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

• 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

Cantilever bending based on humidity-actuated mesoporous silica/silicon bilayers

• Christian Ganser,
• Gerhard Fritz-Popovski,
• Roland Morak,
• Parvin Sharifi,
• Benedetta Marmiroli,
• Barbara Sartori,
• Heinz Amenitsch,
• Thomas Griesser,
• Christian Teichert and
• Oskar Paris

Beilstein J. Nanotechnol. 2016, 7, 637–644, doi:10.3762/bjnano.7.56

• strain and the cantilever deflection. If we have a reliable estimate for the Young’s modulus EF of the film, the expected deflection can be predicted from the experimentally measured strain (see Figure 4). However, EF is not known experimentally for our film. On the other hand, if we know both, the

• cantilever deflection and the sorption-induced strain from experiment, Equation 2 can be used to estimate the Young’s modulus of the porous film. Inserting the experimental values of δ and ε together with the other known parameters (Table 1) we obtain EF ≈ 5.0 GPa. Literature reports values of the order of

• 30–40 GPa for the bulk Young’s modulus in nanostructured amorphous silica systems [32][33]. If we assume quadratic scaling of the Young’s modulus with density [34], EF would be expected to be of the order of 12–16 GPa, which is higher by a factor of 2–3 than the value obtained from Equation 2. This

Correlative infrared nanospectroscopic and nanomechanical imaging of block copolymer microdomains

• Benjamin Pollard and
• Markus B. Raschke

Beilstein J. Nanotechnol. 2016, 7, 605–612, doi:10.3762/bjnano.7.53

• regions, and 3–4 GPa in PS regions. These values of the DMT modulus [24] are closely related to the Young’s modulus, an intrinsic bulk material property of the sample. Measurements of Young’s modulus in polymers often exhibit considerable variation and nonlinearity [25]. However, our values generally

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

• -solid viscoelastic elements. The enhanced model introduces in-plane surface elastic forces that can be approximately related to a two-dimensional (2D) Young’s modulus. Relevant cases are discussed for single- and multifrequency intermittent-contact AFM imaging, with focus on the calculated surface

• ]. In these methods, the surface is modeled as a continuum material with a well-defined Young’s modulus, which interacts with a spherical AFM probe and is assumed to dissipate energy in proportion to the probe’s instantaneous velocity and depth of indentation. Here, an analytical description of the

• techniques such as AFM. In contrast, the Young’s modulus is not an appropriate measure because it is not well defined in a dynamic measurement (especially as the strain oscillation frequency is increased), and because in the case of viscoelastic materials, the stress and strain are not related by a simple

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

• approach may be modified with the introduction of the efficiency parameters. Under such modification, Young’s modulus and the shear modulus of the composite media take the form: In this formula, the properties of the CNT are denoted by a superscript CN and that those belong to matrix are denoted by a

• is free of CNTs and the top has the maximum volume fraction of CNTs. Unlike these three types, in the UD case, each surface of the plate has the same volume fraction of CNTs. Similar to the shear modulus and Young’s modulus, Poisson’s ratio and the mass density of the composite media may be written

• obtained in terms of strain components according to the following generalized Hook law as where the plane-stress stiffnesses of the plate are denote by Qij components (i,j = 1,2,4,5,6). These constants may be obtained in terms of the Poisson’s ratio, shear modulus and Young’s modulus of the composite plate

High-bandwidth multimode self-sensing in bimodal atomic force microscopy

• Michael G. Ruppert and
• S. O. Reza Moheimani

Beilstein J. Nanotechnol. 2016, 7, 284–295, doi:10.3762/bjnano.7.26

• the (3)-direction causes normal stress in the (1)-direction [21]. Then, the constitutive equations reduce to two scalar equations with Young’s modulus Y [N/m2], piezoelectric d [m/V] and dielectric ξ [F/m] material constants. The superscripts E and σ indicate that these constants are measured during

• ] where Ib and Yb are the moment of inertia and Young’s modulus of the beam and α(V) contains geometrical constants of the beam and the piezoelectric layer and is linear in the applied voltage. Thus, a voltage applied to the electrodes results in a bending moment causing the cantilever to deflect

• Young’s modulus, area moment of inertia, mass density and cross section of the beam respectively. A common approach to solve Equation 11 is the modal analysis approach. Here, it is assumed that the solution can be represented by separable space and time functions representing the mode shape Zk(x) and

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

• and determine their Young’s modulus using in situ electric-field-induced mechanical resonance and static bending tests on individual Sb2S3 nanowires with cross-sectional areas ranging from 1.1·104 nm2 to 7.8·104 nm2. Mutually orthogonal resonances are observed and their origin explained by asymmetric

• cross section of nanowires. The results obtained from the two methods are consistent and show that nanowires exhibit Young’s moduli comparable to the value for macroscopic material. An increasing trend of measured values of Young’s modulus is observed for smaller thickness samples. Keywords: antimony

• sulfide; in situ; mechanical properties; nanowires; Young’s modulus; Introduction Antimony sulfide or stibnite is a highly anisotropic semiconductor material with potential applications in thermoelectric and optoelectronic [1][2] devices due to its high achievable thermoelectric power and

Synthesis and applications of carbon nanomaterials for energy generation and storage

• Marco Notarianni,
• Jinzhang Liu,
• Kristy Vernon and
• Nunzio Motta

Beilstein J. Nanotechnol. 2016, 7, 149–196, doi:10.3762/bjnano.7.17

• hexagons around the equatorial plane and exhibits a more oval shape (Figure 4) [26]. The main properties of C60 are [25]: Young’s modulus, ≈14 GPa Electrical resistivity, ≈1014 Ω m Thermal conductivity, ≈0.4 W/mK Band gap, 1.7 eV The other fullerene species show similar properties to C60. Depending on the

• the discovery of CNTs, scientists have made great progress in the experimental and theoretical study of their mechanical, electrical and thermal properties. CNTs exhibit remarkable properties including: Tensile strength of at least 37 GPa and strain to failure of at least 6% [38][39] Young’s modulus

• ][63], high Young’s modulus (≈1 TPa) with an intrinsic strength of 130 GPa [64][65], high thermal conductivity (over 3000 W m−1 K−1) [66] and excellent optical transmittance (≈97.7%) [67]. Additional graphene characteristics include: high theoretical specific surface area (2630 m2 g−1) [68

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

• extract properties such as the Young’s modulus, which describes the bulk stress–strain relation of the material, or the Hamaker constant, which describes the dispersion forces between the tip and the sample. In the case of a viscoelastic surface the extraction of material ‘properties’ is difficult for a

• terms of a real 3D tip interacting with a flat surface, and thus makes it impossible to extract approximate parameters such as the Young’s modulus [12]. It is clear in Figure 1a that the geometry of the tip and its indentation depth into the surface have absolutely no effect on the nature of the tip

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

• Berkovich tip with a maximum load of 0.6 mN, a dwell time at maximum load of 30 s, loading and unloading periods of 30 and 15 s, respectively. Every sample has been measured at 16 different points (in a matrix of 4 × 4, the distance between measurement points was 50 μm). Young’s modulus was calculated

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

• . An indenter probe fabricated with a known tip geometry is used to penetrate into the sample. By utilizing the force and small amount of depth information measured during indentation, material properties such as elastic (Young’s) modulus of the sample can be estimated. For example, a growing

Simulation of thermal stress and buckling instability in Si/Ge and Ge/Si core/shell nanowires

• Suvankar Das,
• Amitava Moitra,
• Mishreyee Bhattacharya and
• Amlan Dutta

Beilstein J. Nanotechnol. 2015, 6, 1970–1977, doi:10.3762/bjnano.6.201

• employs the method of atomistic simulation to estimate the thermal stress experienced by Si/Ge and Ge/Si, ultrathin, core/shell nanowires with fixed ends. The underlying technique involves the computation of Young’s modulus and the linear coefficient of thermal expansion through separate simulations

• normal stresses on clamped Si/Ge and Ge/Si CSNWs due to variation in the operating temperature. The calculation of thermal stress typically involves the measurement of Young’s modulus and the thermal expansion of a solid. Unlike the composite structures of macroscopic dimensions, core–shell nanowires

• , it would be significant only for a nanowire diameter of less than 2–3 nm. As the surface/volume ratio decays rapidly with increasing wire thickness, the surface reconstruction is not expected to dramatically affect the Young’s modulus or thermal expansion coefficient of 10 nm diameter nanowires. 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

• approach has been to estimate the spring constant from plane view geometry and the Young’s modulus of the appropriate crystallographic orientation. In this case, the qPlus sensor is treated as a uniform, rectangular cantilever and the spring constant is predicted from Euler–Bernoulli beam theory [1][7

• uncertainty for moderate tip offsets (less than ±100 μm with this method, see Appendix section). Finally, the agreement between experiment and theory suggests that the spring constant of the tuning fork can be predicted reasonably well from the geometry and Young’s modulus of the tine, being careful to

• simply to estimate the spring constant from the Young’s modulus and geometry of the tuning fork, taking care to measure the dimensions of the cross section. We estimate the uncertainty in this method is closer to 10%, which comes primarily from limited knowledge of the effective cantilever length

Improved atomic force microscopy cantilever performance by partial reflective coating

• Zeno Schumacher,
• Yoichi Miyahara,
• Laure Aeschimann and
• Peter Grütter

Beilstein J. Nanotechnol. 2015, 6, 1450–1456, doi:10.3762/bjnano.6.150

• Sosale et al. [8], derived a quantitative theory of how the internal material friction of a partial coating effects the Q-factor of a microcantilever: with ξ the normalized length (l/L), (ξ) the natural mode shape of the cantilever, E the Young’s modulus and hf, hs being the coating film thickness and

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

• is the Young’s modulus of the cantilever [11]. According to Equation 1, the more molecules are adsorbed on the surface of a cantilever, the larger is the shift of the resonance frequency. Therefore AAO cantilevers hold a great promise for the development of micromechanical sensor arrays. In the

• ). Using Equation 1 and the Young’s modulus of AAO of 340 GPa one can evaluate the quantity of water adsorbed onto the anodic alumina surface. The calculation gives a result of Δm = 20 pg at a sensitivity Δf/Δm of 56 Hz/pg. On the other hand, the amount of absorbed water can be estimated from the Langmuir

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

• , PMMA, gold) and use the same values on both sides. For the sake of quantitative modeling (see Figure 5 below) we keep the Poisson number fixed at v1 = v2 = 0.17 and express the shear modulus as where E is the Young’s modulus and E is a fit parameter. The contact radius, a, is assumed to obey the JKR

• . We fitted the data with the JKR model. (The Tabor parameter of the geometry under study is 10, which says that the JKR model should be applied, rather than the DMT model.) Table 1 shows the derived values of the interfacial energy, γ, and the effective Young’s modulus, E. While the values are

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

• (DMT) model of contact mechanics [54] has been employed to account for short range repulsion: where E* is the effective Young’s modulus that includes the elastic modulus of the tip and of the sample [14]. This profile is shown in Figure 4b. 2) The second profile corresponds to a linear decay in the

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

• -treated at different temperatures. The Young’s modulus of the individual phases can be approximated by using M values for the respective phases and Equation 6. Poisson’s ratio values as a function of heat-treatment temperature for Ti-6Al-4V samples are discussed in detail elsewhere [31]. The Poisson’s

• and α′ phases in the sample and EBS is the average Young’s modulus of the bulk sample. Substituting the values for Eα and Eβ, obtained by AFAM and Vα and Vβ obtained by JMatPro® simulation for specimens heat-treated at 923, 1123 and 1223 K in Equation 9, the EBS values are obtained as 119.1, 116.2 and

Self-assembled anchor layers/polysaccharide coatings on titanium surfaces: a study of functionalization and stability

• Ognen Pop-Georgievski,
• Dana Kubies,
• Josef Zemek,
• Neda Neykova,
• Roman Demianchuk,
• Eliška Mázl Chánová,
• Miroslav Šlouf,
• Milan Houska and
• František Rypáček

Beilstein J. Nanotechnol. 2015, 6, 617–631, doi:10.3762/bjnano.6.63

• strength, appropriate Young’s modulus, outstanding biocompatibility and excellent corrosion resistance make commercially pure titanium a highly favored, biocompatible, metallic material [2]. The biocompatibility and corrosion resistance of titanium surfaces is closely related to the presence of a

Chains of carbon atoms: A vision or a new nanomaterial?

• Florian Banhart

Beilstein J. Nanotechnol. 2015, 6, 559–569, doi:10.3762/bjnano.6.58

• . [19] have related the fracture strength to a specific strength of carbon chains of 6.0–7.5 × 107 Nm/kg which would be the highest of all known materials. A Young’s modulus of 3.3 × 1013 Pa has been calculated [19] which is much higher than for graphene (approx. 1012 Pa). In sp2 networks like graphene

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

• deflection, the strain at the base of the cantilever can be approximated by using Hooke’s law and the Young’s modulus of the cantilever beam. In Figure 5c, the sensor response for four chosen field angles is given. The strain sensitivity (slope of the sensor response) varies quite significantly with the

Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments

• Horacio V. Guzman,
• Pablo D. Garcia and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2015, 6, 369–379, doi:10.3762/bjnano.6.36

• the effective Young modulus of the interface defined by where Et and Es are the Young’s modulus of the tip and sample, respectively, and υt and υs are the Poisson coefficients of the tip and sample, respectively. Derjaguin–Mueller–Toporov contact mechanics (DMT) The DMT model is valid for describing

• with a spring and a dashpot. By assuming a contact mechanism as described by Hertz contact mechanics, we deduce the force as where E0 and E∞ represent the Young’s modulus of the material at fast and slow loading rates, respectively. Customized force The code also enables the definition of other types

• higher in water (Figure 3c). Imaging soft and hard materials The cantilever dynamics in AM-AFM shows some subtle differences depending on the effective Young’s modulus of the interaction. Figure 4 shows the amplitude, phase shift and harmonic components for two materials characterized by an Es of 50 MPa

Mechanical properties of MDCK II cells exposed to gold nanorods

• Anna Pietuch,
• Bastian Rouven Brückner,
• David Schneider,
• Marco Tarantola,
• Christina Rosman,
• Carsten Sönnichsen and
• Andreas Janshoff

Beilstein J. Nanotechnol. 2015, 6, 223–231, doi:10.3762/bjnano.6.21

• atomic force microscope (AFM) by taking force curves at each spot the probe touches the sample surface. These force indentation curves are frequently subject to regression analysis employing Hertzian contact models that permit to assess the cell’s Young’s modulus. The modulus bears invaluable information

• uses Hertzian contact mechanics (Sneddon model for conical indenters) providing a single parameter, the Young’s modulus of the cell (see Materials and Methods section). The range of validity is limited to only a few hundred nanometers (green dotted lines in Figure 3). Due to the well-known shortcomings

• results of employing conventional contact models based on Hertzian mechanics expressing the mechanical properties as a single parameter, the Young’s modulus. However, the fits of the liquid droplet model describe the data very well and show the same trend as the more conventional contact models assuming a

The capillary adhesion technique: a versatile method for determining the liquid adhesion force and sample stiffness

• Daniel Gandyra,
• Stefan Walheim,
• Stanislav Gorb,
• Wilhelm Barthlott and
• Thomas Schimmel

Beilstein J. Nanotechnol. 2015, 6, 11–18, doi:10.3762/bjnano.6.2

• also resulted in the measurement of an elastic modulus (Young’s modulus) for individual hairs of 3.0 × 105 N/cm2, which is within the typical range known for human hair. (3) Finally, the accuracy and validity of the capillary adhesion technique was proven by examining calibrated atomic force microscopy

• -off, the elongation, Δy, of the trichome in the direction of the force was observed. Assuming Hooke’s law, its spring constant is Likewise, other elastic constants such as Young’s modulus can be determined, as shown later in the section where human head hairs are examined. The contribution of the

• the pulling force with respect to the trichome elongation, thus following Hooke’s law. This is valid over the whole range from a smaller force to the maximum force immediately before snap-off. Determining the water adhesion force, elasticity and Young’s modulus of human head hairs As a second

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

• the elastic constants. Therefore, the mechanical properties were investigated in terms of the indentation (or reduced Young’s) modulus M by using an indenter acting with a load F on a contact area A of a half-space, thereby causing a displacement u [20]: Since the elastic constants can consistently be

• spring constant of 39 N/m. The second resonance mode was used for further analysis. The reduced Young’s modulus was measured by using a reference approach with three reference samples: fused silica (M = 75 GPa), silicon (M = 165 GPa) and sapphire (M = 433 GPa), which were demonstrated to be sufficient