Dynamics of atomic stick-slip friction examined with atomic force microscopy and atomistic simulations at overlapping speeds

The Evolution of Nanoscale Third Body Layer Revealed by Graphite Structural Superlubric Contact

Revealing the evolution of nanoscale third bodies confined between sliding surfaces is essential to understanding the friction and electrical properties for solid contacts. Here, with graphite/graphite contacts in structural superlubricity, a state of no wear and ultralow friction, we in situ reveal the morphological evolution of a third body layer introduced by air through measuring friction and conductance during cyclic hold-slide tests. The directional transport of confined molecules causes apparent elastic deformation of the third body layer, leading to local graphite/graphite direct contact. Together with a proposed quantum tunneling effective thickness (deff) model, a constant volume of third bodies with a sub-nm thickness is observed. Our work provides a feasible approach to investigate the kinetics of substances under nanoscale confinement.

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.

Effects of -H and -OH Termination on Adhesion of Si-Si Contacts Examined Using Molecular Dynamics and Density Functional Theory

The contact between nanoscale single-crystal silicon asperities and substrates terminated with -H and -OH functional groups is simulated using reactive molecular dynamics (MD). Consistent with previous MD simulations for self-mated surfaces with -H terminations only, adhesion is found to be low at full adsorbate coverages, be it self-mated coverages of mixtures of -H and -OH groups, or just -OH groups. As the coverage reduces, adhesion increases markedly, by factors of ∼5 and ∼6 for -H-terminated surfaces and -OH-terminated surfaces, respectively, and is due to the formation of covalent Si-Si bonds; for -OH-terminated surfaces, some interfacial Si-O-Si bonds are also formed. Thus, covalent linkages need to be broken upon separation of the tip and substrate. In contrast, replacing -H groups with -OH groups while maintaining complete coverage leads to negligible increases in adhesion. This indicates that increases in adhesion require unsaturated sites. Furthermore, plane-wave density functional theory (DFT) calculations were performed to investigate the energetics of two Si(111) surfaces fully terminated by either -H or -OH groups. Importantly for the adhesion results, both DFT and MD calculations predict the correct trends for the relative bond strengths: Si-O > Si-H > Si-Si. This work supports the contention that prior experimental work observing strong increases in adhesion after sliding Si-Si nanoasperities over each other is due to sliding-induced removal of passivating species on the Si surfaces.

Atomic Defect Quantification by Lateral Force Microscopy

Atomic defects in two-dimensional (2D) materials impact electronic and optoelectronic properties, such as doping and single photon emission. An understanding of defect-property relationships is essential for optimizing material performance. However, progress in understanding these critical relationships is hindered by a lack of straightforward approaches for accurate, precise, and reliable defect quantification on the nanoscale, especially for insulating materials. Here, we demonstrate that lateral force microscopy (LFM), a mechanical technique, can observe atomic defects in semiconducting and insulating 2D materials under ambient conditions. We first improve the sensitivity of LFM through consideration of cantilever mechanics. With the improved sensitivity, we use LFM to locate atomic-scale point defects on the surface of bulk MoSe2. By directly comparing LFM and conductive atomic force microscopy (CAFM) measurements on bulk MoSe2, we demonstrate that point defects observed with LFM are atomic defects in the crystal. As a mechanical technique, LFM does not require a conductive pathway, which allows defect characterization on insulating materials, such as hexagonal boron nitride (hBN). We demonstrate the ability to observe intrinsic defects in hBN and defects introduced by annealing. Our demonstration of LFM as a mechanical defect characterization technique applicable to both conductive and insulating 2D materials will enable routine defect-property determination and accelerate materials research.

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.

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.

Stiffness and Atomic-Scale Friction in Superlubricant MoS2 Bilayers

Molecular dynamics simulations, performed with chemically accurate ab initio machine-learning force fields, are used to demonstrate that layer stiffness has profound effects on the superlubricant state of two-dimensional van der Waals heterostructures. We engineer bilayers of different rigidity but identical interlayer sliding energy surface and show that a 2-fold increase in the intralayer stiffness reduces the friction by a factor of ∼6. Two sliding regimes as a function of the sliding velocity are found. At a low velocity, the heat generated by the motion is efficiently exchanged between the layers and the friction is independent of the layer order. In contrast, at a high velocity, the friction heat flux cannot be exchanged fast enough and a buildup of significant temperature gradients between the layers is observed. In this situation, the temperature profile depends on whether the slider is softer than the substrate.

On the Friction Behavior of SiO2 Tip Sliding on the Au(111) Surface: How Does an Amorphous SiO2 Tip Produce Regular Stick-Slip Friction and Friction Duality?

Friction behaviors of an amorphous SiO₂ tip sliding on the Au(111) surface in atomic force microscopy (AFM) are investigated through molecular dynamics (MD) simulations. We observed a regime of extremely low, close-to-zero friction at low normal loads with clear stick-slip friction signals. The friction is almost independent of the applied normal load below a threshold value. However, above this loading threshold, friction can remain low or increase sharply. Such an unexpected friction duality is attributed to the high probability of defect formation at the sliding interface that can induce plowing friction in a high-friction state. The energy difference between the low-friction state and the high-friction state is surprisingly low, which is comparable to kT (∼25 meV) at room temperature. These findings are consistent with previous AFM friction measurements using silicon AFM tips. Further MD simulations show that one can always use an amorphous SiO₂ tip to image the crystalline surface with regular stick-slip friction signals. This is largely due to the fact that there is always a small fraction of contacting Si and O atoms at the sliding interface that are sitting on the relatively stable, close-to-hollow sites of the crystalline Au(111) surface during the stick stage; thus, they are capable of sampling local energy minima. We anticipate that regular stick-slip friction can be achieved even in the intermediate loading range, so long as the low-friction state is maintained when friction duality occurs.

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'.

Electrotunable friction with ionic liquid lubricants

Room-temperature ionic liquids and their mixtures with organic solvents as lubricants open a route to control lubricity at the nanoscale via electrical polarization of the sliding surfaces. Electronanotribology is an emerging field that has a potential to realize in situ control of friction-that is, turning the friction on and off on demand. However, fulfilling its promise needs more research. Here we provide an overview of this emerging research area, from its birth to the current state, reviewing the main achievements in non-equilibrium molecular dynamics simulations and experiments using atomic force microscopes and surface force apparatus. We also present a discussion of the challenges that need to be solved for future applications of electrotunable friction.

Atomic-scale friction between single-asperity contacts unveiled through in situ transmission electron microscopy

Friction and wear are detrimental to functionality and reduce the service life of products with mechanical elements. Here, we unveil the atomic-scale friction of a single tungsten asperity in real time through a high-resolution transmission electron microscopy investigation of a nanocontact in countermotion, induced through a piezo actuator. Molecular dynamics simulations provide insights into the sliding pathway of interface atoms and the dynamic strain/stress evolution at the interface. We observe a discrete stick-slip behaviour and an asynchronous process for the accumulation and dissipation of the strain energy together with the non-uniform motion of interface atoms. Our methodology allows for studying in situ atomic-friction phenomena and provides insights into friction phenomena at the atomic scale.

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.

Dual-Scale Stick-Slip Friction on Graphene/h-BN Moiré Superlattice Structure

Using atomic force microscopy, we have shown that friction on graphene/h-BN superlattice structures may exhibit unusual moiré-scale stick slip in addition to the regular ones observed at the atomic scale. Such dual-scale slip instability will lead to unique length-scale dependent energy dissipation when the different slip mechanisms are sequentially activated. Assisted by an improved theoretical model and comparative experiments, we find that accumulation and unstable release of the in-plane strain of the graphene layer is the key mechanism underlying the moiré-scale behavior. This work highlights the distinct role of the internal state of the van der Waals interfaces in determining the rich dynamics and energy dissipation of layer-structured materials.

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.

100 MHz large bandwidth preamplifier and record-breaking 50 kHz scanning rate quantum point contact mode probe microscopy imaging with atomic resolution

The high-bandwidth preamplifier is a vital component designed to increase the scanning speed of a high-speed scanning tunneling microscope (STM). However, the bandwidth is limited not only by the characteristic GΩ feedback resistor R_F but also by the characteristic unity-gain-stable operational amplifier (UGS-OPA) in the STM preamplifier. Here, we report that paralleling a resistor with the tunneling junction (PRTJ) can break both limitations. Then, the UGS-OPA can be replaced by a higher rate, higher antinoise ability, decompensated OPA. By doing so, a bandwidth of more than 100 MHz was achieved in the STM preamplifier with decompensated OPA657, and a higher bandwidth is possible. High-clarity atomic resolution STM images were obtained under about 10 MHz bandwidth and quantum point contact microscopy mode with a record-breaking line rate of 50 k lines/s and a record-breaking frame rate of 250 frames/s. Both the PRTJ method and the decompensated OPA will pave the way for higher scanning speeds and play a key role in the design of high-performance STMs.

Phonon dissipation in friction with commensurate-incommensurate transition between graphene membranes

To examine phonon transport during the friction process of commensurate-incommensurate transition, the vibrational density of states of contact surfaces is calculated based on molecular dynamics simulations. The results indicate that, compared with the static state, the relative sliding of the contact surfaces causes a blue shift in the interfacial phonon spectrum in or close to commensurate contact, whereas the contrast of the phonon spectrum in incommensurate contact is almost indiscernible. Further findings suggest that the cause of friction can be attributed to the excitation of new in-plane acoustic modes, which provide the most efficient energy dissipation channels in the friction process. In addition, when the tip and the substrate are subjected to a same biaxial compressive/tensile strain, fewer new acoustic modes are excited than in the no strain case. Thus, the friction can be controlled by applying in-plane strain even in commensurate contact. The contribution of the excited acoustic modes to friction at various frequency bands is also calculated, which provides theoretical guidance for controlling friction by adjusting excitation phonon modes.

Friction Modulation via Photoexcitation in Two-Dimensional Materials

We demonstrate a photoexcitation-friction coupling in bilayered black phosphorus, a two-dimensional semiconductor crystallized via van der Waals interaction, using density functional theory and the Prandtl-Tomlinson model. Under an experimentally accessible electron-hole density of 5 × 10¹³ cm^-2, the energy barrier for interlayer sliding can be reduced by 13% and the resultant reduction of critical force for stick-slip transition can be up to 4.7%. With the carrier density being doubled, the frictional anisotropy can even be eliminated. Analysis based on Born-Oppenheimer approximation shows that photoexcitation-friction coupling can be universal for van der Waals crystals with interlayer electronic states responsive to both photoexcitation and interlayer sliding.

Driven Dynamics of Long-Time Bond-Breaking Events

We present a predict-correct trajectory propagation (PCTP) method for simulating nonequilibrium driven dynamics of the long-time bond-breaking event in an atomic force microscope (AFM). Whereas the parallel replica method can extend the time scale of molecular dynamics (MD) simulations of infrequent-event systems with high parallel efficiency, the second aspect of the time scale difficulty in MD simulations for slow-driven systems, namely, the unphysically high attempt frequency of an infrequent event, cannot be resolved by this method. Here, we take a gold nanojunction under mechanical pulling as a simulation system and demonstrate that the PCTP simulation is capable of capturing key transition dynamics of bond breaking predicted by accurate MD simulations in the activationless regime, such as at cryogenic temperature with high pulling rates. The PCTP algorithm includes three steps: (i) the trajectory prediction of the AFM tip, (ii) the atomic structural relaxation of the nanojunction, and (iii) the trajectory correction of the tip motion predicted by step (i). Application of the PCTP simulation to the bond breaking at AFM experimental pulling rates reveals different rupture mechanisms, depending on temperature and single-atom nanojunction structures, which are consistent with recent AFM bond-breaking observations.

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.

Probing the Self-Assembly and Nonlinear Friction Behavior of Confined Gold Nano-Particles

For the wide application of nanoparticles (NPs) (e.g., in nanotribology), it is of fundamental and practical importance to understand the self-assembly and lubrication behavior of confined NPs. In this work, a systematic study was conducted to probe the assembly and associated surface forces of spherical gold nanoparticles (Au NPs, diameter ∼5 nm) confined between pairs of mica (negatively charged) and (3-aminopropyl)triethoxysilane modified mica (APTES-mica, positively charged) surfaces using a surface forces apparatus (SFA) under aqueous conditions. It is observed that Au NPs were squeezed out of the confined gap between two mica surfaces during the loading process, resulting from the repulsive electric-double layer force. In contrast, multilayers of Au NPs were confined between two APTES-mica surfaces because of the attractive double-layer force between oppositely charged Au NPs and APTES-mica. Interestingly, the interaction between Au NPs and APTES-mica is stronger than the interactions between Au NPs, resulting in the rearrangement of the confined Au NPs under shearing. Importantly, a large friction coefficient (μ > 0.7) with unexpected nonlinear stick-slip friction was observed when sliding two APTES-mica surfaces with thin layers of Au NPs (∼20 nm) confined in between. The observed stick-slip motion could be explained by the velocity-dependent friction model where a critical shear velocity was required for transiting from stick-slip to smooth sliding. Our study provides useful information on the assembly and interaction forces of confined nanoparticles on charged surfaces, with implications for predicting the behaviors of NPs under confinement in various engineering applications.

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.

Effect of Ambient Chemistry on Friction at the Basal Plane of Graphite

Graphite is widely used as a solid lubricant due to its layered structure, which enables ultralow friction. However, the lubricity of graphite is affected by ambient conditions and previous studies have shown a sharp contrast between frictional behavior in vacuum or dry environments compared to humid air. Here, we studied the effect of organic gaseous species in the environment, specifically comparing the adsorption of phenol and pentanol vapor. Atomic force microscopy experiments and reactive molecular dynamics simulations showed that friction was larger with phenol than with pentanol. The simulation results were analyzed to test multiple hypotheses to explain the friction difference, and it was found that mechanically driven chemical bonding between the tip and phenol molecules plays a critical role. Bonding increases the number of phenol molecules in the contact, which increases the adhesion as well as the number of atoms in registry with the topmost graphene layer acting as a pinning site to resist sliding. The findings of this research provide insight into how the chemistry of the operating environment can affect the frictional behavior of graphite and layered materials more generally.

Covalent Bonding and Atomic-Level Plasticity Increase Adhesion in Silicon-Diamond Nanocontacts

Nanoindentation and sliding experiments using single-crystal silicon atomic force microscope probes in contact with diamond substrates in vacuum were carried out in situ with a transmission electron microscope (TEM). After sliding, the experimentally measured works of adhesion were significantly larger than values estimated for pure van der Waals (vdW) interactions. Furthermore, the works of adhesion increased with both the normal stress and speed during the sliding, indicating that applied stress played a central role in the reactivity of the interface. Complementary molecular dynamics (MD) simulations were used to lend insight into the atomic-level processes that occur during these experiments. Simulations using crystalline silicon tips with varying degrees of roughness and diamond substrates with different amounts of hydrogen termination demonstrated two relevant phenomena. First, covalent bonds formed across the interface, where the number of bonds formed was affected by the hydrogen termination of the substrate, the tip roughness, the applied stress, and the stochastic nature of bond formation. Second, for initially rough tips, the sliding motion and the associated application of shear stress produced an increase in irreversible atomic-scale plasticity that tended to smoothen the tips' surfaces, which resulted in a concomitant increase in adhesion. In contrast, for initially smooth tips, sliding roughened some of these tips. In the limit of low applied stress, the experimentally determined works of adhesion match the intrinsic (van der Waals) work of adhesion for an atomically smooth silicon-diamond interface obtained from MD simulations. The results provide mechanistic interpretations of sliding-induced changes and interfacial adhesion and may help inform applications involving adhesive interfaces that are subject to applied shear forces and displacements.

Origin of Nanoscale Friction Contrast between Supported Graphene, MoS2, and a Graphene/MoS2 Heterostructure

Ultralow friction can be achieved with 2D materials, particularly graphene and MoS₂. The nanotribological properties of these different 2D materials have been measured in previous atomic force microscope (AFM) experiments sequentially, precluding immediate and direct comparison of their frictional behavior. Here, friction is characterized at the nanoscale using AFM experiments with the same tip sliding over graphene, MoS₂, and a graphene/MoS₂ heterostructure in a single measurement, repeated hundreds of times, and also measured with a slowly varying normal force. The same material systems are simulated using molecular dynamics (MD) and analyzed using density functional theory (DFT) calculations. In both experiments and MD simulations, graphene consistently exhibits lower friction than the MoS₂ monolayer and the heterostructure. In some cases, friction on the heterostructure is lower than that on the MoS₂ monolayer. Quasi-static MD simulations and DFT calculations show that the origin of the friction contrast is the difference in energy barriers for a tip sliding across each of the three surfaces.

Memory Distance for Interfacial Chemical Bond-Induced Friction at the Nanoscale

Macroscale rate and state friction (RSF) laws include a memory distance, D_c, which is considered to be the distance required for a population of frictional contacts to renew itself via slip, counteracting the effects of aging in slow or static contact. This concept connects static friction and kinetic friction. Here, we use atomic force microscopy to study interfacial chemical bond-induced kinetic friction and the memory distance at the nanoscale for single silica-silica nanocontacts. We observe a logarithmic trend of decreasing friction with sliding velocity (i.e., velocity-weakening) at low velocities and a transition to increasing friction with velocity at higher velocities (i.e., velocity-strengthening). We propose a physically based kinetic model for the nanoscale memory effect, the "activation-passivation loop" model, which accounts for the activation and passivation of chemical reaction sites and the formation of new chemical bonds from dangling bonds during sliding. In the model, we define the memory distance to be the average sliding distance that accrues before an activated reaction site becomes passivated. Results from numerical simulations based on this model match experimental friction data well in the velocity-weakening regime and show that D_c is sensitive to the surface chemistry, and nearly independent of sliding velocity. The simulations also show values of D_c that are consistent with those obtained from the experiments. We propose a semiquantitative physical explanation of the observed logarithmic velocity-weakening behavior based on the conservation of the number of interfacial bonds during sliding. We also extract from the experimental data physically reasonable values of the energy barriers to the activation of reaction sites. Our results provide one possible physical mechanism for the nanoscale memory distance.

Operational and environmental conditions regulate the frictional behavior of two-dimensional materials

The friction characteristics of single-layer h-BN, MoS₂, and graphene were systematically investigated via friction force microscopy measurements at various operational (e.g., normal force and sliding speed) and environmental (e.g., relative humidity and thermal annealing) conditions. The low friction characteristics of these single-layer materials were clearly observed from the normal force-dependent friction results, and their interfacial shear strengths were further estimated using a Hertz-plus-offset model. In addition, speed-dependent friction characteristics clearly demonstrated two regimes of friction as a function of sliding speed - the first is the logarithmic increase in friction with sliding speed regime at sliding speeds smaller than the critical speed and the second is the friction plateau regime at sliding speeds greater than the critical speed. Fundamental parameters such as effective shape of the interaction potential and its corrugation amplitude for these single-layer materials were characterized using the thermally-activated Prandtl-Tomlinson model. Moreover, friction of single-layer h-BN, MoS₂, and graphene was found to increase with relative humidity and decrease with thermal annealing; these trends were attributed to the diffusion of water molecules to the interface between the single-layer materials and their substrates, which leads to an increase in the puckering effect at the tip-material interface and interaction potential corrugation. The enhanced puckering effect was verified via molecular dynamics simulations. Overall, the findings enable a comprehensive understanding of friction characteristics for several classes of two-dimensional materials, which is important to elucidate the feasibility of using these materials as protective and solid-lubricant coating layers for nanoscale devices.

Interface Characterization and Control of 2D Materials and Heterostructures

2D materials and heterostructures have attracted significant attention for a variety of nanoelectronic and optoelectronic applications. At the atomically thin limit, the material characteristics and functionalities are dominated by surface chemistry and interface coupling. Therefore, methods for comprehensively characterizing and precisely controlling surfaces and interfaces are required to realize the full technological potential of 2D materials. Here, the surface and interface properties that govern the performance of 2D materials are introduced. Then the experimental approaches that resolve surface and interface phenomena down to the atomic scale, as well as strategies that allow tuning and optimization of interfacial interactions in van der Waals heterostructures, are systematically reviewed. Finally, a future outlook that delineates the remaining challenges and opportunities for 2D material interface characterization and control is presented.

Static and dynamic calibration of torsional spring constants of cantilevers

A method for calibrating the dynamic torsional spring constant of cantilevers by directly measuring the thermally driven motion of the cantilever with an interferometer is presented. Random errors in calibration were made negligible (<1%) by averaging over multiple measurements. The errors in accuracy of ±5% or ±10% for both of the cantilevers calibrated in this study were limited only by the accuracy of the laser Doppler vibrometer (LDV) used to measure thermal fluctuations. This is a significant improvement over commonly used methods that result in large and untraceable errors resulting from assumptions made about the cantilever geometry, material properties, and/or hydrodynamic physics of the surroundings. Subsequently, the static torsional spring constant is determined from its dynamic counterpart after careful LDV measurements of the torsional mode shape, backed by finite element analysis simulations. A meticulously calibrated cantilever is used in a friction force microscopy experiment that measures the friction difference and interfacial shear strength (ISS) between graphene and a silicon dioxide AFM probe. Accurate calibration can resolve discrepancies between different experimental methods, which have contributed to a large scatter in the reported friction and ISS values in the literature to date.

Rate and State Friction Relation for Nanoscale Contacts: Thermally Activated Prandtl-Tomlinson Model with Chemical Aging

Rate and state friction (RSF) laws are widely used empirical relationships that describe macroscale to microscale frictional behavior. They entail a linear combination of the direct effect (the increase of friction with sliding velocity due to the reduced influence of thermal excitations) and the evolution effect (the change in friction with changes in contact "state," such as the real contact area or the degree of interfacial chemical bonds). Recent atomic force microscope (AFM) experiments and simulations found that nanoscale single-asperity amorphous silica-silica contacts exhibit logarithmic aging (increasing friction with time) over several decades of contact time, due to the formation of interfacial chemical bonds. Here we establish a physically based RSF relation for such contacts by combining the thermally activated Prandtl-Tomlinson (PTT) model with an evolution effect based on the physics of chemical aging. This thermally activated Prandtl-Tomlinson model with chemical aging (PTTCA), like the PTT model, uses the loading point velocity for describing the direct effect, not the tip velocity (as in conventional RSF laws). Also, in the PTTCA model, the combination of the evolution and direct effects may be nonlinear. We present AFM data consistent with the PTTCA model whereby in aging tests, for a given hold time, static friction increases with the logarithm of the loading point velocity. Kinetic friction also increases with the logarithm of the loading point velocity at sufficiently high velocities, but at a different increasing rate. The discrepancy between the rates of increase of static and kinetic friction with velocity arises from the fact that appreciable aging during static contact changes the energy landscape. Our approach extends the PTT model, originally used for crystalline substrates, to amorphous materials. It also establishes how conventional RSF laws can be modified for nanoscale single-asperity contacts to provide a physically based friction relation for nanoscale contacts that exhibit chemical bond-induced aging, as well as other aging mechanisms with similar physical characteristics.

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.

Structural Ordering of Molybdenum Disulfide Studied via Reactive Molecular Dynamics Simulations

Molybdenum disulfide (MoS₂) is a well-known and effective lubricant that provides extremely low values of coefficient of friction. It is known that the sliding process may induce structural transformations of amorphous or disordered MoS₂ to the crystalline phase with basal planes oriented parallel to the sliding direction, which is optimal for reducing friction. However, the key reaction parameters and conditions promoting this structural transformation are still largely unknown. We investigate, by employing reactive molecular dynamics simulations, the formation of MoS₂ layers from an amorphous phase as a function of temperature, initial sample density, and sliding velocity. We show that the formation of ordered crystalline structures can be explained in the framework of classical nucleation theory as it predicts the conditions for their nucleation and growth. These results may have important implications in the fields of coating and thin-film deposition, tribology, and in all technological applications where a fast and effective structural transition to an ordered phase is needed.

Development of a ReaxFF Force Field for Cu/S/C/H and Reactive MD Simulations of Methyl Thiolate Decomposition on Cu (100)

It has been shown that the rate of decomposition of methyl thiolate species on copper is accelerated by sliding on a methyl thiolate covered surface in ultrahigh vacuum at room temperature. The reaction produces small gas-phase hydrocarbons and deposits sulfur on the surface. Here, a new ReaxFF potential was developed to enable investigation of the molecular processes that induce this mechanochemical reaction by using density functional theory calculations to tune force field parameters for the model system. Various processes, including volumetric expansion/compression of CuS, CuS₂, and Cu₂S unit cells; bond dissociation of Cu-S and valence angle bending of Cu-S-C; the binding energies of SCH₃, CH₃, and S atoms on a Cu surface; and energy for the decomposition of methyl thiolate molecular species on copper, were used to identify the new ReaxFF parameters. Molecular dynamics simulations of the reactions of adsorbed methyl thiolate species at various temperatures were performed to demonstrate the validity of the new potential and to study the thermal reaction pathways. It was found that reaction is initiated by C-S bond scission, consistent with experiments, and that the resulting methyl species diffuse on the surface and combine to desorb ethane, also as found experimentally.

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.

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.

Multislip Friction with a Single Ion

A trapped ion transported along a periodic potential is studied as a paradigmatic nanocontact frictional interface. The combination of the periodic corrugation potential and a harmonic trapping potential creates a one-dimensional energy landscape with multiple local minima, corresponding to multistable stick-slip friction. We measure the probabilities of slipping to the various minima for various corrugations and transport velocities. The observed probabilities show that the multislip regime can be reached dynamically at smaller corrugations than would be possible statically, and can be described by an equilibrium Boltzmann model. While a clear microscopic signature of multislip behavior is observed for the ion motion, the frictional force and dissipation are only weakly affected by the transition to multistable potentials.

Interfacial assembly structures and nanotribological properties of saccharic acids

The larger friction of the successfully constructed assembly of saccharic acid indicates the higher potential energy barrier at the interface.

Imaging high-speed friction at the nanometer scale

Friction is a complicated phenomenon involving nonlinear dynamics at different length and time scales. Understanding its microscopic origin requires methods for measuring force on nanometer-scale asperities sliding at velocities reaching centimetres per second. Despite enormous advances in experimental technique, this combination of small length scale and high velocity remain elusive. We present a technique for rapidly measuring the frictional forces on a single asperity over a velocity range from zero to several centimetres per second. At each image pixel we obtain the velocity dependence of both conservative and dissipative forces, revealing the transition from stick-slip to smooth sliding friction. We explain measurements on graphite using a modified Prandtl–Tomlinson model, including the damped elastic deformation of the asperity. With its improved force sensitivity and small sliding amplitude, our method enables rapid and detailed surface mapping of the velocity dependence of frictional forces with less than 10 nm spatial resolution.

It has been a challenge to characterize microscopic origins of friction at high velocities. Here authors extend atomic force microscopy to develop a dynamic technique combining force sensitivity and spatial resolution and able to probe, at each image pixel, frictional forces at velocities up to several cm per second.

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.

Stochastic stick-slip nanoscale friction on oxide surfaces

The force needed to move a nanometer-scale contact on various oxide surfaces has been studied using an atomic force microscope and theoretical modeling. Force-distance traces unveil a stick-slip movement with erratic slip events separated by several nanometers. A linear scaling of friction force with normal load along with low pull-off forces reveals dispersive adhesive interactions at the interface. We model our findings by considering a variable Lennard-Jones-like interaction potential, which accounts for slip-induced variation of the effective contact area. The model explains the formation and fluctuation of stick-slip phases and provides guidelines for predicting transitions from stick-slip to continuous sliding on oxide surfaces.

Effects of Water on Tribochemical Wear of Silicon Oxide Interface: Molecular Dynamics (MD) Study with Reactive Force Field (ReaxFF)

Molecular dynamics (MD) simulations with the ReaxFF reactive force field were carried out to find the atomistic mechanisms for tribochemical reactions occurring at the sliding interface of fully hydroxylated amorphous silica and oxidized silicon as a function of interfacial water amount. The ReaxFF-MD simulations showed a significant amount of atom transfers across the interface occurs during the sliding. In the absence of water molecules, the interfacial mixing is initiated by dehydroxylation followed by the Si-O-Si bond formation bridging two solid surfaces. In the presence of submonolayer thick water, the dissociation of water molecules can provide additions reaction pathways to form the Si-O-Si bridge bonds and atom transfers across the interface. However, when the amount of interfacial water molecules is large enough to form a full monolayer, the degree of atom transfer is substantially reduced since the silicon atoms at the sliding interface are terminated with hydroxyl groups rather than forming interfacial Si-O-Si bridge bonds. The ReaxFF-MD simulations clearly showed the role of water molecules in atomic scale mechanochemical processes during the sliding and provided physical insights into tribochemical wear processes of silicon oxide surfaces observed experimentally.