Structural lubricity in soft and hard matter systems

The effects of disordered edge and vanishing friction in microscale structural superlubric graphite contact

Structural superlubricity (SSL), a state of ultralow friction and no wear between two solid surfaces in contact, offers a fundamental solution for reducing friction and wear. Recent studies find that the edge pinning of SSL contact dominates the friction. However, its nature remains mysterious due to the lack of direct characterizations on atomic scale. Here, for microscale graphite mesa, we unambiguously reveal the atomic structure and chemical composition of the disordered edge. The friction stress for each contact condition, namely, edge/edge, edge/surface, and surface/surface contacts are quantified, with the ratio being 104:103:1. The mechanism is revealed by all-atom molecular dynamic simulations, which reproduce the measured friction qualitatively. Inspired by such understanding, through fabricating SixNy caps with tensile stress, we further eliminate the friction caused by the edges through disengaging the edges from the substrate. As a result, an SSL contact with ultralow friction stress of 0.1 kPa or lower is achieved directly.

Evidence of Directional Structural Superlubricity and Lévy Flights in a van der Waals Heterostructure

Structural superlubricity is a special frictionless contact in which two crystals are in incommensurate arrangement such that relative in-plane translation is associated with vanishing energy barrier crossing. So far, it has been realized in multilayer graphene and other van der Waals (2D crystals with hexagonal or triangular crystalline symmetries, leading to isotropic frictionless contacts. Directional structural superlubricity, to date unrealized in 2D systems, is possible when the reciprocal lattices of the two crystals coincide in one direction only. Here, directional structural superlubricity a α-bismuthene/graphite van der Waals system is evidenced, manifested by spontaneous hopping of the islands over hundreds of nanometers at room temperature, resolved by low-energy electron microscopy and supported by registry simulations. Statistical analysis of individual and collective α-bismuthene islands populations reveal a heavy-tailed distribution of the hopping lengths and sticking times indicative of Lévy flight dynamics, largely unobserved in condensed-matter systems.

Geometry-induced friction at a soft interface

Soft and biological matter come in a variety of shapes and geometries. When soft surfaces that do not fit into each other due to a mismatch in Gaussian curvatures form an interface, beautiful geometry-induced patterns are known to emerge. In this paper, we study the effect of geometry on the dynamical response of soft surfaces moving relative to each other. Using a simple experimental scheme, we measure friction between a highly bendable thin polymer sheet and a hydrogel substrate. At this soft and low-friction interface, we find a strong dependence of friction on the relative geometry of the two surfaces-a flat sheet experiences significantly larger friction on a spherical substrate than on flat or cylindrical substrate. We show that the stress developed in the sheet due to its geometrically incompatible confinement is responsible for the enhanced friction. This mechanism also leads to a transition in the nature of friction as the sheet radius is increased beyond a critical value. Our finding reveals a hitherto unnoticed mechanism based on an interplay between geometry and elasticity that may influence friction significantly in soft, biological, and nanoscale systems. In particular, it provokes us to reexamine our understanding of phenomena such as the curvature dependence of biological cell mobility.

Macroscale Superlubricity on Nanoscale Graphene Moiré Structure-Assembled Surface via Counterface Hydrogen Modulation

Interlayer incommensurateness slippage is an excellent pathway to realize superlubricity of van der Waals materials; however, it is instable and heavily depends on twisted angle and super-smooth substrate which pose great challenges for the practical application of superlubricity. Here, macroscale superlubricity (0.001) is reported on countless nanoscale graphene moiré structure (GMS)-assembled surface via counterface hydrogen (H) modulation. The GMS-assembled surface is formed on grinding balls via sphere-triggered strain engineering. By the H modulation of counterface diamond-like carbon (25 at.% H), the wear of GMS-assembled surface is significantly reduced and a steadily superlubric sliding interface between them is achieved, based on assembly face charge depletion and H-induced assembly edge weakening. Furthermore, the superlubricity between GMS-assembled and DLC25 surfaces holds true in wide ranges of normal load (7-11 N), sliding velocity (0.5-27 cm -1s), contact area (0.4×104-3.7×104 µm2), and contact pressure (0.19-1.82 GPa). Atomistic simulations confirm the preferential formation of GMS on a sphere, and demonstrate the superlubricity on GMS-assembled surface via counterface H modulation. The results provide an efficient tribo-pairing strategy to achieve robust superlubricity, which is of significance for the engineering application of superlubricity.

In Situ Twistronics: A New Platform Based on Superlubricity

Twistronics, an emerging field focused on exploring the unique electrical properties induced by twist interface in graphene multilayers, has garnered significant attention in recent years. The general manipulation of twist angle depends on the assembly of van der Waals (vdW) layered materials, which has led to the discovery of unconventional superconductivity, ferroelectricity, and nonlinear optics, thereby expanding the realm of twistronics. Recently, in situ tuning of interlayer conductivity in vdW layered materials has been achieved based on scanning probe microscope. In this Perspective, the advancements in in situ twistronics are focused on by reviewing the state-of-the-art in situ manipulating technology, discussing the underlying mechanism based on the concept of structural superlubricity, and exploiting the real-time twistronic tests under scanning electron microscope (SEM). It is shown that the real-time manipulation under SEM allows for visualizing and monitoring the interface status during in situ twistronic testing. By harnessing the unique tribological properties of vdW layered materials, this novel platform not only enhances the fabrication of twistronic devices but also facilitates the fundamental understanding of interface phenomena in vdW layered materials. Moreover, this platform holds great promise for the application of twistronic-mechanical systems, providing avenues for the integration of twistronics into various mechanical frameworks.

Tunable, Wide-Temperature, and Macroscale Superlubricity Enabled by Nanoscale Van Der Waals Heterojunction-to-Homojunction Transformation

Achieving macroscale superlubricity of van der Waals (vdW) nanopowders is particularly challenging, due to the difficulty in forming ordered junctions before friction and the friction-induced complex contact restructuration among multiple nanometer-sized junctions. Here, a facile way is reported to achieve vdW nanopowder-to-heterojunction conversion by graphene edge-oxygen (GEO) incorporation. The GEO effectively weakens the out-of-plane edge-edge and in-plane plane-edge states of the vdW nanopowder, leading to a coexistent structure of nanoscale homojunctions and heterojunctions on the grinding balls. When sliding on diamond-like carbon surfaces, the ball-supported structure governs macroscale superlubricity by heterojunction-to-homojunction transformation among the countless nanoscale junctions. Furthermore, the transformation guides the tunable design of superlubricity, achieving superlubricity (µ ≈ 0.005) at wide ranges of load, velocity, and temperature (-200 to 300 °C). Atomistic simulations reveal the GEO-enhanced conversion of vdW nanopowder to heterojunctions and demonstrate the heterojunction-to-homojunction transformation superlubricity mechanism. The findings are of significance for the macroscopic scale-up and engineering application of structural superlubricity.

Superlubricity of Materials: Progress, Potential, and Challenges

This review paper provides a comprehensive overview of the phenomenon of superlubricity, its associated material characteristics, and its potential applications. Superlubricity, the state of near-zero friction between two surfaces, presents significant potential for enhancing the efficiency of mechanical systems, thus attracting significant attention in both academic and industrial realms. We explore the atomic/molecular structures that enable this characteristic and discuss notable superlubric materials, including graphite, diamond-like carbon, and advanced engineering composites. The review further elaborates on the methods of achieving superlubricity at both nanoscale and macroscale levels, highlighting the influence of environmental conditions. We also discuss superlubricity's applications, ranging from mechanical systems to energy conservation and biomedical applications. Despite the promising potential, the realization of superlubricity is laden with challenges. We address these technical difficulties, specifically those related to achieving and maintaining superlubricity, and the issues encountered in scaling up for industrial applications. The paper also underscores the sustainability concerns associated with superlubricity and proposes potential solutions. We conclude with a discussion of the possible future research directions and the impact of technological innovations in this field. This review thus provides a valuable resource for researchers and industry professionals engaged in the development and application of superlubric materials.

Dissipation Mechanisms and Superlubricity in Solid Lubrication by Wet-Transferred Solution-Processed Graphene Flakes: Implications for Micro Electromechanical Devices

Solution-processed few-layer graphene flakes, dispensed to rotating and sliding contacts via liquid dispersions, are gaining increasing attention as friction modifiers to achieve low friction and wear at technologically relevant interfaces. Vanishing friction states, i.e., superlubricity, have been documented for nearly-ideal nanoscale contacts lubricated by individual graphene flakes. However, there is no clear understanding if superlubricity might persist for larger and morphologically disordered contacts, as those typically obtained by incorporating wet-transferred solution-processed flakes into realistic microscale contact junctions. In this study, we address the friction performance of solution-processed graphene flakes by means of colloidal probe atomic force microscopy. We use a state-of-the-art additive-free aqueous dispersion to coat micrometric silica beads, which are then sled under ambient conditions against prototypical material substrates, namely, graphite and the transition metal dichalcogenides (TMDs) MoS₂ and WS₂. High resolution microscopy proves that the random assembly of the wet-transferred flakes over the silica probes results into an inhomogeneous coating, formed by graphene patches that control contact mechanics through tens-of-nanometers tall protrusions. Atomic-scale friction force spectroscopy reveals that dissipation proceeds via stick-slip instabilities. Load-controlled transitions from dissipative stick-slip to superlubric continuous sliding may occur for the graphene-graphite homojunctions, whereas single- and multiple-slips dissipative dynamics characterizes the graphene-TMD heterojunctions. Systematic numerical simulations demonstrate that the thermally activated single-asperity Prandtl-Tomlinson model comprehensively describes friction experiments involving different graphene-coated colloidal probes, material substrates, and sliding regimes. Our work establishes experimental procedures and key concepts that enable mesoscale superlubricity by wet-transferred liquid-processed graphene flakes. Together with the rise of scalable material printing techniques, our findings support the use of such nanomaterials to approach superlubricity in micro electromechanical systems.

Largest Lyapunov exponent as a tool for detecting relative changes in the particle positions

Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent, and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step.

Twisting Dynamics of Large Lattice-Mismatch van der Waals Heterostructures

van der Waals (vdW) homo/heterostructures are ideal systems for studying interfacial tribological properties such as structural superlubricity. Previous studies concentrated on the mechanism of translational motion in vdW interfaces. However, detailed mechanisms and general properties of the rotational motion are barely explored. Here, we combine experiments and simulations to reveal the twisting dynamics of the MoS₂/graphite heterostructure. Unlike the translational friction falling into the superlubricity regime with no twist angle dependence, the dynamic rotational resistances highly depend on twist angles. Our results show that the periodic rotational resistance force originates from structural potential energy changes during the twisting. The structural potential energy of MoS₂/graphite heterostructure increases monotonically from 0° to 30° twist angles, and the estimated relative energy barrier is (1.43 ± 0.36) × 10^-3 J/m². The formation of Moiré superstructures in the graphene layer is the key to controlling the structural potential energy of the MoS₂/graphene heterostructure. Our results suggest that in twisting 2D heterostructures, even if the interface sliding friction is negligible, the evolving potential energy change results in a nonvanishing rotational resistance force. The structural change of the heterostructure can be an additional pathway for energy dissipation in the rotational motion, further enhancing the rotational friction force.

Preparation, properties and applications of two-dimensional superlattices

As a combination concept of a 2D material and a superlattice, two-dimensional superlattices (2DSs) have attracted increasing attention recently. The natural advantages of 2D materials in their properties, dimension, diversity and compatibility, and their gradually improved technologies for preparation and device fabrication serve as solid foundations for the development of 2DSs. Compared with the existing 2D materials and even their heterostructures, 2DSs relate to more materials and elaborate architectures, leading to novel systems with more degrees of freedom to modulate material properties at the nanoscale. Here, three typical types of 2DSs, including the component, strain-induced and moiré superlattices, are reviewed. The preparation methods, properties and state-of-the-art applications of each type are summarized. An outlook of the challenges and future developments is also presented. We hope that this work can provide a reference for the development of 2DS-related research.

Frictionless nanohighways on crystalline surfaces

The understanding of friction at nano-scales, ruled by the regular arrangement of atoms, is surprisingly incomplete. Here we provide a unified understanding by studying the interlocking potential energy of two infinite contacting surfaces with arbitrary lattice symmetries, and extending it to finite contacts. We categorize, based purely on geometrical features, all possible contacts into three different types: a structurally lubric contact where the monolayer can move isotropically without friction, a corrugated and strongly interlocked contact, and a newly discovered directionally structurally lubric contact where the layer can move frictionlessly along one specific direction and retains finite friction along all other directions. This novel category is energetically stable against rotational perturbations and provides extreme friction anisotropy. The finite-size analysis shows that our categorization applies to a wide range of technologically relevant materials in contact, from adsorbates on crystal surfaces to layered two-dimensional materials and colloidal monolayers.

Sliding Friction and Superlubricity of Colloidal AFM Probes Coated by Tribo-Induced Graphitic Transfer Layers

Colloidal probe atomic force microscopy (AFM) allows us to explore sliding friction phenomena in graphite contacts of nominal lateral size up to hundreds of nanometers. It is known that contact formation involves tribo-induced material transfer of graphite flakes from the graphitic substrate to the colloidal probe. In this context, sliding states with nearly vanishing friction, i.e., superlubricity, may set in. A comprehensive investigation of the transfer layer properties is mandatory to ascertain the origin of superlubricity. Here we explore the friction response of micrometric beads, of different size and pristine surface roughness, sliding on graphite under ambient conditions. We show that such tribosystems undergo a robust transition toward a low-adhesion, low-friction state dominated by mechanical interactions at one dominant tribo-induced nanocontact. Friction force spectroscopy reveals that the nanocontact can be superlubric or dissipative, in fact undergoing a load-driven transition from dissipative stick-slip to continuous superlubric sliding. This behavior is excellently described by the thermally activated, single-asperity Prandtl-Tomlinson model. Our results indicate that upon formation of the transfer layer, friction depends on the energy landscape experienced by the topographically highest tribo-induced nanoasperity. We consistently find larger dissipation when the tribo-induced nanoasperity is slid against surfaces with higher atomic corrugation than graphite, like MoS₂ and WS₂, in prototypical van der Waals layered heterojunctions.

Electrotunable friction with ionic liquid lubricants

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

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

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

Mussel-Inspired Interfacial Modification for Ultra-Stable MoS2 Lubricating Films with Improved Tribological Behavior on Nano-Textured ZnO Surfaces Using the AACVD Method

Friction-associated energy loss and mechanical wear leading to failure is a major problem in industries. To mitigate this, the design and testing of novel lubricants is important. Here, we show the facile one-pot synthesis of ZnO/ZnO nanorods (NRs) and MoS2 films on pre-treated glass substrates via aerosol-assisted chemical vapor deposition. The bearing capacity and wear life of ZnO film/ZnO NRs/MoS2 films were improved due to the lubricant retention capabilities of the NRs. Modification of the ZnO/MoS2 nano-arrays using polydopamine (PDA) allowed the realization of robust and ultra-stable solid lubricants through the triple action of chemical chelation, layered materials, and nanotexture, especially under heavy load conditions. Compared with pristine MoS2, the adhesion and bearing strength of the composite film increased by 11 and 30 times, respectively, while the coefficient of friction and wear rate decreased by 94 and 85%, respectively. This is because the chelation between the transition metal and the groups in the interlayer PDA was fully utilized to improve the interface compatibility, which significantly improves the robustness of ZnO NRs and the adhesion of MoS2. This allowed a stable and firm mechanical lock between the substrate, lubricant films, and the steel ball. It demonstrated a convenient method to achieve the antifriction and anti-wear of solid lubricating materials by PDA interface modification for practical industrial applications.

Flexible Superlubricity Unveiled in Sidewinding Motion of Individual Polymeric Chains

A combination of low temperature atomic force microcopy and molecular dynamic simulations is used to demonstrate that soft designer molecules realize a sidewinding motion when dragged over a gold surface. Exploiting their longitudinal flexibility, pyrenylene chains are indeed able to lower diffusion energy barriers via on-surface directional locking and molecular strain. The resulting ultralow friction reaches values on the order of tens of pN reported so far only for rigid chains sliding on an incommensurate surface. Therefore, we demonstrate how molecular flexibility can be harnessed to realize complex nanomotion while retaining a superlubric character. This is in contrast with the paradigm guiding the design of most superlubric nanocontacts (mismatched rigid contacting surfaces).

Critical peeling of tethered nanoribbons

The peeling of an immobile adsorbed membrane is a well-known problem in engineering and macroscopic tribology. In the classic setup, picking up at one extreme and pulling off result in a peeling force that is a decreasing function of the pickup angle. As one end is lifted, the detachment front retracts to meet the immobile tail. At the nanoscale, interesting situations arise with the peeling of graphene nanoribbons (GNRs) on gold, as realized, e.g., by atomic force microscopy. The nanosized system shows a constant-force steady peeling regime, where the tip lifting h produces no retraction of the ribbon detachment point, and just an advancement h of the free tail end. This is opposite to the classic case, where the detachment point retracts and the tail end stands still. Here we characterise, by analytical modeling and numerical simulations, a third, experimentally relevant setup where the nanoribbon, albeit structurally lubric, does not have a freely moving tail end, which is instead elastically tethered. Surprisingly, novel nontrivial scaling exponents appear that regulate the peeling evolution. As the detachment front retracts and the tethered tail is stretched, power laws of h characterize the shrinking of the adhered length, the growth of peeling force and the peeling angle. These exponents precede the final total detachment as a critical point, where the entire ribbon eventually hangs suspended between the tip and the tethering spring. These analytical predictions are confirmed by realistic MD simulations, retaining the full atomistic description, also confirming their survival at finite experimental temperatures.

Shear adhesive strength between epoxy resin and copper surfaces: a density functional theory study

Shear adhesive strengths of epoxy resin for copper and copper oxide surfaces are estimated based on quantum chemical calculations. Shear adhesion has periodicity, and its origin is revealed.

Dissipation from Interlayer Friction in Graphene Nanoelectromechanical Resonators

A unique feature of two-dimensional (2D) materials is the ultralow friction at their van der Waals interfaces. A key question in a new generation of 2D heterostructure-based nanoelectromechanical systems (NEMS) is how the low friction interfaces will affect the dynamic performance. Here, we apply the exquisite sensitivity of graphene nanoelectromechanical drumhead resonators to compare the dissipation from monolayer, Bernal-stacked bilayer, and twisted bilayer graphene membranes. We find a significant difference in the average quality factors of three resonator types: 53 for monolayer, 40 for twisted and 31 for Bernal-stacked membranes. We model this difference as a combination of change in stiffness and additional dissipation from interlayer friction during motion. We find even the lowest frictions measured on sliding 2D interfaces are sufficient to alter dissipation in 2D NEMS. This model provides a generalized approach to quantify dissipation in NEMS based on 2D heterostructures which incorporate interlayer slip and friction.

Thermally active nanoparticle clusters enslaved by engineered domain wall traps

The stable assembly of fluctuating nanoparticle clusters on a surface represents a technological challenge of widespread interest for both fundamental and applied research. Here we demonstrate a technique to stably confine in two dimensions clusters of interacting nanoparticles via size-tunable, virtual magnetic traps. We use cylindrical Bloch walls arranged to form a triangular lattice of ferromagnetic domains within an epitaxially grown ferrite garnet film. At each domain, the magnetic stray field generates an effective harmonic potential with a field tunable stiffness. The experiments are combined with theory to show that the magnetic confinement is effectively harmonic and pairwise interactions are of dipolar nature, leading to central, strictly repulsive forces. For clusters of magnetic nanoparticles, the stationary collective states arise from the competition between repulsion, confinement and the tendency to fill the central potential well. Using a numerical simulation model as a quantitative map between the experiments and theory we explore the field-induced crystallization process for larger clusters and unveil the existence of three different dynamical regimes. The present method provides a model platform for investigations of the collective phenomena emerging when strongly confined nanoparticle clusters are forced to move in an idealized, harmonic-like potential.

Theoretical modeling of structural superlubricity in rotated bilayer graphene, hexagonal boron nitride, molybdenum disulfide, and blue phosphorene

The superior lubrication capabilities of two-dimensional crystalline materials such as graphene, hexagonal boron nitride (h-BN), and molybdenum disulfide (MoS₂) have been well known for many years. It is generally accepted that structural superlubricity in these materials is due to misalignment of the surfaces in contact, known as incommensurability. In this work, we present a detailed study of structural superlubricity in bilayer graphene, h-BN, MoS₂, and the novel material blue phosphorene (b-P) using dispersion-corrected density-functional theory with periodic boundary conditions. Potential energy surfaces for interlayer sliding were computed for the standard (1 × 1) cell and three rotated, Moiré unit cells for each material. The energy barriers to form the rotated structures remain higher than the minimum-energy sliding barriers for the (1 × 1) cells. However, if the rotational barriers can be overcome, nearly barrierless interlayer sliding is observed in the rotated cells for all four materials. This is the first density-functional investigation of friction using rotated, Moiré cells, and the first prediction of structural superlubricty for b-P.

Computational Prediction of Superlubric Layered Heterojunctions

Structural superlubricity has attracted increasing interest in modern tribology. However, experimental identification of superlubric interfaces among the vast number of heterojunctions is a trial-and-error and time-consuming approach. In this work, based on the requirements on the in-plane stiffnesses of layered materials and the interfacial interactions at the sliding incommensurate interfaces of heterojunctions for structural superlubricity, we propose criteria for predicting structural superlubricity between heterojunctions. Based on these criteria, we identify 61 heterojunctions with potential superlubricity features from 208 candidates by screening the data of first-principles calculations. This work provides a universal route for accelerating the discovery of new superlubric heterojunctions.

Pervasive orientational and directional locking at geometrically heterogeneous sliding interfaces

Understanding the drift motion and dynamical locking of crystalline clusters on patterned substrates is important for the diffusion and manipulation of nano- and microscale objects on surfaces. In a previous work, we studied the orientational and directional locking of colloidal two-dimensional clusters with triangular structure driven across a triangular substrate lattice. Here we show with experiments and simulations that such locking features arise for clusters with arbitrary lattice structure sliding across arbitrary regular substrates. Similar to triangular-triangular contacts, orientational and directional locking are strongly correlated via the real- and reciprocal-space Moiré patterns of the contacting surfaces. Due to the different symmetries of the surfaces in contact, however, the relation between the locking orientation and the locking direction becomes more complicated compared to interfaces composed of identical lattice symmetries. We provide a generalized formalism which describes the relation between the locking orientation and locking direction with arbitrary lattice symmetries.