Lateral Contact Stiffness Research Articles

Surroundings affect slip length dynamics in nanoscale friction through contact stiffness and damping

Friction force microscopy (FFM) explores the interaction in a sliding contact on the nanoscale, providing information on the frictional dynamics and lateral contact stiffness with lattice resolution. Recent FFM measurements on a NaCl crystal immersed in liquid (ethanol) surroundings displayed an increase of the effective contact stiffness, Keff, with the applied load, differently from similar measurements performed under ultra-high vacuum (UHV) conditions, where Keff showed negligible load dependency. Additionally, under UHV conditions multiple slip length friction with increasing load was reported, while in ethanol surroundings only single (lattice unit length) slips were observed. Our current understanding of this behavior relates the transition from single jumps to multiple jumps dynamics to the normal load (manifested through the amplitude of the interaction potential at the contact, U0) and to the damping of the system. Here we have incorporated the effect of the load dependency on both U0 and Keff within Prandtl—Tomlinson based simulations, accompanied by variations in the damping coefficient of the system. Introducing the experimentally observed load dependency to Keff resulted indeed in single slip jumps at critical damping, while multiple slip jumps were obtained at constant Keff. The average slip length increased with the normal load, particularly when the system became underdamped. Our work provides a glimpse on the relation between the characteristic observables in atomic-scale sliding friction (maximal slip forces, stiffness, and slip dynamics) with respect to their governing parameters (corrugation energy, effective stiffness, and damping). While common understanding in nanotribology relates the effect of surrounding media mainly to the interaction potential at the contact, here we show that the media can also greatly affect the elastic interaction, and consequently play an important role on the transition from single to multiple stick-slip.

Large lateral contact stiffness on Si nanopillar surfaces

We studied the lateral contact stiffness (kcontactx) between the tip of a frictional force microscope and a pillar surface to identify the sliding behavior of the tip at the submicrometer scale. The kcontactx and mean lateral force (⟨F⟩) were systematically measured as functions of pillar diameter φ. We found that the kcontactx on a single Si pillar surface increased whereas the ⟨F⟩ rapidly decreased as φ decreased from the micrometer to the nanometer scale. This contradiction could be explained by the change in tip behavior from dynamic sliding to static sticking.

AFM measurement of the cuticle of the orchid bee Euglossa sp.: Elastic properties under dehydrated and hydrated conditions

We used experimental resonant data of AFM cantilevers within a finite element analysis (FEA) modeling to study the resonant curves as a function of the normal and lateral contact stiffness, kN and kS, respectively. An analytical function was fitted to the contact-dependent shape modes obtained from FEA to determine the effective stiffness and effective mass of cantilever of each resonant mode. We use this sensitive dynamic information of the cantilever to perform nanomechanical measurements on the cuticle of the orchid bee Euglossa sp. under dehydrated and hydrated conditions. We implemented acoustic microscopy mappings with resonance tracking to monitor the changes caused by the different kN values on the biocomposite. Results showed a reduction of kN from 39–42 to 36–38 N/m caused by the hydration process, indicating a change in the spatial period of the multilayer system at the epicuticle, which agree with Oliver&Pharr analysis (~1.80 GPa-dehydrated and ~1.4 GPa-hydrated).

Influence of heating on the measured friction behavior of graphene evaluated under ultra-high vacuum conditions

Atomic scale friction measurements of exfoliated graphene on a silicon oxide substrate were conducted under ultra-high vacuum (UHV) conditions using an atomic force microscope. Two groups of samples were prepared: one that was heated for 3 h at 800 °C in the UHV chamber and one that was not heated in the UHV chamber. The heated sample showed much lower friction, a lower pull-off force during unloading, and no hysteresis between loading and unloading friction measurements on the heated sample compared with the unheated sample. Additionally, a significantly higher tilt of the friction loop was observed in the unheated sample compared with no or very little tilt of friction loops in the heated sample. Interpretation of lateral forces using the Prandtl–Tomlinson model showed a significantly higher energy corrugation on the unheated sample, but similar lateral contact stiffnesses. Furthermore, no hysteresis in either the energy corrugation or lateral contact stiffness was observed in either sample, suggesting that friction hysteresis is less likely correlated with the energy corrugation and lateral contact stiffness. These observations suggest that surface contamination was present on the unheated sample, which is removed or reduced to undetectable levels on the heated sample. Furthermore, the study distinguishes features in the friction behavior induced by surface contamination with those associated with graphene's intrinsic properties.

Modelling tangential contact problem with surface stress

In this paper, we investigate the effects of surface stress on the spherical contact problem under combined normal and lateral loads. The boundary element method based on fast Fourier transform and conjugate gradient algorithm is employed to perform the contact analysis with partial slip. It is shown that as the size of contact reduces to the characteristic scale that surface stress dominates, the contact behavior will significantly deviate from the classical model. Under the same loading condition, the tangential traction within contact region tends to distribute more evenly and the width of slip zone would be relatively smaller due to the presence of surface stress. In addition, it is found that the variations of the total tangential force and the lateral contact stiffness with respect to the lateral displacement depend strongly on the contact scale. This work provides a theoretical basis for the study of contact and friction of some soft materials and biological systems.

Experimental and theoretical investigations about the nonlinear vibrations of rectangular atomic force microscope cantilevers immersed in different liquids

Nonlinear flexural vibrations of rectangular atomic force microscope cantilever have been investigated by both the theoretical model and experimental works. As for the theoretical model, the Timoshenko beam theory which takes the rotatory inertia and shear deformation effects into consideration has been adopted. To increase the accuracy of the theoretical model, all necessary details for cantilever and sample surface have been taken into account. Differential quadrature method as a simple and fast numerical method has been used for solving the differential equations. During the investigation, the softening behavior was observed for all cases. It was also seen that raising the amplitude of vibrations led to a decrease in the nonlinear resonant frequency to linear resonant frequency ratio. The effects of different parameters such as normal and lateral contact stiffness, cantilever thickness, the angle between cantilever and sample surface and tip height in the presence of air as environment on the softening behavior were also examined. It was also demonstrated that increasing the lateral and normal contact stiffness, but decreasing the Timoshenko beam parameter would lead to an increase in the amplitude of vibrations for the first and second modes. The vibrational behavior of cantilever immersed in different liquids including water, methanol, acetone and carbon tetrachloride has been studied. Results show that increasing the liquid density reduces the nonlinear frequency. Furthermore, experimental works were compared with theoretical model for water and air environments. Results show good agreement.

An Integrated Force Probe and Quartz Crystal Microbalance for High-Speed Microtribology

We have developed a technique for measuring frictional forces and contact areas, over a wide range of applied loads, at microscopic contacts reaching high sliding speeds near 1 m/s. Our approach is based on integrating two stand-alone methods: nanoindentation and quartz crystal microbalance (QCM). Energy dissipation and lateral contact stiffness are monitored by a transverse shear quartz resonator, while a spherical indenter probe is loaded onto its surface. Variations in these two quantities as functions of shear amplitude, with the normal load held fixed, reveal a transition from partial to full slip at a critical amplitude. Average values of both the threshold force for full slip and the kinetic friction during sliding are determined from these trends, and the contact area is inferred from the lateral stiffness at low shear amplitudes. Measurements are performed at loads ranging from 5 µN to 8 mN using an electrostatically actuated indenter probe. For the materials chosen in this study, we find that the full slip threshold force is about a factor of two larger than kinetic friction. The forces increase sublinearly with load in close correspondence with the contact area, and the shear strengths are found to be relatively insensitive to pressure. The threshold shear amplitude scales in proportion to the contact radius. These results demonstrate that the probe–QCM technique is a versatile and full-featured platform for microtribology in the speed range relevant to practical applications.

High resolution lateral force-displacement measurements as a tool for the determination of lateral contact stiffness and Poisson's ratio

A Lateral Force Unit (LFU) as a second measuring head for nanoindenters is now available as a commercial tool with the necessary accuracy to investigate the elastic contact between a sphere and a flat surface with sub-nanometer resolution. The combination of normal and lateral load-displacement measurements at one and the same sample position gives two independent measurement results and can therefore be used to extract beside Young's modulus a second elastic constant. This can be shear modulus or Poisson's ratio for elastically isotropic materials. To realize that, it is necessary to determine all necessary corrections with high precision. This comprises normal and lateral instrument compliance, indenter area function, spring constant of the holding springs of the LFU and the surface slope. Two algorithms were developed and tested for the determination of the Poisson's ratio from fully elastic measurements with a spherical indenter. One is using the ratio of normal and lateral contact stiffness and the other the curvature of the lateral load-displacement curve at the turning points and the transition from sticking to sliding friction. By measuring six different materials it was shown that the ratio of normal and lateral contact stiffness results in relatively large errors for the Poisson's ratio of up to 50% against literature data while the other method had only an error (1σ) between 6% and 20%. The last method is restricted to hard and smooth materials to enable measurements in fully elastic regime but it can also be applied to coatings if they are about 2.5–4 times ticker than the contact radius during the measurement. This is nevertheless a progress against the current situation where the Poisson's ratio of coatings is mostly unknown.

Molecular-scale shear response of the organic semiconductor β -DBDCS (100) surface

In this work we present friction-force microscopy (FFM) lattice-resolved images acquired on the (100) facet of the semiconductor organic oligomer (2Z,2'Z) − 3,3'-(1,4-phenylene)bis(2-(4-butoxyphenyl)acrylonitrile) (β-DBDCS) crystal in water at room temperature. Stick-slip contrast, lateral contact stiffness, and friction forces are found to depend strongly on the sliding direction due to the anisotropic packing of the molecular chains forming the crystal surface along the [010] and [001] directions. The anisotropy also causes the maximum value of the normal force applicable before wearing to increase by a factor of 3 when the scan is performed along the [001] direction on the (100) face. Altogether, our results contribute to achieving a better understanding of the molecular origin of friction anisotropy on soft crystalline surfaces, which has been often hypothesized but rarely investigated in the literature.

Time Strengthening of Crystal Nanocontacts.

We demonstrate how an exponentially saturating increase of the contact area between a nanoasperity and a crystal surface, occurring on time scales governed by the Arrhenius equation, is consistent with measurements of the static friction and lateral contact stiffness on a model alkali-halide surface at different temperatures in ultrahigh vacuum. The "contact ageing" effect is attributed to atomic attrition and is eventually broken by thermally activated slip of the nanoasperity on the surface. The combination of the two effects also leads to regions of strengthening and weakening in the velocity dependence of the friction, which are well-reproduced by an extended version of the Prandtl-Tomlinson model.

Effect of capillary forces on the correlation between nanoscale adhesion and friction of polymer patterned surfaces

A general relation between adhesion and friction was elusive. This was partly due to the limitations in experimentally configuring the wide variety of geometrical and chemical cues encountered at a sliding contact. We study the combined influence of capillary and van der Waals forces on the correlation between the adhesion (pull-off force) and friction of polymer patterns. We report the existence of master curves in plot of adhesion versus friction, spanning nearly two orders of magnitude, characteristic of the effective lateral contact stiffness of the contact determined by geometry and capillary forces. Further, we showed how nanocylindrical patterns, micropatterns and PTFE-coated PMMA flat surfaces subjected to varying capillary forces displayed similar sliding characteristics despite their large differences in contact characteristics.

Atomic force acoustic microscopy: Influence of the lateral contact stiffness on the elastic measurements

Atomic force acoustic microscopy is a dynamic technique where the resonances of a cantilever, that has its tip in contact with the sample, are used to quantify local elastic properties of surfaces. Since the contact resonance frequencies (CRFs) monotonically increase with the tip-sample contact stiffness, they are used to evaluate the local elastic properties of the surfaces through a suitable contact mechanical model. The CRFs depends on both, normal and lateral contact stiffness, kN and kS respectively, where the last one is taken either as constant (kS<1), or as zero, leading to uncertainty in the estimation of the elastic properties of composite materials. In this work, resonance spectra for free and contact vibration were used in a finite element analysis of cantilevers to show the influence of kS in the resonance curves due to changes in the kS/kN ratio. These curves have regions for the different vibrational modes that are both, strongly and weakly dependent on kS, and they can be used in a selective manner to obtain a precise mapping of elastic properties.

Direct torsional actuation of microcantilevers using magnetic excitation

Torsional mode dynamic force microscopy can be used for a wide range of studies including mapping lateral contact stiffness, torsional frequency or amplitude modulation imaging, and dynamic friction measurements of various materials. Piezo-actuation of the cantilever is commonly used, but it introduces spurious resonances, limiting the frequency range that can be sampled, and rendering the technique particularly difficult to apply in liquid medium where the cantilever oscillations are significantly damped. Here, we demonstrate a method that enables direct torsional actuation of cantilevers with high uniformity over wide frequency ranges by attaching a micrometer-scale magnetic bead on the back side of the cantilever. We show that when beads are magnetized along the width of the cantilever, efficient torsional actuation of the cantilevers can be achieved using a magnetic field produced from a solenoid placed underneath the sample. We demonstrate the capability of this technique by imaging atomic steps on graphite surfaces in tapping mode near the first torsional resonance of the cantilever in dodecane. The technique is also applied to map the variations in the lateral contact stiffness on the surface of graphite and polydiacetylene monolayers.

Atomistic study of lateral contact stiffness in friction force microscopy

The effective stiffness of a friction force microscope tip–substrate system is an important parameter that describes the relationship between lateral force and elastic deformation. In this study, we use a multi-spring model to simplify the system, where two contributions, the tip apex stiffness and the lateral contact stiffness, are discussed in detail. Molecular dynamics simulations are used to characterize stiffness by simulating a tip apex subject to shear or sliding over a substrate surface. The results show that, although the height of the tip apex and tip–substrate orientation affect the various stiffness contributions, the contact itself dominates the overall compliance.

A new investigation for double tapered atomic force microscope cantilevers by considering the damping effect

The resonant frequency of flexural vibration for a double tapered atomic force microscope (AFM) cantilever has been investigated by considering the damping effect. In this paper the effects of the contact position, contact stiffness, height of the tip, thickness of the beam, the height and breadth taper ratios of cantilever, the angle between the cantilever and the sample surface and damping parameter based on Timoshenko beam theory on the non‐dimensional frequency and sensitivity have been studied. The differential Quadrature method (DQM) is employed to solve the nonlinear differential equations of motion. The results show that the resonant frequency decreases when Timoshenko beam parameter or cantilever thickness increases and high order modes are more sensitive to it. The first frequency is sensitive only in the lower range of contact stiffness, but the higher order modes are sensitive to the contact stiffness in a larger range. Increasing the tip height increases the sensitivity of the vibrational modes in a limited range of normal contact stiffness. Increasing the lateral contact stiffness increases the sensitivity to the normal contact stiffness after critical normal contact stiffness, but when the normal contact stiffness is lower than critical normal contact stiffness, the situation is reversed. By increasing the lateral damping parameter, the resonant frequency and sensitivity to the contact stiffness decrease. Furthermore, by increasing the breadth taper ratio, the frequency increases.

Frictional properties of native and functionalized type I collagen thin films

Frictional properties of native and fibronectin (FN)-functionalized type I collagen (COL) thin films were studied via atomic force microscopy. The COL lateral contact stiffness was dependent only on the hydration state, indicating that shear deformation was invariant with FN. In contrast, the COL coefficient of friction and shear strength varied with both functionalization and hydration state. The changes in shear strength were found to correlate well with changes in mean cell spread area on the same thin films, suggesting that shear strength is a better indicator of cell spreading than heretofore considerations of film, and thus extracellular matrix, stiffness alone.

Accurate control of friction with nanosculptured thin coatings: Application to gripping in microscale assembly

Chromium thin films were sputter deposited implementing the GLancing Angle Deposition (GLAD) method, which is a thin film deposition technique where the incident vapor flux – composed of atoms and molecules from gas phase – strikes onto the substrate at tilted angles α. Oriented chromium columns were produced with various column angles β (from 0 to 60°) closely linked to the sputtering pressure and incidence angle α. Three sputtering pressures of 0.11, 0.40 and 0.53Pa were used. Incidence angle α of the sputtered particles was systematically changed from 0 to 80°. Tribological properties were investigated as a function of these operating parameters. Results reveal that the tribological behaviour is strongly correlated with the structure and especially the growth mechanism of the films, which are both linked with the operating sputtering parameters. Thus, at the lowest sputtering pressure (0.11Pa), gradual variations of the tribological properties and wettability are observed as a function of the incidence angle α, which are interesting for tailoring surfaces displaying a gradient of wettability. In contrast, at higher sputtering pressures (>0.2Pa), local variations of static friction coefficient, wettability and lateral contact stiffness are systematically observed as a function of the column angle β—and then the incidence angle α. Basically, these results enable to tailor tribological properties by tuning the incidence angle α in order to control the transition from sticking to sliding in micro-gripping.

Torsional Vibrations of a Cantilever with Lateral Friction in a Resonance Friction Microscope

A model of fundamental torsional vibration of a cantilever with lateral friction is presented by using the harmonic balance method. The model demonstrates that the torsional vibration has close relations with the lateral friction threshold, the lateral contact stiffness and the torsional vibration amplitude of the cantilever. When the threshold is larger than a product of the stiffness and the vibration amplitude, the lateral friction is a linear force with the amplitude. If the lateral friction threshold is less than the product, the motions of the tip on the sample can be stick-slip or slip motions. The results are useful to optimize and to manipulate the fundamental flexural vibration of the piezo-cantilever, and give an insight into the tribological characterization of the interface in a resonance friction microscope.

Effects of stick–slip motions on Besocke-style scanners in scanning probe microscopes

In Besocke-style scanners, a theoretical model with stick–slip sliding boundary conditions is presented by Timoshenko beam theory combined with the harmonic-balance method. The flexural vibration characteristics of the piezo-tubes induced by the stick–slip motions of the ball on the rail are investigated. The results show that the flexural vibrations essentially depend on the ratio of the ball–rail lateral friction threshold to the product of the ball–rail lateral contact stiffness and the vibration amplitude of the ball. When the ratio changes from zero to one, the lateral friction applied to the ball induces complex flexural vibrations. The vibrations can be regulated by adjusting an input electric signal to change the vibration amplitude of the ball, or using an external electro-magnetic force to change the preload of the ball–rail interaction, or changing the radius of the ball. Thus, the adverse vibrations of Besocke-style scanner can be eliminated to improve the spatial resolution of the atomic structure in scanning probe microscopes.

Mesoscale friction anisotropy revealed by slidingless tests

Abstract