Low-Speed Atomistic Simulation of Stick–Slip Friction using Parallel Replica Dynamics

Atomic stick–slip friction has been predicted by molecular dynamics simulation and observed in experiments. However, direct quantitative comparison of the two has thus far not been possible because of the large difference between scanning velocities accessible to simulations and experiments. In general, the slowest sliding speeds in MD simulations are at least five orders of magnitude larger than the upper limit available to experimentalists. To take a step toward bridging this gap, we have applied parallel replica dynamics, an accelerated molecular dynamics method, to the simulation of atomic stick–slip. The method allows molecular simulations to run parallel in time in order to extend their duration, thereby enabling lower scanning velocities. We show here that this method is able to predict atomic stick–slip friction accurately and efficiently at scanning speeds several orders of magnitude slower than standard molecular dynamics simulations. The accuracy and usefulness of this method is illustrated by correct prediction of the logarithmic dependence of friction on velocity.     

Atomic friction studies on well-defined surfaces

Atomic friction studies have been performed by means of a friction force microscope (FFM) in ultrahigh vacuum, where well-defined surfaces can be prepared. A home-built FFM allows us to study lateral forces as low as 0.05 nN using rectangular silicon cantilevers. Furthermore, comparison with dissipation measurements performed in non-contact mode are possible. Recent experimental results are presented and discussed in the framework of a one-dimensional Tomlinson model which includes thermal activation. Atomic-scale stick–slip processes on a metallic surface could be repeatedly measured on Cu(111), while the Cu(100) surface was distorted by the tip during the scanning process. A logarithmic velocity dependence of atomic friction has been measured on Cu(111) and NaCl(100) for low scanning velocities. The dissipation found in stick–slip measurements is compared to the power loss detected in dynamic non-contact measurement.     

Consequence of contact local kinematics of sliding bodies on the surface temperatures generated

When studying contact with friction between two bodies, it is not possible to obtain data on real contact conditions on the basis of steady-state situations. Indeed, contacts with friction usually lead to dynamic instabilities generated at the contact interface. It is therefore necessary to take into account contact dynamics in order to better understand the phenomena involved during sliding with friction. The explicit dynamic finite element code PlastD in 2D is used to simulate the contact between two bodies. A constant Coulomb friction coefficient is imposed at the interface. The simulations carried out permitted identifying local contact conditions (kinematics, tribological state, stresses, etc.). They revealed that different instability regimes can be generated (stick–slip, slip–separation, stick–slip–separation, etc.). Local contact stresses and the sliding velocity oscillate through time when instabilities are generated and their maximum values can be much higher than those expected for steady-state conditions. The aim of this paper is to analyse the frictional instabilities and their consequences on the heat generated in the contact. First, the influence of the different instability regimes is studied on a simple contact. Then, an industrial mechanism is studied (wheel–rail contact) to investigate the influence of local contact conditions on the temperature of the rail surface.     

Measurements of friction-induced surface strains in a steel/polymer contact

The paper describes an experimental study combined with analyses and numerical simulations of the surface strains developed in a metal–polymer contact under a variety of loading configurations. Specifically, a steel ball is caused to slide over a poly(methylmethacrylate) flat counterface under a fixed normal load where the imposed motions are small and consist of sliding and rotation and the combination of both. The surface strains have been measured directly using conventional strain gauges in two types of configurations specifically designed to monitor the strains for sliding and rotation. Calculations of frictional forces provide friction coefficients which are self-consistent and the computed ‘friction displacement loops’ correspond closely to those measured. In addition, the surface strain measurements provide a convenient and accurate insight into the stick–slip transitions in fretting contacts.     

Atomic Friction Modulation on the Reconstructed Au(111) Surface

Friction between a nanoscale tip and a reconstructed Au(111) surface is investigated both by atomic force microscopy (AFM) and molecular statics calculations. Lateral force AFM images exhibit atomic lattice stick–slip behavior with a superstructure corresponding to the herringbone reconstruction pattern. However, the superstructure contrast is not primarily due to variations in the local frictional dissipation (which corresponds to the local width of the friction loop). Rather, the contrast occurs primarily because the local centerline position of the friction loop is periodically shifted from its usual value of zero. Qualitatively, similar behavior is reproduced in atomistic simulations of an AFM tip sliding on the reconstructed Au(111) substrate. In both simulations and experiments, this centerline modulation effect is not observed on unreconstructed surfaces. Similarly, using a topographically flat surface as a hypothetical control system, the simulations show that the centerline modulation is not caused by variations in the reconstructed surface’s topography. Rather, we attribute it to the long-range variation of the local average value of the tip-sample interaction potential that arises from the surface reconstruction. In other words, surface atoms located at unfavorable sites, i.e., in the transition between face-centered-cubic (FCC) and hexagonal-close-packed (HCP) regions, have a higher surface free energy. This leads to a varying conservative force which locally shifts the centerline position of the friction force. This demonstrates that stick–slip behavior in AFM can serve as a rather sensitive probe of the local energetics of surface atoms, with an attainable lateral spatial resolution of a few nanometers.     

Modification of Boundary Lubrication by Oil-Soluble Friction Modifier Additives

The molecular-level function of model and commercial friction modifier additives in lubricants of the type used at the wet clutch interface in automatic transmissions has been studied using a surface forces apparatus (SFA) modified for oscillatory shear. The nanorheological properties of tetradecane with and without a model friction modifier additive (1-hexadecylamine) were examined in the boundary lubrication regime and compared to a fully-formulated automatic transmission fluid (ATF). 1-Hexadecylamine adsorbed as a single layer on the sliding surfaces, reduced the static frictional force and the limiting shear stress, and eliminated the stick–slip transition that exists in pure tetradecane. The ATF, which contains commercial-grade friction modifiers, showed nanorheological properties similar to those observed for tetradecane containing 0.1–0.2 wt% 1-hexadecylamine.     

Friction-induced vibration of oscillating multi-degree of freedom polymeric sliding systems

The purpose of this study is to investigate friction-induced vibration of oscillating systems. Special attention is focused on modeling polymer-on-metal systems. Past experimental and analytical friction results from non-oscillating or unidirectional translational sliding modes are extended into the oscillating sliding mode. Specifically, this refers to the incorporation of a representative functional shape of the friction–velocity relationships estimated from experimental results. Dependent on the relative sliding velocity between the frictionally coupled subsystems, the modeled system exhibits behavior such as a single stick–slip at the beginning of oscillatory motion, a single stick–slip at each motion reversal, or multiple stick-slip events during each half cycle of motion. Additionally, the boundary of incipient friction-induced vibration was identified via a rigorous definition of friction-induced vibration.     

Stick–Slip and Temperature Effect in the Scratching of Materials

The stick–slip process and temperature effect in scratch testing of materials have been studied. For a poly(methyl methacrylate) (PMMA) polymer scratched by a conical diamond indenter, both the amplitude and period of the stick–slip at room temperature increase with the normal load and decrease with the driving speed. An increase in temperature leads to an increase in stick–slip amplitude and period, as well as in the average horizontal force. For bismuth metal scratched by a conical tungsten indenter, the surface temperature in the contact area reveals fluctuations related to the stick–slip motion.     

Influence of surface texture and roughness parameters on friction and transfer layer formation during sliding of aluminium pin on steel plate

Surface texture of harder mating surfaces plays an important role during sliding against softer materials and hence the importance of characterizing the surfaces in terms of roughness parameters. In the present investigation, basic studies were conducted using inclined pin-on-plate sliding tester to understand the surface texture effect of hard surfaces on coefficient of friction and transfer layer formation. A tribological couple made of a super purity aluminium pin against steel plate was used in the tests. Two surface parameters of steel plates, namely roughness and texture, were varied in the tests. It was observed that the transfer layer formation and the coefficient of friction along with its two components, namely, the adhesion and plowing, are controlled by the surface texture and are independent of surface roughness (R_a). Among the various surface roughness parameters, the average or the mean slope of the profile was found to explain the variations best. Under lubricated conditions, stick–slip phenomena was observed, the amplitude of which depends on the plowing component of friction. The presence of stick–slip motion under lubricated conditions could be attributed to the molecular deformation of the lubricant component confined between asperities.     

Spanning Time Scales in Dynamic Simulations of Atomic-Scale Friction

We investigate the sliding dynamics of atomic-scale friction at different time scales. Depending on the dynamic inertia and sliding velocity of a cantilever, different dynamic behaviors are observed from both conventional molecular dynamics (MD) simulation and temporally hybrid molecular simulation methods. The mechanism of friction dissipation is also investigated. For either smooth sliding or stick–slip, a non-zero work of friction is obtained, while surface forces are no longer conservative.     

The structural origin of the complex rheology in thin dodecane films: Three routes to low friction

The effective viscosity of confined lubricant films less than 6–7 molecular layers is usually enhanced by many orders of magnitude. For dodecane the high friction film has a strong in-plane order with “mosaic-like” structures that extend across the film and effectively form “crystalline bridges” [Jabbarzadeh A, Harrowell P, Tanner RI. Crystal bridge formation marks the transition to rigidity in a thin lubrication film. Phys Rev Lett 2006; 96: 206102-1/4] resulting in high friction. Using molecular dynamics simulations, we have identified three routes to lower the friction. We show that the structure of confined films and their response to shearing are affected by atomic in-plane order and smoothness of the confining surfaces, the relative orientation of two crystalline surfaces and the direction of shear. We show a small increase in surface roughness in going from crystalline to amorphous surfaces can lead to a much lower friction. We demonstrate that misaligning (twisting) one surface with respect to the other by 45° results in a much lower effective viscosity. Application of shear for extended times induces alignment of lubricant molecules into a nematic-like order with ultra-low effective viscosity. The magnitude of reduction in the friction and the physical process through which it happens varies for each of these three routes. Depending on the method used, destruction of crystalline bridges, multilayer or fault plane slip provides a route for dramatic reduction in friction.     

Thermomechanical modeling and transient analysis of sliding contacts between an elastic–plastic asperity and a rigid isothermal flat

To investigate thermomechanical contacts between an elastic–plastic sphere and a rigid flat, simulations with slip rates ranging from 0.1 m/s to 10 m/s were performed. As interfaces with strong interfacial bonding but weak substrate were specifically targeted, slip initiation was treated as shear failure of the softer material in numerical simulations. The simulations show that both sliding friction coefficient and friction stress are significantly dependent on slip rate while the maximum static friction coefficient is independent of that. Moreover, the energy release during the transition from full stick to full slip is comparable to the shear fracture energy of the material.     

Multiple Slips in Atomic-Scale Friction: An Indicator for the Lateral Contact Damping

The occurrence of multiple jumps in 2D atomic-scale friction measurements is used to quantify the viscous damping accompanying the stick–slip motion of a sharp tip in contact with a NaCl(001) surface. Multiple slips are observed without apparent wear for normal forces between 13 and 91 nN. For scans parallel to [100] directions, the tip jumps between minima of the substrate corrugation potential in a zigzag fashion. An algorithm is applied to determine histograms of lateral force jumps which characterize multiple slips. The same algorithm is used to classify multiple slips occurring in calculated lateral force maps. Comparisons between simulations and experiments indicate that the nanometer-sized contact is underdamped at intermediate loads (13–26 nN) and becomes slightly overdamped at higher loads. The proposed procedure is a novel way to estimate the lateral contact damping which plays an important role in the interpretation of measurements of the velocity and temperature dependence of friction, of slip duration, and of the reduction of friction by applied perpendicular or parallel oscillations.     

Stick–slip friction in dissimilar polymer pairs used in automobile interiors

The static and dynamic friction of dissimilar pairs of plastics used in automotive interiors was measured as a function of normal load, system stiffness, and surface roughness. Glass fiber filled polypropylene (FPP) was slid on polycarbonate (PC) and glass fiber filled styrene–maleic–anhydride copolymer (SMAC) in a single pass, unidirectional sliding test. The friction was characterized by the value of static coefficient of friction (COF) and the number of stick–slip cycles during sliding. It was found that the FPP/PC and FPP/SMAC pairs had fewer instances of stick slip than FPP/FPP, PC/PC, and SMAC/SMAC pairs except for one of the SMAC polymers. The surface texture which had the smallest average radius of peak curvature, had the lowest value of static COF. The decrease in the static COF of polypropylene (PP) caused by the addition of glass fiber was most likely caused by the increase in elastic modulus and hardness.     

Computer simulation of sliding hydroxylated alumina surfaces

A molecular dynamics simulation is performed to investigate the frictional force and energy transfer dynamics associated with sliding hydroxylated alumina surfaces. The calculated coefficient of friction is in good agreement with a recent experimental study. The dynamics of energy transfer from the interface of the sliding surface is investigated by calculating the surface–surface intermolecular potential and the energy in surface hydroxyl groups. The simulations indicate the experimental friction force arises from energy relaxation. A transition from stick–slip to smooth sliding is observed as the sliding velocity is increased. This revised version was published online in September 2006 with corrections to the Cover Date.     

Friction-induced vibration and noise generation of instrument panel material pairs

This study investigated the effect of various parameters of the friction–velocity relationship on the friction-induced vibration of simulated instrument panel components. The effect of subsystem stiffness and damping on the system response was also studied. A simple discretized model was utilized with subsystem properties that were intended to realistically model values of low, medium, and high stiffness components. Specifically, the metric of mean squared velocity was used as an indicator of the noise generated during the stick–slip process. It was found that the difference between the static and the asymptotic kinetic value of friction was the most important friction parameter in determining the resulting behavior. As stiffness and damping are increased, the mean squared velocity decreases. Additionally, results from single excursion tests on a variety of instrument panel material pairs showed good correlation between mean squared velocity and the difference in static and kinetic friction.     

A study of fiber-capstan friction. 2. Stick–slip phenomena

A study was made of the friction of nylon fiber (monofilament fishing line) rubbing against spinning aluminum and nylon capstans (cylinders), in the presence of various lubricants. Use of variable speed drives with appropriate gear reducers allowed variation of sliding speed over four orders of magnitude and monitoring of the entire Stribeck curves, from boundary through mixed to hydrodynamic sliding, for these systems. The effects on friction of seven system variables—cylinder material, sliding speed, system elasticity, input tension, lubricant viscosity, lubricant additives and cylinder surface roughness—were investigated. Special attention was given to the effects of elasticity on friction and the character of sliding. Factors which determine the critical speed where stick–slip sliding just appears or disappears are defined.     

Frictional dynamics of perfluorinated self-assembled monolayers on amorphous SiO<Subscript>2</Subscript>

Silicon micromachines in microelectromechanical systems (MEMS) are coated with self-assembled monolayers (SAMs) in order to reduce the wear and stiction that are commonplace during operation. Recently, perfluorinated SAMs have been the focus of attention because they have better processing properties than hydrocarbon SAMs. In this study, we perform molecular dynamics simulations that model adhesive contact and friction for perfluorinated alkylsilane (Si(OH)₃(CF₂)₁₀CF₃) self-assembled monolayers (SAMs), which are commonly used in MEMS devices. Amorphous silica is used as the substrate for the SAMs in the simulations. The frictional behavior is investigated as a function of applied pressure (50 MPa–1 GPa) for a shear velocity of 2 m/s and compared to recent simulation results of hydrocarbon alkylsilane SAMs. The microscopic friction coefficient for the perfluorinated SAMs is the same as was measured for the hydrocarbon SAMs, but the shear stress is slightly larger than in the case of the hydrocarbon SAMs on amorphous silica.     

Stick–slip motion in the atomic force microscope

Measurements of atomic friction in the atomic force microscope frequently show periodic variations at the lattice spacing of the surface being scanned, which have the saw‐tooth wave form characteristic of “stick–slip” motion. Simple models of this behaviour have been proposed, in which the “dynamic element” of the system is provided by the elastic stiffness and inertia of the cantilever which supports the tip of the microscope, in its lateral, i.e., torsional mode of vibration. These models have been successful in predicting the observed motion, but only by assuming that the cantilever is heavily damped. However, the source of this damping in a highly elastic cantilever is not explained. To resolve the paradox, it is shown in this note that it is necessary to introduce the elastic stiffness of the contact into the model. The relationship between the contact stiffness, the cantilever stiffness and the amplitude of the periodic friction force is derived in order for stick–slip motion at lattice spacing to be achieved. This revised version was published online in July 2006 with corrections to the Cover Date.     

A novel long-travel piezoelectric-driven linear nanopositioning stage

This study presents a novel long-travel piezoelectric-driven linear nanopositioning stage capable of operating in either a stepping mode or in a scanning mode. In the stepping mode, the stick–slip friction effect between a linear micropositioner and a sliding stage is used to drive the stage step-by-step through an extended displacement range. The straightness precision of the stage displacement is ensured by running the stage along two high-precision cylindrical guide rails as it moves. The developed linear micropositioner delivers a high amplification of the piezoelectric actuator input and ensures minimum angular deviation. In the scanning mode, the micropositioner acts as an elastic deformation-type linear displacement amplification device and drives the stage through displacements in the micrometer level range. In practical applications, the scanning mode can be utilized to compensate for the final stage positioning error introduced during the stepping motion of the stage. In a series of experiments, a laser interferometer is employed to measure the displacement responses of the stage under the application of input driving voltages with various waveforms. The results demonstrate that in the stepping mode, the stage is capable of performing precision positioning over an extended displacement range in incremental step sizes ranging from 70 nm to 35 μm. Meanwhile, in the scanning mode, the stage can perform a scanning motion over a displacement range of 50 μm with a displacement resolution of less than 10 nm. Finally, it is shown that the high-precision cylindrical guide rails ensure a straightness error of the stage displacement of less than 50 nm within 10 mm motion range.