Thermal effects on atomic friction

Tribological metamaterial: how feathers reduce drag and friction through hidden energy dissipation structures

The lateral moving resistance of a liquid droplet on a solid surface generally increases with velocity and is dominated by the non-viscous wetting line friction. Many superhydrophobic man-made and biological surfaces have minimal, nevertheless speed-sensitive, water droplet friction, limiting their potential to reduce drag at high speeds in natural situations. Using an in situ surface force apparatus, we demonstrated low and remarkably speed-insensitive (over 300-fold) water bridge sliding friction on a goose feather vane. Detailed analyses suggest a dominant, hidden energy dissipation channel probably related to the deformation and elastic recovery of feather's characteristic metamaterial-like structure, which also results in feather's speed insensitive (from 0.1 to 1 mm s-1) ultra-low dry sliding friction coefficient observed in this study (approx. 0.07). The new insights gained have the potential to motivate novel approaches to the design of all-weather and speed-insensitive low-friction surfaces with practical applications in aviation and lubrication technology.

Nonmonotonic Velocity Dependence of Atomic Friction Induced by Multiple Slips

The transition from single to multiple atomic slips, theoretically expected and important in atomic-scale friction, has never been demonstrated experimentally as a function of velocity. Here we show by high-resolution friction force microscopy on monolayer MoS_{2}/Au(111) that multiple slips leave a unique footprint-a frictional velocity weakening. Specifically, in a wide velocity interval from 10 to 100  nm/s, friction surprisingly decreases. Model simulations show a similar nonmonotonic behavior at velocities in quantitative agreement with experiment. Results suggest a velocity-corrugation phase diagram, whose validity is proposed more generally.

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.

Coupling Effect of Structural Lubrication and Thermal Excitation on Phononic Friction

This work investigates the coupling effect of structural lubrication and thermal excitation on phononic friction between black phosphorus (BP) layers. As the rotation angle increases from commensurate to incommensurate states, the friction gradually decreases at any temperature. However, the role of temperature in friction depends on commensurability. For a rotation angle less than 10°, increasing temperature leads to a decrease in friction due to thermal excitation. Conversely, when the rotation angle exceeds 10°, elevated temperature results in an increase in friction due to the effect of thermal collision. At a critical rotation angle of 10°, higher temperatures lead to reduced friction through thermal lubrication at low speeds, and at large speeds, the thermal excitation duration becomes so short that the role of thermal lubrication is weakened, and instead thermal collision dominates. Further research reveals that BP's ability to withstand different maximum speeds is also determined by commensurability. Finally, a method to measure the sliding period length of a rotated tip through an unrotated substrate potential energy topography is proposed and simply verified by using the phonon spectrum.

Reexamination of Damping in Sliding Friction

Friction is responsible for about one-third of the primary energy consumption in the world. So far, a thorough atomistic understanding of the frictional energy dissipation mechanisms is still lacking. The Amontons' law states that kinetic friction is independent of the sliding velocity while the Prandtl-Tomlinson model suggests that damping is proportional to the relative sliding velocity between two contacting objects. Through careful analysis of the energy dissipation process in atomic force microscopy measurements, here we propose that damping force is proportional to the tip oscillation speed induced by friction. It is shown that a physically well-founded damping term can better reproduce the multiple peaks in the velocity-dependent friction force observed in both experiments and molecular dynamics simulations. Importantly, the analysis gives a clear physical picture of the dynamics of energy dissipation in different friction phases, which provides insight into long-standing puzzles in sliding friction, such as velocity weakening and spring-stiffness-dependent friction.

Atomic Friction Processes of Two-Dimensional Materials

In this Perspective, we present the recent advances in atomic friction measured of two-dimensional materials obtained by friction force microscopy. Starting with the atomic-scale stick-slip behavior, a beautiful highly nonequilibrium process, we discuss the main factors that contribute to determine sliding friction between single asperity and a two-dimensional sheet including chemical identity of material, thickness, external load, sliding direction, velocity/temperature, and contact size. In particular, we focus on the latest progress of the more complex friction behavior of moiré systems involving 2D layered materials. The underlying mechanisms of these frictional characteristics observed during the sliding process by theoretical and computational studies are also discussed. Finally, a discussion and outlook on the perspective of this field are provided.

Temperature-Dependent Friction-Induced Surface Amorphization Mechanism of Crystal Silicon

Friction-induced surface amorphization of silicon is one of the most important surface wear and damage forms, changing the material properties and harming the reliability of silicon-based devices. However, knowledge regarding the amorphization mechanisms as well as the effects of temperature is still insufficient, because the experimental measurements of the crystal-amorphous interface structures and evolutions are extremely difficult. In this work, we aim to fully reveal the temperature dependence of silicon amorphization behaviors and relevant mechanisms by using reactive molecular dynamics simulations. We first show that the degree of amorphization is suppressed by the increasing temperature, contrary to our initial expectations. Then, we further revealed that the observed silicon amorphization behaviors are attributed to two independent processes: One is a thermoactivated and shear-driven amorphization process where the theoretical amorphization rate shows an interesting valley-like temperature dependence because of the competition between the increased thermal activation effect and the reduction of shear stress, and another one is a thermoactivated recrystallization process which shows a monotonically increasing trend with temperature. Thus, the observed reduction of amorphization with temperature is mainly due to the recrystallization effect. Additionally, analytical models are proposed in this work to describe both the amorphization and the recrystallization processes. Overall, the present findings provide deep insights into the temperature-dependent amorphization and recrystallization processes of silicon, benefiting the further development of silicon-based devices and technologies.

Transition between the stick and slip states in a simplified model of magnetic friction

We introduce a simplified model of magnetic friction and investigate its behavior using both numerical and analytical methods. When resistance coefficient γ is large, the movement of the system obeys the thermally activated process. In contrast, when γ is sufficiently small, the slip and stick states behave as separate metastable states, and the lattice velocity depends on the probability that the slip state appears. We evaluate the velocities in both cases using several approximations and compare the results with those of numerical simulations.

Phonon mechanism of angle-dependent superlubricity between black phosphorus layers

Based on a combination of molecular dynamics simulations and quantum theories, this study discloses the phonon mechanism of angle-dependent superlubricity between black phosphorus layers. Friction exhibits 180° periodicity, i.e., the highest friction at 0° and 180° and lowest at 90°. Thermal excitation reduces friction at 0° due to thermal lubrication. However, at 90°, high temperature increases friction caused by thermal collision owing to lower interfacial constraints. Phonon spectra reveal that with 0°, energy dissipation channels can be formed at the interface, thus enhancing dissipation efficiency, while the energy dissipation channels are destroyed, thus hindering frictional dissipation at 90°. Besides, for both commensurate and incommensurate cases, more phonons are excited on atoms adjacent to the contact interface than those excited from nonadjacent interface atoms.

Velocity-Dependent Friction of Graphene at Electrical Contact Interfaces

Graphene has enormous potential as a solid lubricant at sliding electrical contact interfaces of micro-/nanoelectromechanical systems that suffer severe wear. Understanding the velocity-dependent friction of graphene under different applied voltages contributes to the application of graphene in sliding electrical contact scenarios. The friction of graphene, measured by conductive atomic force microscopy, under low applied voltage increases logarithmically with sliding velocity─the same as when no voltage is applied but at a faster rate of increase. The variation of friction was explained by the thermally activated Prandtl-Tomlinson model with increased potential barrier and temperature because of the applied voltage. An opposite trend in which friction decreases with sliding velocity is observed under high applied voltage. Topography, adhesion measurements, and SEM characterization demonstrate the wear of the tip. Moreover, the tip wears more severely at low sliding velocity compared to a high sliding velocity. It was interpreted that the excessive Joule heat at the electrical contact interface under high applied voltage weakens the mechanical properties of the tip, resulting in wear and high friction. The increase in the sliding velocity could accelerate the Joule heat transfer and reduce wear and friction. The studies provide beneficial guidelines for the design of graphene-lubricated sliding electrical contact interfaces.

Effect of Amorphous-Crystalline Phase Transition on Superlubric Sliding

Structural superlubricity describes the state of greatly reduced friction between incommensurate atomically flat surfaces. Theory predicts that, in the superlubric state, the remaining friction sensitively depends on the exact structural configuration. In particular the friction of amorphous and crystalline structures for, otherwise, identical interfaces should be markedly different. Here, we measure friction of antimony nanoparticles on graphite as a function of temperature between 300 and 750 K. We observe a characteristic change of friction when passing the amorphous-crystalline phase transition above 420 K, which shows irreversibility upon cooling. The friction data is modeled with a combination of an area scaling law and a Prandtl-Tomlinson type temperature activation. We find that the characteristic scaling factor γ, which is a fingerprint of the structural state of the interface, is reduced by 20% when passing the phase transition. This validates the concept that structural superlubricity is determined by the effectiveness of atomic force canceling processes.

Temperature dependent model for the quasi-static stick-slip process on a soft substrate

The classical Prandtl-Tomlinson model is the most famous and efficient method to describe the stick-slip phenomenon and the resulting friction between a slider and a corrugated substrate. It is widely used in all studies of frictional physics and notably in nanotribology. However, it considers a rigid or undeformable substrate and therefore is hardly applicable for investigating the physics of soft matter and in particular biophysics. For this reason, we introduce here a modified model that is capable of taking into consideration a soft or deformable substrate. It is realized by a sequence of elastically bound quadratic energy wells, which represent the corrugated substrate. We study the quasi-static behavior of the system through the equilibrium statistical mechanics. We thus determine the static friction and the deformation of the substrate as a function of temperature and substrate stiffness. The results are of interest for the study of cell motion in biophysics and for haptic and tactile systems in microtechnology.

Nanoscale Friction across the First-Order Charge Density Wave Phase Transition of 1T-TaS2

Nanotribology using atomic force microscopy (AFM) can be considered as a unique approach to analyze phase transition materials by localized mechanical interaction. In this work, we investigate friction on the lamellar transition metal dichalcogenide 1T-TaS₂, which can undergo first-order charge density wave (CDW) phase transitions. Based on temperature-dependent atomic force microscopy under ultrahigh vacuum conditions (UHV), we can characterize the general friction levels across the first-order phase transitions and for the different phases. While structural and electronic properties for different phases appear to be of minor influence on friction, a distinct peak in friction is observed during the phase transition when cooling the sample from the nearly commensurate CDW (NC-CDW) phase to the commensurate CDW (C-CDW) phase. By performing systematic measurements as a function of load, scan velocity, and scan time, a recently proposed friction mechanism can be corroborated, where the AFM tip gradually induces local transformations of the material close to the spinodal point in a thermally activated and shear-assisted process until the surface is fully "harvested". Our results demonstrate that repeated nanomechanical stress can trigger local first-order phase transitions constituting a so far little explored mechanical energy dissipation channel.

Velocity Dependence of Moiré Friction

Friction force microscopy experiments on moiré superstructures of graphene-coated platinum surfaces demonstrate that in addition to atomic stick-slip dynamics, a new dominant energy dissipation route emerges. The underlying mechanism, revealed by atomistic molecular dynamics simulations, is related to moiré ridge elastic deformations and subsequent relaxation due to the action of the pushing tip. The measured frictional velocity dependence displays two distinct regimes: (i) at low velocities, the friction force is small and nearly constant; and (ii) above some threshold, friction increases logarithmically with velocity. The threshold velocity, separating the two frictional regimes, decreases with increasing normal load and moiré superstructure period. Based on the measurements and simulation results, a phenomenological model is derived, allowing us to calculate friction under a wide range of room temperature experimental conditions (sliding velocities of 1-10⁴ nm/s and a broad range of normal loads) and providing excellent agreement with experimental observations.

Force Dependent Barriers from Analytic Potentials within Elastic Environments

Bond rupture under the action of external forces is usually induced by temperature fluctuations, where the key quantity is the force dependent barrier that needs to be overcome. Using analytic potentials we find that these barriers are fully determined by the dissociation energy and the maximal force the potential can withstand. The barrier shows a simple dependence on these two quantities that allows for a re-interpretation of the Eyring-Zhurkov-Bell length Δ x ‡ and the expressions in theories going beyond that. It is shown that solely elastic environments do not change this barrier in contrast to the predictions of constraint geometry simulate external force (COGEF) strategies. The findings are confirmed by explicit calculations of bond rupture in a polydimethylsiloxane model.

A modified multibond model for nanoscale static friction

Several key features of nanoscale friction phenomena observed in experiments, including the stick-slip to smooth sliding transition and the velocity and temperature dependence of friction, are often described by reduced-order models. The most notable of these are the thermal Prandtl-Tomlinson model and the multibond model. Here we present a modified multibond (mMB) model whereby a physically-based criterion-a critical bond stretch length-is used to describe interfacial bond breaking. The model explicitly incorporates damping in both the cantilever and the contacting materials. Comparison to the Fokker-Planck formalism supports the results of this new model, confirming its ability to capture the relevant physics. Furthermore, the mMB model replicates the near-logarithmic trend of increasing friction with lateral scanning speed seen in many experiments. The model can also be used to probe both correlated and uncorrelated stick slip. Through greater understanding of the effects of damping and noise in the system and the ability to more accurately simulate a system with multiple interaction sites, this model extends the range of frictional systems and phenomena that can be investigated. This article is part of the theme issue 'Nanocracks in nature and industry'.

Will Polycrystalline Platinum Tip Sliding on a Gold(111) Surface Produce Regular Stick-Slip Friction?

Friction measurements by an atomic force microscope (AFM) frequently showed regular stick-slip friction signals with atomic-scale resolutions. Typically, for an AFM metal tip sliding on a metal crystal surface, the microstructure of the tip made from the thermally evaporated metal coating on a silicon cantilever was polycrystalline. Our detailed molecular dynamics(MD) simulations of a polycrystalline Pt tip (R = 10 nm in radius) sliding on an Au(111) surface revealed how the geometry of the polycrystalline tip took effect on the friction behavior at the contact interface. We found that the apex of the Pt tip with multiple grains near the edge of contact could induce severe plastic deformations of the gold substrate, leading to irregular stick-slip frictions upon sliding. Simulation results showed that in order to achieve a clear stick-slip friction signal with single atomic slips, the apex of the Pt tip must adopt a single crystalline protrusion without any neighboring grains involved in the metal contact. We showed that such a single crystalline protrusion, which presumably could be achieved during initial run-in or wear-out of high-energy Pt atoms in the neighboring grains, was passivated by a large number of gold atoms due to metal adhesion in the contact periphery. Using such a crystalline protrusion tip, we demonstrated that the stick-slip friction produced was very "tolerant" to the adhesion of a large number of gold atoms on the tip apex. We further showed that AFM tip mass used in MD simulations also played an important role in determining the transition between friction regimes, which could be well explained by the Prandtl-Tomlinson thermal activation model.

Tuning the interfacial friction force and thermal conductance by altering phonon properties at contact interface

Controlling friction force and thermal conductance at solid/solid interface is of great importance but remains a significant challenge. In this work, we propose a method to control the matching degree of phonon spectra at the interface through modifying the atomic mass of contact materials, thereby regulating the interfacial friction force and thermal conductance. Results of Debye theory and molecular dynamics simulations show that the cutoff frequency of phonon spectrum decreases with increasing atomic mass. Thus, two contact surfaces with equal atomic mass have same vibrational characteristics, so that more phonons could pass through the interface. In these regards, the coupling strength of phonon modes on contact surfaces makes it possible to gain insight into the nonmonotonic variation of interfacial friction force and thermal conductance. Our investigations suggest that the overlap of phonon modes increases energy scattering channels and therefore phonon transmission at the interface, and finally, an enhanced energy dissipation in friction and heat transfer ability at interface.

Thermal Friction Enhancement in Zwitterionic Monolayers

We introduce a model for zwitterionic monolayers and investigate its tribological response to changes in applied load, sliding velocity, and temperature by means of molecular-dynamics simulations. The proposed model exhibits different regimes of motion depending on temperature and sliding velocity. We find a remarkable increase of friction with temperature, which we attribute to the formation and rupture of transient bonds between individual molecules of opposite sliding layers, triggered by the out-of-plane thermal fluctuations of the molecules' orientations. To highlight the effect of the molecular charges, we compare these results with analogous simulations for the charge-free system. These findings are expected to be relevant to nanoscale rheology and tribology experiments of locally-charged lubricated systems such as, e.g., experiments performed on zwitterionic monolayers, phospholipid micelles, or confined polymeric brushes in a surface force apparatus.

100 km wear-free sliding achieved by microscale superlubric graphite/DLC heterojunctions under ambient conditions

Wear-free sliding between two contacted solid surfaces is the ultimate goal in the effort to extend the lifetime of mechanical devices, especially when it comes to inventing new types of micro-electromechanical systems where wear is often a major obstacle. Here we report experimental observations of wear-free sliding for a micrometer-sized graphite flake on a diamond-like-carbon (DLC) surface under ambient conditions with speeds up to 2.5 m/s, and over a distance of 100 km. The coefficient of friction (COF) between the microscale graphite flake, a van der Waals (vdW) layered material and DLC, a non-vdW-layered material, is measured to be of the order of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}${10^{ - 3}}$\end{document}, which belongs to the superlubric regime. Such ultra-low COFs are also demonstrated for a microscale graphite flake sliding on six other kinds of non-vdW-layered materials with sub-nanometer roughness. With a synergistic analysis approach, we reveal the underlying mechanism to be the combination of interfacial vdW interaction, atomic-smooth interfaces and the low normal stiffness of the graphite flake. These features guarantee a persistent full contact of the interface with weak interaction, which contributes to the ultra-low COFs. Together with the extremely high in-plane strength of graphene, wear-free sliding is achieved. Our results broaden the scope of superlubricity and promote its wider application in the future.

Relaxation process of magnetic friction under sudden changes in velocity

Although there have been many studies of statistical mechanical models of magnetic friction, most of these have focused on the behavior in the steady state. In this study, we prepare a system composed of a chain and a lattice of Ising spins that interact with each other, and we investigate the relaxation of the system when the relative velocity v changes suddenly. The situation where v is given is realized by attaching the chain to a spring, the other end of which moves with a constant velocity v. Numerical simulation finds that, when the spring constant has a moderate value, the relaxation of the frictional force is divided into two processes, which are a sudden change and a slow relaxation. This behavior is also observed on regular solid surfaces, although caused by different factors than our model. More specifically, the slow relaxation process is caused by relaxation of the magnetic structure in our model but is caused by creep deformation in regular solid surfaces.

Resonance in Atomic-Scale Sliding Friction

Friction represents a major energy dissipation mode, yet the atomistic mechanism of how friction converts mechanical motion into heat remains elusive. It has been suggested that excess phonons are mainly excited at the washboard frequency, the fundamental frequency at which relative motion excites the interface atoms, and the subsequent thermalization of these nonequilibrium phonons completes the energy dissipation process. Through combined atomic force microscopy measurements and atomistic modeling, here we show that the nonlinear interactions between a sliding tip and the substrate can generate excess phonons at not only the washboard frequency but also its harmonics. These nonequilibrium phonons can induce resonant vibration of the tip and lead to multiple peaks in the friction force as the tip sliding velocity ramps up. These observations disclose previously unrecognized energy dissipation channels associated with tip vibration and provide insights into engineering friction force through adjusting the resonant frequency of the tip-substrate system.

Stochastic thermodynamics of nanoscale friction

Developing the thermodynamics of nanoscale friction is needed in a wide range of tribological applications, where the key objective is to optimally control the energy dissipation. Here we show that modern stochastic thermodynamics allows us to interpret the measurements obtained by friction force microscopy, which is the standard tool for investigating the frictional properties of materials, in terms of basic thermodynamics concepts such as fluctuating work and entropy. We show that this allows the identification of the heat produced during the friction process as an unambiguous measure of thermodynamic irreversibility. We have applied this procedure to quantify the heat produced during the frictional sliding in a broad velocity range, and we observe velocity-dependent scaling behavior, which is useful for interpreting the experimental outcomes.

Polaronic Contributions to Friction in a Manganite Thin Film

Despite the huge importance of friction in regulating movement in all natural and technological processes, the mechanisms underlying dissipation at a sliding contact are still a matter of debate. Attempts to explain the dependence of measured frictional losses at nanoscale contacts on the electronic degrees of freedom of the surrounding materials have so far been controversial. Here, it is proposed that friction can be explained by considering the damping of stick-slip pulses in a sliding contact. Based on friction force microscopy studies of La(1- x )Sr x MnO3 films at the ferromagnetic-metallic to a paramagnetic-polaronic conductor phase transition, it is confirmed that the sliding contact generates thermally-activated slip pulses in the nanoscale contact, and argued that these are damped by direct coupling into the phonon bath. Electron-phonon coupling leads to the formation of Jahn-Teller polarons and to a clear increase in friction in the high-temperature phase. There is neither evidence for direct electronic drag on the atomic force microscope tip nor any indication of contributions from electrostatic forces. This intuitive scenario, that friction is governed by the damping of surface vibrational excitations, provides a basis for reconciling controversies in literature studies as well as suggesting possible tactics for controlling friction.

Negative friction coefficient in microscale graphite/mica layered heterojunctions

The friction of a solid contact typically shows a positive dependence on normal load according to classic friction laws. A few exceptions were recently observed for nanoscale single-asperity contacts. Here, we report the experimental observation of negative friction coefficient in microscale monocrystalline heterojunctions at different temperatures. The results for the interface between graphite and muscovite mica heterojunction demonstrate a robust negative friction coefficient both in loading and unloading processes. Molecular dynamics simulations reveal that the underlying mechanism is a synergetic and nontrivial redistribution of water molecules at the interface, leading to larger density and more ordered structure of the confined subnanometer-thick water film. Our results are expected to be applicable to other hydrophilic van der Waals heterojunctions.

Shear Thinning in the Prandtl Model and Its Relation to Generalized Newtonian Fluids

The Prandtl model is certainly the simplest and most generic microscopic model describing solid friction. It consists of a single, thermalized atom attached to a spring, which is dragged past a sinusoidal potential representing the surface energy corrugation of a counterface. While it was primarily introduced to rationalize how Coulomb’s friction law can arise from small-scale instabilities, Prandtl argued that his model also describes the shear thinning of liquids. Given its success regarding the interpretation of atomic-force-microscopy experiments, surprisingly little attention has been paid to the question how the Prandtl model relates to fluid rheology. Analyzing its Langevin and Brownian dynamics, we show that the Prandtl model produces friction–velocity relationships, which, converted to a dependence of effective (excess) viscosity on shear rate η ( γ ˙ ) , is strikingly similar to the Carreau–Yasuda (CY) relation, which is obeyed by many non-Newtonian liquids. The two dimensionless parameters in the CY relation are found to span a broad range of values. When thermal energy is small compared to the corrugation of the sinusoidal potential, the leading-order γ ˙ 2 corrections to the equilibrium viscosity only matter in the initial part of the cross-over from Stokes friction to the regime, where η obeys approximately a sublinear power law of 1 / γ ˙ .

Single-asperity sliding friction across the superconducting phase transition

In sliding friction, different energy dissipation channels have been proposed, including phonon and electron systems, plastic deformation, and crack formation. However, how energy is coupled into these channels is debated, and especially, the relevance of electronic dissipation remains elusive. Here, we present friction experiments of a single-asperity sliding on a high-T c superconductor from 40 to 300 kelvin. Overall, friction decreases with temperature as generally expected for nanoscale energy dissipation. However, we also find a large peak around T c. We model these results by a superposition of phononic and electronic friction, where the electronic energy dissipation vanishes below T c. In particular, we find that the electronic friction constitutes a constant offset above T c, which vanishes below T c with a power law in agreement with Bardeen-Cooper-Schrieffer theory. While current point contact friction models usually neglect such friction contributions, our study shows that electronic and phononic friction contributions can be of equal size.

Understanding the friction of atomically thin layered materials

Friction is a ubiquitous phenomenon that greatly affects our everyday lives and is responsible for large amounts of energy loss in industrialised societies. Layered materials such as graphene have interesting frictional properties and are often used as (additives to) lubricants to reduce friction and protect against wear. Experimental Atomic Force Microscopy studies and detailed simulations have shown a number of intriguing effects such as frictional strengthening and dependence of friction on the number of layers covering a surface. Here, we propose a simple, fundamental, model for friction on thin sheets. We use our model to explain a variety of seemingly contradictory experimental as well as numerical results. This model can serve as a basis for understanding friction on thin sheets, and opens up new possibilities for ultimately controlling their friction and wear protection.

Despite the fact that layered materials are often employed as lubricants, many of the underlying mechanisms are still controversial. Here the authors present a fundamental model for describing friction on atomically thin sheets that reveals the dynamics of strengthening and layer-number dependence of the friction.

A new methodology for a detailed investigation of quantized friction in ionic liquids

When confined at the nanoscale between smooth surfaces, an ionic liquid forms a structured film responding to shear in a quantized way, i.e., with a friction coefficient indexed by the number of layers in the gap. So far, only a few experiments have been performed to study this phenomenon, because of the delicate nature of the measurements. We propose a new methodology to measure friction with a surface force balance, based on the simultaneous application of normal and lateral motions to the surfaces, allowing for a more precise, comprehensive and rapid determination of the friction response. We report on proof-of-concept experiments with an ionic liquid confined between mica surfaces in dry or wet conditions, showing the phenomenon of quantized friction with an unprecedented resolution. First, we show that the variation of the kinetic friction force with the applied load for a given layer is not linear, but can be quantitatively described by two additive contributions that are respectively proportional to the load and to the contact area. Then, we find that humidity improves the resistance of the layers to be squeezed-out and extends the range of loads in which the liquid behaves as a superlubricant, interpreted by an enhanced dissolution of the potassium ions on the mica leading to a larger surface charge. There, we note a liquid-like friction behavior, and observe in certain conditions a clear variation of the kinetic friction force over two decades of shearing velocities, that does not obey a simple Arrhenius dynamics.

Sliding History-Dependent Adhesion of Nanoscale Silicon Contacts Revealed by in Situ Transmission Electron Microscopy

Nanoscale asperity-on-asperity sliding experiments were conducted using a nanoindentation apparatus inside a transmission electron microscope, allowing for atomic-scale resolution of contact formation, sliding, and adhesive separation of two silicon nanoasperities in real time. The formation and separation of the contacts without sliding revealed adhesion forces often below detectable limits (ca. 5 nN) or at most equal to values expected from van der Waals forces. Lateral sliding during contact by distances ranging from 3.7 μm down to as little as 20 nm resulted in an average 19× increase in the adhesive pull-off force, with increases as large as 32× seen. Adhesion after sliding increased with both the sliding speed and the applied normal contact stress. Unlike cold welding, where irreversible material changes like flow occur, these effects were repeatable and reversible multiple times, for multiple pairs of asperities. We hypothesize that sliding removes passivating surface terminal species, most likely hydrogen or hydroxyl groups, making sites available to form strong covalent bonds across the interface that increase adhesion. Upon separation, repassivation occurs within the experimentally limited lower bound time frame of 5 s, with full recovery of low adhesion. The results demonstrate the strong sliding history-dependence of adhesion, which hinges on the interplay between tribologically induced removal of adsorbed species and repassivation of unsaturated bonds on freshly separated surfaces by dissociative chemisorption.

Integrated QCM-Microtribometry: Friction of Single-Crystal MoS2 and Gold from μm/s to m/s

Two opposing microtribometry approaches have been developed over the past decade to help connect the dots between fundamental and practical tribology measurements: spring-based (e.g., AFM) approaches use low speed, low stiffness, and long relative slip length to quantify friction, while quartz crystal microbalance (QCM)-based approaches use high speed, high stiffness, and short relative slip length. Because the friction forces generated in these experiments are attributed to entirely different phenomena, it is unclear if or how the resulting friction forces are related. This study aims to resolve this uncertainty by integrating these distinct techniques into a single apparatus that allows two independent measurements of friction at a single interface. Alumina microspheres were tested against single-crystal MoS₂, a model nominally wear-free solid lubricant, and gold, a model metal control, at loads between 0.01 and 1 mN. The combined results from both measurement approaches gave friction coefficients (mean ± standard error) of 0.087 ± 0.007 and 0.27 ± 0.02 for alumina-MoS₂ and alumina-gold, respectively. The observed agreement between these methods for two different material systems suggests that friction in microscale contacts can be far less sensitive to external effects from compliance and slip speed than currently thought. Perhaps more importantly, this Article describes and validates a novel approach to closing the "tribology gap" while demonstrating how integration creates new opportunities for fundamental studies of practical friction.

Velocity-dependent friction enhances tribomechanical differences between monolayer and multilayer graphene

The influence of sliding speed in the nanoscale friction forces between a silicon tip and monolayer and multilayer graphene were investigated with the use of an atomic force microscope. We found that the friction forces increase linearly with the logarithm of the sliding speed in a highly layer-dependent way. The increase in friction forces with velocity is amplified at the monolayer. The amplification of the friction forces with velocity results from the introduction of additional corrugation in the interaction potential driven by the tip movement. This effect can be interpreted as a manifestation of local thermally induced surface corrugations in nanoscale influencing the hopping dynamics of the atoms at the contact. These experimental observations were explained by modeling the friction forces with the thermally activated Prandtl-Tomlinson model. The model allowed determination of the interaction potential between tip and graphene, critical forces, and attempt frequencies of slip events. The latter was observed to be dominated by the effective contact stiffness and independent of the number of layers.

Load and Velocity Dependence of Friction Mediated by Dynamics of Interfacial Contacts

Studying the frictional properties of interfaces with dynamic chemical bonds advances understanding of the mechanism underlying rate and state laws, and offers new pathways for the rational control of frictional response. In this work, we revisit the load dependence of interfacial chemical-bond-induced (ICBI) friction experimentally and find that the velocity dependence of friction can be reversed by changing the normal load. We propose a theoretical model, whose analytical solution allows us to interpret the experimental data on timescales and length scales that are relevant to experimental conditions. Our work provides a promising avenue for exploring the dynamics of ICBI friction.

A Langevin equation that governs the irregular stick-slip nano-scale friction

Friction force at the nanoscale, as measured from the lateral deflection of the tip of an atomic force microscope, usually shows a regular stick-slip behavior superimposed by a stochastic part (fluctuations). Previous studies showed the overall fluctuations to be correlated and multi-fractal, and thus not describable simply by e.g. a white noise. In the present study, we investigate whether one can extract an equation to describe nano-friction fluctuations directly from experimental data. Analysing the raw data acquired by a silicon tip scanning the NaCl(001) surface (of lattice constant 5.6 Å) at room temperature and in ultra-high vacuum, we found that the fluctuations possess a Markovian behavior for length scales greater than 0.7 Å. Above this characteristic length, the Kramers-Moyal approach applies. However, the fourth-order KM coefficient turns out to be negligible compared to the second order coefficients, such that the KM expansion reduces to the Langevin equation. The drift and diffusion terms of the Langevin equation show linear and quadratic trends with respect to the fluctuations, respectively. The slope 0.61 ± 0.02 of the drift term, being identical to the Hurst exponent, expresses a degree of correlation among the fluctuations. Moreover, the quadratic trend in the diffusion term causes the scaling exponents to become nonlinear, which indicates multifractality in the fluctuations. These findings propose the practical way to correct the prior models that consider the fluctuations as a white noise.

Plowing-Induced Structuring of Compliant Surfaces

The structures produced by a sharp tip scraping a compliant surface are modeled in the illustrative case of scan patterns formed by a series of parallel lines. This is made possible by a modified version of the Prandtl model for stick-slip friction, with an interaction energy landscape replicating the morphology of the evolving surface. As a result, a ripple motif emerges with a tilt angle increasing linearly with the distance between the scan lines, except for the region close to the left boundary of the scanned area, where the ripples are oriented at 90°. This region can penetrate considerably to the right, forming a complex branched pattern. These predictions are substantiated by atomic force microscopy nanolithography experiments on polystyrene surfaces at room temperature. A simple and robust theoretical protocol for reproducing early-stage wear processes (potentially going beyond single contacts) is thus made available.

Nanotribological Properties of ALD-Made Ultrathin MoS2 Influenced by Film Thickness and Scanning Velocity

Solid lubricating films are usually applied to reduce friction and adhesion of micro-/nano-electromechanical systems (MEMS/NEMS). Due to the special structure, MoS₂ is endowed with excellent lubricity. Layer-controlled ultrathin MoS₂ films with strong interactions to the underlying substrates were prepared by atomic layer deposition (ALD) using MoCl₅ and H₂S and characterized by various measures. Nanotribological properties of the MoS₂ films with different thicknesses were observed by an atomic force microscope tip under various loads. In the initial stage of ALD, bigger roughness induced by discontinuous nanoparticles can increase friction. However, when the number of ALD cycles is more than 3, the friction force can be effectively reduced by about 40-55% because of interlayer sliding and lower adhesion. Finally, friction properties against sliding velocities of the MoS₂ films were also observed. The ultrathin MoS₂ film obtained by ALD exhibits a huge application value as reducing friction surface in MEMS/NEMS.

On the Non-trivial Origin of Atomic-Scale Patterns in Friction Force Microscopy

Friction between two surfaces is due to nano- and micro-asperities at the interface that establish true contact and are responsible for the energy dissipation. To understand the friction mechanism, often single-asperity model experiments are conducted in atomic-force microscopes. Here, we show that the conventional interpretation of the typical results of such experiments, based on a simple mass-spring model, hides a fundamental contradiction. Via an estimate of the order of magnitude of the dissipative forces required to produce atomic-scale patterns in the stick-slip motion of a frictional nano-contact, we find that the energy dissipation must be dominated by a very small, highly dynamic mass at the very end of the asperity. Our conclusion casts new light on the behavior of sliding surfaces and invites us to speculate about new ways to control friction by manipulation of the contact geometry.

What is the origin of macroscopic friction?

What is the origin of molecular friction, and how can macroscopic friction be explained in terms of molecular friction? To elucidate the origins of molecular and macroscopic friction, we conducted density functional theory calculations and double-direct shear tests at normal stresses ranging from 5 to 60 MPa for mica surfaces. Frictional forces between mica surfaces were theoretically predicted to oscillate periodically every 30° of sliding direction, in agreement with previous experimental findings. This result affirms that the potential energy roughness of mica under sliding is the origin of molecular friction, which depends on the normal stress and sliding direction. The discovered mechanism of molecular friction can quantitatively explain experimentally observed macroscopic friction of mica when the presence of wear particles is taken into consideration.

Exploring load, velocity, and surface disorder dependence of friction with one-dimensional and two-dimensional models

The effect of surface disorder, load, and velocity on friction between a single asperity contact and a model surface is explored with one-dimensional and two-dimensional Prandtl-Tomlinson (PT) models. We show that there are fundamental physical differences between the predictions of one-dimensional and two-dimensional models. The one-dimensional model estimates a monotonic increase in friction and energy dissipation with load, velocity, and surface disorder. However, a two-dimensional PT model, which is expected to approximate a tip-sample system more realistically, reveals a non-monotonic trend, i.e. friction is inert to surface disorder and roughness in wearless friction regime. The two-dimensional model discloses that the surface disorder starts to dominate the friction and energy dissipation when the tip and the sample interact predominantly deep into the repulsive regime. Our numerical calculations address that tracking the minimum energy path and the slip-stick motion are two competing effects that determine the load, velocity, and surface disorder dependence of friction. In the two-dimensional model, the single asperity can follow the minimum energy path in wearless regime; however, with increasing load and sliding velocity, the slip-stick movement dominates the dynamic motion and results in an increase in friction by impeding tracing the minimum energy path. Contrary to the two-dimensional model, when the one-dimensional PT model is employed, the single asperity cannot escape to the minimum energy minimum due to constraint motion and reveals only a trivial dependence of friction on load, velocity, and surface disorder. Our computational analyses clarify the physical differences between the predictions of the one-dimensional and two-dimensional models and open new avenues for disordered surfaces for low energy dissipation applications in wearless friction regime.

Friction Determination by Atomic Force Microscopy in Field of Biochemical Science

Atomic force microscopy (AFM) is an analytical nanotechnology in friction determination between microscale and nanoscale surfaces. AFM has advantages in mechanical measurement, including high sensitivity, resolution, accuracy, and simplicity of operation. This paper will introduce the principles of mechanical measurement by using AFM and reviewing the progress of AFM methods in determining frictions in the field of biochemical science over the past decade. While three friction measurement assays-friction morphology, friction curve and friction process in experimental cases-are mainly introduced, important advances of technology, facilitating future development of AFM are also discussed. In addition to the principles and advances, the authors also give an overview of the shortcomings and restrictions of current AFM methods, and propose potential directions of AFM techniques by combining it with other well-established characterization techniques. AFM methods are expected to see an increase in development and attract wide attention in scientific research.

Sliding states of a soft-colloid cluster crystal: Cluster versus single-particle hopping

We study a two-dimensional model for interacting colloidal particles which displays spontaneous clustering. Within this model we investigate the competition between the pinning to a periodic corrugation potential and a sideways constant pulling force which would promote a sliding state. For a few sample particle densities and amplitudes of the periodic corrugation potential we investigate the depinning from the statically pinned to the dynamically sliding regime. This sliding state exhibits the competition between a dynamics where entire clusters are pulled from a minimum to the next and a dynamics where single colloids or smaller groups leave a cluster and move across the corrugation energy barrier to join the next cluster downstream in the force direction. Both kinds of sliding states can occur either coherently across the entire sample or asynchronously: the two regimes result in different average mobilities. Finite temperature tends to destroy separate sliding regimes, generating a smoother dependence of the mobility on the driving force.

Frictional lubricity enhanced by quantum mechanics

The quantum motion of nuclei, generally ignored in the physics of sliding friction, can affect in an important manner the frictional dissipation of a light particle forced to slide in an optical lattice. The density matrix-calculated evolution of the quantum version of the basic Prandtl-Tomlinson model, describing the dragging by an external force of a point particle in a periodic potential, shows that purely classical friction predictions can be very wrong. The strongest quantum effect occurs not for weak but for strong periodic potentials, where barriers are high but energy levels in each well are discrete, and resonant Rabi or Landau-Zener tunneling to states in the nearest well can preempt classical stick-slip with nonnegligible efficiency, depending on the forcing speed. The resulting permeation of otherwise unsurmountable barriers is predicted to cause quantum lubricity, a phenomenon which we expect should be observable in the recently implemented sliding cold ion experiments.

Interface bonding in silicon oxide nanocontacts: interaction potentials and force measurements

The interface bonding between two silicon-oxide nanoscale surfaces has been studied as a function of atomic nature and size of contacting asperities. The binding forces obtained using various interaction potentials are compared with experimental force curves measured in vacuum with an atomic force microscope. In the limit of small nanocontacts (typically <10³ nm²) measured with sensitive probes the bonding is found to be influenced by thermal-induced fluctuations. Using interface interactions described by Morse, embedded atom model, or Lennard-Jones potential within reaction rate theory, we investigate three bonding types of covalent and van der Waals nature. The comparison of numerical and experimental results reveals that a Lennard-Jones-like potential originating from van der Waals interactions captures the binding characteristics of dry silicon oxide nanocontacts, and likely of other nanoscale materials adsorbed on silicon oxide surfaces. The analyses reveal the importance of the dispersive surface energy and of the effective contact area which is altered by stretching speeds. The mean unbinding force is found to decrease as the contact spends time in the attractive regime. This contact weakening is featured by a negative aging coefficient which broadens and shifts the thermal-induced force distribution at low stretching speeds.

Estimation of interaction energy and contact stiffness in atomic-scale sliding on a model sodium chloride surface in ethanol

Friction force microscopy (FFM) in aqueous environments has recently proven to be a very effective method for lattice-resolution imaging of crystal surfaces. Here we demonstrate the use of ethanol for similar measurements on water-soluble materials. Lattice resolved frictional stick-slip traces of a cleaved NaCl(100) surface submerged in ethanol are compared with previous obtained FFM results in ultrahigh vacuum (UHV). We use the Prandtl-Tomlinson framework to estimate the amplitude of the corrugation potential and the contact stiffness. The surface potential amplitude scales with the applied normal loads are in good agreement with data obtained for NaCl measured under UHV conditions, but demonstrates deviations from the ideal periodic potential given by the Prandtl-Tomlinson model. An additional finding is that the use of ethanol allows us to explore higher load ranges without detectable evidence of surface wear. The contact stiffness does not vary significantly with the normal load up to 38 nN, while above it a sudden increase by almost one order of magnitude was observed. Comparing this to previous results suggests that considerable atom rearrangements may occur in the contact region, although the (100) surface structure is preserved by ethanol-assisted diffusion of Na and Cl ions.

Dependence of the friction strengthening of graphene on velocity

Graphene shows great potential applications as a solid lubricant in micro- and nanoelectromechanical systems (MEMS/NEMS). An atomic-scale friction strengthening effect in a few initial atomic friction periods usually occurred on few-layer graphene. Here, velocity dependent friction strengthening was observed in atomic-scale frictional behavior of graphene by atomic force microscopy (AFM). The degree of the friction strengthening decreases with the increase of velocity first and then reaches a plateau. This could be attributed to the interaction potential between the tip and graphene at high velocity which is weaker than that at low velocity, because the strong tip-graphene contact interface needs a longer time to evolve. The subatomic-scale stick-slip behavior in the conventional stick-slip motion supports the weak interaction between the tip and graphene at high velocity. These findings can provide a deeper understanding of the atomic-scale friction mechanism of graphene and other two-dimensional materials.

Stick-Slip Instabilities for Interfacial Chemical Bond-Induced Friction at the Nanoscale

Earthquakes are generally caused by unstable stick-slip motion of faults. This stick-slip phenomenon, along with other frictional properties of materials at the macroscale, is well-described by empirical rate and state friction (RSF) laws. Here we study stick-slip behavior for nanoscale single-asperity silica-silica contacts in atomic force microscopy experiments. The stick-slip is quasiperiodic, and both the amplitude and spatial period of stick-slip increase with normal load and decrease with the loading point (i.e., scanning) velocity. The peak force prior to each slip increases with the temporal period logarithmically, and decreases with velocity logarithmically, consistent with stick-slip behavior at the macroscale. However, unlike macroscale behavior, the minimum force after each slip is independent of velocity. The temporal period scales with velocity in a nearly power law fashion with an exponent between -1 and -2, similar to macroscale behavior. With increasing velocity, stick-slip behavior transitions into steady sliding. In the transition regime between stick-slip and smooth sliding, some slip events exhibit only partial force drops. The results are interpreted in the context of interfacial chemical bond formation and rate effects previously identified for nanoscale contacts. These results contribute to a physical picture of interfacial chemical bond-induced stick-slip, and further establish RSF laws at the nanoscale.

Dependence of the sliding distance of a one-dimensional atom chain on initial velocity

In our daily lives, a body with a high initial velocity sliding freely on a rough surface moves a longer distance than that with a low initial velocity. However, such a phenomenon may not occur in the microscopic world. The dynamical behavior of a one-dimensional atom chain (1DAC) sliding on a substrate is investigated in this study by using a modified Frenkel–Kontorova model, in which the vibration of atoms on the substrate is considered. The dependence of sliding distance on initial velocity is examined. Result shows that although sliding distance is proportional to the initial value for most velocities, such a linear relation does not exist in some special velocities. This phenomenon is explained by a theoretical analysis of phonon excitation. The physical process is divided into three stages. The first stage is a superlubric sliding process with small amplitude of the vibrication of the atoms. The single-mode phonon is excited in the second stage. In the third stage, the system exhibits instability because of multiple-mode phonon excitations. In addition, the dependence of the coupling strength between 1DAC and the substrate is investigated. The findings are helpful in understanding the energy dissipation mechanism of friction.

Velocity dependence of sliding friction on a crystalline surface

We introduce and study a minimal 1D model for the simulation of dynamic friction and dissipation at the atomic scale. This model consists of a point mass (slider) that moves over and interacts weakly with a linear chain of particles interconnected by springs, representing a crystalline substrate. This interaction converts a part of the kinetic energy of the slider into phonon waves in the substrate. As a result, the slider experiences a friction force. As a function of the slider speed, we observe dissipation peaks at specific values of the slider speed, whose nature we understand by means of a Fourier analysis of the excited phonon modes. By relating the phonon phase velocities with the slider velocity, we obtain an equation whose solutions predict which phonons are being excited by the slider moving at a given speed.

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.

Multibond Model of Single-Asperity Tribochemical Wear at the Nanoscale

Single-asperity wear experiments and simulations have identified different regimes of wear including Eyring- and Archard-like behaviors. A multibond dynamics model has been developed based on the friction model of Filippov et al. [Phys. Rev. Lett. 92, 135503 (2004)]. This new model captures both qualitatively distinct regimes of single-asperity wear under a unified theoretical framework. In this model, the interfacial bond formation, wearless rupture, and transfer of atoms are governed by three competing thermally activated processes. The Eyring regime holds under the conditions of low load and low adhesive forces; few bonds form between the asperity and the surface, and wear is a rare and rate-dependent event. As the normal stress increases, the Eyring behavior of wear rate breaks down. A nearly rate-independent regime arises under high load or high adhesive forces, in which wear becomes very nearly, but not precisely, proportional to sliding distance. In this restricted regime, the dependence of wear rate per unit contact area is nearly independent of the normal stress at the point of contact. In true contact between rough elastic surfaces, where contact area is expected to grow linearly with normal load, this would lead to behavior very similar to that described by the Archard equation. Detailed comparisons to experimental and molecular dynamics simulation investigations illustrate both Eyring and Archard regimes, and an intermediate crossover regime between the two.