Atomic-scale friction of a tungsten tip on a graphite surface

Structural superlubricity and ultralow friction across the length scales

Structural superlubricity, a state of ultralow friction and wear between crystalline surfaces, is a fundamental phenomenon in modern tribology that defines a new approach to lubrication. Early measurements involved nanometre-scale contacts between layered materials, but recent experimental advances have extended its applicability to the micrometre scale. This is an important step towards practical utilization of structural superlubricity in future technological applications, such as durable nano- and micro-electromechanical devices, hard drives, mobile frictionless connectors, and mechanical bearings operating under extreme conditions. Here we provide an overview of the field, including its birth and main achievements, the current state of the art and the challenges to fulfilling its potential.

Graphene used as a lateral force microscopy calibration material in the low-load non-linear regime

A lateral force microscopy (LFM) calibration technique utilizing a random low-profile surface is proposed that is successfully employed in the low-load non-linear frictional regime using a single layer of graphene on a supporting oxide substrate. This calibration at low loads and on low friction surfaces like graphene has the benefit of helping to limit the wear of the LFM tip during the calibration procedure. Moreover, the low-profiles of the calibration surface characteristic of these layered 2D materials, on standard polished oxide substrates, result in a nearly constant frictional, adhesive, and elastic response as the tip slides over the surface, making the determination of the calibration coefficient robust. Through a detailed calibration analysis that takes into account non-linear frictional response, it is found that the adhesion is best described by a nearly constant vertical orientation, rather than the more commonly encountered normally directed adhesion, as the single asperity passes over the low-profile graphene-coated oxide surface.

Superlubricity of Graphite Sliding against Graphene Nanoflake under Ultrahigh Contact Pressure

Superlubricity of graphite sliding against graphene can be easily attained at the nanoscale when it forms the incommensurate contact under a low contact pressure. However, the achievement of superlubricity under an ultrahigh contact pressure (>1 GPa), which has more applications in the lubrication of micromachine and nanomachine, remains unclear. Here, this problem is addressed and the robust superlubricity of graphite is obtained under ultrahigh contact pressures of up to 2.52 GPa, by the formation of transferred graphene nanoflakes on a silicon tip. The friction coefficient becomes as low as 0.0003, a state that is attributed to the extremely low shear strength of the graphene/graphite interface in the incommensurate contact. When the pressure exceeds some threshold, the superlubricity state collapses suddenly with the friction coefficient increasing ≈10 times. The failure of superlubricity originates from the delamination of the topmost graphene layers on graphite under ultrahigh contact pressures, which requires the tip to provide additional exfoliation energies during the sliding process. The results demonstrate that the superlubricity of graphite sliding against graphene can exist stably under ultrahigh contact pressure, which would appear to accelerate its application in nanoscale lubrication.

Graphene Nanoribbons with Atomically Sharp Edges Produced by AFM Induced Self-Folding

The ability to create graphene nanoribbons with atomically sharp edges is important for various graphene applications because these edges significantly influence the overall electronic properties and support unique magnetic edge states. The discovery of graphene self-folding induced by traveling wave excitation through atomic force microscope scanning under a normal force of less than 15 nN is reported. Most remarkably, the crystallographic direction of self-folding may be either along a chosen direction defined by the scan line or along the zigzag or armchair direction in the presence of a pre-existing crack in the vicinity. The crystalline direction of the atomically sharp edge is confirmed via careful lateral force microscopy measurements. Multilayer nanoribbons with lateral dimensions of a few tens of nanometers are realized on the same graphene sheet with different folding types (e.g., z-type or double parallel). Molecular dynamics simulations reveal the folding dynamics and suggest a monotonic increase of the folded area with the applied normal force. This method may be extended to other 2D van der Waals materials and lead to nanostructures that exhibit novel edge properties without the chemical instability that typically hinders applications of etched or patterned graphene nanostructures.

Spatial dimensions in atomic force microscopy: Instruments, effects, and measurements

Atomic force microscopes (AFMs) are commonly and broadly regarded as being capable of three-dimensional imaging. However, conventional AFMs suffer from both significant functional constraints and imaging artifacts that render them less than fully three dimensional. To date a widely accepted consensus is still lacking with respect to characterizing the spatial dimensions of various AFM measurements. This paper proposes a framework for describing the dimensional characteristics of AFM images, instruments, and measurements. Particular attention is given to instrumental and measurement effects that result in significant non-equivalence among the three axes in terms of both data characteristics and instrument performance. Fundamentally, our position is that no currently available AFM should be considered fully three dimensional in all relevant aspects.

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

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

Superlubricity Enabled by Pressure-Induced Friction Collapse

From daily intuitions to sophisticated atomic-scale experiments, friction is usually found to increase with normal load. Using first-principle calculations, here we show that the sliding friction of a graphene/graphene system can decrease with increasing normal load and collapse to nearly zero at a critical point. The unusual collapse of friction is attributed to an abnormal transition of the sliding potential energy surface from corrugated, to substantially flattened, and eventually to counter-corrugated states. The energy dissipation during the mutual sliding is thus suppressed sufficiently under the critical pressure. The friction collapse behavior is reproducible for other sliding systems, such as Xe/Cu, Pd/graphite, and MoS₂/MoS₂, suggesting its universality. The proposed mechanism for diminishing energy corrugation under critical normal load, added to the traditional structural lubricity, enriches our fundamental understanding about superlubricity and isostructural phase transitions and offers a novel means of achieving nearly frictionless sliding interfaces.

Friction fluctuations of gold nanoparticles in the superlubric regime

Superlubricity, or alternatively termed structural (super)lubrictiy, is a concept where ultra-low friction is expected at the interface between sliding surfaces if these surfaces are incommensurate and thus unable to interlock. In this work, we now report on sudden, reversible, friction changes that have been observed during AFM-based nanomanipulation experiments of gold nanoparticles sliding on highly oriented pyrolythic graphite. These effects can be explained by rotations of the gold nanoparticles within the concept of structural superlubricity, where the occurrence of ultra-low friction can depend extremely sensitively on the relative orientation between the slider and the substrate. From our theoretical simulations it will become apparent how even miniscule magnitudes of rotation are compatible to the observed effects and how size and shape of the particles can influence the dependence between friction and relative orientation.

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.

Velocity dependence of sliding friction on a crystalline surface

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

Non-contact lateral force microscopy

The goal of atomic force microscopy (AFM) is to measure the short-range forces that act between the tip and the surface. The signal recorded, however, includes long-range forces that are often an unwanted background. Lateral force microscopy (LFM) is a branch of AFM in which a component of force perpendicular to the surface normal is measured. If we consider the interaction between tip and sample in terms of forces, which have both direction and magnitude, then we can make a very simple yet profound observation: over a flat surface, long-range forces that do not yield topographic contrast have no lateral component. Short-range interactions, on the other hand, do. Although contact-mode is the most common LFM technique, true non-contact AFM techniques can be applied to perform LFM without the tip depressing upon the sample. Non-contact lateral force microscopy (nc-LFM) is therefore ideal to study short-range forces of interest. One of the first applications of nc-LFM was the study of non-contact friction. A similar setup is used in magnetic resonance force microscopy to detect spin flipping. More recently, nc-LFM has been used as a true microscopy technique to systems unsuitable for normal force microscopy.

Unconventional Behavior of Friction at the Nanoscale beyond Amontons' Law

By means of a many-body van der Waals (vdW)-corrected density functional theory approach, the atomic-scale friction of a prototypical tip-substrate system consisting of an Si tip and a graphene substrate is studied. In a loading-sliding process, the tip-substrate distance is found to be essential for nanofrictional behavior, through determining the competition between vdW contributions and electronic contributions. As the tip approaches the substrate, this competition results in a smooth transition of normal forces from attraction to repulsion, and the friction coefficient in turn undergoes a sign change from negative to positive with possible giant magnitude and strong anisotropy. The loading-sliding process does not introduce any chemical modification of the underlying system. These findings reveal the boundary of validity of Amontons' law, unify negative and giant friction coefficients, rationalize the experimentally observed anisotropy of nanofriction, and are universal when vdW interactions are crucial, all of which are helpful to establish a comprehensive picture of nanofriction.

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.

Single-file mobility of water-like fluid in a generalized Frenkel-Kontorova model

In this work, we used a generalized Frenkel-Kontorova model to study the mobility of water molecules inside carbon nanotubes with small radius at low temperatures. Our simulations show that the mobility of confined water decreases monotonically increasing the amplitude of the substrate potential at fixed commensurations. On the other hand, the mobility of the water molecules shows a non-monotonic behavior when varying the commensuration. This result indicates that the mobility of the confined fluid presents different behavior regimes depending on the amplitude of the water-nanotube interaction. In order to qualitatively understand these results, we study analytically the driven Frenkel-Kontorova model at finite temperatures. This analysis allows us to obtain the curves of the mobility versus commensurations, at fixed substrate potentials. Such curves show the existence of three regimes of mobility behavior as a function of the commensuration ratio. Additionally, our study indicates a nontrivial and strong dependence of the mobility with a quantity that can be interpreted as an effective amplitude of the substrate potential, depending on the bare amplitude of the substrate potential, the commensuration ratio, and temperature.

Nanotribological Properties of Hexadecanethiol Self-Assembled Monolayers on Au(111): Structure, Temperature, and Velocity

Self-assembled monolayers (SAM) are promising building blocks for the optimization of a large variety of systems both on the nano- and on the microscale. Among other applications, SAM are often used as protective coating or friction modifiers. In this work, we have used hexadecanethiol SAM on Au(111) as a model system and studied the different mechanisms of energy dissipation during temperature and velocity dependent friction force microscopy (FFM). In a number of cases, the SAM remained stable during atomic force microscopy experiments and friction-velocity isotherms related dissipation to an activation energy. In other cases, friction experiments lead to an irreversible deterioration of the SAM. This can rather be associated with the general SAM structure that was analyzed by scanning tunneling microscopy and showed a large variety of potential breakdown points like, for example, grain boundaries, step edges, or substrate-related holes in the SAM.

Effect of sliding friction in harmonic oscillators

Sliding friction is ubiquitous in nature as are harmonic oscillators. However, when treating harmonic oscillators the effect of sliding friction is often neglected. Here, we propose a simple analytical model to include both viscous and sliding friction in common harmonic oscillator equations, allowing to separate these different types of dissipation. To compare this model with experimental data, a nanometric vibration was imposed on a quartz tuning fork, while an atomic force microscope tip was used to disturb its motion. We analyzed tuning fork resonance and ‘ring down’ experimental curves and for each case calculated the amount of sliding friction and of viscous damping, finding an agreement between the two different experiments and the model proposed.

A universal and ultrasensitive vectorial nanomechanical sensor for imaging 2D force fields

The miniaturization of force probes into nanomechanical oscillators enables ultrasensitive investigations of forces on dimensions smaller than their characteristic length scales. It also unravels the vectorial character of the force field and how its topology impacts the measurement. Here we present an ultrasensitive method for imaging two-dimensional vectorial force fields by optomechanically following the bidimensional Brownian motion of a singly clamped nanowire. This approach relies on angular and spectral tomography of its quasi-frequency-degenerated transverse mechanical polarizations: immersing the nanoresonator in a vectorial force field not only shifts its eigenfrequencies but also rotates the orientation of the eigenmodes, as a nanocompass. This universal method is employed to map a tunable electrostatic force field whose spatial gradients can even dominate the intrinsic nanowire properties. Enabling vectorial force field imaging with demonstrated sensitivities of attonewton variations over the nanoprobe Brownian trajectory will have a strong impact on scientific exploration at the nanoscale.

Stacking stability and sliding mechanism in weakly bonded 2D transition metal carbides by van der Waals force

The stability of the stacked two-dimensional (2D) transition metal carbides and their interlayered friction in different configurations are comparatively studied by means of density functional theory (DFT).

Dynamics of bacterial streamers induced clogging in microfluidic devices

Using a microfabricated porous media mimic platform, we investigated the clogging dynamics of bacterial biomass that accumulated in the device due to the formation of bacterial streamers. Particularly, we found the existence of a distinct clogging front which advanced via pronounced 'stick-slip' of the viscoelastic bacterial biomass over the solid surface of the micro pillar. Thus, the streamer, the solid surface, and the background fluidic media defined a clear three-phase front influencing these advancing dynamics. Interestingly, we also found that once the clogging became substantial, contrary to a static homogenous saturation state, the clogged mimic exhibited an instability phenomena marked by localized streamer breakage and failure leading to extended water channels throughout the mimic. These findings have implications for design and fabrication of biomedical devices and membrane-type systems such as porous balloon catheters, porous stents and filtration membranes prone to bacteria induced clogging as well as understanding bacterial growth and proliferation in natural porous media such as soil and rocks.

Universal Aging Mechanism for Static and Sliding Friction of Metallic Nanoparticles

The term "contact aging" refers to the temporal evolution of the interface between a slider and a substrate usually resulting in increasing friction with time. Current phenomenological models for multiasperity contacts anticipate that such aging is not only the driving force behind the transition from static to sliding friction, but at the same time influences the general dynamics of the sliding friction process. To correlate static and sliding friction on the nanoscale, we show experimental evidence of stick-slip friction for nanoparticles sliding on graphite over a wide dynamic range. We can assign defined periods of aging to the stick phases of the particles, which agree with simulations explicitly including contact aging. Additional slide-hold-slide experiments for the same system allow linking the sliding friction results to static friction measurements, where both friction mechanisms can be universally described by a common aging formalism.

Atomistic Mechanisms of Chemical Mechanical Polishing of a Cu Surface in Aqueous H2O2: Tight-Binding Quantum Chemical Molecular Dynamics Simulations

We applied our original chemical mechanical polishing (CMP) simulator based on the tight-binding quantum chemical molecular dynamics (TB-QCMD) method to clarify the atomistic mechanism of CMP processes on a Cu(111) surface polished with a SiO2 abrasive grain in aqueous H2O2. We reveal that the oxidation of the Cu(111) surface mechanically induced at the friction interface is a key process in CMP. In aqueous H2O2, in the first step, OH groups and O atoms adsorbed on a nascent Cu surface are generated by the chemical reactions of H2O2 molecules. In the second step, at the friction interface between the Cu surface and the abrasive grain, the surface-adsorbed O atom intrudes into the Cu bulk and dissociates the Cu-Cu bonds. The dissociation of the Cu-Cu back-bonds raises a Cu atom from the surface that is mechanically sheared by the abrasive grain. In the third step, the raised Cu atom bound to the surface-adsorbed OH groups is removed from the surface by the generation and desorption of a Cu(OH)2 molecule. In contrast, in pure water, there are no geometrical changes in the Cu surface because the H2O molecules do not react with the Cu surface, and the abrasive grain slides smoothly on the planar Cu surface. The comparison between the CMP simulations in aqueous H2O2 and pure water indicates that the intrusion of a surface-adsorbed O atom into the Cu bulk is the most important process for the efficient polishing of the Cu surface because it induces the dissociation of the Cu-Cu bonds and generates raised Cu atoms that are sheared off by the abrasive grain. Furthermore, density functional theory calculations show that the intrusion of the surface-adsorbed O atoms into the Cu bulk has a high activation energy of 28.2 kcal/mol, which is difficult to overcome at 300 K. Thus, we suggest that the intrusion of surface-adsorbed O atoms into the Cu bulk induced by abrasive grains at the friction interface is a rate-determining step in the Cu CMP process.

Voltage assisted asymmetric nanoscale wear on ultra-smooth diamond like carbon thin films at high sliding speeds

The understanding of tribo- and electro-chemical phenomenons on the molecular level at a sliding interface is a field of growing interest. Fundamental chemical and physical insights of sliding surfaces are crucial for understanding wear at an interface, particularly for nano or micro scale devices operating at high sliding speeds. A complete investigation of the electrochemical effects on high sliding speed interfaces requires a precise monitoring of both the associated wear and surface chemical reactions at the interface. Here, we demonstrate that head-disk interface inside a commercial magnetic storage hard disk drive provides a unique system for such studies. The results obtained shows that the voltage assisted electrochemical wear lead to asymmetric wear on either side of sliding interface.

Atomic-Scale Sliding Friction on Graphene in Water

The sliding of a sharp nanotip on graphene completely immersed in water is investigated by molecular dynamics (MD) and atomic force microscopy. MD simulations predict that the atomic-scale stick-slip is almost identical to that found in ultrahigh vacuum. Furthermore, they show that water plays a purely stochastic role in sliding (solid-to-solid) friction. These observations are substantiated by friction measurements on graphene grown on Cu and Ni, where, oppositely of the operation in air, lattice resolution is readily achieved. Our results promote friction force microscopy in water as a robust alternative to ultra-high-vacuum measurements.

Characterising the nanoscale kinetic friction using force-equilibrium and energy-conservation models with optical manipulation

SiC nanowires were manipulated under an optic microscope to investigate the nanoscale friction between nanowires and a flat substrate. The deflection of the nanowires was modeled as that of an Euler-Bernoulli beam subjected to a uniformly distributed load. A simple formula was developed to calculate the kinetic friction from the normalized deflections at the two ends of a nanowire. The frictional force per unit area determined ranges from 0.18-0.51 MPa. Both experimental and simulated results demonstrated that the proposed approach was reliable. The results were also compared with those estimated using an energy-conservation model, which produced a frictional force ranging from 0.21-0.62 MPa. The results obtained from the two different methods are in excellent agreement.

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.

Single-Molecule Tribology: Force Microscopy Manipulation of a Porphyrin Derivative on a Copper Surface

The low-temperature mechanical response of a single porphyrin molecule attached to the apex of an atomic force microscope (AFM) tip during vertical and lateral manipulations is studied. We find that approach-retraction cycles as well as surface scanning with the terminated tip result in atomic-scale friction patterns induced by the internal reorientations of the molecule. With a joint experimental and computational effort, we identify the dicyanophenyl side groups of the molecule interacting with the surface as the dominant factor determining the observed frictional behavior. To this end, we developed a generalized Prandtl-Tomlinson model parametrized using density functional theory calculations that includes the internal degrees of freedom of the side group with respect to the core and its interactions with the underlying surface. We demonstrate that the friction pattern results from the variations of the bond length and bond angles between the dicyanophenyl side group and the porphyrin backbone as well as those of the CN group facing the surface during the lateral and vertical motion of the AFM tip.

Exploring and Explaining Friction with the Prandtl-Tomlinson Model

The Prandtl-Tomlinson model of friction, first introduced in 1928 as a "conceptual model" for a single-atom contact, consists of a point mass that is dragged over a sinusoidal potential by a spring. After decades of virtual oblivion, it has recently found impressive validation for contacts comprising tens or even hundreds of atoms. To date, the Prandtl-Tomlinson model enjoys widespread popularity as depicting arguably the most insightful mechanical analogue to atomic-scale effects occurring at sliding interfaces. In this issue of ACS Nano, Pawlak et al. demonstrate the model's applicability to a true single-atom contact, thereby illustrating that simple mechanical representations can indeed go a long way toward explaining interactions at atomically defined interfaces.

Stick-slip behavior identified in helium cluster growth in the subsurface of tungsten: effects of cluster depth

We have performed a molecular dynamics study on the growth of helium (He) clusters in the subsurface of tungsten (W) (1 0 0) at 300 K, focusing on the role of cluster depth. Irregular 'stick-slip' behavior exhibited during the evolution of the He cluster growth is identified, which is due to the combined effects of the continuous cluster growth and the loop punching induced pressure relief. We demonstrate that the He cluster grows via trap-mutation and loop punching mechanisms. Initially, the self-interstitial atom SIA clusters are almost always attached to the He cluster; while they are instantly emitted to the surface once a critical cluster pressure is reached. The repetition of this process results in the He cluster approaching the surface via a 'stop-and-go' manner and the formation of surface adatom islands (surface roughening), ultimately leading to cluster bursting and He escape. We reveal that, for the Nth loop punching event, the critical size of the He cluster to trigger loop punching and the size of the emitted SIA clusters are correspondingly increased with the increasing initial cluster depth. We tentatively attribute the observed depth effects to the lower formation energies of Frenkel pairs and the greatly reduced barriers for loop punching in the stress field of the W subsurface. In addition, some intriguing features emerge, such as the morphological transformation of the He cluster from 'platelet-like' to spherical, to ellipsoidal with a 'bullet-like' tip, and finally to a 'bottle-like' shape after cluster rupture.

Static friction between rigid fractal surfaces

Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.

Experimental and Theoretical Investigations on the Nanoscale Kinetic Friction in Ambient Environmental Conditions

The liquid lubrication, thermolubricity and dynamic lubricity due to mechanical oscillations are investigated with an atomic force microscope in ambient environmental conditions with different relative humidity (RH) levels. Experimental results demonstrate that high humidity at low-temperature regime enhances the liquid lubricity while at high-temperature regime it hinders the effect of the thermolubricity due to the formation of liquid bridges. Friction response to the dynamic lubricity in both high- and low-temperature regimes keeps the same trends, namely the friction force decreases with increasing the amplitude of the applied vibration on the tip regardless of the RH levels. An interesting finding is that for the dynamic lubricity at high temperature, high-humidity condition leads to the friction forces higher than that at low-humidity condition while at low temperature the opposite trend is observed. An extended two-dimensional dynamic model accounting for the RH is proposed to interpret the frictional mechanism in ambient conditions.

Solid friction between soft filaments

Any macroscopic deformation of a filamentous bundle is necessarily accompanied by local sliding and/or stretching of the constituent filaments. Yet the nature of the sliding friction between two aligned filaments interacting through multiple contacts remains largely unexplored. Here, by directly measuring the sliding forces between two bundled F-actin filaments, we show that these frictional forces are unexpectedly large, scale logarithmically with sliding velocity as in solid-like friction, and exhibit complex dependence on the filaments' overlap length. We also show that a reduction of the frictional force by orders of magnitude, associated with a transition from solid-like friction to Stokes's drag, can be induced by coating F-actin with polymeric brushes. Furthermore, we observe similar transitions in filamentous microtubules and bacterial flagella. Our findings demonstrate how altering a filament's elasticity, structure and interactions can be used to engineer interfilament friction and thus tune the properties of fibrous composite materials.

β-Relaxation of PMMA: Tip Size and Stress Effects in Friction Force Microscopy

The kinetic signature of the β-relaxation of poly(methyl methacrylate) (PMMA) is investigated by friction force microscopy. The variation in friction force was measured as a function of scan velocity, temperature (300 K-410 K), and applied load using both sharp and blunt probe tips. The friction data show distinct maxima, which can be ascribed to the β-relaxation of PMMA. The contact area was varied over the ranges of approximately 20 to 70 nm(2) and 12,000 to 43,000 nm(2) through the use of probe tips with radii of approximately 15, 18, 1350, and 2650 nm. Kinetic analysis shows that the apparent activation energy of the β-relaxation decreases with the tip radius. Accompanying finite element simulations indicate that for the sharp tips a substantial subvolume of the polymer underneath the tip exceeds the yield stress of PMMA. This suggests that for small contact sizes and high stresses the activation barrier of the β-process decreases through the activation of the α-process by material yielding.

Molecular dynamics simulations of nanoscale and sub-nanoscale friction behavior between graphene and a silicon tip: analysis of tip apex motion

A sliding object on a crystal surface with a nanoscale contact will always experience stick-slip movement. However, investigation of the slip motion itself is rarely performed due to the short slip duration. In this study, we performed molecular dynamics simulation and frictional force microscopy experiments for the precise observation of slip motion between a graphene layer and a crystalline silicon tip. The simulation results revealed a hierarchical structure of stick and slip motion. Nanoscale stick and slip motion is composed of sub-nanoscale stick and slip motion. Sub-nanoscale stick and slip motion occurred on a timescale of a few ps and a force scale of 10(-1) nN. The relationship between the trajectories of the silicon tip and stick-slip peak revealed that in-plane and vertical motions of the tip provide information about stick and slip motion in the sub-nanoscale and nanoscale ranges, respectively. Parametric studies including tip size, scan angle, layer thickness, and flexibility of the substrate were also carried out to compare the simulation results with findings on lateral force microscopy.

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

Atomic force microscopy (AFM) and atomistic simulations of atomic friction with silicon oxide tips sliding on Au(111) are conducted at overlapping speeds. Experimental data unambiguously reveal a stick-slip friction plateau above a critical scanning speed, in agreement with the thermally activated Prandtl-Tomlinson (PTT) model. However, friction in experiments is larger than in simulations. PTT energetic parameters for the two are comparable, with minor differences attributable to the contact area's influence on the barrier to slip. Recognizing that the attempt frequency may be determined by thermal vibrations of the larger AFM tip mass or instrument noise fully resolves the discrepancy. Thus, atomic stick-slip is well described by the PTT model if sources of slip-assisting energy are accounted for.

Nanoprocessing of layered crystalline materials by atomic force microscopy

By taking advantage of the mechanical anisotropy of crystalline materials, processing at a single-layer level can be realized for layered crystalline materials with periodically weak bonds. Mica (muscovite), graphite, molybdenum disulfide (MoS2), and boron nitride have layered structures, and there is little interaction between the cleavage planes existing in the basal planes of these materials. Moreover, it is easy to image the atoms on the basal plane, where the processed shape can be observed on the atomic level. This study reviews research evaluating the nanometer-scale wear and friction as well as the nanometer-scale mechanical processing of muscovite using atomic force microscopy (AFM). It also summarizes recent AFM results obtained by our research group regarding the atomic-scale mechanical processing of layered materials including mica, graphite, MoS2, and highly oriented pyrolytic graphite.

Chemically grafted graphite nanosheets dispersed in poly(ethylene-glycol) by γ-radiolysis for enhanced lubrication

The γ-radiolysis derived chemical grafting of graphite nanosheets with poly(ethylene-glycol) results in a remarkable decrease in the friction coefficient and significantly enhanced antiwear characteristics of steel–steel sliding interfaces.

Theoretical study of electronic and tribological properties of h-BNC2/graphene, h-BNC2/h-BN and h-BNC2/h-BNC2bilayers

Density functional theory methods are used to investigate the interlayer sliding energy landscape, binding energy and interlayer spacing between h-BNC₂/graphene (I), h-BNC₂/h-BN (II) and h-BNC₂/h-BNC₂(III) bilayer structures.

A non-contact, thermal noise based method for the calibration of lateral deflection sensitivity in atomic force microscopy

Calibration of lateral forces and displacements has been a long standing problem in lateral force microscopies. Recently, it was shown by Wagner et al. that the thermal noise spectrum of the first torsional mode may be used to calibrate the deflection sensitivity of the detector. This method is quick, non-destructive and may be performed in situ in air or liquid. Here we make a full quantitative comparison of the lateral inverse optical lever sensitivity obtained by the lateral thermal noise method and the shape independent method developed by Anderson et al. We find that the thermal method provides accurate results for a wide variety of rectangular cantilevers, provided that the geometry of the cantilever is suitable for torsional stiffness calibration by the torsional Sader method, in-plane bending of the cantilever may be eliminated or accounted for and that any scaling of the lateral deflection signal between the measurement of the lateral thermal noise and the measurement of the lateral deflection is eliminated or corrected for. We also demonstrate that the thermal method may be used to characterize the linearity of the detector signal as a function of position, and find a deviation of less than 8% for the instrument used.

Ex situ and in situ characterization of patterned photoreactive thin organic surface layers using friction force microscopy

Photolithographic methods allow an easy lateral top-down patterning and tuning of surface properties with photoreactive molecules and polymers. Employing friction force microscopy (FFM), we present here different FFM-based methods that enable the characterization of several photoreactive thin organic surface layers. First, three ex situ methods have been evaluated for the identification of irradiated and non-irradiated zones on the same organosilane sample by irradiation through different types of masks. These approaches are further extended to a time dependent ex situ FFM measurement, which allows to study the irradiation time dependent evolution of the resulting friction forces by sequential irradiation through differently sized masks in crossed geometry. Finally, a newly designed in situ FFM measurement, which uses a commercial bar-shaped cantilever itself as a noncontact shadow mask, enables the determination of time dependent effects on the surface modification during the photoreaction.

Reinterpretation of velocity-dependent atomic friction: influence of the inherent instrumental noise in friction force microscopes

We have applied both the master equation method and harmonic transition state theory to interpret the velocity-dependent friction behavior observed in atomic friction experiments. To understand the discrepancy between attempt frequencies measured in atomic force microscopy experiments and those estimated by theoretical models, both thermal noise and instrumental noise are introduced into the model. It is found that the experimentally observed low attempt frequency and the transition point at low velocity regimes can be interpreted in terms of the instrumental noise inherent in atomic force microscopy. In contrast to previous models, this model also predicts (1) the existence of a two-slope curve of velocity dependence and (2) the decrease of critical velocity with temperature, which provides clues for further experimental verification of the influence of instrumental noise in friction measurements.

Stick-slip and force chain evolution in a granular bed in response to a grain intruder

The mechanical response of granular beds under applied stresses is often characterized by repeated cycles of stick-slip. Using the discrete element method, we examine stick-slip from a concentrated force loading-imposed by a single grain that is drawn through a densely packed, periodic granular bed via a stiff virtual spring. Force chains continually form and collapse ahead of the intruder grain. A comprehensive characterization of the birth-death evolution of these load-bearing structures, along with their surrounding contact cycles, reveals a well-defined shear zone of around eight particle diameters from the intruder, encapsulating: (i) long force chains that form buttresses with the fixed bottom wall for support, (ii) a region where the collapse of the most stable, persistent three-cycles preferentially occur to the point where they are essentially depleted by the end of the first cycle of stick-slip, and (iii) an inner core where force chain buckling events concentrate. Dilatancy is greatest in this inner core, and in the region next to the free surface. During slip, secondary force chains briefly form behind the intruder: these transient force chains, most of which comprise only 3 particles, form in the direction that is roughly perpendicular to the intruder motion.

The diversity of friction behavior between bi-layer graphenes

For relative sliding between two rigid graphene sheets that are interacted on by a van der Waals force, we show that the friction behavior is significantly dependent on the interlayer separation distance h. Around the equilibrium interlayer distance he, the friction behavior exactly obeys a linear law. When h is far smaller than he, the linear friction behavior transforms to overlinear behavior. On the other hand, when h is larger than he, there is another critical value of the interlayer distance, hc; when h is larger than he and smaller than hc, the friction behavior transforms from linear to sublinear behavior; however, when h is larger than hc, the coefficient of friction becomes negative. Further, the different friction behaviors are found to be well described by a universal power law, τ = μ*(σ + σ0)(n).