Determination of the radii of coated and uncoated silicon AFM sharp tips using a height calibration standard grating and a nonlinear regression function

• Perawat Boonpuek and
• Jonathan R. Felts

Beilstein J. Nanotechnol. 2023, 14, 1200–1207, doi:10.3762/bjnano.14.99

• force curves with contact mechanics models and extracting the adhesion and friction forces [5][6]. If we do not know the exact value of the tip radius, the sample image with the observation of scanning frequency and the calculation results are not accurate. This indicates that the measurement results

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

• and velocity distribution are not well defined and one has to resort to an atomistic description, for example, via molecular dynamics (MD) simulations. Also, the contact mechanics at the nanoscale is very different from the macroscopic case since specific pair interactions have to be taken into

A new method for obtaining model-free viscoelastic material properties from atomic force microscopy experiments using discrete integral transform techniques

• Berkin Uluutku,
• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2021, 12, 1063–1077, doi:10.3762/bjnano.12.79

• geometry correction factor discussed above, . For this calculation Δt is a known experimental parameter, and r is chosen by the researcher. Demonstration with AFM contact mechanics So far, we have demonstrated our method for stress–strain inputs using the generalized Voigt model. However, in AFM

Physical constraints lead to parallel evolution of micro- and nanostructures of animal adhesive pads: a review

• Thies H. Büscher and
• Stanislav N. Gorb

Beilstein J. Nanotechnol. 2021, 12, 725–743, doi:10.3762/bjnano.12.57

• of the same microstructures, in contrast, is a result of similar demands for adhesion in the respective habitats, which means that the physical rules of contact mechanics have a very strong influence on the adaptive evolution of the attachment structures in general. The reason is that similar AMS

• bend during contact formation with the substrate (Figure 6A and Figure 6B). The pad can, therefore, work as a damper at high-speed deformations during jumping or landing. More importantly, in terms of contact mechanics, deformability functions as a basis for replicating a complex substrate profile

Quantitative determination of the interaction potential between two surfaces using frequency-modulated atomic force microscopy

• Nicholas Chan,
• Carrie Lin,
• Tevis Jacobs,
• Robert W. Carpick and
• Philip Egberts

Beilstein J. Nanotechnol. 2020, 11, 729–739, doi:10.3762/bjnano.11.60

• LJ pair potential is an over-simplification, we demonstrate that it is significantly misleading for the near-contact behavior of silicon oxide and diamond. There are several factors that may have led to this discrepancy. First, the LJ potential, which is extremely widely used in contact mechanics and

• experiments is often challenging as the measured adhesion and friction forces cannot provide direct mechanistic understanding of atomic-scale interactions that occur at the contact interface. Thus, it is often desirable to incorporate complementary atomistic simulation techniques [18][19][20][21] or contact

• mechanics models [22][23][24][25] to allow better visualization of surface interactions. While useful insights can be obtained using fully atomistic simulations, such as molecular dynamics simulations or density functional theory, these techniques are impractical for describing larger contacts with a large

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

• studies are presented in Figure 18 and Figure 19 by employing contact mechanics models that are in compliance with other studies. Moradi et al. [8] studied the manipulation dynamics of a cylindrical nanorod made from polystyrene using a classical theory of continuum mechanics. In this section, by

The effect of heat treatment on the morphology and mobility of Au nanoparticles

• Sven Oras,
• Sergei Vlassov,
• Simon Vigonski,
• Boris Polyakov,
• Mikk Antsov,
• Vahur Zadin,
• Rünno Lõhmus and
• Karine Mougin

Beilstein J. Nanotechnol. 2020, 11, 61–67, doi:10.3762/bjnano.11.6

• should decrease the contact area compared to faceted particles, and hence reduce the friction forces in accordance with the known relation τ = F/A [6], where τ is the contact strength, F is the friction force and A is the contact area. For a round particle, the contact area is determined by contact

• mechanics [14][26]. The contact area of a perfect sphere can be two orders of magnitude smaller than that of a polyhedron-like NP, as was shown by Vlassov and co-workers [6]. The mobility of the Au NPs was evaluated by means of the power dissipated in tapping-mode AFM, which has previously been shown to be

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

• the cantilever and the contact mechanics between the tip and the multilayer sample. Finite element analysis (FEA) was also carried out for comparison. Some qualitative clues were obtained for optimizing the imaging contrast, which were experimentally proved. Finally, imaging of structural defects in

• convenient modeling of the contact mechanics for multilayers without the requirement of a rigid substrate. In their approach, the stress and displacement fields for each layer and the substrate are first expressed in terms of harmonic Papkovich–Neuber potentials. Then, the unknown functions in the potential

• the dispersion curve. The cantilever dynamics analysis and the tip–sample contact mechanics model can provide the dispersion relation between contact resonance frequency and contact stiffness, and the relationship between contact stiffness and local mechanical properties, respectively [16][44]. The

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

• stiffness. A logical approach is to apply the basic equations of a contact mechanics model to determine the mechanical properties. In principle either the Hertzian [30] or Derjaguin–Muller–Toporov (DMT) models [31] can be employed to calculate the mechanical properties of the contact. However, this approach

Mechanical and thermodynamic properties of Aβ₄₂, Aβ₄₀, and α-synuclein fibrils: a coarse-grained method to complement experimental studies

• Adolfo B. Poma,
• Horacio V. Guzman,
• Mai Suan Li and
• Panagiotis E. Theodorakis

Beilstein J. Nanotechnol. 2019, 10, 500–513, doi:10.3762/bjnano.10.51

• considered. The former refers to the way that the indentation load is measured by the deflection of the AFM cantilever. The latter is an assumption of the semi-infinite half-space approximation. Once the AFM data is obtained, it requires interpretation by using a contact mechanics theory. There is no

• experiment at the nanoscale where the influence of the indenter could be neglected. Depending on the type of forces between the indenter and the biomaterial, we might describe the process by non-adhesive [12] or adhesive contact mechanics theories [58][59]. Here, we suggest our particle-based CG method as a

Biological and biomimetic surfaces: adhesion, friction and wetting phenomena

• Stanislav N. Gorb,
• Kerstin Koch and
• Lars Heepe

Beilstein J. Nanotechnol. 2019, 10, 481–482, doi:10.3762/bjnano.10.48

• Keywords: adhesion; air retention; contact mechanics; fluid transport; friction; functional gradients; wetting; This Thematic Series is the continuation of the previous series on the broad topic of biological and bioinspired materials and surfaces [1][2][3]. This collection of articles displays a current

Friction reduction through biologically inspired scale-like laser surface textures

• Johannes Schneider,
• Vergil Djamiykov and
• Christian Greiner

Beilstein J. Nanotechnol. 2018, 9, 2561–2572, doi:10.3762/bjnano.9.238

• arguments based on indentation depth do change for a sliding contact (e.g., Hamilton’s [42] instead of Hertz’s [43] solution) should be applied for the stress field. We made use of the contact mechanics solver developed and provided by Pastewka [44]. This program allows uploading white light profilometry

• images and analysing the contact mechanics. Profilometry images of all four scale sizes were taken and attention was focused on the ratio of the true to the projected contact area for a contact with a sapphire counter body. This analysis showed that, in agreement with what was postulated by Baum et al

• or micro-hydrodynamic pressure build-up as these experiments were performed under dry sliding. Understanding and exploiting this size effect phenomenon therefore will be the focus of future research. These investigations will mainly involve a detailed modelling of the contact mechanics for each

Evidence of friction reduction in laterally graded materials

• Roberto Guarino,
• Gianluca Costagliola,
• Federico Bosia and
• Nicola Maria Pugno

Beilstein J. Nanotechnol. 2018, 9, 2443–2456, doi:10.3762/bjnano.9.229

• have also been applied to tribological studies, where it is well known that the behaviour of a system is governed by multiphysics and multiscale interactions [19]. The first application of graded materials to contact mechanics was proposed by Giannakopoulos and Suresh, who presented an analytical study

Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy

• Miead Nikfarjam,
• Enrique A. López-Guerra,
• Santiago D. Solares and
• Babak Eslami

Beilstein J. Nanotechnol. 2018, 9, 1116–1122, doi:10.3762/bjnano.9.103

• the material, therefore the tip–sample force not only depends on tip position but also on tip velocity and higher displacement derivatives, in addition to force derivatives [11][16]. This contact-mechanics problem for viscoelastic half spaces has been formulated by independent studies [18][19][20][21

• 1 (Figure S1). The contact mechanics described by Equation 4 are strictly only valid for the approach portion of the indenter trajectory. A generalized approach has been derived by Ting, which is applicable for any arbitrary (a priori) known loading history [21]. In our simulations, where a priori

Review on nanoparticles and nanostructured materials: history, sources, toxicity and regulations

• Jaison Jeevanandam,
• Ahmed Barhoum,
• Yen S. Chan,
• Alain Dufresne and
• Michael K. Danquah

Beilstein J. Nanotechnol. 2018, 9, 1050–1074, doi:10.3762/bjnano.9.98

• are exposed via an extensive microscopic study. It has been shown that adhesion is ensured by sub-micrometric devices whereas flies and beetles rely on terminal setae that are of micrometer dimensions. The principle of contact mechanics, which shows that the adhesion leads to the splitting of contacts

• force in the physical form contribute to their adhesion. In recent reports, the reason for adhesion of gecko setae is due to van der Waals interaction through strong evidence [237] and rejects the capillary adhesion mechanisms. It was predicted that application of contact mechanics may help in smaller

Tuning adhesion forces between functionalized gold colloidal nanoparticles and silicon AFM tips: role of ligands and capillary forces

• Sven Oras,
• Sergei Vlassov,
• Marta Berholts,
• Rünno Lõhmus and
• Karine Mougin

Beilstein J. Nanotechnol. 2018, 9, 660–670, doi:10.3762/bjnano.9.61

• form a highly compact thin film [44]. It is important that although the absolute adhesion values measured on the films are different compared to the particles, the trend from least to most adhesive remains similar. We have estimated the effect of the particle size on adhesion by contact mechanics

Scaling law to determine peak forces in tapping-mode AFM experiments on finite elastic soft matter systems

• Horacio V. Guzman

Beilstein J. Nanotechnol. 2017, 8, 968–974, doi:10.3762/bjnano.8.98

• bidimensional deformation contact mechanics model. The equation enables to estimate the peak force based on the tapping mode observables, probe characteristics and the material properties of the sample. The accuracy of the equation has been verified by comparing it to numerical simulations for the archetypical

• matter Tatara’s contact mechanics model could be more appropriate to describe the elastic interactions between tip and sample. In particular when the sample is very soft and has finite dimensions conditions that would imply that the deformation happens symmetrically at both, the tip–sample and the sample

• mass of the fluid [39], and ω0, Q, k and Fts are the angular resonant frequency, quality factor, spring constant and tip–sample interaction forces, respectively. The latter has been modelled according to the Tatara contact mechanics [35][36][37] which is given by with the constitutive material

Measuring adhesion on rough surfaces using atomic force microscopy with a liquid probe

• Juan V. Escobar,
• Cristina Garza and
• Rolando Castillo

Beilstein J. Nanotechnol. 2017, 8, 813–825, doi:10.3762/bjnano.8.84

• two solid surfaces (force of adhesion per unit area) that governs contact stresses and strongly influences friction. In such method, the force, Fadh, required to separate a tip from a flat solid sample is measured. Subsequently, a single-asperity continuum contact mechanics model is used to extract

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

• are sensitive to the tip–sample nanomechanical interaction parameters. To demonstrate this, a generalized theoretical framework for extracting nanomechanical sample properties from bimodal experiments is presented based on Hertzian contact mechanics. Three modes of operation for measuring cantilever

• parameters are considered: amplitude, phase, and frequency modulation. The experimental equivalence of all three modes is demonstrated on measurements of the second eigenmode parameters. The contact mechanics theory is then extended to power-law tip shape geometries, which is applied to analyze the

• experimental data and extract a shape and size of the tip interacting with a polystyrene surface. Keywords: bimodal atomic force microscopy; bimodal spectroscopy; contact mechanics; multifrequency; nanomechanical mapping; nanomechanics; Introduction Over the decades since its invention [1] the atomic force

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

• can be explained by nanoroughness. In other words, contact splitting (i.e., a transport of shear stress across many small contacts, rather than a few large ones) can be exploited to reduce partial slip. Keywords: contact mechanics; contact splitting; contact stiffness; partial slip; quartz crystal

• water, respectively. The fact that Δf0 increases with normal load is easy to understand. With increasing load, the contact radius increases and the contact stiffness increases correspondingly. The dotted lines show an attempt to bring this understanding in line with the known models of contact mechanics

• far, the discussion has been concerned with linear contact mechanics. The experiment is easy and there are few other techniques that give access to the same data (mostly the AFM and ultrasonic reflectometry). Importantly, the QCM also accesses the (weakly) nonlinear regime and it does so rather easily

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

• moment of inertia. By using an appropriate contact mechanics model, one can convert the obtained stiffness values to the reduced elastic modulus E* and then to the indentation modulus M. The contact mechanics for AFM tips is very difficult to model as the exact shape of the tip in contact with the sample

• is usually unknown. The Hertz model is a simplified and the most widely used contact mechanics model for AFM contacts. It assumes each contact to be an elastic half space with relatively small strains at the frictionless contact with elliptical shape [26]. The tip radius and the applied load are

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

• instantaneous deflection and tip–surface force, velocity, virial, dissipated energy, sample deformation and peak force as a function of time or distance. The simulator includes a variety of interactions and contact mechanics models to describe AFM experiments including: van der Waals, Hertz, DMT, JKR, bottom

• tip–surface charge density and σs is the sample surface charge density. Hertz contact mechanics The elastic contact between the tip and sample is usually modelled with the Hertz model [46] whereby for a spherical tip and a half-space sample the force is given by where δ is the indentation and Eeff is

• 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

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

• 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

Modeling viscoelasticity through spring–dashpot models in intermittent-contact atomic force microscopy

• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 2149–2163, doi:10.3762/bjnano.5.224

• contact mechanics to incorporate the contact area and sample deformation [7]. The dissipative part of this model, originally introduced by García and coworkers [34] has the following form: where η is the viscosity, R is the tip radius and δ is the sample deformation (tip–sample indentation). In this model

• SLS is the simplest model that is able to describe stress relaxation and creep, and the DMT is a widely used model in contact mechanics that is typically used in the context of AFM. We include both DMT contact forces and long-range van der Waals forces [6][32]. where H is the Hammaker constant, R is