Superlubric Sliding of Graphene Auto-Kirigami with Interfaces Containing Self-Assembled Stripe-Pattern Adsorbates.

Van der Waals heterostructures formed by stacked 2D materials show exceptional electronic, mechanical, and optical properties. Superlubricity, a condition where atomically flat, incommensurate planes of atoms result in ultra-low friction, is a prime example enabling, for example, self-assembly of optically visible graphene nanostructures in air via a sliding auto-kirigami process. Here, it is demonstrated that a subtle but ubiquitous adsorbate stripe structure found on graphene and graphitic surfaces in ambient conditions remains stable within the interface between twisted graphene layers as they slide over each other. Despite this contamination, the interface retains an exceptional superlubricious state with an estimated upper bound frictional shear strength of 10 kPa, indicating that direct atomic incommensurate contact is not required to achieve ambient superlubricity for 2D materials. The results suggest that any phenomena depending on 2D heterostructure interfaces such as exotic electronic behavior may need to consider the presence of stripe adsorbate structures that remain intercalated.

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.

What stress components drive mechanochemistry? A study of ZDDP tribofilm formation.

Zinc dialkyldithiophosphate (ZDDP), the most widely used antiwear additive in engine oils, has been extensively studied over the last few decades to help understand the origin of its effectiveness. Glassy phosphate-based tribofilms, approximately 100 nm thick, are often formed on surfaces sliding in ZDDP-containing oils, which help to prevent or reduce wear. Recent studies reveal that a combination of applied shear and compressive stresses drive mechanochemical reactions that promote tribofilm growth, and that growth is further accelerated by increased temperature. While recent work has shown that compressive stress alone is insufficient to form tribofilms, the individual effects of the shear stress and compressive stress are not fully understood. Here, shear and compressive stresses are studied separately by using different ratios of high-viscosity, high-traction fluids for testing. This allows the areal mean compressive and shear stresses in the fluid when confined at a loaded sliding interface, to be independently controlled while driving tribofilm growth, which is a system we refer to as a stress-controlled mechanochemical reactor. Tribofilms derived from a secondary ZDDP were generated using a tungsten carbide/tungsten carbide ball-on-disk contact in the full elastohydrodynamic lubrication (EHL) regime using a mini-traction machine (MTM), meaning that solid-solid contact is avoided. The MTM was equipped with a spacer layer imaging (SLIM) capability, permitting in situ measurement of the tribofilm thickness during its growth. The well-separated sliding surfaces generated by the high-viscosity fluids confirm that solid-solid contact is not required for tribofilm formation. Under these full fluid film EHL conditions, shear stress and temperature promote tribofilm growth in accordance with stress-augmented thermal activation. In contrast, under constant shear stress and temperature, compressive stress has the opposite effect, inhibiting tribofilm growth. Using the extended Eyring model for shear- and hydrostatic pressure-affected reaction kinetics, an activation energy of 0.54 ± 0.04 eV is found, consistent with prior studies of ZDDPs. The activation volume for shear stress is found to be 0.18 ± 0.06 nm3, while that for the compressive stress component is much smaller, at 0.010 ± 0.004 nm3. This not only confirms prior work supporting that shear stress drives tribofilm growth, but demonstrates and quantifies how compressive stress inhibits growth, consistent with the rate-limiting step in tribofilm growth involving a bond-breaking reaction. Implications of these findings are discussed.

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'.

The evolving quality of frictional contact with graphene.

Graphite and other lamellar materials are used as dry lubricants for macroscale metallic sliding components and high-pressure contacts. It has been shown experimentally that monolayer graphene exhibits higher friction than multilayer graphene and graphite, and that this friction increases with continued sliding, but the mechanism behind this remains subject to debate. It has long been conjectured that the true contact area between two rough bodies controls interfacial friction. The true contact area, defined for example by the number of atoms within the range of interatomic forces, is difficult to visualize directly but characterizes the quantity of contact. However, there is emerging evidence that, for a given pair of materials, the quality of the contact can change, and that this can also strongly affect interfacial friction. Recently, it has been found that the frictional behaviour of two-dimensional materials exhibits traits unlike those of conventional bulk materials. This includes the abovementioned finding that for few-layer two-dimensional materials the static friction force gradually strengthens for a few initial atomic periods before reaching a constant value. Such transient behaviour, and the associated enhancement of steady-state friction, diminishes as the number of two-dimensional layers increases, and was observed only when the two-dimensional material was loosely adhering to a substrate. This layer-dependent transient phenomenon has not been captured by any simulations. Here, using atomistic simulations, we reproduce the experimental observations of layer-dependent friction and transient frictional strengthening on graphene. Atomic force analysis reveals that the evolution of static friction is a manifestation of the natural tendency for thinner and less-constrained graphene to re-adjust its configuration as a direct consequence of its greater flexibility. That is, the tip atoms become more strongly pinned, and show greater synchrony in their stick-slip behaviour. While the quantity of atomic-scale contacts (true contact area) evolves, the quality (in this case, the local pinning state of individual atoms and the overall commensurability) also evolves in frictional sliding on graphene. Moreover, the effects can be tuned by pre-wrinkling. The evolving contact quality is critical for explaining the time-dependent friction of configurationally flexible interfaces.

Friction and Adhesion Govern Yielding of Disordered Nanoparticle Packings: A Multiscale Adhesive Discrete Element Method Study.

Recent studies have demonstrated that amorphous materials, from granular packings to atomic glasses, share multiple striking similarities, including a universal onset strain level for yield. This is despite vast differences in length scales and in the constituent particles' interactions. However, the nature of localized particle rearrangements is not well understood, and how local interactions affect overall performance remains unknown. Here, we introduce a multiscale adhesive discrete element method to simulate recent novel experiments of disordered nanoparticle packings indented and imaged with single nanoparticle resolution. The simulations exhibit multiple behaviors matching the experiments. By directly monitoring spatial rearrangements and interparticle bonding/debonding under the packing's surface, we uncover the mechanisms of the yielding and hardening phenomena observed in experiments. Interparticle friction and adhesion synergistically toughen the packings and retard plastic deformation. Moreover, plasticity can result from bond switching without particle rearrangements. These results furnish insights for understanding yielding in amorphous materials generally.

Hollow Atomic Force Microscopy Cantilevers with Nanoscale Wall Thicknesses.

In atomic force microscopy, the cantilever probe is a critical component whose properties determine the resolution and speed at which images with nanoscale resolution can be obtained. Traditional cantilevers, which have moderate resonant frequencies and high quality factors, have relatively long response times and low bandwidths. In addition, cantilevers can be easily damaged by excessive deformation, and tips can be damaged by wear, requiring them to be replaced frequently. To address these issues, new cantilever probes that have hollow cross-sections and walls of nanoscale thicknesses made of alumina deposited by atomic layer deposition are introduced. It is demonstrated that the probes exhibit spring constants up to ≈100 times lower and bandwidths up to ≈50 times higher in air than their typical solid counterparts, allowing them to react to topography changes more quickly. Moreover, it is shown that the enhanced robustness of the hollow cantilevers enables them to withstand large bending displacements more readily and to be more resistant to tip wear.

Unraveling the Friction Evolution Mechanism of Diamond-Like Carbon Film during Nanoscale Running-In Process toward Superlubricity.

Diamond-like carbon (DLC) films are capable of achieving superlubricity at sliding interfaces by a rapid running-in process. However, fundamental mechanisms governing the friction evolution during this running-in processes remain elusive especially at the nanoscale, which hinders strategic tailoring of tribosystems for minimizing friction and wear. Here, it is revealed that the running-in governing superlubricity of DLC demonstrates two sub-stages in single-asperity nanocontacts. The first stage, mechanical removal of a thin oxide layer, is described quantitatively by a stress-activated Arrhenius model. In the second stage, a large friction decrease occurs due to a structural ordering transformation, with the kinetics well described by the Johnson-Mehl-Avrami-Kolmogorov model with a modified load dependence of the activation energy. The direct observation of a graphitic-layered transfer film formation together with the measured Avrami exponent reveal the primary mechanism of the ordering transformation. The findings provide fundamental insights into friction evolution mechanisms, and design criteria for superlubricity.

Linescan Lattice Microscopy: A Technique for the Accurate Measurement and Mapping of Lattice Spacing and Strain with Atomic Force Microscopy.

Lateral resolution and accuracy in scanning probe microscopies are limited by the nonideality of piezoelectric scanning elements due to phenomena including nonlinearity, hysteresis, and creep. By taking advantage of the well-established atomic-scale stick-slip phenomenon in contact-mode atomic force microscopy, we have developed a method for simultaneously indexing and measuring the spacing of surface atomic lattices using only Fourier analysis of unidirectional linescan data. The first step of the technique is to calibrate the X-piezo response using the stick-slip behavior itself. This permits lateral calibration to better than 1% error between 2.5 nm and 9 µm, without the use of calibration gratings. Lattice indexing and lattice constant determination are demonstrated in this way on the NaCl(001) crystal surface. After piezo calibration, lattice constant measurement on a natural bulk MoS2(0001) surface is demonstrated with better than 0.2% error. This is used to measure nonuniform thermal mismatch strain for chemical vapor deposition (CVD)-grown monolayer MoS2 as small as 0.5%. A spatial mapping technique for the lattice spacing is developed and demonstrated, with absolute accuracy better than 0.2% and relative accuracy better than 0.1%, within a map of 12.5 × 12.5 nm2 pixels using bulk highly oriented pyrolytic graphite (HOPG) and MoS2 as reference materials.

Origin of Friction in Superlubric Graphite Contacts.

More than thirty years ago, it was theoretically predicted that friction for incommensurate contacts between atomically smooth, infinite, crystalline materials (e.g., graphite, MoS_{2}) is vanishing in the low speed limit, and this corresponding state was called structural superlubricity (SSL). However, experimental validation of this prediction has met challenges, since real contacts always have a finite size, and the overall friction arises not only from the atoms located within the contact area, but also from those at the contact edges which can contribute a finite amount of friction even when the incommensurate area does not. Here, we report, using a novel method, the decoupling of these contributions for the first time. The results obtained from nanoscale to microscale incommensurate contacts of graphite under ambient conditions verify that the average frictional contribution of an inner atom is no more than 10^{-4} that of an atom at the edge. Correspondingly, the total friction force is dominated by friction between the contact edges for contacts up to 10 µm in lateral size. We discuss the physical mechanisms of friction observed in SSL contacts, and provide guidelines for the rational design of large-scale SSL contacts.

Linear Aging Behavior at Short Timescales in Nanoscale Contacts.

Nanoscale silica-silica contacts were recently found to exhibit logarithmic aging for times ranging from 0.1 to 100 s, consistent with the macroscopic rate and state friction laws and several other aging processes. Nanoscale aging in this system is attributed to progressive formation of interfacial siloxane bonds between surface silanol groups. However, understanding or even data for contact behavior for aging times <0.1 s, before the onset of logarithmic aging, is limited. Using a combination of atomic force microscopy experiments and kinetic Monte Carlo simulations, we find that aging is nearly linear with aging time at short timescales between ∼ 5 and 90 ms. We demonstrate that aging at these timescales requires the existence of a particular range of reaction energy barriers for interfacial bonding. Specifically, linear aging behavior consistent with experiments requires a narrow peak close to the upper bound of this range of barriers. These new insights into the reaction kinetics of interfacial bonding in nanoscale aging advance the development of physically based rate and state friction laws for nanoscale contacts.

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.

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.

Disordered Nanoparticle Packings under Local Stress Exhibit Avalanche-Like, Environmentally Dependent Plastic Deformation.

Nanoindentation experiments on disordered nanoparticle packings performed both in an atomic force microscope and in situ in a transmission electron microscope are used to investigate the mechanics of plastic deformation. Under an applied load, these highly porous films exhibit load drops, the magnitudes of which are consistent with an exponential population distribution. These load drops are attributed to local rearrangements of a small number of particles, which bear similarities to shear transformation zones and to the T1 process, both of which have been previously predicted for disordered packings. An increase in the relative humidity results in an increase in the number of observed load drops, indicating that the strength of the particle interactions has a significant effect on the modes of plastic deformation. These results suggest how disordered nanoparticle packings may be expected to behave in devices operating under varying environments.

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.

Thermally Induced Structural Evolution of Silicon- and Oxygen-Containing Hydrogenated Amorphous Carbon: A Combined Spectroscopic and Molecular Dynamics Simulation Investigation.

Silicon- and oxygen-containing hydrogenated amorphous carbon (a-C:H:Si:O) coatings are amorphous thin-film materials composed of hydrogenated amorphous carbon (a-C:H), doped with silicon and oxygen. Compared to a-C:H, a-C:H:Si:O exhibits much lower susceptibility to oxidative degradation and higher thermal stability, making a-C:H:Si:O attractive for many applications. However, the physical mechanisms for this improved behavior are not understood. Here, the thermally induced structural evolution of a-C:H:Si:O was investigated in situ by X-ray photoelectron and absorption spectroscopy, as well as molecular dynamics (MD) simulations. The spectroscopy results indicate that upon high vacuum annealing, two thermally activated processes with a Gaussian distribution of activation energies with mean value E and standard deviation σ take place in a-C:H:Si:O: (a) ordering and clustering of sp2 carbon ( E ± σ = 0.22 ± 0.08 eV) and (b) conversion of sp3- to sp2-bonded carbon ( E ± σ = 3.0 ± 1.1 eV). The experimental results are in qualitative agreement with the outcomes of MD simulations performed using a ReaxFF potential. The MD simulations also indicate that the higher thermal stability of a-C:H:Si:O compared to a-C:H (with similar fraction of sp2-bonded carbon and hydrogen content) derives from the significantly lower fraction of strained carbon-carbon sp3 bonds in a-C:H:Si:O compared to a-C:H, which are more likely to break at elevated temperatures.

Load and Time Dependence of Interfacial Chemical Bond-Induced Friction at the Nanoscale.

Rate and state friction (RSF) laws are widely used empirical relationships that describe the macroscale frictional behavior of a broad range of materials, including rocks found in the seismogenic zone of Earth's crust. A fundamental aspect of the RSF laws is frictional "aging," where friction increases with the time of stationary contact due to asperity creep and/or interfacial strengthening. Recent atomic force microscope (AFM) experiments and simulations found that nanoscale silica contacts exhibit aging due to the progressive formation of interfacial chemical bonds. The role of normal load (and, thus, normal stress) on this interfacial chemical bond-induced (ICBI) friction is predicted to be significant but has not been examined experimentally. Here, we show using AFM that, for nanoscale ICBI friction of silica-silica interfaces, aging (the difference between the maximum static friction and the kinetic friction) increases approximately linearly with the product of the normal load and the log of the hold time. This behavior is attributed to the approximately linear dependence of the contact area on the load in the positive load regime before significant wear occurs, as inferred from sliding friction measurements. This implies that the average pressure, and thus the average bond formation rate, is load independent within the accessible load range. We also consider a more accurate nonlinear model for the contact area, from which we extract the activation volume and the average stress-free energy barrier to the aging process. Our work provides an approach for studying the load and time dependence of contact aging at the nanoscale and further establishes RSF laws for nanoscale asperity contacts.

Frictional ageing from interfacial bonding and the origins of rate and state friction.

Earthquakes have long been recognized as being the result of stick-slip frictional instabilities. Over the past few decades, laboratory studies of rock friction have elucidated many aspects of tectonic fault zone processes and earthquake phenomena. Typically, the static friction of rocks grows logarithmically with time when they are held in stationary contact, but the mechanism responsible for this strengthening is not understood. This time-dependent increase of frictional strength, or frictional ageing, is one manifestation of the 'evolution effect' in rate and state friction theory. A prevailing view is that the time dependence of rock friction results from increases in contact area caused by creep of contacting asperities. Here we present the results of atomic force microscopy experiments that instead show that frictional ageing arises from the formation of interfacial chemical bonds, and the large magnitude of ageing at the nanometre scale is quantitatively consistent with what is required to explain observations in macroscopic rock friction experiments. The relative magnitude of the evolution effect compared with that of the 'direct effect'--the dependence of friction on instantaneous changes in slip velocity--determine whether unstable slip, leading to earthquakes, is possible. Understanding the mechanism underlying the evolution effect would enable us to formulate physically based frictional constitutive laws, rather than the current empirically based 'laws', allowing more confident extrapolation to natural faults.