Interaction potential and hopping dynamics governing sliding friction

The friction force on a nanometer-sized tip sliding on a surface is related to the thermally activated hopping of the contact atoms on an effective atomic interaction potential. A general analytical expression relates the height of this potential and the hopping attempt frequency to measurements of the velocity dependence of the friction force performed with an atomic force microscope. While the height of the potential is roughly proportional to the normal load, the attempt frequency falls in the range of mechanical eigenfrequencies of the probing tip in contact with the surface.     

Dynamical theory of topological defects

A method is presented to obtain stochastic equations of motion for topological defects from the underlying TDGL-like stochastic dissipative field equations. The method makes use of virtual displacements of the Goldstone coordinates of topological defects. Effects of kinematical constraints among Goldstone coordinates are studied. The method is applied to modulated systems and we obtain stochastic equations of motion for interfaces (domain walls) and vortex lines (dislocation or defect lines). The driving force for a vortex line is found to include besides the usual surface tension force a new force due to misfit, which is an analogue of the Magnus force on a quantized vortex line and the Peach-Kochler force on a dislocation. A general expression for interactions between parts of interfaces is obtained in terms of asymptotic forms of field variables far from interfaces.     

Ultrasonic excitation affects friction interactions between food materials and cutting tools

In the food industry, ultrasonic cutting is used to improve separation by a reduction of the cutting force. This reduction can be attributed to the modification of tool–workpiece interactions at the cutting edge and along the tool flanks because of the superposition of the cutting movement with ultrasonic vibration of the cutting tool. In this study, model experiments were used to analyze friction between the flanks of a cutting tool and the material to be cut. Friction force at a commercial cutting sonotrode was quantified using combined cutting–friction experiments, and sliding friction tests were carried out by adapting a standard draw-off assembly and using an ultrasonic welding sonotrode as sliding surface. The impact of material parameters, ultrasonic amplitude, and the texture of the contacting food surface on friction force was investigated. The results show that ultrasonic vibration significantly reduces the sliding friction force. While the amplitude showed no influence within the tested range, the texture of the contact surface of the food affects the intensity of ultrasonic transportation effects. These effects are a result of mechanical interactions and of changes in material properties of the contact layer, which are induced by the deformation of contact points, friction heating and absorption heating because of the dissipation of mechanical vibration energy.     

Crystalline misfit-angle implications for solid sliding

For the contact of two finite portions of interacting rigid crystalline surfaces, we compute the pinning energy barrier dependency on the misfit angle and contact area. This simple model allows us to investigate a broad contact-size and angular range, thus obtaining the statistical properties of the energy barriers opposing sliding for a single asperity. These data are used to generate the distribution of static frictional thresholds for the contact of polycrystals, as in dry or even lubricated friction. This distribution is used as the input of a master equation to predict the sliding properties of macroscopic contacts.     

Observed transition from linear to non-linear friction-load behavior using a lateral force microscope

The most commonly observed friction behavior for sliding systems is that described by Amontons laws of friction. In this case, sliding friction is independent of the gross or apparent area of contact between the materials and a linear function of the applied normal load, where the constant of proportionality is called the friction coefficient. However, for dry sliding solids in contact via a single-asperity junction, Amontons (linear) friction-load behavior is not strictly relevant. In experiments measuring sliding friction between a silicon tip and a quartz surface using an atomic force microscope (AFM), a transition from linear to non-linear friction-load behavior has been observed. This is proposed to result from a nanoscale ‘conditioning’ of a multiple-contact tip-surface interface to form a single-asperity contact.     

Frictional coupling between sliding and spinning motion

The tangential motion at the contact of two solid objects is studied. It consists of a sliding and a spinning degree of freedom (no rolling). We show that the friction force and torque are inherently coupled. As a simple test system, a sliding and spinning disk on a horizontal flat surface is considered. We calculate, and also measure, how the disk slows down and find that it always stops its sliding and spinning motion at the same moment. We discuss the impact of this coupling between friction force and torque on the physics of granular materials.     

基底支撑刚度梯度变化对石墨烯层间摩擦力的影响

基于纳米摩擦能耗理论,利用分子动力学方法建立了公度接触下支撑刚度梯度变化的石墨烯层间摩擦力模型,分析了基底质心刚度和支撑刚度梯度变化对基底和薄片各接触区摩擦能耗的贡献.结果表明:软边界区始终贡献驱动力;硬边界区贡献的摩擦力最大,且随着支撑刚度的增大,硬边界区对总摩擦的贡献比也越高.各接触区的摩擦力是薄片和基底之间的褶皱势和接触区产生的法向变形差两部分的共同作用.前者是公度接触下阻碍滑移的界面势垒和刚度梯度方向上不同刚度支撑原子热振动引起的势梯度;后者是接触边界过渡区两侧原子的非对称变形和自由度约束突变引起的非平衡边界势垒相耦合的结果.本文对研究公度接触下刚度梯度支撑的纳米器件的相对运动规律有指导意义.     

Contact mechanics analysis of oscillatory sliding of a rigid fractal surface against an elastic–plastic half-space

Oscillatory sliding contact between a rigid rough surface and an elastic–plastic half-space is examined in the context of numerical simulations. Stick-slip at asperity contacts is included in the analysis in the form of a modified Mindlin theory. Two friction force components are considered – adhesion (depending on the real area of contact, shear strength and interfacial adhesive strength) and plowing (accounting for the deformation resistance of the plastically deformed half-space). Multi-scale surface roughness is described by fractal geometry, whereas the interfacial adhesive strength is represented by a floating parameter that varies between zero (adhesionless surfaces) and one (perfectly adhered surfaces). The effects of surface roughness, apparent contact pressure, oscillation amplitude, elastic–plastic properties of the half-space and interfacial adhesion on contact deformation are interpreted in the light of numerical results of the energy dissipation, maximum tangential (friction) force and slip index. A non-monotonic trend of the energy dissipation and maximum tangential force is observed with increasing surface roughness, which is explained in terms of the evolution of the elastic and plastic fractions of truncated asperity contact areas. The decrease of energy dissipation with increasing apparent contact pressure is attributed to the increase of the elastic contact area fraction and the decrease of the slip index. For a half-space with fixed yield strength, a lower elastic modulus produces a higher tangential force, whereas a higher elastic modulus yields a higher slip index. These two competing effects lead to a non-monotonic dependence of the energy dissipation on the elastic modulus-to-yield strength ratio of the half-space. The effect of interfacial adhesion on the oscillatory contact behaviour is more pronounced for smoother surfaces because the majority of asperity contacts deform elastically and adhesion is the dominant friction mechanism. For rough surfaces, higher interfacial adhesion yields less energy dissipation because more asperity contacts exhibit partial slip.     

Transition from stick-slip to continuous sliding in atomic friction: entering a new regime of ultralow friction

A transition from stick-slip to continuous sliding is observed for atomically modulated friction by means of a friction force microscope. When the stick-slip instabilities cease to exist, a new regime of ultralow friction is encountered. The transition is described in the framework of the Tomlinson model using a parameter eta which relates the strength of the lateral atomic surface potential and the stiffness of the contact under study. Experimentally, this parameter can be tuned by varying the normal load on the contact. We compare our results to a recently discussed concept called superlubricity.     

超声驱动的超声波振动减摩作用研究

借助于动力学原理,对超声驱动中的垂直超声波振动的减摩作用进行了理论研究。将超声电机定子和转子接触区定子表面一点的超声波振动分解成水平振动和垂直振动,并分析了两个方向振动对超声电机驱动作用的影响。提出水平振动产生摩擦驱动力,垂直振动影响水平驱动的效果,将垂直方向超声波振动的作用等效为普通滑动试验中垂直于滑动方向超声波振动的作用,揭示了垂直方向超声波振动是导致超声驱动动摩擦系数降低的原因。试验结果与理论分析定性地一致。     

Effects of non-flat contact and interference on self-assembled monolayers under sliding friction

The nanotribology mechanism of alkanethiol self-assembled monolayers (SAM) chemisorbed on a gold surface under a non-flat contact by a tilt plane was studied using molecular dynamics (MD) simulations. The molecular trajectories, tilt angles, normal forces, shear forces, and frictional coefficient of the SAM were evaluated during the friction and relaxation processes for various parameters, including the tilt angle of the slider, interference magnitude, and SAM length. At the nanoscale, the magnitude of interface interactional forces is strongly dependent on the magnitude of the contact area, not on the surface geometry. The contact area and the exerted normal force of the SAM increase with decreasing the tilt angle of the slider at the same contact interference. In contrast, the periods in both normal force and shear force are gradually delayed as the tilt angle of the slider increases. Once the contact interference increases, the normal force and shear force increase together. During the sliding friction process with a smaller tilt slider angle, SAM molecules can maintain a better collective ordered structure. Short SAM molecules are more sensitive to a compressive loading and react to a larger normal force under the same contact interference due to the deformation of a larger tilt angle and decrease in chain length. The friction coefficient of SAM is significantly more dependent on the tilt angle of the slider than the contact interference.     

Friction and normal forces of model friction modifier additives in simulations of boundary lubrication

ABSTRACT

Interaction forces between solid surfaces are often mitigated by adsorbed molecules that control normal and friction forces at nanoscale separations. Molecular dynamics simulations were conducted of opposing semi-ordered monolayers of united-atom chains on sliding surfaces to relate friction and normal forces to imposed sliding velocity and inter-surface separation. Practical examples include adsorbed friction-modifier molecules in automatic transmission fluids. Friction scenarios in the simulations had zero, one, or two fluid layers trapped between adsorbed monolayers. Sliding friction forces increased with sliding velocity at each stable separation. Lower normal forces were obtained than in most previous nanotribology molecular simulations and were relatively independent of sliding speed. Distinguishing average frictional force from its fluctuations showed the importance of system size. Uniform velocities were obtained in the sliding direction across each adsorbed film, with a gradient across the gap containing trapped fluid. The calculated friction stress was consistent with measurements reported using a surface forces apparatus, indicating that drag between an adsorbed layer and trapped fluid can account sufficiently for sliding friction in friction modifier systems. An example is shown in which changes in molecular organisation parallel to the surface led to a large change in normal force but no change in friction force.     

Electron and probe microscopy investigation of the surface of elastomers modified with antifriction fillers

The surface of frost-resistant elastomers (rubbers) based on nitrile-butadiene rubber and propylene- oxide rubber (pure and modified with fillers: ultrafine PTFE and carbon black) is investigated. Tribological tests show that the addition of carbon black produced the greatest effect: the friction coefficient decreases to 0.2 and remains virtually constant during cooling. Surface and subsurface defects are detected by SEM. These defects can affect the processes in the zone of friction and destruction of the sliding surface of rubber. It is demonstrated that the modification of propylene-oxide rubber results in surface smoothing; the effect is the most pronounced in the samples modified with carbon black. The potential to use scanning probe microscopy for local investigation of the surface of rubber is assessed. A conclusion is made about the adhesive properties of surfaces based on the obtained force–distance curves. The investigation of vibration parameters of a probe in contact with the surface provides an opportunity to estimate the surface elasticity. It is shown that the addition of carbon black results in an increase in hardness of the rubber samples and a drastic reduction in adhesion. At the same time, the introduction of ultrafine PTFE leads to a slight enhancement of the adhesion and hardness. It is concluded that carbon black is the best modifying additive for the studied elastomers.     

Superlubricity of graphite

Using a home-built frictional force microscope that is able to detect forces in three dimensions with a lateral force resolution down to 15 pN, we have studied the energy dissipation between a tungsten tip sliding over a graphite surface in dry contact. By measuring atomic-scale friction as a function of the rotational angle between two contacting bodies, we show that the origin of the ultralow friction of graphite lies in the incommensurability between rotated graphite layers, an effect proposed under the name of "superlubricity" [Phys. Rev. B 41, 11 837 (1990)]].     

Tribological behavior of micro/nano-patterned surfaces in contact with AFM colloidal probe

In effort to investigate the influence of the micro/nano-patterning or surface texturing on the nanotribological properties of patterned surfaces, the patterned polydimethylsiloxane (PDMS) surfaces with pillars were fabricated by replica molding technique. The surface morphologies of patterned PDMS surfaces with varying pillar sizes and spacing between pillars were characterized by atomic force microscope (AFM) and scanning electron microscope (SEM). The AFM/FFM was used to acquire the friction force images of micro/nano-patterned surfaces using a colloidal probe. A difference in friction force produced a contrast on the friction force images when the colloidal probe slid over different regions of the patterned polymer surfaces. The average friction force of patterned surface was related to the spacing between the pillars and their size. It decreased with the decreasing of spacing between the pillars and the increasing of pillar size. A reduction in friction force was attributed to the reduced area of contact between patterned surface and colloidal probe. Additionally, the average friction force increased with increasing applied load and sliding velocity.     

Tribological properties of silicate materials on nano and microscale

We studied the friction properties of four model silicate materials at the nanoscale and microscale. From nanotribology, we characterized the tribological properties at single asperity contact scale and from microtribology, we characterized the tribological properties at multi asperity contact scale. First, for each material we measured chemical composition by XPS, Young's modulus by acoustical microscopy and roughness σ by atomic force microscopy (AFM). Second, we measured the nanofriction coefficients with an AFM and the microfriction coefficients with a ball probe tribometer, for three hardnesses of the ball probe. We identified one friction mechanism at the nanoscale (sliding friction) and two friction mechanisms at the microscale (sliding friction and yielding friction). Comparison of the nano and microfriction coefficients at the same sliding friction regime shown, that the tribological properties of these materials didn’t depend on roughness.     

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.     

Frictional properties of confined polymers

We present molecular dynamics friction calculations for confined hydrocarbon solids with molecular lengths from 20 to 1400 carbon atoms. Two cases are considered: a) polymer sliding against a hard substrate, and b) polymer sliding on polymer. In the first setup the shear stresses are relatively independent of molecular length. For polymer sliding on polymer the friction is significantly larger, and dependent on the molecular chain length. In both cases, the shear stresses are proportional to the squeezing pressure and finite at zero load, indicating an adhesional contribution to the friction force. The friction decreases when the sliding distance is of the order of the molecular length indicating a strong influence of molecular alignment during run-in. The results of our calculations show good correlation with experimental work.     

Adhesion between an elastic body and a randomly rough hard surface

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account that partial contact may occur between the solids on all length scales. I present numerical results for the case where the substrate surface is self-affine fractal. When the fractal dimension is close to 2, complete contact typically occurs in the macro-asperity contact areas, while when the fractal dimension is larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased. An important result is that even when the surface roughness is so high that no adhesion can be detected in a pull-off experiment, the area of real contact (when adhesion is included) may still be several times larger than when the adhesion is neglected. Since it is the area of real contact which determines the sliding friction force, the adhesion interaction may strongly affect the friction force even when no adhesion can be detected in a pull-off experiment. Received 3 April 2002     

Texture-induced modulations of friction force: the fingerprint effect

Modulations of the friction force in dry solid friction are usually attributed to macroscopic stick-slip instabilities. Here we show that a distinct, quasistatic mechanism can also lead to nearly periodic force oscillations during sliding contact between an elastomer patterned with parallel grooves, and abraded glass slides. The dominant oscillation frequency is set by the ratio between the sliding velocity and the grooves period. A model is derived which quantitatively captures the dependence of the force modulations amplitude with the normal load, the grooves period, and the slides roughness characteristics. The model's main ingredient is the nonlinearity of the friction law. Since such nonlinearity is ubiquitous for soft solids, this "fingerprint effect" should be relevant to a large class of frictional configurations and have important consequences in human digital touch.