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

Mechanical properties of sol–gel derived SiO₂ nanotubes

• Boris Polyakov,
• Mikk Antsov,
• Sergei Vlassov,
• Leonid M Dorogin,
• Mikk Vahtrus,
• Roberts Zabels,
• Sven Lange and
• Rünno Lõhmus

Beilstein J. Nanotechnol. 2014, 5, 1808–1814, doi:10.3762/bjnano.5.191

• performed by atomic force microscopy (AFM) under ambient conditions. Half-suspended and three-point bending tests were processed in the framework of linear elasticity theory. Finite element method simulations were used to extract Young’s modulus values from the nanoindentation data. Finally, the Young’s

• ), which were prepared by sol–gel synthesis using organic NT templates, by using three point bending [15]. The differences of the values of the Young’s modulus measured by the listed methods were approximately 40%, which can probably be attributed to peculiarities of the measurement techniques. The effect

• of the experimental technique on the measured values of the Young’s modulus was demonstrated by Rohlig et al. for ZnO NWs by comparing the resonant technique, nanoindentation, bending of bridges, and tensile and compressive strain tests [16]. In the case of SiO2 NTs it is also important to consider

On the structure of grain/interphase boundaries and interfaces

• K. Anantha Padmanabhan and
• Herbert Gleiter

Beilstein J. Nanotechnol. 2014, 5, 1603–1615, doi:10.3762/bjnano.5.172

• temperature has a significant effect on properties. From structural studies and the measurements of interfacial properties (e.g., density, Young’s modulus) of metallic nano-glasses it is known that the atomic arrangements and electronic structures are different from what is found in the interface of relaxed

• actually increased [12][13]) but the Young’s modulus was similar to or higher than that of the crystalline and the denser, conventional glassy counterparts [9][10][14]. This could indicate a change in the nature of electronic interactions, e.g., from metallic to covalent bonding. The heat capacity was 20

Influence of the PDMS substrate stiffness on the adhesion of Acanthamoeba castellanii

• Sören B. Gutekunst,
• Carsten Grabosch,
• Alexander Kovalev,
• Stanislav N. Gorb and
• Christine Selhuber-Unkel

Beilstein J. Nanotechnol. 2014, 5, 1393–1398, doi:10.3762/bjnano.5.152

• increases with a decreasing Young’s modulus of the substrate. Conclusion: The dependence of A. castellanii adhesion on the elastic properties of the substrate is the first study suggesting a mechanosensory effect for a eukaryotic human pathogen. Interestingly, the main targets of A. castellanii infections

• cool down to room temperature. Elasticity measurements Mechanical properties of PDMS substrates were determined by microindentation using a micro-force measurements device (Basalt-BT01, Tetra GmbH, Ilmenau, Germany) [24]. The recorded force–distance curves were used to calculate the Young’s modulus of

• Young’s modulus (4 kPa), A. castellanii occupy a larger area compared to acanthamoebae on substrates with a higher Young’s modulus (128 kPa). The substrate with a Young’s modulus of 29 kPa gave an intermediate value. On the control sample, the cell adhesion area was similar to the one on the 4 kPa

Surface topography and contact mechanics of dry and wet human skin

• Alexander E. Kovalev,
• Kirstin Dening,
• Bo N. J. Persson and
• Stanislav N. Gorb

Beilstein J. Nanotechnol. 2014, 5, 1341–1348, doi:10.3762/bjnano.5.147

• a rather complex topic due to the layered morphology and the viscoelastic–plastic nature of the human skin. A modern view about this topic is presented in [3]. The top-layer of the skin (stratum corneum, about 20 μm thick) has a Young’s modulus of E ≈ 1–3 GPa, which is similar to rubber in the

• layer of stratum corneum has a Young’s modulus of E0 = 7 MPa in the wet state and of E0 = 1 GPa in the dry state with a Poisson ratio of ν0 = 0.5. Plastic deformation must be taken into account for the dry skin, because of the the high contact pressure. In the following calculations the plastic yield

• stress (or penetration hardness) of human skin was taken as σY = 50 MPa [10], which is similar to the yield stress of most polymers, which are of the order of 100 MPa. We note that the yield stress of the skin is about 5% of its Young’s modulus, which is typical for many materials, e.g., for dry

Physical principles of fluid-mediated insect attachment - Shouldn’t insects slip?

• Jan-Henning Dirks

Beilstein J. Nanotechnol. 2014, 5, 1160–1166, doi:10.3762/bjnano.5.127

• case of insect (and tree frog) attachment, with very smooth and adaptable pads [49][50], it is very questionable whether this assumption is justified. In fact, recent and more comprehensive tribological models show that for certain ratios of adhesive pad size and stiffness, the Young’s modulus of the

Organic and inorganic–organic thin film structures by molecular layer deposition: A review

• Pia Sundberg and
• Maarit Karppinen

Beilstein J. Nanotechnol. 2014, 5, 1104–1136, doi:10.3762/bjnano.5.123

A nanometric cushion for enhancing scratch and wear resistance of hard films

• Katya Gotlib-Vainshtein,
• Olga Girshevitz,
• Chaim N. Sukenik,
• David Barlam and
• Sidney R. Cohen

Beilstein J. Nanotechnol. 2014, 5, 1005–1015, doi:10.3762/bjnano.5.114

• qualitatively similar to those observed on kapton (Figure 3) which is in line with the similarity in Young’s modulus of kapton and PC: 2.5 and 2.6 GPa, respectively. The dependence of sliding velocity on scratch resistance was checked for TiO2 on PC samples over the range of 0.05–1 µm/s, using a constant normal

• nm X motion). Young’s modulus E and Poisson ratio used in FEA calculations. Acknowledgements We gratefully acknowledge the support of this work by the Minerva Center for Biomaterial Interfaces and the Edward and Judith Steinberg Chair in Nanotechnology, both at Bar Ilan University, as well as the

Scale effects of nanomechanical properties and deformation behavior of Au nanoparticle and thin film using depth sensing nanoindentation

• Dave Maharaj and
• Bharat Bhushan

Beilstein J. Nanotechnol. 2014, 5, 822–836, doi:10.3762/bjnano.5.94

• understanding of materials behavior during contact. Mechanical properties of interest comprise hardness, Young’s modulus of elasticity, bulk modulus, elastic–plastic deformation, scratch resistance, residual stresses, time-dependent creep and relaxation properties, fracture toughness, fatigue and yield strength

• mechanical properties such as hardness and Young’s modulus of elasticity can be directly obtained as a function of depth. This can be done with a high degree of accuracy, not easily obtained with an AFM. This advancement in technology has proven useful for understanding the mechanical behavior of micro- and

• the elastic modulus. By using this method the Young’s modulus of elasticity and Poisson’s ratio for diamond were taken as 1140 GPa and 0.07, respectively. Poisson’s ratio for Au was taken as 0.42. The data from these experiments is the average of five measurements on five different nanoparticles for

Resonance of graphene nanoribbons doped with nitrogen and boron: a molecular dynamics study

• Ye Wei,
• Haifei Zhan,
• Kang Xia,
• Wendong Zhang,
• Shengbo Sang and
• Yuantong Gu

Beilstein J. Nanotechnol. 2014, 5, 717–725, doi:10.3762/bjnano.5.84

• been reported to have supreme stiffness (Young’s modulus ≈ 1 TPa), very high electron mobility, electrical and thermal conductivity, optical absorption as well as many other excellent properties [2][3]. These properties of graphene open up huge potential applications in the area of electronics

Analytical development and optimization of a graphene–solution interface capacitance model

• Hediyeh Karimi,
• Rasoul Rahmani,
• Reza Mashayekhi,
• Leyla Ranjbari,
• Amir H. Shirdel,
• Niloofar Haghighian,
• Parisa Movahedi,
• Moein Hadiyan and
• Razali Ismail

Beilstein J. Nanotechnol. 2014, 5, 603–609, doi:10.3762/bjnano.5.71

• stiffness with a Young’s modulus of approximately 1000 GPa, a significant heat conductivity of 3000 W·(m·K)−1, and large specific surface area of 2600 m2·g−1 [15][16][17]. Intrinsic graphene is a semi metal or a zero band gap semiconductor, which results in a high electron mobility at room temperature [18

Calibration of quartz tuning fork spring constants for non-contact atomic force microscopy: direct mechanical measurements and simulations

• Jens Falter,
• Marvin Stiefermann,
• Gernot Langewisch,
• Philipp Schurig,
• Hendrik Hölscher,
• Harald Fuchs and
• André Schirmeisen

Beilstein J. Nanotechnol. 2014, 5, 507–516, doi:10.3762/bjnano.5.59

• epoxy glue. Commonly, spring constants of kqPlus = 1800–2000 N/m are used for the force transformation. These values are estimated from the geometric dimensions of the free prong of the tuning fork and the Young’s modulus of quartz by using the beam formula according to Equation 1 [16]. In this equation

• w and t are the width and thickness of the free prong, respectively and Equartz is the Young’s modulus of quartz. The limitations for the validity of this formula are small deformations leading to only elastic stress/stain inside the uniform, rectangular cross section of the beam, which consists of

• L0 as it is commonly done in the nc-AFM literature in order to avoid inaccuracies in later discussions. Inserting our measured values of ΔL1 = 2139 μm, w = 207.3 μm and t = 120.8 μm into Equation 1 together with the Young’s modulus of quartz of Equartz = 78.7 GPa results in a stiffness of the free

The softening of human bladder cancer cells happens at an early stage of the malignancy process

• Jorge R. Ramos,
• Joanna Pabijan,
• Ricardo Garcia and
• Malgorzata Lekka

Beilstein J. Nanotechnol. 2014, 5, 447–457, doi:10.3762/bjnano.5.52

• are stiffer (higher Young’s modulus) than cancerous cells (HTB-9, HT1376, and T24 cell lines). However, independently of the histological grade of the studied bladder cancer cells, all cancerous cells possess a similar level of the deformability of about a few kilopascals, significantly lower than non

• mechanical properties of the extracellular matrix [2][4]. Remarkably, in this case the ECM of the malignant cells is stiffer (reflected by a higher Young’s modulus) as compared to the ECM of non-malignant tissues [2]. Those studies underline the connection between changes in the mechanical properties of the

• extended also to primary cells [6][13] and tissue sections [5][12] that were collected from human patients. For example, a comparison of the elastic properties of normal and benign breast tissues gives a wide distribution of the Young’s modulus, in which a peak at lower values characterizes malignant

Single-asperity contact mechanics with positive and negative work of adhesion: Influence of finite-range interactions and a continuum description for the squeeze-out of wetting fluids

• Martin H. Müser

Beilstein J. Nanotechnol. 2014, 5, 419–437, doi:10.3762/bjnano.5.50

• deformed tip (in the small-slope approximation) as where E is the effective modulus, E = EY/(1 − ν2), EY being the Young’s modulus and ν the Poisson ratio. The convention of using the symbol E* for the effective modulus is abandoned for clarity, because primes will be used later to indicate scaled

Tensile properties of a boron/nitrogen-doped carbon nanotube–graphene hybrid structure

• Kang Xia,
• Haifei Zhan,
• Ye Wei and
• Yuantong Gu

Beilstein J. Nanotechnol. 2014, 5, 329–336, doi:10.3762/bjnano.5.37

• with different dopants. It is found that with the presence of dopants, the hybrid structures usually exhibit lower yield strength, Young’s modulus, and earlier yielding compared to that of a pristine hybrid structure. For dopant concentrations below 2.5% no significant reduction of Young’s modulus or

• materials. Keywords: doping; graphene; molecular dynamics simulation; nanotubes; tension; Young’s modulus; Introduction In recent years, low-dimensional structures such as carbon nanotubes (CNT) and graphene have attracted huge attention of the scientific community, because of their excellent performance

• ) simulations, Bohayra et al. [10] conclude that the content of nitrogen atoms (up to 6%) has a negligible effect on the Young’s modulus of a nitrogen-doped graphene layer, while the presence of nitrogen substitutions reduces the layer strength significantly. Only a few works have been devoted to examine the

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

• cantilever is described by its Young’s modulus E, second moment of area of its cross section I, mass density ρ, and cross-sectional area A, and ηair characterizes the damping of the oscillations in air. The general solution of Equation 1 is in the form of y(x,t) = y(x)eiωt, with with A1, A2, A3, and A4

• length L = 225.03 µm, width w = 30.00 µm, and thickness T = 4.89 µm. With mass density ρSi = 2329.00 kg/m3 and Young’s modulus ESi = 130.00 GPa, the cantilever’s spring constant was calculated as kc = 10.00 N/m. Using these parameters and considering ηair = 2.50 s−1 in Equation 1, the first two