations of self-assembled photovoltaic donor–acceptor dyads

• Benjamin Grévin,
• Pierre-Olivier Schwartz,
• Laure Biniek,
• Martin Brinkmann,
• Nicolas Leclerc,
• Elena Zaborova and
• Stéphane Méry

Beilstein J. Nanotechnol. 2016, 7, 799–808, doi:10.3762/bjnano.7.71

• Omicron VT-AFM setup under UHV at room temperature. For each image, the frequency shift, Δf, and vibration amplitude, AVib, are indicated in the corresponding figure caption. Silicon cantilevers (SuperSharpSilicon, Nanosensors, n+-doped, stiffness 40 N/m, resonance frequency in the 280–300 kHz range) were

Assembling semiconducting molecules by covalent attachment to a lamellar crystalline polymer substrate

• Rainhard Machatschek,
• Patrick Ortmann,
• Renate Reiter,
• Stefan Mecking and
• Günter Reiter

Beilstein J. Nanotechnol. 2016, 7, 784–798, doi:10.3762/bjnano.7.70

Magnetic switching of nanoscale antidot lattices

• Ulf Wiedwald,
• Joachim Gräfe,
• Kristof M. Lebecki,
• Maxim Skripnik,
• Felix Haering,
• Gisela Schütz,
• Paul Ziemann,
• Eberhard Goering and
• Ulrich Nowak

Beilstein J. Nanotechnol. 2016, 7, 733–750, doi:10.3762/bjnano.7.65

• material parameters and temperature dependent input functions. The latter are the exchange stiffness, the equilibrium magnetisation, and the parallel and perpendicular susceptibilities. The parallel susceptibility can be related to the uniaxial anisotropy [34][35]. In the past, these input functions were

• anisotropy and the exchange stiffness at 0 K for the particular material. A realistic value for the micromagnetic damping constant is in the range of 0.1 [36][37]. In case one is not interested in the dynamics but only in the equilibrium state of the system, the damping can be increased to 1. Magnetic

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

• can usually be neglected as long as they are not excited on purpose [24][25][26]. Therefore it suffices to let the z-component of the center of mass, zs, of the simulated tip move in a harmonic potential, . The equilibrium position of the center of mass is denoted by z0, and kz is the stiffness of the

• -component of the center of mass of the tip and x0 and y0 the associated equilibrium positions. The potential is applied to all atoms of the simulated tip, where kx denotes the stiffness for the oscillation parallel to the x–y-plane. Correspondingly, the frequency of the lateral oscillations is given by

• the center of mass. The stiffness ks should generally be much larger than kz and kx. Prior to the simulation, the initial configuration is obtained in the following way: First, we set up a system that consists only of the substrate atoms. For the Lennard-Jones crystal, these were placed on regular fcc

Characterization of spherical domains at the polystyrene thin film–water interface

• Khurshid Ahmad,
• Xuezeng Zhao,
• Yunlu Pan and
• Danish Hussain

Beilstein J. Nanotechnol. 2016, 7, 581–590, doi:10.3762/bjnano.7.51

• films. This study employs AFM and optical microscopy to characterize the spherical-shaped domains that readily nucleate on the PS film after immersion in DI water. The radius, height, contact angle (CA) and line tension are analyzed in detail. The coalescence, stiffness and phase contrast analysis were

• nitride cantilevers with a nominal tip radius of 20 nm and nominal stiffness of 0.05 N/m. The resonance frequency of the cantilever immersed in DI water was 35.0 kHz. Furthermore, an average scan rate of 1 Hz was used to image the surface topography and the micro/nano spherical domains. Moreover, the

• (approximately), have an almost spherical shape (see Supporting Information File 1, Figure S1). Stiffness of the spherical objects Nanobubbles are softer and the tip–bubble interaction can affect the shape and movement of the bubbles [19][29][36][37][38]. In order to differentiate the spherical domains from

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

• the tip protrusion and the rest of the tip (this happens when in-plane surface elasticity is weak or nonexistent [22]) to a regime in which only the protrusion interacts with the surface (this happens for large in-plane surface stiffness). Notice that there can be a transition between the two regimes

• traces is inverted, in agreement with the force versus distance curves of Figure 10b). Additionally, Figure 10b shows that as the in-plane surface stiffness increases, the force curves resemble those obtained for the 1D SLS model (see Figure 7), since the effect of increasing contact surface area between

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

• Mostafa Mirzaei and
• Yaser Kiani

Beilstein J. Nanotechnol. 2016, 7, 511–523, doi:10.3762/bjnano.7.45

• matrix and, K is the stiffness matrix. Additionally, the mechanical displacement vector is denoted by X, which consists of the unknown displacements Uij, Vij, Wij, Xij and Yij. Since the free vibration response is under investigation, X = sin(ω t+φ) may be considered, where ω is the natural frequency

• stiffness matrices. In numerical integration, the interval is divided into 100 segments. Results and Discussion The free vibration characteristics of FG-CNTRC rectangular plates with a centric rectangular hole were formulated in the previous sections. In the following, to assure the effectiveness and

Contact-free experimental determination of the static flexural spring constant of cantilever sensors using a microfluidic force tool

• John D. Parkin and
• Georg Hähner

Beilstein J. Nanotechnol. 2016, 7, 492–500, doi:10.3762/bjnano.7.43

• employed as freestanding sensors [8][9][10][11][12][13]. In many applications where a cantilever-type sensor is involved, the calibration of the sensor stiffness (spring constant, k) is a prerequisite for obtaining quantitative data. Several methods describing how the static flexural spring constant can be

Active multi-point microrheology of cytoskeletal networks

• Tobias Paust,
• Tobias Neckernuss,
• Lina Katinka Mertens,
• Ines Martin,
• Michael Beil,
• Paul Walther,
• Thomas Schimmel and
• Othmar Marti

Beilstein J. Nanotechnol. 2016, 7, 484–491, doi:10.3762/bjnano.7.42

• generated in such a way that the calculated potential matches the theoretical potential of the trap with a stiffness kTr = 1 pN/µm. Afterwards, the noise was added to a generated sinusoidal motion with a frequency f = 10 Hz and a data length of 16000 points. The calculation of the SNR in the lock-in method

• is determined with 3σ (95%) accuracy and depends on the stiffness of the trap. However, with this method it is possible to measure with trap stiffnesses and applied displacements that are at the lower limit of what is experimentally possible and to still obtain a satisfying SNR. At an excitation of

• improve the SNR and to shift the error to smaller amplitudes, data sets with a length of 106 data points have to be generated. With this change a minimum amplitude of about 1 nm can be achieved. Another possibility to improve the measurement is the change of the trap stiffness. This can be seen in the

Length-extension resonator as a force sensor for high-resolution frequency-modulation atomic force microscopy in air

• Hannes Beyer,
• Tino Wagner and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2016, 7, 432–438, doi:10.3762/bjnano.7.38

• avoid stability issues such as “jump-to-contact” while working with small amplitudes, sensors with a high stiffness, e.g., short cantilevers, quartz tuning forks, or length-extension resonators are required [3]. In UHV tuning forks have outperformed conventional cantilevers because the high stiffness (k

• resonance frequency of about 1 MHz, a Q-factor of approximately 15,000 in air and an effective stiffness of keff = 1.08 MN/m. The effective stiffness amounts to twice the stiffness of a single beam (k = 540 kN/m) because the LER consists of two oscillating beams fixed at the center [9]. The very high

• stiffness allows for operation at very small amplitudes down to tens of picometres and atomic resolution has already been achieved in UHV [10][11][12][13]. The sensor is also suited for simultaneous measurements of the frequency shift and tunnelling current [12][13][14]. Only a few applications of the LER

Efficiency improvement in the cantilever photothermal excitation method using a photothermal conversion layer

• Natsumi Inada,
• Hitoshi Asakawa,
• Taiki Kobayashi and
• Takeshi Fukuma

Beilstein J. Nanotechnol. 2016, 7, 409–417, doi:10.3762/bjnano.7.36

• 0.58 and 0.12 N/m and a visible laser beam were used. However, since the excitation efficiency decreases with increasing cantilever stiffness (or with increasing the excitation laser beam wavelength), it is important to experimentally confirm the applicability of such a coating method with a relatively

Functional fusion of living systems with synthetic electrode interfaces

• Oskar Staufer,
• Sebastian Weber,
• C. Peter Bengtson,
• Hilmar Bading,
• Joachim P. Spatz and
• Amin Rustom

Beilstein J. Nanotechnol. 2016, 7, 296–301, doi:10.3762/bjnano.7.27

• . Indeed, several cell/NW-related papers based on experimental and theoretical considerations including mathematical and mechanical models predict a narrow window for the aspect ratio and density of electrodes as well as for factors such as cell stiffness, cell spreading, substrate adhesion or cell

Determination of Young’s modulus of Sb₂S₃ nanowires by in situ resonance and bending methods

• Liga Jasulaneca,
• Raimonds Meija,
• Alexander I. Livshits,
• Juris Prikulis,
• Subhajit Biswas,
• Justin D. Holmes and
• Donats Erts

Beilstein J. Nanotechnol. 2016, 7, 278–283, doi:10.3762/bjnano.7.25

• NWs over the examined cross sectional area range, with the apparent stiffness increasing for NWs with smaller cross sectional area. A linear fit added to the data points marks the tendency with a negative slope of ΔE/ΔA ≈ 230 GPa/μm². This can be explained by a nanoscale surface effect that arises

Single-molecule mechanics of protein-labelled DNA handles

• Vivek S. Jadhav,
• Dorothea Brüggemann,
• Florian Wruck and
• Martin Hegner

Beilstein J. Nanotechnol. 2016, 7, 138–148, doi:10.3762/bjnano.7.16

• lengths, one can choose a certain trap separation during experiments that minimizes contributions due to crosstalk. DH lengths of 1000, 3034 and 4056 bp were chosen for the PDHs in this study. Short handles with greater stiffness could be produced quite easily and increase the signal-to-noise ratio (SNR

• increasing the distance between the two optically trapped beads. For nanomechanical experiments short molecular handles are preferred due to their increased mechanical stiffness, resulting in a favourable signal-to-noise ratio [14]. In order to achieve optimal positional and force resolution a balance had to

• be found between minimising the parasitic optical crosstalk signal in the dual-trap instrument and maximising the stiffness of the tethers. Double handle experiments with DNA handles of 1000 bp (contour lengths of more than 340 nm each), were the shortest possible constructs that still featured the

Dependence of lattice strain relaxation, absorbance, and sheet resistance on thickness in textured ZnO@B transparent conductive oxide for thin-film solar cell applications

• Kuang-Yang Kou,
• Yu-En Huang,
• Chien-Hsun Chen and
• Shih-Wei Feng

Beilstein J. Nanotechnol. 2016, 7, 75–80, doi:10.3762/bjnano.7.9

• , εxx, and in the y-direction, εyy, of ZnO films can be determined by the frequency shift, Δω = ω−ω0 [21], as: where a = −774 cm−1 and b = −375 cm−1 are the deformation potential constants of the A1(TO) mode [22]. The elastic stiffness constants, C33 and C13, are 216 and 104 GPa, respectively [1]. The

Controlled graphene oxide assembly on silver nanocube monolayers for SERS detection: dependence on nanocube packing procedure

• Martina Banchelli,
• Bruno Tiribilli,
• Roberto Pini,
• Luigi Dei,
• Paolo Matteini and
• Gabriella Caminati

Beilstein J. Nanotechnol. 2016, 7, 9–21, doi:10.3762/bjnano.7.2

• . Possibility to obtain these structures relies on the ratio between the in-plane stiffness and out-of-plane bending stiffness: large values of this parameter translate in membrane-like material that more easily bend and crumple. Optical microscopy in reflection mode images (Figure 4) of the two systems

Nanoscale rippling on polymer surfaces induced by AFM manipulation

• Mario D’Acunto,
• Franco Dinelli and
• Pasqualantonio Pingue

Beilstein J. Nanotechnol. 2015, 6, 2278–2289, doi:10.3762/bjnano.6.234

• cantilever longitudinal and lateral stiffness, the scan direction and velocity, the spacing between successive lines (named ‘feeding’). Depending on these parameters, the nanoripple patterns form in either one or several scan frames. The most significant physical observables of the process are the lateral

• upon penetration of the tip. If one knows the time dependence N(t) and the indenter width, the process is found to be governed only by the scan velocity v and the lateral stiffness k. Specifically, the amplitude A and ripple periodicity increase when N exceeds a critical value Nc or, vice versa, when k

• or v fall below the critical values of vc and kc, respectively (Figure 7). A transition from stick–slip to gliding can be also predicted for an indentation rate below a critical value or, alternatively, for large values of the sliding velocity, the lateral stiffness or the tip width. It is suggested

A simple and efficient quasi 3-dimensional viscoelastic model and software for simulation of tapping-mode atomic force microscopy

• Santiago D. Solares

Beilstein J. Nanotechnol. 2015, 6, 2233–2241, doi:10.3762/bjnano.6.229

• analyze the depth dependence of the contact stiffness by performing a fit to appropriate models of elastic, viscous and adhesive forces, as is demonstrated in [13] for polymer blends. This approach is associated with small tip oscillations and is sensitive to the speed at which the base of the cantilever

Fabrication of hybrid nanocomposite scaffolds by incorporating ligand-free hydroxyapatite nanoparticles into biodegradable polymer scaffolds and release studies

• Balazs Farkas,
• Marina Rodio,
• Ilaria Romano,
• Alberto Diaspro,
• Romuald Intartaglia and
• Szabolcs Beke

Beilstein J. Nanotechnol. 2015, 6, 2217–2223, doi:10.3762/bjnano.6.227

• concentration. The MPExSL process yielded PPF thin films with a stable and homogenous dispersion of the embedded HA nanoparticles. Here, it was not possible to tune the stiffness and hardness of the scaffolds by varying the laser parameters, although this was observed for regular PPF scaffolds. Finally, the

• also proved that these scaffolds did not cause immune rejection [21]. A constant release of HA NPs during scaffold degradation may vastly improve the healing process. Also, certain tuning capabilities emerge with PPF:DEF resins when fabrication parameters are changed [22][23]: The stiffness/Young

• nanoindentation (Figure 2b) measurements show that the stiffness of the fabricated samples can be considered identical, independent of the concentration of the nanoparticles, as well as the laser parameters. Also, the samples (samples 1–6) fabricated with three different HA concentrations (50, 100 and 300 ppm

Development of a novel nanoindentation technique by utilizing a dual-probe AFM system

• Eyup Cinar,
• Ferat Sahin and
• Dalia Yablon

Beilstein J. Nanotechnol. 2015, 6, 2015–2027, doi:10.3762/bjnano.6.205

• . Therefore, stiffness can be approximated with the slope of unloading curve as shown in Figure 1a. If the unloading curve is fit to a power law such as F = α(h − hf)m where α and m are power-law fitting constants then the unloading stiffness S can be approximated as in Equation 1 by the slope of the fitting

• force curve such as that in Figure 1a is obtained, one can calculate elastic unloading stiffness through Equation 2 defined as the slope of the upper part on the unloading curve as shown in Figure 1a: where Eeff is effective elastic modulus including both the elastic modulus of the indenter (E1) and of

• calculate the stiffness parameter S from the slope of the unloading part and use Equation 2 and Equation 3 to extract the unknown elastic modulus of the sample (E2). In the next section we introduce an overview of the proposed system and its components in detail. We also present the calibration data and the

A simple method for the determination of qPlus sensor spring constants

• John Melcher,
• Julian Stirling and
• Gordon A. Shaw

Beilstein J. Nanotechnol. 2015, 6, 1733–1742, doi:10.3762/bjnano.6.177

• System of Units (SI) [19][21][37], measures a force vs displacement curve by pressing a sharp indenter tip into the qPlus sensor surface at a known axial distance from the distal edge of the tine. From the indentation curve, a stiffness kI is inferred, taking care to remove the machine compliance and

• were acquired along the axis of the tine and additionally at the base of the sensor in order to remove the contact stiffness and machine compliance from the spring constant prediction. To avoid interference with the indenter tip, tips were not attached to the tine. Figure 7 shows the indentation

• (less than 3%) in stiffness by testing at a lateral offset from the beam axis. Finally, we note that for sufficiently long tips, the compliance of the tip contributes to the parasitic tip motion [32][33]. This, in turn, influences the spring constant and force spectroscopy results presented here. To