Effect of Interlayer Bonding on Superlubric Sliding of Graphene Contacts: A Machine-Learning Potential Study.

Surface defects and their mutual interactions are anticipated to affect the superlubric sliding of incommensurate layered material interfaces. Atomistic understanding of this phenomenon is limited due to the high computational cost of ab initio simulations and the absence of reliable classical force-fields for molecular dynamics simulations of defected systems. To address this, we present a machine-learning potential (MLP) for bilayer defected graphene, utilizing state-of-the-art graph neural networks trained against many-body dispersion corrected density functional theory calculations under iterative configuration space exploration. The developed MLP is utilized to study the impact of interlayer bonding on the friction of bilayer defected graphene interfaces. While a mild effect on the sliding dynamics of aligned graphene interfaces is observed, the friction coefficients of incommensurate graphene interfaces are found to significantly increase due to interlayer bonding, nearly pushing the system out of the superlubric regime. The methodology utilized herein is of general nature and can be adapted to describe other homogeneous and heterogeneous defected layered material interfaces.

Liquid-Phase Friction of Two-Dimensional Molybdenum Disulfide at the Atomic Scale.

Tribological properties depend strongly on environmental conditions such as temperature, humidity, and operation liquid. However, the origin of the liquid effect on friction remains largely unexplored. Herein, taking molybdenum disulfide (MoS2) as a model system, we explored the nanoscale friction of MoS2 in polar (water) and nonpolar (dodecane) liquids through friction force microscopy. The friction force exhibits a similar layer-dependent behavior in liquids as in air; i.e., thinner samples have a larger friction force. Interestingly, friction is significantly influenced by the polarity of the liquid, and it is larger in polar water than in nonpolar dodecane. Atomically resolved friction images together with atomistic simulations reveal that the polarity of the liquid has a substantial effect on friction behavior, where liquid molecule arrangement and hydrogen-bond formation lead to a higher resistance in polar water in comparison to that in nonpolar dodecane. This work provides insights into the friction on two-dimensional layered materials in liquids and holds great promise for future low-friction technologies.

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'.

Nanoscale Friction Behavior of Transition-Metal Dichalcogenides: Role of the Chalcogenide.

Despite extensive research on the tribological properties of MoS2, the frictional characteristics of other members of the transition-metal dichalcogenide (TMD) family have remained relatively unexplored. To understand the effect of the chalcogen on the tribological behavior of these materials and gain broader general insights into the factors controlling friction at the nanoscale, we compared the friction force behavior for a nanoscale single asperity sliding on MoS2, MoSe2, and MoTe2 in both bulk and monolayer forms through a combination of atomic force microscopy experiments and molecular dynamics simulations. Experiments and simulations showed that, under otherwise identical conditions, MoS2 has the highest friction among these materials and MoTe2 has the lowest. Simulations complemented by theoretical analysis based on the Prandtl-Tomlinson model revealed that the observed friction contrast between the TMDs was attributable to their lattice constants, which differed depending on the chalcogen. While the corrugation amplitudes of the energy landscapes are similar for all three materials, larger lattice constants permit the tip to slide more easily across correspondingly wider saddle points in the potential energy landscape. These results emphasize the critical role of the lattice constant, which can be the determining factor for frictional behavior at the nanoscale.

Steric Effects Control Dry Friction of H- and F-Terminated Carbon Surfaces.

A stable passivation of surface dangling bonds underlies the outstanding friction properties of diamond and diamond-like carbon (DLC) coatings in boundary lubrication. While hydrogen is the simplest termination of a carbon dangling bond, fluorine can also be used as a monoatomic termination, providing an even higher chemical stability. However, whether and under which conditions a substitution of hydrogen with fluorine can be beneficial to friction is still an open question. Moreover, which of the chemical differences between C-H and C-F bonds are responsible for the change in friction has not been unequivocally understood yet. In order to shed light on this problem, we develop a density functional theory-based, nonreactive force field that describes the relevant properties of hydrogen- and fluorine-terminated diamond and DLC tribological interfaces. Molecular dynamics and nudged elastic band simulations reveal that the frictional stress at such interfaces correlates with the corrugation of the contact potential energy, thus ruling out a significant role of the mass of the terminating species on friction. Furthermore, the corrugation of the contact potential energy is almost exclusively determined by steric factors, while electrostatic interactions only play a minor role. In particular, friction between atomically flat diamond surfaces is controlled by the density of terminations, by the C-H and C-F bond lengths, and by the H and F atomic radii. For sliding DLC/DLC interfaces, the intrinsic atomic-scale surface roughness plays an additional role. While surface fluorination decreases the friction of incommensurate diamond contacts, it can negatively affect the friction performance of carbon surfaces that are disordered and not atomically flat. This work provides a general framework to understand the impact of chemical structure of surfaces on friction and to generate design rules for optimally terminated low-friction systems.

Sequential Bending and Twisting around C-C Single Bonds by Mechanical Lifting of a Pre-Adsorbed Polymer.

Bending and twisting around carbon-carbon single bonds are ubiquitous in natural and synthetic polymers. Force-induced changes were so far not measured at the single-monomer level, owing to limited ways to apply local forces. We quantified down to the submolecular level the mechanical response within individual poly-pyrenylene chains upon their detachment from a gold surface with an atomic force microscope at 5 K. Computer simulations based on a dedicated force field reproduce the experimental traces and reveal symmetry-broken bent and rotated conformations of the sliding physisorbed segment besides steric hindrance of the just lifted monomer. Our study also shows that the tip-molecule bond remains intact but remarkably soft and links force variations to complex but well-defined conformational changes.

In-Plane Potential Gradient Induces Low Frictional Energy Dissipation during the Stick-Slip Sliding on the Surfaces of 2D Materials.

Understanding the nanoscale friction properties of 2D materials and further manipulating their friction behaviors is of great significance for the development of various micro/nanodevices. Recent studies, taking advantage of the close relationship between friction and surface charges, use an external out-of-plane electric field to control the interfacial friction. Nevertheless, friction increases with the application of the out-of-plane electric field in most cases. Here, an in-plane potential gradient is applied for the investigation of the contribution of electric charges to friction on the surfaces of 2D materials. Experimental results show that the friction between an atomic force microscope tip and the flakes of 2D materials decreases with the application of the in-plane potential gradient, and the higher the potential gradient, the greater the friction decrease. By comparing the in situ atomic-level stick-slip maps before and after the application of the in-plane potential gradient, it is proposed that the promotion of low friction dissipative motion during the stick-slip process owing to the presence of the potential gradient gives rise to the friction reduction. These results not only help to reveal the origin of friction, but also provide a novel way to manipulate friction through an electrically-controlled sliding process.

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.

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.

Nanoserpents: Graphene Nanoribbon Motion on Two-Dimensional Hexagonal Materials.

We demonstrate snake-like motion of graphene nanoribbons atop graphene and hexagonal boron nitride ( h-BN) substrates using fully atomistic nonequilibrium molecular dynamics simulations. The sliding dynamics of the edge-pulled nanoribbons is found to be determined by the interplay between in-plane ribbon elasticity and interfacial lattice mismatch. This results in an unusual dependence of the friction-force on the ribbon's length, exhibiting an initial linear rise that levels-off above a junction-dependent threshold value dictated by the pre-slip stress distribution within the slider. As part of this letter, we present the LAMMPS implementation of the registry-dependent interlayer potentials for graphene, h-BN, and their heterojunctions that were used herein, which provides enhanced performance and accuracy.

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.

Phononic Origins of Friction in Carbon Nanotube Oscillators.

Phononic coupling can have a significant role in friction between nanoscale surfaces. We find frictional dissipation per atom in carbon nanotube (CNT) oscillators to depend significantly on interface features such as contact area, commensurability, and by end-capping of the inner core. We perform large-scale phonon wavepacket MD simulations to study phonon coupling between a 250 nm long (10,10) outer tube and inner cores of four different geometries. Five different phonon polarizations known to have dominant roles in thermal transport are selected, and transmission coefficient plots for a range of phonon energies along with phonon scattering dynamics at specific energies are obtained. We find that the length of interface affects friction only through LA phonon scattering and has a significant nonlinear effect on total frictional force. Incommensurate contact does not always give rise to superlubricity: the net effect of two competing interaction mechanisms shown by longitudinal and transverse phonons decides the role of commensurability. Capping of the core has no effect on acoustic phonons but destroys the coherence of transverse optical phonons and creates diffusive scattering. In contrast, the twisting and radial breathing phonon modes have perfect transmission at all energies and can be deemed as the enablers of ultralow friction in CNT oscillators. Our work suggests that tuning of interface geometries can give rise to desirable friction properties in nanoscale devices.

Size Dependence of Nanoscale Wear of Silicon Carbide.

Nanoscale, single-asperity wear of single-crystal silicon carbide (sc-SiC) and nanocrystalline silicon carbide (nc-SiC) is investigated using single-crystal diamond nanoindenter tips and nanocrystalline diamond atomic force microscopy (AFM) tips under dry conditions, and the wear behavior is compared to that of single-crystal silicon with both thin and thick native oxide layers. We discovered a transition in the relative wear resistance of the SiC samples compared to that of Si as a function of contact size. With larger nanoindenter tips (tip radius ≈ 370 nm), the wear resistances of both sc-SiC and nc-SiC are higher than that of Si. This result is expected from the Archard's equation because SiC is harder than Si. However, with the smaller AFM tips (tip radius ≈ 20 nm), the wear resistances of sc-SiC and nc-SiC are lower than that of Si, despite the fact that the contact pressures are comparable to those applied with the nanoindenter tips, and the plastic zones are well-developed in both sets of wear experiments. We attribute the decrease in the relative wear resistance of SiC compared to that of Si to a transition from a wear regime dominated by the materials' resistance to plastic deformation (i.e., hardness) to a regime dominated by the materials' resistance to interfacial shear. This conclusion is supported by our AFM studies of wearless friction, which reveal that the interfacial shear strength of SiC is higher than that of Si. The contributions of surface roughness and surface chemistry to differences in interfacial shear strength are also discussed.

Molecular machines operating on the nanoscale: from classical to quantum.

The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation-dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.

Frictional Properties of Nanojunctions Including Atomically Thin Sheets.

Using nonequilibrium molecular dynamics simulations and a coarse-grained description of a system, we have investigated frictional properties of nanojunctions including atomically thin sheets embedded between metal surfaces. We found that the frictional properties of the junctions are determined by the interplay between the lattice mismatch of the contacting surfaces and out-of-plane displacements of the sheet. The simulations provide insight into how and why the frictional characteristics of the nanojunctions are affected by the commensurate-incommensurate transition. We demonstrated that in order to achieve a superlow friction, the graphene sheet should be grown on or transferred to the surface with morphology, which is close to that of the graphene (for instance, Cu), while the second confining surface should be incommensurate with the graphene (e.g., Au). Our results suggest an avenue for controlling nanoscale friction in layered materials and provide insights in the design of heterojunctions for nanomechanical applications.

Friction Force Microscopy Analysis of Self-Adaptive W-S-C Coatings: Nanoscale Friction and Wear.

Transition metal dichalcogenides (TMD) are increasingly popular due to unique structural and mechanical properties. They belong, together with graphene and similar 2D materials, to a small family of solid lubricants with potential to produce ultralow friction state. At the macroscale, low friction stems from the ability to form well-oriented films on the sliding surface (typically up to 10 nm thick), with the TMD basal planes aligned parallel to the surface. In this study, we quantitatively evaluate tribological properties of three sputtered tungsten-sulfur-carbon (W-S-C) coatings at a nanoscale using friction force microscopy. In particular, we investigate possible formation of well-ordered tungsten disulfide (WS2) layers on the coating surface. The coefficient of friction decreased with increasing load independently of coating composition or mechanical properties. In contrast, hard coatings with high tungsten carbide content were more resistant to wear. We successfully identified a WS2 tribolayer at the sliding interface, which peeled off as ultrathin flakes and attached to AFM tip. Nanoscale tribological behavior of WSC coatings replicates deviation of Amonton's law observed in macroscale testing and strongly suggests that the tribolayer is formed almost immediately after the start of sliding.