Frictional Forces and Amontons' Law: From the Molecular to the Macroscopic Scale

Alternatives to Friction Coefficient: Role of Frictional Instabilities on Fine Touch Perception

Fine touch perception is often correlated to material properties and friction coefficients, but the inherent variability of human motion has led to low correlations and contradictory findings. Instead, we hypothesized that humans use frictional instabilities to discriminate between objects. We constructed a set of coated surfaces with minimal physical differences that by themselves, are not perceptible to people, but instead, due to modification in surface chemistry, the surfaces created different types of instabilities based on how quickly a finger is slid and how hard a human finger is pressed during sliding. We found that participant accuracy in tactile discrimination most strongly correlated with formations of steady sliding, and response times negatively correlated with stiction spikes. Conversely, traditional metrics like surface roughness or average friction coefficient did not predict tactile discriminability. In fact, the typical method of averaging friction coefficients led to a spurious correlation which erroneously suggests that distinct objects should feel identical and identical objects should feel distinct. Identifying the central role of frictional instabilities as an alternative to using friction coefficients should accelerate the design of tactile interfaces for psychophysics and haptics.

Ndc80 complex, a conserved coupler for kinetochore-microtubule motility, is a sliding molecular clutch

Chromosome motion at spindle microtubule plus-ends relies on dynamic molecular bonds between kinetochores and proximal microtubule walls. Under opposing forces, kinetochores move bi-directionally along these walls while remaining near the ends, yet how continuous wall-sliding occurs without end-detachment remains unclear. Using ultrafast force-clamp spectroscopy, we show that single Ndc80 complexes, the primary microtubule-binding kinetochore component, exhibit processive, bi-directional sliding. Plus-end-directed forces induce a mobile catch-bond in Ndc80, increasing frictional resistance and restricting sliding toward the tip. Conversely, forces pulling Ndc80 away from the plus-end trigger mobile slip-bond behavior, facilitating sliding. This dual behavior arises from force-dependent modulation of the Nuf2 calponin-homology domain's microtubule binding, identifying this subunit as a friction regulator. We propose that Ndc80c's ability to modulate sliding friction provides the mechanistic basis for the kinetochore's end coupling, enabling its slip-clutch behavior.

One Sentence Summary

Direction-dependent mobile catch- and slip-bond behavior of the microtubule-binding Ndc80 protein.

Characterizing sliding and rolling contacts between single particles

Contacts between particles in dense, sheared suspensions are believed to underpin much of their rheology. Roughness and adhesion are known to constrain the relative motion of particles, and thus globally affect the shear response, but an experimental description of how they microscopically influence the transmission of forces and relative displacements within contacts is lacking. Here, we show that an innovative colloidal-probe atomic force microscopy technique allows the simultaneous measurement of normal and tangential forces exchanged between tailored surfaces and microparticles while tracking their relative sliding and rolling, unlocking the direct measurement of coefficients of rolling friction, as well as of sliding friction. We demonstrate that, in the presence of sufficient traction, particles spontaneously roll, reducing dissipation and promoting longer-lasting contacts. Conversely, when rolling is prevented, friction is greatly enhanced for rough and adhesive surfaces, while smooth particles coated by polymer brushes maintain well-lubricated contacts. We find that surface roughness induces rolling due to load-dependent asperity interlocking, leading to large off-axis particle rotations. In contrast, smooth, adhesive surfaces promote rolling along the principal axis of motion. Our results offer direct values of friction coefficients for numerical studies and an interpretation of the onset of discontinuous shear thickening based on them, opening up ways to tailor rheology via contact engineering.

Tuning Colloidal Gel Properties: The Influence of Central and Noncentral Forces

Colloidal gels, ubiquitous in industrial applications, can undergo reversible solid-to-liquid transitions. Recent work demonstrates that adding surface roughness to primary particles enhances the toughness and influences the self-healing properties of colloidal gels. In the present work, we first use colloidal probe atomic force microscopy (CP-AFM) to assess the quantitative changes in adhesive and frictional forces between thermoresponsive particles as a function of their roughness. The presence of static friction, generated by interparticle adhesion results in noncentral forces, leading to network structures that are more readily constrained in their nodes. Systems with higher friction exhibited increased sedimentation stability, a decrease in percolation threshold and a more abrupt elastic to plastic transition, but an enhanced capacity in storing elastic energy until fluidification. Additional experiments with geometrically smooth but "chemically rough" (patchy) particles further emphasized the importance of static interparticle friction in the macroscopic yielding and recovery behavior of colloidal gels.

Compressing slippery surface-assembled amphiphiles for tunable haptic energy harvesters

A recurring challenge in extracting energy from ambient motion is that devices must maintain high harvesting efficiency and a positive user experience when the interface is undergoing dynamic compression. We show that small amphiphiles can be used to tune friction, haptics, and triboelectric properties by assembling into specific conformations on the surfaces of materials. Molecules that form multiple slip planes under pressure, especially through π-π stacking, produce 80 to 90% lower friction than those that form disordered mesostructures. We propose a scaling framework for their friction reduction properties that accounts for adhesion and contact mechanics. Amphiphile-coated surfaces tend to resist wear and generate distinct tactile perception, with humans preferring more slippery materials. Separately, triboelectric output is enhanced through the use of amphiphiles with high electron affinity. Because device adoption is tied to both friction reduction and electron-withdrawing potential, molecules that self-organize into slippery planes under pressure represent a facile way to advance the development of haptic power harvesters at scale.

Signal Detection by Sensors and Determination of Friction Coefficient During Brake Lining Movement

This article presents a laboratory device by which the course of two signals can be detected using two types of sensors-strain gauges and the DEWESoft DS-NET measuring apparatus. The values of the coefficient of friction of the brake lining when moving against the rotating shell of the brake drum were determined from the physical quantities sensed by tensometric sensors and transformed into electrical quantities. The friction coefficient of the brake lining on the circumference of the rotating brake disc shell can be calculated from the known values measured by the sensors, the design dimensions of the brake, and the revolutions of the rotating parts system. The values of the friction coefficient were measured during brake lining movement. A woven asbestos-free material, Beral 1126, which contained brass fibers and resin additives, showed slightly higher values when rotating at previously tested speeds compared to the friction coefficient values obtained when the brake drum rotation was uniformly delayed. The methodology for determining the friction coefficient of the brake lining allowed the laboratory device to verify its magnitude for different friction materials under various operating conditions.

Control of interlayer friction in two-dimensional ferromagnetic CrBr3

Two-dimensional (2D) magnetic materials may offer new opportunities in the field of lubrication at the nanoscale. It is essential to investigate the interfacial properties, particularly magnetic coupling, at the interfaces of 2D magnetic materials from the point of view of friction. In the present study, we investigated the tribological and interfacial properties at the interface of bilayer CrBr3 by performing first-principles calculations. The effects of normal load, biaxial strain and carrier doping on interlayer magnetic coupling were also studied. Our calculations identify the ferromagnetic (FM)-antiferromagnetic (AFM) conversion of the interlayer magnetic couplings, which leads to the reduction of the sliding energy barriers. Importantly, our calculations demonstrate the lower sliding energy barrier at the interface of 2D FM CrBr3, implying lower friction and better lubricating properties. Additionally, we found that a normal load of 0.5-1.0 eV Å-1, a biaxial compressive strain of 0% to -5%, and a carrier doping of -0.2 to 0.2 e f.u.-1 are effective in reducing the sliding energy barrier and the friction. It is also found that the biaxial strain tunes the interlayer electron redistribution and thus alters the interlayer interaction and friction. The differences between the lubricating properties of 2D magnetic CrX3 (X = Cl, Br and I) have also been studied. The present findings are inspiring for the application of 2D magnetic materials as solid lubricants in the fields of lubrication at the nanoscale.

Self-assembled thin films as alternative surface textures in assistive aids with users who are blind

Current tactile graphics primarily render tactile information for blind users through physical features, such as raised bumps or lines. However, the variety of distinctive physical features that can be created is effectively saturated, and alternatives to these physical features are not currently available for static tactile aids. Here, we explored the use of chemical modification through self-assembled thin films to generate distinctive textures in tactile aids. We used two silane precursors, n-butylaminopropyltrimethoxysilane and n-pentyltrichlorosilane, to coat playing card surfaces and investigated their efficacy as a tactile coating. We verified the surface coating process and examined their durability to repeated use by traditional materials characterization and custom mesoscale friction testing. Finally, we asked participants who were both congenitally blind and braille-literate to sort the cards based on touch. We found that participants were able to identify the correct coated card with 82% accuracy, which was significantly above chance, and two participants achieved 100% accuracy. This success with study participants demonstrates that surface coatings and surface modifications might augment or complement physical textures in next-generation tactile aids.

Behavioral biometric optical tactile sensor for instantaneous decoupling of dynamic touch signals in real time

Decoupling dynamic touch signals in the optical tactile sensors is highly desired for behavioral tactile applications yet challenging because typical optical sensors mostly measure only static normal force and use imprecise multi-image averaging for dynamic force sensing. Here, we report a highly sensitive upconversion nanocrystals-based behavioral biometric optical tactile sensor that instantaneously and quantitatively decomposes dynamic touch signals into individual components of vertical normal and lateral shear force from a single image in real-time. By mimicking the sensory architecture of human skin, the unique luminescence signal obtained is axisymmetric for static normal forces and non-axisymmetric for dynamic shear forces. Our sensor demonstrates high spatio-temporal screening of small objects and recognizes fingerprints for authentication with high spatial-temporal resolution. Using a dynamic force discrimination machine learning framework, we realized a Braille-to-Speech translation system and a next-generation dynamic biometric recognition system for handwriting.

Friction Force Mapping of Molecular Ordering and Mesoscopic Phase Transformations in Layered-Crystalline Organic Semiconductor Films

It is critical to understand molecular ordering processes in small-molecule organic semiconductor (OSC) films in optimizing electronic device applications, although it is difficult to observe and investigate the ordering characteristics at a mesoscopic or device scale. Here, we report that friction force microscopy (FFM) allows visualizing the ordering transformation process from a thermodynamically metastable phase to a stable phase at a mesoscopic scale. We utilized 2-octyl-benzothieno[3,2-b]naphtho[2,3-b]thiophene (2-C8-BTNT) as a typical highly layered-crystalline OSC. We found that the friction force between an AFM tip and spin-coated OSC films significantly depends on whether local film states are in metastable monolayer phase or stable bilayer-type herringbone (b-LHB) phase that exhibits high carrier mobility. The formation of the stable b-LHB phase leads to lower friction than the metastable monolayer phase, clearly visualizing the molecular order. Force map (Fmap) analysis indicates that the lower friction in the b-LHB phase should be associated with the reduction of interfacial adhesion force. Notably, the observed results demonstrate that the spin-coated thin film changes from continuous film with the monolayer phase to rugged microcrystal grains with the b-LHB phase when left at ambient conditions. By contrast, an appropriate post-thermal annealing process facilitates the phase transformation without inducing such morphological changes. The technique provides a unique and effective tool for revealing the relationship between processing conditions and device performance in polycrystalline OSC films.

Substrate deformability and applied normal force are coupled to change nanoscale friction

Amonton's law of friction states that the friction force is proportional to the normal force in magnitude, and the slope gives a constant friction coefficient. In this work, with molecular dynamics simulation, we study how the kinetic friction at the nanoscale deviates qualitatively from the relation. Our simulation demonstrates that the friction behavior between a nanoscale AFM tip and an elastic graphene surface is regulated by the coupling of the applied normal force and the substrate deformability. First, it is found that the normal load-induced substrate deformation could lower friction at low load while increasing it at high load. In addition, when the applied force exceeds a certain threshold another abrupt change in friction behavior is observed, i.e., the stick-slip friction changes to the paired stick-slip friction. The unexpected change in friction behavior is then ascribed to the change of the microscopic contact states between the two surfaces: the increase in normal force and the substrate deformability together lead to a change in the energy landscape experienced by the tip. Finally, the Prandtl-Tomlinson model also validates that the change in friction behavior can be interpreted in terms of the energy landscape.

Measuring Rolling Friction at the Nanoscale

Colloidal probe microscopy, a technique whereby a microparticle is affixed at the end of an atomic force microscopy (AFM) cantilever, plays a pivotal role in enabling the measurement of friction at the nanoscale and is of high relevance for applications and fundamental studies alike. However, in conventional experiments, the probe particle is immobilized onto the cantilever, thereby restricting its relative motion against a countersurface to pure sliding. Nonetheless, under many conditions of interest, such as during the processing of particle-based materials, particles are free to roll and slide past each other, calling for the development of techniques capable of measuring rolling friction alongside sliding friction. Here, we present a new methodology to measure lateral forces during rolling contacts based on the adaptation of colloidal probe microscopy. Using two-photon polymerization direct laser writing, we microfabricate holders that can capture microparticles, but allow for their free rotation. Once attached to an AFM cantilever, upon lateral scanning, the holders enable both sliding and rolling contacts between the captured particles and the substrate, depending on the interactions, while simultaneously giving access to normal and lateral force signals. Crucially, by producing particles with optically heterogeneous surfaces, we can accurately detect the presence of rotation during scanning. After introducing the workflow for the fabrication and use of the probes, we provide details on their calibration, investigate the effect of the materials used to fabricate them, and report data on rolling friction as a function of the surface roughness of the probe particles. We firmly believe that our methodology opens up new avenues for the characterization of rolling contacts at the nanoscale, aimed, for instance, at engineering particle surface properties and characterizing functional coatings in terms of their rolling friction.

Effects of surface chemistry on the mechanochemical decomposition of tricresyl phosphate

The growth of protective tribofilms from lubricant antiwear additives on rubbing surfaces is initiated by mechanochemically promoted dissociation reactions. These processes are not well understood at the molecular scale for many important additives, such as tricresyl phosphate (TCP). One aspect that needs further clarification is the extent to which the surface properties affect the mechanochemical decomposition. Here, we use nonequilibrium molecular dynamics (NEMD) simulations with a reactive force field (ReaxFF) to study the decomposition of TCP molecules confined and pressurised between sliding ferrous surfaces at a range of temperatures. We compare the decomposition of TCP on native iron, iron carbide, and iron oxide surfaces. We show that the decomposition rate of TCP molecules on all the surfaces increases exponentially with temperature and shear stress, implying that this is a stress-augmented thermally activated (SATA) process. The presence of base oil molecules in the NEMD simulations decreases the shear stress, which in turn reduces the rate constant for TCP decomposition. The decomposition is much faster on iron surfaces than iron carbide, and particularly iron oxide. The activation energy, activation volume, and pre-exponential factor from the Bell model are similar on iron and iron carbide surfaces, but significantly differ for iron oxide surfaces. These findings provide new insights into the mechanochemical decomposition of TCP and have important implications for the design of novel lubricant additives for use in high-temperature and high-pressure environments.

Experimental and analytical study on insertion force of composite-coated needle in soft tissue material

Medical interventions require control over surgical needle insertion to minimize tissue damage and target inaccuracies during percutaneous procedures. The composite coating of the needle using Polydopamine (PDA), Polytetrafluoroethylene (PTFE), and Activated Carbon (C) has been used to reduce the damaging needle insertion force. This research aims to further understand the interfacial mechanics of coated needle insertion by studying the forces at the needle and tissue interface and developing an analytical insertion force model through a combined experimental and numerical method. The proposed analytical force model is divided into two components: (1) Friction force on the needle shaft, modeled using a modified Karnopp model that includes an elastic force component; (2) Cutting force on the needle tip, modeled using a constant cutting coefficient for a given tissue and insertion speed. In this work, the analytical model was established by incorporating experiments conducted at a reasonable 35 mm insertion depth in tissues. In a bovine kidney with a 35 mm insertion depth, the insertion force evaluated through experimentation and modeling differed by 6.5% for a bare needle and 17.1% for a coated needle. It is important to note that this difference in the analytical insertion force model is anticipated when dealing with real tissues with a highly complex structured tissue. Prediction of the insertion force could potentially be utilized in robotic needle systems for needle control to improve the success of percutaneous procedures.

Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids

Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length λ growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law λ(t)∝tα, with α≃1/3, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a "universal" evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential.

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

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

Nanoscale friction of biomimetic hair surfaces

We investigate the nanoscale friction between biomimetic hair surfaces using chemical colloidal probe atomic force microscopy experiments and nonequilibrium molecular dynamics simulations. In the experiments, friction is measured between water-lubricated silica surfaces functionalised with monolayers formed from either octadecyl or sulfonate groups, which are representative of the surfaces of virgin and ultimately bleached hair, respectively. In the simulations, friction is monitored between coarse-grained model hair surfaces with different levels of chemical damage, where a specified amount of grafted octadecyl groups are randomly replaced with sulfonate groups. The sliding velocity dependence of friction in the simulations can be described using an extended stress-augmented thermally activation model. As the damage level increases in the simulations, the friction coefficient generally increases, but its sliding velocity-dependence decreases. At low sliding velocities, which are closer to those encountered experimentally and physiologically, we observe a monotonic increase of the friction coefficient with damage ratio, which is consistent with our new experiments using biomimetic surfaces and previous ones using real hair. This observation demonstrates that modified surface chemistry, rather than roughness changes or subsurface damage, control the increase in nanoscale friction of bleached or chemically damaged hair. We expect the methods and biomimetic surfaces proposed here to be useful to screen the tribological performance of hair care formulations both experimentally and computationally.

Nanoscale friction on MoS2/graphene heterostructures

Stacked hetero-structures of two-dimensional materials allow for a design of interactions with corresponding electronic and mechanical properties. We report structure, work function, and frictional properties of 1 to 4 layers of MoS₂ grown by chemical vapor deposition on epitaxial graphene on SiC(0001). Experiments were performed by atomic force microscopy in ultra-high vacuum. Friction is dominated by adhesion which is mediated by a deformation of the layers to adapt the shape of the tip apex. Friction decreases with increasing number of MoS₂ layers as the bending rigidity leads to less deformation. The dependence of friction on applied load and bias voltage can be attributed to variations in the atomic potential corrugation of the interface, which is enhanced by both load and applied bias. Minimal friction is obtained when work function differences are compensated.

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

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

Nanofriction Properties of Mono- and Double-Layer Ti3C2Tx MXenes

Unique structure and ability to control the surface termination groups of MXenes make these materials extremely promising for solid lubrication applications. Due to the challenging delamination process, the tribological properties of two-dimensional MXenes particles have been mostly investigated as additive components in the solvents working in the macrosystem, while the understanding of the nanotribological properties of mono- and few-layer MXenes is still limited. Here, we investigate the nanotribological properties of mono- and double-layer Ti₃C₂T_x MXenes deposited by the Langmuir-Schaefer technique on SiO₂/Si substrates. The friction of all of the samples demonstrated superior lubrication properties with respect to SiO₂ substrate, while the friction force of the monolayers was found to be slightly higher compared to double- and three-layer flakes, which demonstrated similar friction. The coefficient of friction was estimated to be 0.087 ± 0.002 and 0.082 ± 0.003 for mono- and double-layer flakes, respectively. The viscous regime was suggested as the dominant friction mechanism at high scanning velocities, while the meniscus forces affected by contamination of the MXenes surface were proposed to control the friction at low sliding velocities.

Atomic force microscopy probing interactions and microstructures of ionic liquids at solid surfaces

Ionic liquids (ILs) are room temperature molten salts that possess preeminent physicochemical properties and have shown great potential in many applications. However, the use of ILs in surface-dependent processes, e.g. energy storage, is hindered by the lack of a systematic understanding of the IL interfacial microstructure. ILs on the solid surface display rich ordering, arising from coulombic, van der Waals, solvophobic interactions, etc., all giving near-surface ILs distinct microstructures. Therefore, it is highly important to clarify the interactions of ILs with solid surfaces at the nanoscale to understand the microstructure and mechanism, providing quantitative structure-property relationships. Atomic force microscopy (AFM) opens a surface-sensitive way to probe the interaction force of ILs with solid surfaces in the layers from sub-nanometers to micrometers. Herein, this review showcases the recent progress of AFM in probing interactions and microstructures of ILs at solid interfaces, and the influence of IL characteristics, surface properties and external stimuli is thereafter discussed. Finally, a summary and perspectives are established, in which, the necessities of the quantification of IL-solid interactions at the molecular level, the development of in situ techniques closely coupled with AFM for probing IL-solid interfaces, and the combination of experiments and simulations are argued.

Cohesion Gain Induced by Nanosilica Consolidants for Monumental Stone Restoration

Mineral nanoparticle suspensions with consolidating properties have been successfully applied in the restoration of weathered architectural surfaces. However, the design of these consolidants is usually stone-specific and based on trial and error, which prevents their robust operation for a wide range of highly heterogeneous monumental stone materials. In this work, we develop a facile and versatile method to systematically study the consolidating mechanisms in action using a surface forces apparatus (SFA) with real-time force sensing and an X-ray surface forces apparatus (X-SFA). We directly assess the mechanical tensile strength of nanosilica-treated single mineral contacts and show a sharp increase in their cohesion. The smallest used nanoparticles provide an order of magnitude stronger contacts. We further resolve the microstructures and forces acting during evaporation-driven, capillary-force-induced nanoparticle aggregation processes, highlighting the importance of the interactions between the nanoparticles and the confining mineral walls. Our novel SFA-based approach offers insight into nano- and microscale mechanisms of consolidating silica treatments, and it can aid the design of nanomaterials used in stone consolidation.

Rough Surface Contact Modelling—A Review

It has been shown experimentally that boundary friction is proportional to load (commonly known as Amontons’ law) for more than 500 years, and the fact that it holds true over many scales (from microns to kilometres, and from nano-Newtons to Mega-Newtons) and for materials which deform both elastically and plastically has been the subject of much research, in order to more fully understand its wide applicability (and also to find any deviations from the law). Attempts to explain and understand Amontons’ law recognise that real surfaces are rough; as such, many researchers have studied the contact of rough surfaces under both elastic and plastic deformation conditions. As the focus on energy efficiency is ever increasing, machines are now being used with lower-viscosity lubricants, operating at higher loads and temperatures, such that the oil films separating the moving surfaces are becoming thinner, and there is a greater chance of mixed/boundary lubrication occurring. Because mixed/boundary lubrication occurs when the two moving rough surfaces come into contact, it is thought timely to review this topic and the current state of the theoretical and experimental understanding of rough-surface contact for the prediction of friction in the mixed/boundary lubrication regime.

Friction Coefficients for Droplets on Solids: The Liquid-Solid Amontons' Laws

The empirical laws of dry friction between two solid bodies date back to the work of Amontons in 1699 and are pre-dated by the work of Leonardo da Vinci. Fundamental to those laws are the concepts of static and kinetic coefficients of friction relating the pinning and sliding friction forces along a surface to the normal load force. For liquids on solid surfaces, contact lines also experience pinning and the language of friction is used when droplets are in motion. However, it is only recently that the concept of coefficients of friction has been defined in this context and that droplet friction has been discussed as having a static and a kinetic regime. Here, we use surface free energy considerations to show that the frictional force per unit length of a contact line is directly proportional to the normal component of the surface tension force. We define coefficients of friction for both contact lines and droplets and provide a droplet analogy of Amontons' first and second laws but with the normal load force of a solid replaced by the normal surface tension force of a liquid. In the static regime, the coefficient of static friction, defined by the maximum pinning force of a droplet, is proportional to the contact angle hysteresis, whereas in the kinetic regime, the coefficient of kinetic friction is proportional to the difference in dynamic advancing and receding contact angles. We show the consistency between the droplet form of Amontons' first and second laws and an equation derived by Furmidge. We use these liquid-solid Amontons' laws to describe literature data and report friction coefficients for various liquid-solid systems. The conceptual framework reported here should provide insight into the design of superhydrophobic, slippery liquid-infused porous surfaces (SLIPS) and other surfaces designed to control droplet motion.

Hydrophobic Recovery of PDMS Surfaces in Contact with Hydrophilic Entities: Relevance to Biomedical Devices

Polydimethylsiloxane (PDMS), a silicone elastomer, is increasingly being used in health and biomedical fields due to its excellent optical and mechanical properties. Its biocompatibility and resistance to biodegradation led to various applications (e.g., lung on a chip replicating blood flow, medical interventions, and diagnostics). The many advantages of PDMS are, however, partially offset by its inherent hydrophobicity, which makes it unsuitable for applications needing wetting, thus requiring the hydrophilization of its surface by exposure to UV or O2 plasma. Yet, the elastomeric state of PDMS translates in a slow, hours to days, process of reducing its surface hydrophilicity-a process denominated as hydrophobic recovery. Using Fourier transform infrared spectroscopy (FTIR) and atomic force microscopy (AFM), the present study details the dynamics of hydrophobic recovery of PDMS, on flat bare surfaces and on surfaces embedded with hydrophilic beads. It was found that a thin, stiff, hydrophilic, silica film formed on top of the PDMS material, following its hydrophilization by UV radiation. The hydrophobic recovery of bare PDMS material is the result of an overlap of various nano-mechanical, and diffusional processes, each with its own dynamics rate, which were analyzed in parallel. The hydrophobic recovery presents a hysteresis, with surface hydrophobicity recovering only partially due to a thin, but resilient top silica layer. The monitoring of hydrophobic recovery of PDMS embedded with hydrophilic beads revealed that this is delayed, and then totally stalled in the few-micrometer vicinity of the embedded hydrophilic beads. This region where the hydrophobic recovery stalls can be used as a good approximation of the depth of the resilient, moderately hydrophilic top layer on the PDMS material. The complex processes of hydrophilization and subsequent hydrophobic recovery impact the design, fabrication, and operation of PDMS materials and devices used for diagnostics and medical procedures. Consequently, especially considering the emergence of new surgical procedures using elastomers, the impact of hydrophobic recovery on the surface of PDMS warrants more comprehensive studies.

Robust Superlubric Interface across Nano- and Micro-Scales Enabled by Fluoroalkylsilane Self-Assembled Monolayers and Atomically Thin Graphene

Robust superlubrication across nano- and microscales is highly desirable at the interface with asperities of different sizes in durable micro/nanoelectromechanical systems under a harsh environment. A novel method to fabricate superlubric interfaces across nano- and microscales is developed by combining a batch of surface modification with atomically thin graphene. The robust superlubric interface across nano- and microscales between hydrophobic 1H,1H,2H,2H-perfluorodecyltrichlorosilane (FDTS) self-assembly monolayers (SAMs) and graphene was achieved under high relative humidity, sliding speed, and contact pressure. The superlubric mechanisms at the interface of FDTS/graphene could be attributed to the following at different scales: the hydrophobicity of FDTS SAMs and graphene preventing the capillary interaction of the interfacial friction under high relative humidity; the high elastic modulus of graphene leading to small interfacial contact area; the compressing and orientating of FDTS SAMs decreasing interfacial shear strength under high contact pressure; the surface modification of FDTS molecules reducing the interfacial potential barriers when sliding on the atomically thin graphene. The robust superlubric interface across nano- and microscales reducing the friction at the complicated interfaces with asperities at different scales and improving the performance and durability have great potentials in the field of micro/nano mechanical systems.

Elementary, Atomic-Level Friction Processes in Systems with Metallic Inclusions-Systematic Simulations for a Wide Range of Local Pressures

In this work, simulations of friction at the atomic level were performed to evaluate the influence of inclusions coming from metallic nanoadditives in the friction pair. The simple 2D model was applied considering appropriate values of Lennard–Jones potential parameters for given sets of interacting atoms. The real sliding pairs were replaced by effective equivalents consisting of several atoms. The calculations were based on the pseudo-static approximation. The simplicity of the model enabled to repeat the fast calculations in a very wide range of local pressures and for several types of atomic tribopairs. The performed simulations demonstrated a strong dependence of the coefficient of friction (COF) on the atomic environment of the atoms constituting a tribopair. It was confirmed theoretically that the Mo-Fe pair is characterized by lower atomic COF than Fe-Fe, Cu-Fe, and Ag-Fe pairs. This points to the great applicational potential of metallic molybdenum coating applications in tribological systems. Moreover, it was demonstrated that, although Cu-Cu and Ag-Ag pairs are characterized by relatively high COF, they lower the friction as inclusions in Fe surfaces.

A facile and industrial method for synthesis of modified magnetic lipophilic graphene as a super oil additive

Friction and wear are the two major reasons for energy and material losses in mechanical processes. In this research, a simple, industrial and fast exfoliation technique for the production of graphene using sodium azide and graphite in a water solvent without the need for a specific device has been presented following by lipophilizing with octylamine and only with Fe (II). Magnetic nanoparticles were applied on graphene surface, and simultaneously the graphene surface was both lipophilic and magnetic. The method used for graphene production is unique up to now and also it does not oxidize in production procedure. Performed analyzes demonstrate non-destructive properties without any changes in surface functional groups.

Polaronic Contributions to Friction in a Manganite Thin Film

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

On the physicochemical origin of nanoscale friction: the polarizability and electronegativity relationship tailoring nanotribology

Friction is a ubiquitous manifestation of nature, and when it is studied at the nanoscale, complex and interesting effects arise from fundamental physical and chemical surface properties. Surprisingly, and probably due to the complexity of nanofriction studies, this aspect has not been completely discussed in prior studies. To fully consider the physicochemical influence in nanoscale friction, amorphous carbon films with different amounts of hydrogen and fluorine were prepared, chemically characterized, and evaluated via lateral force microscopy. Hydrogen and fluorine were selected because although they exhibit different physicochemical properties, both contribute to frictional force reduction. Indeed, to explain the experimental behavior, it is necessary to propose a new damping constant unifying both polarizability (physical) and electronegativity (chemical) properties. The satisfactory agreement between theory and experiments may encourage and enhance deeper discussion and new experiments that take into account the chemical peculiarities of frictional behavior relating to nanoscale elastic regimes.

Non-Empirical Law for Nanoscale Atom-by-Atom Wear

Wear of contact materials results in energy loss and device failure. Conventionally, wear is described by empirical laws such as the Archard's law; however, the fundamental physical and chemical origins of the empirical law have long been elusive, and moreover empirical wear laws do not always hold for nanoscale contact, collaboratively hindering the development of high-durable tribosystems. Here, a non-empirical and robustly applicable wear law for nanoscale contact situations is proposed. The proposed wear law successfully unveils why the nanoscale wear behaviors do not obey the description by Archard's law in all cases although still obey it in certain experiments. The robustness and applicability of the proposed wear law is validated by atomistic simulations. This work affords a way to calculate wear at nanoscale contact robustly and theoretically, and will contribute to developing design principles for wear reduction.

Identifying Physical and Chemical Contributions to Friction: A Comparative Study of Chemically Inert and Active Graphene Step Edges

Friction has both physical and chemical origins. To differentiate these origins and understand their combined effects, we study friction at graphene step edges with the same height and different terminating chemical moieties using atomic force microscopy (AFM) and reactive molecular dynamics (MD) simulations. A step edge produced by physical exfoliation of graphite layers in ambient air is terminated with hydroxyl (OH) groups. Measurements with a silica countersurface at this exposed step edge in dry nitrogen provide a reference where both physical topography effects and chemical hydrogen-bonding (H-bonding) interactions are significant. H-bonding is then suppressed in AFM experiments performed in alcohol vapor environments, where the OH groups at the step edge are covered with physisorbed alcohol molecules. Finally, a step edge buried under another graphene layer provides a chemically inert topographic feature with the same height. These systems are modeled by reactive MD simulations of sliding on an OH-terminated step edge, a step edge with alkoxide group termination, or a buried step edge. Results from AFM experiments and MD simulations demonstrate hysteresis in friction measured during the step-up versus step-down processes in all cases except the buried step edge. The origin of this hysteresis is shown to be the anisotropic deflection of terminal groups at the exposed step edge, which varies depending on their chemical functionality. The findings explain why friction is high on atomically corrugated and chemically active surfaces, which provides the insight needed to achieve superlubricity more broadly.

Lubricated friction around nanodefects

The lubrication properties of nanoconfined liquids underpin countless natural and industrial processes. However, our current understanding of lubricated friction is still limited, especially for nonideal interfaces exhibiting nanoscale chemical and topographical defects. Here, we use atomic force microscopy to explore the equilibrium and dynamical behavior of a model lubricant, squalane, confined between a diamond tip and graphite in the vicinity of an atomic step. We combine high-resolution imaging of the interface with highly localized shear measurements at different velocities and temperatures to derive a quantitative picture of the lubricated friction around surface defects. We show that defects tend to promote local molecular order and increase friction forces by reducing the number of stable molecular configurations in their immediate vicinity. The effect is general, can propagate over hundreds of nanometers, and can be quantitatively described by a semiempirical model that bridges the molecular details and mesoscale observations.

Negative friction coefficient in microscale graphite/mica layered heterojunctions

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

Bioinspired Adhesion Polymers: Wear Resistance of Adsorption Layers

Mussel adhesive polymers owe their ability to strongly bind to a large variety of surfaces under water to their high content of 3,4-dihydroxy-l-phenylalanine (DOPA) groups and high positive charge. In this work, we use a set of statistical copolymers that contain medium-length poly(ethylene oxide) side chains that are anchored to the surface in three different ways: by means of (i) electrostatic forces, (ii) catechol groups (as in DOPA), and (iii) the combination of electrostatic forces and catechol groups. A nanotribological scanning probe method was utilized to evaluate the wear resistance of the formed layers as a function of normal load. It was found that the combined measurement of surface topography and stiffness provided an accurate assessment of the wear resistance of such thin layers. In particular, surface stiffness maps allowed us to identify the initiation of wear before a clear topographical wear scar was developed. Our data demonstrate that the molecular and abrasive wear resistance on silica surfaces depends on the anchoring mode and follows the order catechol groups combined with electrostatic forces > catechol groups alone > electrostatic forces alone. The devised methodology should be generally applicable for evaluating wear resistance or "robustness" of thin adsorbed layers on a variety of surfaces.

Bidirectional Transport of Nanoparticles and Cells with a Bio-Conveyor Belt

The bidirectional transport of nanoparticles and biological cells is of great significance in efficient biological assays and precision cell screening, and can be achieved with optical conveyor belts in a noncontact and noninvasive manner. However, implantation of these belts into biological systems can present significant challenges owing to the incompatibility of the artificial materials. In this work, an optical conveyor belt assembled from natural biological cells is proposed. The diameter of the belt (500 nm) is smaller than the laser wavelength (980 nm) and, therefore, the evanescent wave stably traps the nanoparticles and cells on the belt surface. By adjusting the relative power of the lasers injected into the belt, the particles or cells can be bidirectionally transported along the bio-conveyor belt. The experimental results are numerically interpreted and the transport velocities are investigated based on simulations. Further experiments show that the bio-conveyor belt can also be assembled with mammalian cells and then applied to dynamic cell transport in vivo. The bio-conveyor belt might provide a noninvasive and biocompatible tool for biomedical assays, drug delivery, and biological nanoarchitectonics.

Multi-Scale Surface Texturing in Tribology—Current Knowledge and Future Perspectives

Surface texturing has been frequently used for tribological purposes in the last three decades due to its great potential to reduce friction and wear. Although biological systems advocate the use of hierarchical, multi-scale surface textures, most of the published experimental and numerical works have mainly addressed effects induced by single-scale surface textures. Therefore, it can be assumed that the potential of multi-scale surface texturing to further optimize friction and wear is underexplored. The aim of this review article is to shed some light on the current knowledge in the field of multi-scale surface textures applied to tribological systems from an experimental and numerical point of view. Initially, fabrication techniques with their respective advantages and disadvantages regarding the ability to create multi-scale surface textures are summarized. Afterwards, the existing state-of-the-art regarding experimental work performed to explore the potential, as well as the underlying effects of multi-scale textures under dry and lubricated conditions, is presented. Subsequently, numerical approaches to predict the behavior of multi-scale surface texturing under lubricated conditions are elucidated. Finally, the existing knowledge and hypotheses about the underlying driven mechanisms responsible for the improved tribological performance of multi-scale textures are summarized, and future trends in this research direction are emphasized.

The interplay between drift and electrical measurement in conduction atomic force microscopy

In Conduction Atomic Force Microscopy (CAFM), it is sometimes required to monitor electrical data at a single location over an extended period of time. However, thermal drift of the microscope will cause the tip to move with respect to the sample and thus limit the collection of data. We investigate a method to prolong the time a tip dwells at a location by choosing the AFM cantilever to have small spring constants in the lateral directions. The basis of the approach is that the tip can only move (or slip) once the lateral forces caused by drift overcome the friction force pinning the tip to the surface. We demonstrate the effect experimentally using platinum wire tips and diamond coated tips on SiO₂ and HfO₂ dielectric films. Simultaneous measurement of the current flow and lateral force signals show that the onset of tip slipping correlates with the beginning of a decrease in the measured current flow, and the onset of slip is prolonged for blunt tips or cantilevers having soft lateral spring constants. The approach not only provides a way to improve the CAFM method for time dependent measurements but also assists in interpreting CAFM data in the presence of drift.

Surface Characterization and Tribological Performance of Anodizing Micro-Textured Aluminum-Silicon Alloys

Eutectic aluminum-silicon alloys present high frictional coefficient and a high wear rate due to the low hardness under sliding friction conditions. In this paper, the eutectic aluminum-silicon alloy was textured firstly by micro-milling operations. Then, the micro-textured specimen was subjected to anodizing to fabricate alumina films. The surface topography, surface roughness, and bearing area ratio of micro-textured and anodizing micro-textured specimens were measured and characterized. For the anodizing micro-textured specimens, the surface roughness and superficial hardness increase compared with those for micro-textured ones. Tribological tests indicate that anodizing micro-textured samples present lower friction coefficient of 0.37 than that of flat samples of 0.43 under dry sliding conditions. However, they exhibit higher friction coefficient at 0.16 than that of flat samples of 0.13 under oil-lubricated conditions. The difference between the friction coefficient of anodizing micro-textured and flat samples under dry and oil-lubricated conditions is ascribed to the influence mechanism of surface roughness, bearing area ratio curves, and its relative parameters on the tribological performance of testing samples. The dry sliding friction coefficient has a positive correlation with bearing area ratio curves, while they present negative correlation with bearing area ratio curves under oil-lubricated conditions. The synergy method treated with micro-milling and anodizing provides an effective approach to enhance the dry sliding friction property of eutectic aluminum-silicon alloys.

Mutual Identification between the Pressure-Induced Superlubricity and the Image Contrast Inversion of Carbon Nanostructures from AFM Technology

Previous studies predict pressure-induced superlubricity, but that is still undetermined due to the absence of a probing technique. Here, we present unprecedented mutual identification between the superlubricity and atomic-scale image from atomic force microscopy (AFM) measurement by the first-principles simulation of metallic Cu tip scanning on carbon nanostructures. With decreasing tip height, the sliding potential evolves from anticorrugated, to substantially flattened, and eventually to corrugated patterns, inducing superlubricity of the flattened potential at the critical height. Correspondingly, both the normal forces and the contrast of atomic image patterns also undergo similar inversions at the respective critical tip heights, in accordance with recent experimental observation. On the basis of the underlying mechanism elucidated, the mutual identification between the image contrast inversion and the superlubricity is confirmed. This may advance AFM technology to stimulate the experimental observation of superlubricity from its theoretical studies and may thus promote the development of theory systems of superlubticity.

Effect of Micro- and Nano-Sized Carbonous Solid Lubricants as Oil Additives in Nanofluid on Tribological Properties

The tribological behavior of graphene and graphite as additives in canola oil was investigated with a pin-on-disk tribometer. The wear surfaces of the aluminum pins lubricated with the additive-containing canola oil were analyzed by scanning electron microscopy (SEM). It was found that graphene and graphite as additives in oil show a lower coefficient of friction and wear rate in comparison with neat canola oil. The graphene sheets are more effective than graphite flakes to reduce friction and wear. In addition, there is a proper concentration where the coefficient of friction (COF) and wear are in minimum value. The optimal concentration of the additive in canola oil is about 0.7 wt %. Therefore, the load-carrying capacity and antiwear ability of the lubricating oil are improved. Moreover, the worn surface of aluminum pins is smother in the presence of solid lubricant rather than neat oil.

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

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

Shear heating, flow, and friction of confined molecular fluids at high pressure

Understanding the molecular-scale behavior of fluids confined and sheared between solid surfaces is important for many applications, particularly tribology where this often governs the macroscopic frictional response. In this study, nonequilibrium molecular dynamics simulations are performed to investigate the effects of fluid and surface properties on the spatially resolved temperature and flow profiles, as well as friction. The severe pressure and shear rate conditions studied are representative of the elastohydrodynamic lubrication regime. In agreement with tribology experiments, flexible lubricant molecules give low friction, which increases linearly with logarithmic shear rate, while bulky traction fluids show higher friction, but a weaker shear rate dependence. Compared to lubricants, traction fluids show more significant shear heating and stronger shear localization. Models developed for macroscopic systems can be used to describe both the spatially resolved temperature profile shape and the mean film temperature rise. The thermal conductivity of the fluids increases with pressure and is significantly higher for lubricants compared to traction fluids, in agreement with experimental results. In a subset of simulations, the efficiency of the thermostat in one of the surfaces is reduced to represent surfaces with lower thermal conductivity. For these unsymmetrical systems, the flow and the temperature profiles become strongly asymmetric and some thermal slip can occur at the solid-fluid interface, despite the absence of velocity slip. The larger temperature rises and steeper velocity gradients in these cases lead to large reductions in friction, particularly at high pressure and shear rate.

Friction forces of saliva and red wine on hydrophobic and hydrophilic surfaces

The physical aspect of human oral astringency perception - the mouthfeel - of red wine has not been quantitatively studied in depth. In this study, the interfacial friction/lubrication properties of saliva (mucin from bovine submaxillary glands or human saliva) with red wines (cv. Cabernet sauvignon and Pinot noir) were measured with a surface force apparatus (SFA). In SFA measurements sliding occurs between smooth, undamaged surfaces with a well-defined contact area and film thickness. The surfaces were either hard, hydrophilic mica or soft, hydrophobic PDMS-coated mica which mimic in-mouth conditions. Saliva was a better lubricant than mucin with the soft, hydrophobic surfaces. In addition, saliva's lubricity was 2.5 times better on the soft hydrophobic surfaces than hard hydrophilic surfaces. The addition of red wine with saliva further decreased friction and improved lubrication. Surprisingly, the coefficient of friction measured for red wine with saliva as the lubricant was higher for Pinot noir than Cabernet sauvignon wine. The aggregation and precipitation of salivary proteins by tannins is well known. The lower friction of high tannin Cabernet sauvignon compared to lower tannin Pinot noir was attributed to exclusion of these aggregates and depletion of more polymeric and protein material from the interfacial sliding region.

Influence of wall heterogeneity on nanoscopically confined polymers

We investigate via molecular dynamics simulations the behaviour of a polymer melt confined between surfaces with increasing spatial correlation (patchiness) of weakly and strongly interacting sites. Beyond a critical patchiness, we find a dramatic dynamic decoupling, characterized by a steep growth of the longest relaxation time and a constant diffusion coefficient. This arises from dynamic heterogeneities induced by the walls in the adjacent polymer layers, leading to the coexistence of fast and slow chain populations. Structural variations are also present, but they are not easy to detect. Our work opens the way to a better understanding of adhesion, friction, rubber reinforcement by fillers, and many other open issues involving the dynamics of polymeric materials on rough, chemically heterogeneous and possibly "dirty" surfaces.