3D solid supported inter-polyelectrolyte complexes obtained by the alternate deposition of poly(diallyldimethylammonium chloride) and poly(sodium 4-styrenesulfonate)

• Eduardo Guzmán,
• Armando Maestro,
• Sara Llamas,
• Jesús Álvarez-Rodríguez,
• Francisco Ortega,
• Ángel Maroto-Valiente and
• Ramón G. Rubio

Beilstein J. Nanotechnol. 2016, 7, 197–208, doi:10.3762/bjnano.7.18

• processed using the software WSxM from Nanotec Electronica [28]. Results and Discussion Wet films vs dry films The growth of polyelectrolyte multilayers of (PDADMAC + PSS)N was followed by monitoring the frequency shift (Δf) of the QCM-D normalized by the overtone number (ν), −Δf/ν, as a function of the

• number of bilayers (N) [19][29]. It is well known that the adsorbed mass calculated using Sauerbrey’s equation underestimates the real mass of viscoelastic films [30][31][32]. Figure 1 shows the frequency shift as a function of N for wet and dry multilayers (PDADMAC + PSS)N. The differences between wet

• , among them the most evident is the adsorbed mass (see Figure 1). Because the QCM-D detects both the polymer adsorbed and the hydration water, drying of the films reduces the adsorbed mass (lower resonance frequency shift). The drying process makes the polymer matrix shrink, which is critically related

Fabrication and characterization of novel multilayered structures by stereocomplexion of poly(D-lactic acid)/poly(L-lactic acid) and self-assembly of polyelectrolytes

• Elena Dellacasa,
• Li Zhao,
• Gesheng Yang,
• Laura Pastorino and
• Gleb B. Sukhorukov

Beilstein J. Nanotechnol. 2016, 7, 81–90, doi:10.3762/bjnano.7.10

• after synthesis and purification. QCM measurements As a first step, the LBL assembly of PEM and PLA polymers was carried out on QCM electrodes in order to monitor the effective multilayer growth. The QCM frequency shift, due to the deposition of material onto the electrode surface, was measured and the

• the quartz crystal surface is mostly negatively charged, PAH was deposited as the first layer. The PEM structure shows a mean mass of 85.38 ng, with a mean frequency shift of 155.4 Hz. The total mass of adsorbed PLA layers with PEM precursor was found to be 1468 ng with a mean mass of 245 ng/layer

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

• six-fold symmetry of the hexagonal polar c-ZnO dictates an isotropic in-plane strain in the basal plane, i.e., εxx = εyy = ε. The frequency shift,s Δω, for the A1(TO) mode are shown in Table 1. The in-plane strain ε can be deduced from Equation 1. The in-plane tensile strain, ε, of the c-20, c-40, c

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

• substrates were simultaneously coated by the same AgNC layer. Quartz crystal microbalance measurements. QCM experiments with impedance monitoring were performed on a QCM-Z500 (KSV Instruments Ltd) equipped with a thermoelectric (TE) module (Oven Instruments). The resonant frequency shift and the change in

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

• parameters constant. The most common example of a spectroscopic measurement in AFM is the recording of an observable (e.g., phase shift, frequency shift, deflection, specific harmonic amplitudes, etc.), while the base of the microcantilever is brought closer to the sample with a relatively small constant

Kelvin probe force microscopy for local characterisation of active nanoelectronic devices

• Tino Wagner,
• Hannes Beyer,
• Patrick Reissner,
• Philipp Mensch,
• Heike Riel,
• Bernd Gotsmann and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2015, 6, 2193–2206, doi:10.3762/bjnano.6.225

• finding the noise power spectral density of the frequency shift signal in FM-AFM [24]. When the narrow-band conditions are not met (β >> 1), the iterative scheme for the sideband amplitudes in Equation 4 and Equation 5 still approaches the Bessel functions describing the sideband amplitudes in a general

• . Nevertheless, the averaging effect of the cantilever beam remains (see below in Figure 1). An alternative approach typically applied in vacuum is based on frequency modulation [15]. To this end, the frequency of the cantilever is usually tracked by a phase-locked loop (PLL). Its output signal, the frequency

• shift Δf, exhibits a frequency component at the electrostatic modulation frequency, which is nullified by the Kelvin feedback loop. Frequency modulated KFM (FM-KFM) [16][17] thus provides a map of potentials required to minimise the electrostatic force gradient, proportional to Δf for small mechanical

Virtual reality visual feedback for hand-controlled scanning probe microscopy manipulation of single molecules

• Philipp Leinen,
• Matthew F. B. Green,
• Taner Esat,
• Christian Wagner,
• F. Stefan Tautz and
• Ruslan Temirov

Beilstein J. Nanotechnol. 2015, 6, 2148–2153, doi:10.3762/bjnano.6.220

• position of the SPM tip during manipulation in real time, while simultaneously plotting the experimentally measured frequency shift (Δf) of the non-contact atomic force microscope (NC-AFM) tuning fork sensor as well as the magnitude of the electric current (I) flowing between the tip and the surface. The

• for additional information). Supporting Information File 132: Interactive 3D models of the data shown in Figure 4. In order to view it unpack and open either ’df.html’ (frequency shift) or ’I.html’ (logarithm of the current) file.

Electrospray deposition of organic molecules on bulk insulator surfaces

• Antoine Hinaut,
• Rémy Pawlak,
• Ernst Meyer and
• Thilo Glatzel

Beilstein J. Nanotechnol. 2015, 6, 1927–1934, doi:10.3762/bjnano.6.195

• distributed all over the surface and appear up to 3 nm high. However, no clear organization of the molecules was observed. Large electrostatic forces have been observed and measured via frequency shift versus voltage curves df(V) [40] after the deposition process. These could not be compensated during

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

• possible for qPlus sensors [10], and other sensors with cantilevered geometries [11], to reach quality factors in excess of 106 without inertial cancelling. Several methods have been developed to reconstruct the tip–sample interaction force from the frequency shift of an oscillating tip in ncAFM [12][13

• ][14][15][16][17]. This analysis requires four separate experimental inputs: the frequency shift Δω as a probe interacts with a surface relative to the unperturbed resonant frequency ω0, the sensor oscillation amplitude a, which is held constant, and z is the distance of nearest approach between a

• surface and the oscillating probe tip, and the spring constant k. The reconstructed tip–sample force is given by [17]: where Ω(z) = Δω(z)/ω0. The reconstruction requires that the z-separation between the tip and sample is varied while the frequency shift is monitored. Force reconstruction using other

Lower nanometer-scale size limit for the deformation of a metallic glass by shear transformations revealed by quantitative AFM indentation

• Arnaud Caron and
• Roland Bennewitz

Beilstein J. Nanotechnol. 2015, 6, 1721–1732, doi:10.3762/bjnano.6.176

• close to a sample surface at its resonance frequency. The tip–sample distance is of the order of a few nanometers. Changes in tip–sample distance during scanning over a sample surface due to sample topography yield changes in the oscillation amplitude and in a frequency shift of the cantilever resonance

• . In order to measure topography both amplitude and frequency shift are tracked by a feedback loop so as to keep the cantilever oscillation in resonance [15]. For indentation and imaging we used a diamond-coated silicon single crystalline cantilever (Type: CDT-NCLR, manufactured by NanoSensors). The

Nanomechanical humidity detection through porous alumina cantilevers

• Olga Boytsova,
• Alexey Klimenko,
• Vasiliy Lebedev,
• Alexey Lukashin and
• Andrey Eliseev

Beilstein J. Nanotechnol. 2015, 6, 1332–1337, doi:10.3762/bjnano.6.137

• of the pores the cantilevers exhibit an exceptional sensitivity to absorbed mass. The resonance frequency shift in water vapor absorption experiments over a humidity range of 10–22% fits well to the monolayer adsorption isotherm. A strong response to environmental change enables the use of AAO

• responses of Si rectangular cantilever (2 μm thick, 100 μm long and 30 μm wide) in the air (black line) and in vacuum (red solid line). The frequency shift is 780 Hz. b) Frequency responses of AAO cantilever (2 μm thick, 800 μm long and 100 μm wide) in the air (black line) and in vacuum (red solid line

Nano-contact microscopy of supracrystals

• Adam Sweetman,
• Nicolas Goubet,
• Ioannis Lekkas,
• Marie Paule Pileni and
• Philip Moriarty

Beilstein J. Nanotechnol. 2015, 6, 1229–1236, doi:10.3762/bjnano.6.126

• qPlus probe became nanocrystal- (or thiol-)terminated. Imaging was performed in constant current STM, constant frequency shift (Δf) DFM, and constant height DFM modes. In addition to traditional STM, we also carried out dynamic STM (dSTM) imaging and spectroscopy, where the tip was oscillated with a

• small amplitude (of order 0.1−0.3 nm, see below) normal to the surface. The use of constant height imaging (using a similar protocol to that described previously [30][33]) allows us to probe the tip–sample interaction on the repulsive branch of the frequency shift curve, which is typically not available

• height DFM mode, producing a map of Δf, with dark regions corresponding to attractive interaction (more negative frequency shift), and brighter regions corresponding to repulsive interactions (more positive frequency shifts). The result of imaging the nanocrystal at progressively smaller tip–sample

Attenuation, dispersion and nonlinearity effects in graphene-based waveguides

• Almir Wirth Lima Jr.,
• João Cesar Moura Mota and
• Antonio Sergio Bezerra Sombra

Beilstein J. Nanotechnol. 2015, 6, 1221–1228, doi:10.3762/bjnano.6.125

• the right side of Equation 8 are responsible for the spectral broadening of the pulse, self-steepening and shock formation and self-frequency shift, respectively. In a previous work, the Fourier transform was applied to find the broadening of a pulse that propagates on a nanophotonic metal/dielectric

Graphene on SiC(0001) inspected by dynamic atomic force microscopy at room temperature

• Mykola Telychko,
• Jan Berger,
• Zsolt Majzik,
• Pavel Jelínek and
• Martin Švec

Beilstein J. Nanotechnol. 2015, 6, 901–906, doi:10.3762/bjnano.6.93

• signal from the tuning fork piezo [22][23]. The tip has been treated by annealing to 1200 °C in contact with a hot tungsten filament. The simultaneous current and frequency shift measurements were done in constant height mode. A very slow tunneling current feedback was applied for compensation of the

• sample tilt. The reason to use current as a feedback, as opposed to using the frequency shift (Δf), is the possibility of doing measurements in the region of a negative frequency shift gradient (repulsive regime), even at room temperature, without enhanced risk of losing the tip apex. This approach is

• (Vbias = 100 mV, I = 0.46 nA, 5.5 nm × 7.1 nm and (b) frequency shift Δf acquired on the same area of graphene/SiC(0001). The q-6 modulation is apparent in both channels, whereas the × modulation due to scattering on armchair boundary is detected only in the map. The insets on the top show zoomed

Stiffness of sphere–plate contacts at MHz frequencies: dependence on normal load, oscillation amplitude, and ambient medium

• Jana Vlachová,
• Rebekka König and
• Diethelm Johannsmann

Beilstein J. Nanotechnol. 2015, 6, 845–856, doi:10.3762/bjnano.6.87

• of an intuitive understanding. Roughly speaking, the apparent contact stiffness decreases at elevated amplitudes because the sticking portion of the contact decreases. The “apparent contact stiffness” here is the stiffness as derived from the frequency shift (Equation 2 below). This intuitive picture

• contacts: linear and nonlinear regime We first consider the viscoelastic contact. According to the small-load approximation, the complex frequency shift at small amplitude is given as [35][36] Δf and ΔΓ are the shifts of the frequency and the half-bandwidth at half-height, respectively. The parameter Γ is

• materials involved, but also to interfacial processes (as long as these obey linear mechanics). Equation 1 can be inverted as As shown in Equation 2, the complex frequency shift is easily converted to a complex contact stiffness. Up to now, linear force–displacement relations were assumed. If linearity does

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

• frequency shift (Ω) that occur by decreasing the cantilever-surface separation (z). This is shown in Equation 2 where dmin is related to z and to A as: dmin ≈ z − A. The normalized frequency shift Ω is derived from observables in AM-AFM. When f = f0, Equation 3 is obtained [38]. where Φ is the phase lag

A scanning probe microscope for magnetoresistive cantilevers utilizing a nested scanner design for large-area scans

• Tobias Meier,
• Alexander Förste,
• Ali Tavassolizadeh,
• Karsten Rott,
• Dirk Meyners,
• Roland Gröger,
• Günter Reiss,
• Eckhard Quandt,
• Thomas Schimmel and
• Hendrik Hölscher

Beilstein J. Nanotechnol. 2015, 6, 451–461, doi:10.3762/bjnano.6.46

• tracked with a phase-locked-loop (PLL) while its frequency shift was used as a feedback for the topography feedback loop [6]. As the frequency tracking loop feeds back the cantilevers resonance frequency to the driving signal at a 90°phase shift, the contrast in the phase signal disappears as shown Figure

Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM

• Kfir Kuchuk and
• Uri Sivan

Beilstein J. Nanotechnol. 2015, 6, 149–156, doi:10.3762/bjnano.6.14

• resonance frequency. In frequency modulation-AFM (FM-AFM), the force is usually reconstructed from the resonance frequency shift, which in the small amplitude regime is proportional to the derivative of the force with respect to tip–surface distance. Similarly, it has been recognized that higher harmonics

• cantilever is brought close to a surface, the tip–surface interaction forces shift the resonance frequency. The relation between the frequency shift and Fts, in the case where the force depends only on tip position, was first derived by Giessibl as [14] Here, Δω is the frequency shift, a is the oscillation

• amplitude in AM-AFM. Second, there is evidence [5][6][7][8][9][10][11] that higher harmonics are more sensitive to short-range forces than the fundamental harmonic. This becomes evident when the cantilever oscillation amplitude is small compared with the interaction length. As we show, the frequency shift

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

• materials contrast imaging. For imaging in air, we used a FastScan A cantilever with the fundamental and first higher flexural resonant modes at 1.3 MHz and 6.6 MHz, respectively. Figure 4a shows the resulting topography image, while Figure 4b and Figure 4c show the frequency shift and dissipation images

• were set to 8 nm free amplitude with a setpoint of around 50–60% for both air and water imaging. The second eigenmode was set to 54 pm in air and 86 pm in water. Figure 4d–f present the topography, frequency shift and dissipation images, respectively. The dissipation images show a very clear step

• resonance. Panels b and e show the resonance frequency shift of the first higher resonant mode, and panels c and f show the drive amplitude needed to keep the first higher resonant mode at constant amplitude, related to the energy dissipation in the tip–sample interaction. a) Schematic of the drive

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

• -modulated atomic force microscopy (FM-AFM), the physical processes involved have been studied intensively in the past [1]. This includes the relation between tip–surface interaction and frequency-shift [2], as well as features such as the energy dissipation during the scan [3], which is an interesting side

• vary the values of x0 and z0 between 0 and 0.5 nm and between 10 and 12 nm, respectively, in order to have different ratios between lateral and normal force. The amplitude is always equal 10 nm. We discard parameter sets for which the reduced frequency shift [2] lies outside the interval −7 fN m1/2 and

• the relaxation procedure each time. The forces are interpolated linearly for the use in Equation 1 and Equation 2. In order to simulate an FM-AFM, we start at a certain position (x0, z0) and integrate Equation 1 and Equation 2 for 10 cycles. The usual reduced frequency shift is adjusted to a given

Patterning a hydrogen-bonded molecular monolayer with a hand-controlled scanning probe microscope

• Matthew F. B. Green,
• Taner Esat,
• Christian Wagner,
• Philipp Leinen,
• Alexander Grötsch,
• F. Stefan Tautz and
• Ruslan Temirov

Beilstein J. Nanotechnol. 2014, 5, 1926–1932, doi:10.3762/bjnano.5.203

• for a stable and precise positioning of the tip, while simultaneously measuring the current flowing through the junction (I) and the frequency shift of the oscillating tip (Δf). Measuring Δf provides additional information about the microscopic junction structure [15][16]. For the AFM functionality we

• quality factor of Q ≈ 70,000. Contacting and manipulation were performed with the qPlus sensor oscillating with an amplitude of A0 ≈ 0.2–0.3 Å. Interactions in the junction were monitored by measuring the frequency shift Δf(z) ≈ −(f0/2k0)dFz/dz, where k0 = 1800 N/m is the stiffness of the quartz tuning

• junction and the frequency shift Δf were displayed on the screen of an oscilloscope and served as feedback signals for the operator. Formation (loss) of the contact was monitored in real time by a sharp increase (decrease) of I (cf. Figure 1b) or a kink in Δf [15][16]. After establishing the contact

Dynamic calibration of higher eigenmode parameters of a cantilever in atomic force microscopy by using tip–surface interactions

• Stanislav S. Borysov,
• Daniel Forchheimer and
• David B. Haviland

Beilstein J. Nanotechnol. 2014, 5, 1899–1904, doi:10.3762/bjnano.5.200

• calibration method is similar to that described in [29], in which stiffness of the second eigenmode is experimentally defined by using consecutive measurements of the frequency shift caused by the tip–surface interaction for different eigenmodes. In contrast, we propose a simultaneous one-point measurement by

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

• , which requires the use of a constant-response-amplitude method such as constant-amplitude frequency-modulation [27]. However, if the frequency shift is significantly different for different regions, according to the results of Figure 4a, they may not be directly comparable since the interplay of

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

• slightly for larger amplitudes). In the second case (Figure 5b), we see that the level of perturbation increases, accompanied by a greater frequency shift (due to a greater influence of the repulsive forces in the range of conditions considered), as the cantilever is lowered towards the sample

• eigenmode frequency shift increases as its free amplitude is decreased while keeping the other higher amplitudes constant, in agreement with previous results [20] and with Figure 5a, although the shape of the response curve remains distorted for most of the range of amplitudes considered. Despite the

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

• setpoint of 45%. The scale bar is 100 nm. Illustration of the ideal response of a harmonic oscillator [22]. (a) Amplitude and phase vs excitation frequency (at the resonance frequency the phase is 90 degrees); (b) phase and effective frequency shift vs external force gradient (at zero force gradient the