Micro-structures, nanomechanical properties and flight performance of three beetles with different folding ratios

• Jiyu Sun,
• Pengpeng Li,
• Yongwei Yan,
• Fa Song,
• Nuo Xu and
• Zhijun Zhang

Beilstein J. Nanotechnol. 2022, 13, 845–856, doi:10.3762/bjnano.13.75

• contact depth. S is the contact stiffness. A Berkovich tip with a tip radius of approximately 100 nm was used for the tests. In order to study the effect of nanomechanical properties of different veins on the lift of the beetle hind wings, the same location of the same vein of three beetles was selected

Determination of elastic moduli of elastic–plastic microspherical materials using nanoindentation simulation without mechanical polishing

• Hongzhou Li and
• Jialian Chen

Beilstein J. Nanotechnol. 2021, 12, 213–221, doi:10.3762/bjnano.12.17

• that the shear modulus is equal to E/[2(1 + ν)], differentiating P with respect to h leads to where S = dP/dh is the initial stiffness of the unloading curve, defined as the slope of the upper portion of the unloading curve during the initial stages of unloading (also called contact stiffness), and E

• . Knowing the contact depth and the shape of the indenter, determined through the “area function”, the contact area is then determined. If contact stiffness and contact area are known, Equation 3 and Equation 4 can be used to determine the elastic modulus of a material. Effects of non-rigid indenters on the

Application of contact-resonance AFM methods to polymer samples

• Sebastian Friedrich and
• Brunero Cappella

Beilstein J. Nanotechnol. 2020, 11, 1714–1727, doi:10.3762/bjnano.11.154

• underlying physical phenomena and of factors influencing the measurements. A commonly used method to analyze CR data requires the determination of the relative position of the tip, the calculation of the normalized contact stiffness, and the use of a calibration sample for the calculation of the elastic

• interactions. Such models allow one to calculate the contact stiffness from the measured CR frequency. Then, from the contact stiffness, the elastic modulus of the sample can be determined. This technique has been successfully applied on rather stiff materials such as silicon [11] or chalcogenide glasses [12

• of the contact stiffness. Several methods to obtain this parameter, such as direct measurement via scanning electron microscopy [14] or identification of the value for which two different modes of the same cantilever yield the same contact stiffness (“mode crossing” method), may lead to different

Stochastic excitation for high-resolution atomic force acoustic microscopy imaging: a system theory approach

• Edgar Cruz Valeriano,
• José Juan Gervacio Arciniega,
• Christian Iván Enriquez Flores,
• Susana Meraz Dávila,
• Joel Moreno Palmerin,
• Martín Adelaido Hernández Landaverde,
• Yuri Lizbeth Chipatecua Godoy,
• Aime Margarita Gutiérrez Peralta,
• Rafael Ramírez Bon and
• José Martín Yañez Limón

Beilstein J. Nanotechnol. 2020, 11, 703–716, doi:10.3762/bjnano.11.58

• distance and zs is the distance from the sample to the tip of the undeflected cantilever, which is described by the force f(t) linearized around a point z0 as In this equation represents the contact stiffness. Then, the linearized model around z0 according to Equation 3 is where Using the boundary

• cantilever that can be fitted best to these frequencies. For a cantilever in contact with the sample, the simulation is shown for three cantilevers with a contact stiffness of 10 N/m and different lengths of L = 300, 400 and 500 µm (Figure 4b). The behavior of the resonance frequencies is similar to that of

• cantilever with L = 400 µm is used and its contact stiffness is changed, it can be seen how the resonance frequencies increase with increasing contact stiffness. Three simulations are shown for contact stiffness values of = 1, 10 and 100 N/m (Figure 4c). The simulation results offer enough support for an

Nonclassical dynamic modeling of nano/microparticles during nanomanipulation processes

• Moharam Habibnejad Korayem,
• Ali Asghar Farid and
• Rouzbeh Nouhi Hefzabad

Beilstein J. Nanotechnol. 2020, 11, 147–166, doi:10.3762/bjnano.11.13

• cantilever frequencies to contact stiffness and investigated the variation of sensitivity with cantilever slope [3][4]. Shi and Zhao examined the contact models at the nanoscale and compared Derjaguin–Muller–Toporov (DMT), Johnson–Kendall–Roberts–Sperling (JKRS) and Maugis–Dugdale (MD) models with the Hertz

• . The results showed that for a lower contact stiffness, the sensitivity of V-shaped cantilevers based on MCST is less than that based on classical theory. They concluded that stiffer cantilevers are suitable for scanning stiffer plates while softer cantilevers, which have a higher sensitivity, could be

Atomic force acoustic microscopy reveals the influence of substrate stiffness and topography on cell behavior

• Yan Liu,
• Li Li,
• Xing Chen,
• Ying Wang,
• Meng-Nan Liu,
• Jin Yan,
• Liang Cao,
• Lu Wang and
• Zuo-Bin Wang

Beilstein J. Nanotechnol. 2019, 10, 2329–2337, doi:10.3762/bjnano.10.223

• describe the vibrations of the cantilever, the contact stiffness of the tip–sample interaction can be estimated [27][28]. For one-phase homogeneous materials, the detected vibrations will remain relatively uniform, while for inhomogeneous materials, the vibrational amplitude depends on the elastic

Subsurface imaging of flexible circuits via contact resonance atomic force microscopy

• Wenting Wang,
• Chengfu Ma,
• Yuhang Chen,
• Lei Zheng,
• Huarong Liu and
• Jiaru Chu

Beilstein J. Nanotechnol. 2019, 10, 1636–1647, doi:10.3762/bjnano.10.159

• embedded metal layer leads to an obvious CR-AFM frequency shift and therefore its unambiguous differentiation from the polymer matrix. The contact stiffness contrast, determined from the tracked frequency images, was employed for quantitative evaluation. The influence of various parameter settings and

• force microscopy (AFM); contact resonance atomic force microscopy (CR-AFM); contact stiffness; defect detection; flexible circuits; subsurface imaging; Introduction With the rapid shrinkage of microelectronic devices, flexible circuits are intensively used while being functionalized as supercapacitors

• heterogeneous structures in the contact volume will alter the local contact stiffness and then the contact resonance of the cantilever. Its usage in detecting buried structures such as defects [21][22][23][24][25] and nanofillers [26][27][28] has thus gained much attention. Although a few investigations have

Nanoscale spatial mapping of mechanical properties through dynamic atomic force microscopy

• Zahra Abooalizadeh,
• Leszek Josef Sudak and
• Philip Egberts

Beilstein J. Nanotechnol. 2019, 10, 1332–1347, doi:10.3762/bjnano.10.132

• the reduced stiffness of the cantilever and contact. This conversion was accomplished by modeling the cantilever stiffness in series with the contact stiffness that represents the boundary conditions at the tip–sample contact. The conversion of the measured oscillation amplitude to an effective

• stiffness was accomplished with the following equation: where Fdr is the drive force obtained on the silicon surface, AHOPG is the amplitude response of the cantilever measured along the HOPG surface, and keff is the effective stiffness. In the next step, the contact stiffness, required for the

• determination of the elastic modulus, must be deconvolved from the effective stiffness using the following equation: where kn is the normal stiffness of the cantilever and kcon is the normal contact stiffness. The next step is to determine the effective elastic modulus by employing the calculated contact

Pull-off and friction forces of micropatterned elastomers on soft substrates: the effects of pattern length scale and stiffness

• Peter van Assenbergh,
• Marike Fokker,
• Julian Langowski,
• Jan van Esch,
• Marleen Kamperman and
• Dimitra Dodou

Beilstein J. Nanotechnol. 2019, 10, 79–94, doi:10.3762/bjnano.10.8

• . The decreased Eeff of a fibrillar geometry also leads to decreased contact stiffness [11] and higher conformability to substrate roughness [12]. The abovementioned effects of fibrillary geometries can be further enhanced with altering the pillar geometry. For example, Gorb et al. fabricated

• features has an effect on the Eeff of micropatterned adhesives. Varenberg et al. reasoned that finer micropillars have a lower contact stiffness, resulting in a lower contact reaction force, which might, in turn, result in higher pull-off forces, as long as the formed real contact area of the finer

• material is used for the micropattern, the Eeff is low, leading to better defect control, stress distribution, and contact stiffness compared to micropatterns made of stiffer materials [22]. Also, the strength of the contacts formed between the adhesive and the substrate is affected by the material

Atomistic modeling of tribological properties of Pd and Al nanoparticles on a graphene surface

• Alexei Khomenko,
• Miroslav Zakharov,
• Denis Boyko and
• Bo N. J. Persson

Beilstein J. Nanotechnol. 2018, 9, 1239–1246, doi:10.3762/bjnano.9.115

• different temperatures, and showed how the static friction and contact stiffness depend on the contact area. They observed “contact aging” due to stress-aided, thermally activated atomic rearrangement processes. The term “contact aging” [6] is related to time-dependent atomic reconstructions at the

Scanning speed phenomenon in contact-resonance atomic force microscopy

• Christopher C. Glover,
• Jason P. Killgore and
• Ryan C. Tung

Beilstein J. Nanotechnol. 2018, 9, 945–952, doi:10.3762/bjnano.9.87

• define the tip location parameter such that . The beam equation is solved, and a characteristic equation relating the n-th non-dimensional contact wavenumbers of the beam to the normalized contact stiffness α and the tip parameter is generated (see Rabe et al. [22]). The normalized contact stiffness

• parameter ks for our mica sample. It was found that the stiffness for mica, for our experimental parameters, is approximately 350 N/m. In Figure 4, we show the measured normalized sample contact stiffness α as a function of the scan speed Vs calculated using data from the 1st and 2nd in-contact natural

• affected by scan speed. Additionally, this phenomenon is observed at a speed two orders of magnitude lower than reported by Picco and co-workers [15]. Error bars represent one standard deviation from the mean. Measured normalized sample contact stiffness as a function of the scan speed. The red data

Nanotribological behavior of deep cryogenically treated martensitic stainless steel

• Germán Prieto,
• Konstantinos D. Bakoglidis,
• Walter R. Tuckart and
• Esteban Broitman

Beilstein J. Nanotechnol. 2017, 8, 1760–1768, doi:10.3762/bjnano.8.177

• . According to [26], hardness (H) is defined as: where P is the maximum normal load and A is the contact area between the tip and the specimen. The contact area can be related to the contact stiffness by using Sneddon’s law [27]: Nanoindentation tests were performed using a Berkovich diamond tip, with an apex

• method utilizes the ratio between the hardness and the square of the elastic modulus (H/E2) as an independent characteristic parameter. The proposed method utilizes the maximum force applied during the test (P) and the calculated contact stiffness (S) from the nanoindentation data. S is defined as the

• control condition, and the force required to reach each depth was the same for both groups of specimens. Hence, the DCT samples must have a higher elastic limit [38][39]. The aforementioned phenomenon can be seen more clearly from the analysis of the contact stiffness, as DCT specimens showed

Relationships between chemical structure, mechanical properties and materials processing in nanopatterned organosilicate fins

• Gheorghe Stan,
• Richard S. Gates,
• Qichi Hu,
• Kevin Kjoller,
• Craig Prater,
• Kanwal Jit Singh,
• Ebony Mays and
• Sean W. King

Beilstein J. Nanotechnol. 2017, 8, 863–871, doi:10.3762/bjnano.8.88

• measurements, the tip–sample contact is mechanically vibrated at various frequencies to detect the so called “contact resonance frequencies”. These CR-frequencies are characteristic of the tip–sample contact stiffness (higher frequencies for stiffer contacts) and depend on the mechanical properties of the tip

• considering the blanket film as a reference with a modulus of 3.5 GPa and reporting all the measured values of contact stiffness to the contact stiffness measured on the blanket film. The tip–sample contacts were treated as Hertz contacts [33]. Results and Discussion To monitor changes in the chemical

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

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

• 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

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

• results from experiments undertaken in the dry state and in water are compared. Building on the shifts in the resonance frequency and resonance bandwidth, the instrument determines the real and the imaginary part of the contact stiffness, where the imaginary part quantifies dissipative processes. The

• method is closely analogous to related procedures in AFM-based metrology. The real part of the contact stiffness as a function of normal load can be fitted with the Johnson–Kendall–Roberts (JKR) model. The contact stiffness was found to increase in the presence of liquid water. This finding is

• tentatively explained by the rocking motion of the spheres, which couples to a squeeze flow of the water close to the contact. The loss tangent of the contact stiffness is on the order of 0.1, where the energy losses are associated with interfacial processes. At high amplitudes partial slip was found to occur

Mapping of elasticity and damping in an α + β titanium alloy through atomic force acoustic microscopy

• M. Kalyan Phani,
• Anish Kumar,
• T. Jayakumar,
• Walter Arnold and
• Konrad Samwer

Beilstein J. Nanotechnol. 2015, 6, 767–776, doi:10.3762/bjnano.6.79

• in the present study. The real and imaginary parts of the contact stiffness k* are obtained from the contact-resonance spectra and by using these two quantities, the maps of local elastic stiffness and the damping factor are derived. The evaluation of the data is based on the mass distribution of the

• -resonance spectra are used to calculate the contact stiffness k* and the local contact damping E″/E′ by employing suitable models for the tip–specimen contact, and in turn enabling one to image and to measure the local elasticity or the storage modulus E′ and the damping or loss modulus E″ of the specimen

• contact damping E″/E′, which we observe in our experiments, we neglect this effect. The values for an and bn are obtained by fitting Lorentzians to the experimentally obtained resonances curves of the free and contact resonances. Due to the local damping in the contact zone the contact stiffness becomes a

Nanometer-resolved mechanical properties around GaN crystal surface steps

• Jörg Buchwald,
• Marina Sarmanova,
• Bernd Rauschenbach and
• Stefan G. Mayr

Beilstein J. Nanotechnol. 2014, 5, 2164–2170, doi:10.3762/bjnano.5.225

• a FEM model (Figure 5) in which surface stresses were omitted. The indentation modulus was calculated by evaluating the contact stiffness S = dF/du of the stationary solution. The flatpunch indenter was modeled by a cylinder of hard material with a contact area A2 and a force of |F|= −Fz = 30 nN as

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

• 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

• along the cantilever for the UAFM (Figure 3a) and AFAM (Figure 3c) configurations for the same contact stiffness, k* = 20 N/m, and three different contact damping values: mild (p = 0.10), medium (p = 0.25), and strong (p = 0.50) contact damping. In both configurations, the calculated displacement along

• and second eigenmodes of the cantilever, we can conclude that for a given contact stiffness, the amplitude changes significantly with the contact damping and this change is qualitatively and quantitatively similar in UAFM and AFAM. However, the phases of the two configurations differ significantly

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

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

• approximately 1 nm when the z-piezo is displaced by 1 nm [10]). The sensitivity of the fourth eigenmode could not be obtained in this way because the modal stiffness was too high (relative to the tip–sample contact stiffness). Therefore the fourth eigenmode sensitivity was estimated based on Euler–Bernoulli

Friction and durability of virgin and damaged skin with and without skin cream treatment using atomic force microscopy

• Bharat Bhushan,
• Si Chen and
• Shirong Ge

Beilstein J. Nanotechnol. 2012, 3, 731–746, doi:10.3762/bjnano.3.83

• and the Poisson’s ratio of the indenter tip respectively; ν is the Poisson’s ratio of skin assumed to be 0.5 [6]; Er is the reduced modulus given as follows: where S is the contact stiffness obtained from the slope of the unloading curve. Results and Discussion The nanoindentation properties are

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

• , while off-resonance actuation reduces fluid-related cantilever dynamics. Consequently, FMM can map even slight differences in the sample surface stiffness (i.e., the contact stiffness). While these advantages were shown in some FMM studies performed on monolayers [38][39], the understanding of amplitude

• angular frequency of the actuation, kc is the spring constant of the AFM cantilever, and k* is the contact stiffness, The contact stiffness is a function of the reduced Young’s modulus, E*, the tip radius, R, and the applied force, F. Equation 1 explains how the amplitude of the AFM cantilever deflection

• force and actuation frequency. Here we use contact force as a variable to change the contact stiffness (Equation 2) and monitor the response of the amplitude and phase behavior of the cantilever. In our parameter-selection process we acquire force–distance curves while the cantilever is modulated at the