Multifrequency AFM integrating PeakForce tapping and higher eigenmodes for heterogeneous surface characterization

• Yanping Wei,
• Jiafeng Shen,
• Yirong Yao,
• Xuke Li,
• Ming Li and
• Peiling Ke

Beilstein J. Nanotechnol. 2025, 16, 2077–2085, doi:10.3762/bjnano.16.142

• constant The inverse optical lever sensitivity (InvOLS) and the spring constant (k) of each cantilever were calibrated following a standard procedure, which is built into the Bruker Nanoscope software. Briefly, InvOLS (in nm·V−1) was determined by averaging the slope of the constant compliance region from

• at least five force–distance curves acquired on a rigid sapphire surface. The standard deviation of these measurements was consistently less than 5%. Subsequently, the spring constant was calibrated using the thermal tune method. The cantilever was retracted more than 5 μm from the sample surface to

• record its thermal vibration power spectral density. A fit to the fundamental resonance peak, based on the equipartition theorem, yielded the spring constant. Characterization of higher eigenmodes The resonant frequencies of the higher eigenmodes were characterized by performing a frequency sweep using

Molecular and mechanical insights into gecko seta adhesion: multiscale simulations combining molecular dynamics and the finite element method

• Yash Jain,
• Saeed Norouzi,
• Tobias Materzok,
• Stanislav N. Gorb and
• Florian Müller-Plathe

Beilstein J. Nanotechnol. 2025, 16, 2055–2076, doi:10.3762/bjnano.16.141

• from the spatulae. To mitigate excessive deformation or drift, harmonic springs connect the FE nodes in the bridging domain to their initial positions at the start of each FEM iteration. These springs have a stiffness referred to as the FE-coupling spring constant. These FE-coupling harmonic springs

• used this multiscale approach to simulate crystalline and amorphous polymers [43]. Once the FEM calculation is complete, the updated positions of the FE nodes in the bridging domain, and hence of the APs, are passed back to the particle domain. The FE-coupling spring constant was optimized, starting

• from the same value as the MD-coupling spring constant and then reduced until forces across the domains matched [43]. Further discussion on the choice of the spring constants is provided in Supporting Information File 1. The FE calculation is static (no inertia), and the MD employs thermostats

Mechanical property measurements enabled by short-term Fourier-transform of atomic force microscopy thermal deflection analysis

• Thomas Mathias,
• Roland Bennewitz and
• Philip Egberts

Beilstein J. Nanotechnol. 2025, 16, 1952–1962, doi:10.3762/bjnano.16.136

• -CONT), and harder cantilevers with an integrated tip (Nanosensors PPP-NCL). The soft cantilevers have a nominal stiffness in the normal bending direction of 0.2 N·m−1, and the hard cantilevers have a nominal stiffness of 40 N·m−1. For each cantilever used, the spring constant of the cantilever in the

• same value as the one obtained using the Sader method (74.3 mN·m−1 for this cantilever in Figure 2) [20]. Similar observations were made for the other cantilevers used in the experiments conducted within this paper, with the difference between the value of D1 and the normal spring constant calculated

• dimensions in the determination of the Sader spring constant or other calculations of the normal spring constant are important. Finally, it has been demonstrated that the Sader method can consistently show a difference compared with the thermal noise method used above, particularly for soft cantilevers as

Mechanical stability of individual bacterial cells under different osmotic pressure conditions: a nanoindentation study of Pseudomonas aeruginosa

• Lizeth García-Torres,
• Idania De Alba Montero,
• Eleazar Samuel Kolosovas-Machuca,
• Facundo Ruiz,
• Sumati Bhatia,
• Jose Luis Cuellar Camacho and
• Jaime Ruiz-García

Beilstein J. Nanotechnol. 2025, 16, 1171–1183, doi:10.3762/bjnano.16.86

• a NanoScope V controller operated in fluid conditions throughout all experiments, using a pre-assembled fluid chamber with the appropriate solutions within a sealed O-ring. The instrument was operated in contact mode using MLCT probes from Bruker, cantilever D with a nominal spring constant of 0.03

Piezoelectricity of hexagonal boron nitrides improves bone tissue generation as tested on osteoblasts

• Sevin Adiguzel,
• Nilay Cicek,
• Zehra Cobandede,
• Feray B. Misirlioglu,
• Hulya Yilmaz and
• Mustafa Culha

Beilstein J. Nanotechnol. 2025, 16, 1068–1081, doi:10.3762/bjnano.16.78

• microscopy (PFM, Nanomagnetic Instruments, UK) was applied to evaluate nanoscale piezoelectric behavior using self-aligned conducting EFM probes with a spring constant of 2.8 N/m and a resonance frequency of 75 kHz. In vitro analyses To investigate the influence of hBNs and BaTiO3 with US therapy on

The impact of tris(pentafluorophenyl)borane hole transport layer doping on interfacial charge extraction and recombination

• Konstantinos Bidinakis and
• Stefan A. L. Weber

Beilstein J. Nanotechnol. 2025, 16, 678–689, doi:10.3762/bjnano.16.52

• lock-in amplifier (Zurich Instruments), in an argon atmosphere glove box (less than 1% ppm O2 and negligible humidity). The cantilever used was SCM PIT V2 (resonance frequency: 75 kHz, spring constant: 3 N/m, Bruker). The scan rate of the measurement was 0.5 Hz. To increase the reliability of our data

Nanoscale capacitance spectroscopy based on multifrequency electrostatic force microscopy

• Pascal N. Rohrbeck,
• Lukas D. Cavar,
• Franjo Weber,
• Peter G. Reichel,
• Mara Niebling and
• Stefan A. L. Weber

Beilstein J. Nanotechnol. 2025, 16, 637–651, doi:10.3762/bjnano.16.49

• capacitance gradient, we need to calculate the electrostatic force from the detected amplitude signal, Adet, taking into account the cantilever’s frequency-dependent spring constant or transfer function, k(ω): Interestingly, the forces in Equation 11 only depend on the frequency difference, Δωe, of the

• ). To enhance the signal, we select ωE such that 2ωE coincides with the second resonance of the cantilever (2ωE = ωm,2). We connect the numerical value of the capacitance gradient to the detected amplitude using the cantilever’s frequency-dependent transfer function or spring constant k(ω) by For the

• the Pt/Ir-coated conductive cantilevers (NuNano SPARK-150Pt and MikroMasch HQ:NSC18/Pt) was ≈75 kHz; the levers had a spring constant of 2–3 N·m−1, a tip radius of 18 nm, and a tip height of 10–18 μm. The topography feedback measurements were performed with amplitude modulation on the first eigenmode

A biomimetic approach towards a universal slippery liquid infused surface coating

• Ryan A. Faase,
• Madeleine H. Hummel,
• AnneMarie V. Hasbrook,
• Andrew P. Carpenter and
• Joe E. Baio

Beilstein J. Nanotechnol. 2024, 15, 1376–1389, doi:10.3762/bjnano.15.111

• Innova instrument in tapping mode. RTESPA-300 (Bruker, Billerica, MA) probes were used with a tip radius of 12 nm, a spring constant of 40 N/m, and a frequency of 300 kHz. A minimum of six images from two different samples were produced with dimensions of 5 × 5 μm at a scan rate of 0.5 Hz. Post

New design of operational MEMS bridges for measurements of properties of FEBID-based nanostructures

• Bartosz Pruchnik,
• Krzysztof Kwoka,
• Ewelina Gacka,
• Dominik Badura,
• Piotr Kunicki,
• Andrzej Sierakowski,
• Paweł Janus,
• Tomasz Piasecki and
• Teodor Gotszalk

Beilstein J. Nanotechnol. 2024, 15, 1273–1282, doi:10.3762/bjnano.15.103

• spectral analysis of vibrations [49]. The thermomechanical noise analysis approximates the bridge as a simple harmonic oscillator with one DOF, as has been used for determining the spring constant of AFM cantilevers [50]. This approach provides an approximation for the stiffness k in terms of the measured

Design, fabrication, and characterization of kinetic-inductive force sensors for scanning probe applications

• August K. Roos,
• Ermes Scarano,
• Elisabet K. Arvidsson,
• Erik Holmgren and
• David B. Haviland

Beilstein J. Nanotechnol. 2024, 15, 242–255, doi:10.3762/bjnano.15.23

• comes the spring constant k, which should match the maximum tip–surface force gradient. For a given k, the mechanical resonant frequency is set by meff, A larger mechanical resonant frequency gives a larger integration bandwidth for a given mechanical quality factor Qm = ωm/γm. However, increasing ωm

• fabricating a wafer of sensor chips. We design the cantilever’s plane-view dimensions to achieve ωm/2π in the range of 0.5–10 MHz, corresponding to mechanical spring constant values k in the range of 2–160 N/m for typical device parameters. The wide frequency range allows us to fabricate devices working in

• ωm, quality factor Qm, and spring constant k of the cantilever. These trade-offs affect the transduction efficiency and force sensitivity. Although a large single-photon coupling rate g0 is desirable, we prioritize a cavity that we can pump to large intra-cavity photon numbers while maintaining

Quantitative wear evaluation of tips based on sharp structures

• Ke Xu and
• Houwen Leng

Beilstein J. Nanotechnol. 2024, 15, 230–241, doi:10.3762/bjnano.15.22

• , making it ideal for reverse imaging of the AFM probe tip to detect tip wear. AFM images were acquired using a Bruker Icon AFM system in tapping mode. The AFM probe used for AFM imaging was a Bruker FESPA-V2 probe. The cantilever was 225 µm long, 35 µm wide, and had a spring constant of 2.8 N/m. The

CdSe/ZnS quantum dots as a booster in the active layer of distributed ternary organic photovoltaics

• Gabriela Lewińska,
• Piotr Jeleń,
• Zofia Kucia,
• Maciej Sitarz,
• Łukasz Walczak,
• Bartłomiej Szafraniak,
• Jerzy Sanetra and
• Konstanty W. Marszalek

Beilstein J. Nanotechnol. 2024, 15, 144–156, doi:10.3762/bjnano.15.14

• carried out for three incidence angles (65°, 70°, and 75°). A Bruker atomic force microscope (AFM) MULTIMODE 8 was used in the measurements in the ScanAsyst in Air mode, using silicon nitride probes (with a nominal tip radius of 2 nm and a spring constant equal to 0.4 N/m). The substrate was

Enhanced feedback performance in off-resonance AFM modes through pulse train sampling

• Mustafa Kangül,
• Navid Asmari,
• Santiago H. Andany,
• Marcos Penedo and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2024, 15, 134–143, doi:10.3762/bjnano.15.13

• setpoint value, as shown in Figure 2C-ii. The slope of the force–distance curve depends on the effective spring constant between the tip and the sample. To mitigate this issue, we select a small time window around the maximum deflection point, where the tip–sample relative velocity is the smallest because

Carbon nanotube-cellulose ink for rapid solvent identification

• Tiago Amarante,
• Thiago H. R. Cunha,
• Claudio Laudares,
• Ana P. M. Barboza,
• Ana Carolina dos Santos,
• Cíntia L. Pereira,
• Vinicius Ornelas,
• Bernardo R. A. Neves,
• André S. Ferlauto and
• Rodrigo G. Lacerda

Beilstein J. Nanotechnol. 2023, 14, 535–543, doi:10.3762/bjnano.14.44

• contact mode. AC160TS silicon cantilevers from Olympus with a typical spring constant of k ≈ 46 N/m, a nominal radius of curvature of r ≈ 7 nm, and a resonant frequency of ω0 ≈ 300 kHz were employed. Heat flow and weight changes of selected solvents were determined by thermogravimetric analysis (TGA

High–low Kelvin probe force spectroscopy for measuring the interface state density

• Ryo Izumi,
• Masato Miyazaki,
• Yan Jun Li and
• Yasuhiro Sugawara

Beilstein J. Nanotechnol. 2023, 14, 175–189, doi:10.3762/bjnano.14.18

• advantages, namely high sensitivity to the electrostatic force gradient, high detection sensitivity using a cantilever with a weak spring constant at the first resonance, ease of implementation in adding FM-AFM, and no need to enhance the bandwidth of the cantilever deflection sensor. FM-KPFM is used to

• vibration cos 2πf0t, f0 ± fm components of the electrostatic force Fele,L(f0 ± fm) appear: When the electrostatic force is detected by the FM method, the electrostatic force Fele,L(f0 ± fm) is demodulated into the fm component of the frequency shift ΔfL(fm), which is expressed as where k is the spring

• constant of the cantilever. This equation indicates that the slope of the dependence of the fm component of the frequency shift ΔfL(fm) on the DC bias voltage Vdc (ΔfL(fm)–Vdc curve) is proportional to the capacitance inside the semiconductor at a low-frequency AC bias (CD + Cit). High KPFS Next, we

Characterisation of a micrometer-scale active plasmonic element by means of complementary computational and experimental methods

• Ciarán Barron,
• Giulia Di Fazio,
• Samuel Kenny,
• Silas O’Toole,
• Robin O’Reilly and
• Dominic Zerulla

Beilstein J. Nanotechnol. 2023, 14, 110–122, doi:10.3762/bjnano.14.12

• setup used to perform such measurements. An Adama NM-RC probe (spring constant: 290.3 N/m, nominal resonance frequency: 814 kHz) has been used in contact mode to scan the topography of an electrically modulated sample with a loading force of 1.9 μN. This particular probe is intended for use in

• nanomechanical operations such as lithography and machining. The high spring constant of this cantilever has the advantage of minimising the unwanted deflection of the cantilever resulting from electrostatic interaction of the potential on the surface and the probe. The tip is constructed from wear-resistant

Utilizing the surface potential of a solid electrolyte region as the potential reference in Kelvin probe force microscopy

• Nobuyuki Ishida

Beilstein J. Nanotechnol. 2022, 13, 1558–1563, doi:10.3762/bjnano.13.129

• spring constant of 3 N/m. The CPD was detected using the sideband KPFM mode [18][19][4]. The amplitude and frequency of the modulation voltage were 1.5 V and 3.2 kHz, respectively. The modulation voltage and DC voltage were applied to the tip to minimize the electrostatic force between the tip and sample

Studies of probe tip materials by atomic force microscopy: a review

• Ke Xu and
• Yuzhe Liu

Beilstein J. Nanotechnol. 2022, 13, 1256–1267, doi:10.3762/bjnano.13.104

• percussive mode AFM imaging, and the growth of PdNWCNT does not significantly decrease the cantilever spring constant and cantilever mass factor. PdNWCNTs showed better performance than standard CNTs in some SPM applications. For example, because it is difficult to form good ohmic contact CNTs, the existence

• , especially large colloidal probes, where the intrinsic static deflection sensitivity and spring coefficient need to be verified. Chighizola et al. [58] proposed an accurate method for calibrating large CPs. This method is applied to calibrate the intrinsic spring constant kTL of a topless cantilever beam by

Comparing the performance of single and multifrequency Kelvin probe force microscopy techniques in air and water

• Jason I. Kilpatrick,
• Emrullah Kargin and
• Brian J. Rodriguez

Beilstein J. Nanotechnol. 2022, 13, 922–943, doi:10.3762/bjnano.13.82

• in the response of the lever proportional to the quality factor of that mode, Qn, where n is the mode number [36][55]. KPFM techniques can be applied off resonance (ω ≠ ωn), where ∝ 1/kn, where kn is the spring constant of the n-th eigenmode. More generally, KPFM techniques are applied at, or close

• constant, T is the temperature, Nd is the detector noise, and ωn, kn, and Qn are, respectively, the resonance frequency, spring constant, and quality factor of the n-th eigenmode (n = 1, 2). The corresponding gain at a given frequency is then defined as We note that more complex expressions for the

Gelatin nanoparticles with tunable mechanical properties: effect of crosslinking time and loading

• Agnes-Valencia Weiss,
• Daniel Schorr,
• Julia K. Metz,
• Metin Yildirim,
• Saeed Ahmad Khan and
• Marc Schneider

Beilstein J. Nanotechnol. 2022, 13, 778–787, doi:10.3762/bjnano.13.68

• same day. AFM measurements were carried out with a JPK NanoWizard® 3 AFM (JPK Instruments, Berlin, Germany) using the MLCT cantilever tip D (Bruker France Nano Surfaces, Wissembourg, France) with a nominal resonance frequency of 15 kHz and a spring constant of 0.03 N/m. Before each measurement, the

• actual sensitivity and the spring constant of the used cantilever were calibrated on a cleaned silica wafer by the thermal noise method by Hutter et al. [27] using a correction factor of 0.251. The data was acquired using the quantitative imaging mode (QI™) with image sizes of 5 × 5 µm and a resolution

• single nanoparticles. For the values of Young’s moduli, the respective curves were treated as follows: The determined spring constant and sensitivity must be applied to calibrate the cantilever deflection. To correct the vertical offset, a baseline subtraction is applied, and the contact point is

Direct measurement of surface photovoltage by AC bias Kelvin probe force microscopy

• Masato Miyazaki,
• Yasuhiro Sugawara and
• Yan Jun Li

Beilstein J. Nanotechnol. 2022, 13, 712–720, doi:10.3762/bjnano.13.63

• was arranged in front of a photodetector of the OBD system to suppress the influence of the UV light on the deflection sensor. We used a commercial Ir-coated Si cantilever (NANOSENSORS, SD-T7L100) with a resonant frequency f0 of 913 kHz, a spring constant k of 650 N/m, and a quality factor Q of 7748

Quantitative dynamic force microscopy with inclined tip oscillation

• Philipp Rahe,
• Daniel Heile,
• Reinhard Olbrich and
• Michael Reichling

Beilstein J. Nanotechnol. 2022, 13, 610–619, doi:10.3762/bjnano.13.53

• for technical reasons. Consequences of this inclined AFM cantilever mount have been identified before, in particular for atomic force microscopy performed in static (“contact”) mode where an effective spring constant [6][7][8] has been introduced and a torque [9][10] as well as load [11] correction

Effects of substrate stiffness on the viscoelasticity and migration of prostate cancer cells examined by atomic force microscopy

• Xiaoqiong Tang,
• Yan Zhang,
• Jiangbing Mao,
• Yuhua Wang,
• Zhenghong Zhang,
• Zhengchao Wang and
• Hongqin Yang

Beilstein J. Nanotechnol. 2022, 13, 560–569, doi:10.3762/bjnano.13.47

• Germany) for 2 h to prevent damage to the cells. Before the experiment, the thermal noise method was used to adjust the cantilever spring constant, and then the experiment was carried out in contact mode. The AFM probe (MLCT probe, Bruker, USA) slightly contacted the cell surface and a constant force was

• maintained. An indentation area of 3 μm × 3 μm was selected at the nuclear region where 36 force curves were recorded for each cell in force spectroscopy mode. The indentation force of 1 nN, spring constant values of 0.01 N·m−1, Z length of 5 μm, and an approach speed of approximately 2 μm·s−1 were employed

Nanoscale friction and wear of a polymer coated with graphene

• Robin Vacher and
• Astrid S. de Wijn

Beilstein J. Nanotechnol. 2022, 13, 63–73, doi:10.3762/bjnano.13.4

• of the chains in the lower quarter of the substrate are tethered to their original positions using springs with spring constant 1 eV/Å2. Graphene deposition After the solidification of the semicrystalline substrate a layer of graphene is deposited on top. We use two different graphene sheets in our

• surface and indents it. After 1 ns, the tip has reached a stable depth. The tip is then attached to the support with a harmonic spring that acts along the sliding direction. The spring constant is equal to 30 N/m. The support is moving at a constant velocity in the x-direction of 2 m/s. We run the sliding

Effect of lubricants on the rotational transmission between solid-state gears

• Huang-Hsiang Lin,
• Jonathan Heinze,
• Alexander Croy,
• Rafael Gutiérrez and
• Gianaurelio Cuniberti

Beilstein J. Nanotechnol. 2022, 13, 54–62, doi:10.3762/bjnano.13.3

• no passivation and complete passivation. Therefore, in our case, it can be viewed as the easiest case to have bond formation. Also, to constrain the rotational axle, we connect a stiff spring with spring constant k = 1600 N/m (1000 eV/Å2) to the center-of-mass of either gear. To fix the temperature