Dependence of kinetic friction on velocity: master equation approach

Substrate deformability and applied normal force are coupled to change nanoscale friction

Amonton's law of friction states that the friction force is proportional to the normal force in magnitude, and the slope gives a constant friction coefficient. In this work, with molecular dynamics simulation, we study how the kinetic friction at the nanoscale deviates qualitatively from the relation. Our simulation demonstrates that the friction behavior between a nanoscale AFM tip and an elastic graphene surface is regulated by the coupling of the applied normal force and the substrate deformability. First, it is found that the normal load-induced substrate deformation could lower friction at low load while increasing it at high load. In addition, when the applied force exceeds a certain threshold another abrupt change in friction behavior is observed, i.e., the stick-slip friction changes to the paired stick-slip friction. The unexpected change in friction behavior is then ascribed to the change of the microscopic contact states between the two surfaces: the increase in normal force and the substrate deformability together lead to a change in the energy landscape experienced by the tip. Finally, the Prandtl-Tomlinson model also validates that the change in friction behavior can be interpreted in terms of the energy landscape.

Measurement of Frictional Properties of Aortic Stent Grafts and Their Delivery Systems

Stent grafts are medical devices used to treat abdominal aortic aneurysms (AAAs) in endovascular aneurysm repair (EVAR). Computational and experimental models have been developed to study stent graft delivery and deployment during EVAR; however, frictional properties have not been taken into account in most previous studies. The objective of this study was to determine the coefficients of friction of three commercially available stent grafts (Cook Zenith, Medtronic Endurant, and Vascutek Anaconda), their delivery sheaths, a porcine aorta, and two mock arterial materials. Stent grafts were obtained and separated into stents, graft fabric, and sheaths. Using a custom-made friction measurement apparatus, the coefficients of friction were measured between five material pairs: (i) the stents and inner surface of the sheath, (ii) the graft fabric and inner surface of the sheath, (iii) the outer surface of the sheath and a porcine aorta, (iv) the outer surface of the sheath and three different polyvinyl alcohol (PVA) cryogels, and (v) the outer surface of the sheath and a polydimethylsiloxane (PDMS) sheet. The results show that the coefficients of friction between the graft fabric and the sheath were higher than those between the stents and the sheath. The PVA cryogels showed more comparable frictional properties to the porcine aorta than did the PDMS sheet, suggesting that PVA cryogels provide a more accurate approximation for the in vivo frictional properties. These results can be used to improve the accuracy of computational models for stent graft delivery and deployment and to select appropriate materials for vascular phantoms.

Recent highlights in nanoscale and mesoscale friction

Friction is the oldest branch of non-equilibrium condensed matter physics and, at the same time, the least established at the fundamental level. A full understanding and control of friction is increasingly recognized to involve all relevant size and time scales. We review here some recent advances on the research focusing of nano- and mesoscale tribology phenomena. These advances are currently pursued in a multifaceted approach starting from the fundamental atomic-scale friction and mechanical control of specific single-asperity combinations, e.g., nanoclusters on layered materials, then scaling up to the meso/microscale of extended, occasionally lubricated, interfaces and driven trapped optical systems, and eventually up to the macroscale. Currently, this "hot" research field is leading to new technological advances in the area of engineering and materials science.

Contact Dependence and Velocity Crossover in Friction between Microscopic Solid/Solid Contacts

Friction at the nanoscale differs markedly from that between surfaces of macroscopic extent. Characteristically, the velocity dependence of friction between apparent solid/solid contacts can strongly deviate from the classically assumed velocity independence. Here, we show that a nondestructive friction between solid tips with radius on the scale of hundreds of nanometers and solid hydrophobic self-assembled monolayers has a strong velocity dependence. Specifically, using laterally oscillating quartz tuning forks, we observe a linear scaling in the velocity at the lowest accessed velocities, typically hundreds of micrometers per second, crossing over into a logarithmic velocity dependence. This crossover is consistent with a general multicontact friction model that includes thermally activated breaking of the contacts at subnanometric elongation. We find as well a strong dependence of the friction on the dimensions of the frictional probe.

Effect of Surface Charge on the Nanofriction and Its Velocity Dependence in an Electrolyte Based on Lateral Force Microscopy

The nanofriction between a silicon nitride probe and both a silicon wafer and an octadecyltrichlorosilane (OTS)-coated surface is studied in saline solution by using lateral force microscopy (LFM). The effects of surface charge on the nanofriction in an electrolyte as well as its velocity dependence are studied, while the surface charge at the solid-liquid interface is adjusted by changing the pH value of the electrolyte. The results show that the nanofrictional behavior between the probe and the samples in an electrolyte depends strongly on the surface charge at the solid-liquid interface. When the probe and the sample in the electrolyte are charged with the same sign, a repulsive electrostatic interaction between the probe and the sample is produced, leading to a reduction in nanofriction. In contrast, when the two surfaces are charged with the opposite sign, nanofriction is enhanced by the attractive electrostatic interaction between the probe and the sample. The velocity dependence of nanofriction in an electrolyte is believed to be tied to charge regulation referring to a decreasing trend in surface charge densities for the two approaching charged surfaces in an electrolyte. When the probe slides on the sample at a low velocity, charge regulation occurs and weakens the electrostatic interaction between the probe and the sample. As a result, nanofriction is reduced for surfaces charged with the opposite sign, and it is enhanced for surfaces charged with the same sign. When the sliding velocity between the probe and the sample is high, there is insufficient time for charge regulation to occur. Thus, the friction pair shows a larger nanofriction when the surfaces are charged with the opposite sign and a smaller nanofriction when the surfaces are charged with the same sign when compared to the case of a lower sliding velocity.

Effect of Changing Table Tennis Ball Material from Celluloid to Plastic on the Post-Collision Ball Trajectory

The official material used in table tennis balls was changed from celluloid to plastic, a material free of celluloid, in 2014. The purpose of this study was to understand the differences and similarities in the two types of ball materials by comparing their behavior upon collision with a table. The behavior of the balls before and after collision with a table, at various initial speeds ranging from 15 to 115 km/h, was captured using high-speed cameras. Velocities and spin rates before collision and velocities after collision were computed to calculate the coefficients of restitution and friction. Based on the computed variables, the post-collision trajectories of both balls were calculated by integrating the equation of motion of the ball for simulated service, smash and drive conditions with respect to time. The coefficients of restitution were higher for the plastic balls than the celluloid ones when the initial vertical velocities were higher. The coefficients of friction were higher for plastic balls when the initial horizontal contact point velocities were slower. Because of the differences in the material characteristics, the plastic ball trajectories of services with backspin and drives with great topspin were expected to be different from those of celluloid balls. Since the extent of differences between the two ball types varied depending on the initial conditions, testing at various initial conditions was suggested for comparing and understanding the characteristics of the balls.

Determining friction and effective loading for sled sprinting

Understanding the impact of friction in sled sprinting allows the quantification of kinetic outputs and the effective loading experienced by the athlete. This study assessed changes in the coefficient of friction (µ_k) of a sled sprint-training device with changing mass and speed to provide a means of quantifying effective loading for athletes. A common sled equipped with a load cell was towed across an athletics track using a motorised winch under variable sled mass (33.1-99.6 kg) with constant speeds (0.1 and 0.3 m · s^-1), and with constant sled mass (55.6 kg) and varying speeds (0.1-6.0 m · s^-1). Mean force data were analysed, with five trials performed for each condition to assess the reliability of measures. Variables were determined as reliable (ICC > 0.99, CV < 4.3%), with normal-force/friction-force and speed/coefficient of friction relationships well fitted with linear (R² = 0.994-0.995) and quadratic regressions (R² = 0.999), respectively (P < 0.001). The linearity of composite friction values determined at two speeds, and the range in values from the quadratic fit (µ_k = 0.35-0.47) suggested µ_k and effective loading were dependent on instantaneous speed on athletics track surfaces. This research provides a proof-of-concept for the assessment of friction characteristics during sled towing, with a practical example of its application in determining effective loading and sled-sprinting kinetics. The results clarify effects of friction during sled sprinting and improve the accuracy of loading applications in practice and transparency of reporting in research.

Complex tribomechanical characterization of ZnO nanowires: nanomanipulations supported by FEM simulations

In the present work, we demonstrate a novel approach to nanotribological measurements based on the bending manipulation of hexagonal ZnO nanowires (NWs) in an adjustable half-suspended configuration inside a scanning electron microscope. A pick-and-place manipulation technique was used to control the length of the adhered part of each suspended NW. Static and kinetic friction were found by a 'self-sensing' approach based on the strain profile of the elastically bent NW during manipulation and its Young's modulus, which was separately measured in a three-point bending test with an atomic force microscope. The calculation of static friction from the most bent state was completely reconsidered and a novel more realistic crack-based model was proposed. It was demonstrated that, in contrast to assumptions made in previously published models, interfacial stresses in statically bent NW are highly localized and interfacial strength is comparable to the bending strength of NW measured in respective bending tests.

Friction and nonlinear dynamics

The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.

Speed of fast and slow rupture fronts along frictional interfaces

The transition from stick to slip at a dry frictional interface occurs through the breaking of microjunctions between the two contacting surfaces. Typically, interactions between junctions through the bulk lead to rupture fronts propagating from weak and/or highly stressed regions, whose junctions break first. Experiments find rupture fronts ranging from quasistatic fronts, via fronts much slower than elastic wave speeds, to fronts faster than the shear wave speed. The mechanisms behind and selection between these fronts are still imperfectly understood. Here we perform simulations in an elastic two-dimensional spring-block model where the frictional interaction between each interfacial block and the substrate arises from a set of junctions modeled explicitly. We find that material slip speed and rupture front speed are proportional across the full range of front speeds we observe. We revisit a mechanism for slow slip in the model and demonstrate that fast slip and fast fronts have a different, inertial origin. We highlight the long transients in front speed even along homogeneous interfaces, and we study how both the local shear to normal stress ratio and the local strength are involved in the selection of front type and front speed. Last, we introduce an experimentally accessible integrated measure of block slip history, the Gini coefficient, and demonstrate that in the model it is a good predictor of the history-dependent local static friction coefficient of the interface. These results will contribute both to building a physically based classification of the various types of fronts and to identifying the important mechanisms involved in the selection of their propagation speed.

History-dependent friction and slow slip from time-dependent microscopic junction laws studied in a statistical framework

To study how macroscopic friction phenomena originate from microscopic junction laws, we introduce a general statistical framework describing the collective behavior of a large number of individual microjunctions forming a macroscopic frictional interface. Each microjunction can switch in time between two states: a pinned state characterized by a displacement-dependent force and a slipping state characterized by a time-dependent force. Instead of tracking each microjunction individually, the state of the interface is described by two coupled distributions for (i) the stretching of pinned junctions and (ii) the time spent in the slipping state. This framework allows for a whole family of microjunction behavior laws, and we show how it represents an overarching structure for many existing models found in the friction literature. We then use this framework to pinpoint the effects of the time scale that controls the duration of the slipping state. First, we show that the model reproduces a series of friction phenomena already observed experimentally. The macroscopic steady-state friction force is velocity dependent, either monotonic (strengthening or weakening) or nonmonotonic (weakening-strengthening), depending on the microscopic behavior of individual junctions. In addition, slow slip, which has been reported in a wide variety of systems, spontaneously occurs in the model if the friction contribution from junctions in the slipping state is time weakening. Next, we show that the model predicts a nontrivial history dependence of the macroscopic static friction force. In particular, the static friction coefficient at the onset of sliding is shown to increase with increasing deceleration during the final phases of the preceding sliding event. We suggest that this form of history dependence of static friction should be investigated in experiments, and we provide the acceleration range in which this effect is expected to be experimentally observable.