The Registry Index: A Quantitative Measure of Materials′ Interfacial Commensurability

Superlubric Graphullerene

Graphullerene (GF), an extended quasi-two-dimensional network of C60 molecules, is proposed as a multicontact platform for constructing superlubric interfaces with layered materials. Such interfaces are predicted to present very small and comparable sliding energy corrugation regardless of the identity of the underlying flat layered material surface. It is shown that, beyond the geometrical effect, covalent interlinking between the C60 molecules results in reduction of the sliding energy barrier. For extended GF supercells, negligible sliding energy barriers are found along all sliding directions considered, even when compared to the case of the robust superlubric graphene/h-BN heterojunction. This suggests that multicontact architectures can be used to design ultrasuperlubric interfaces, where superlubricity may persist under extreme sliding conditions.

Deducing the internal interfaces of twisted multilayer graphene via moiré-regulated surface conductivity

The stacking state of atomic layers critically determines the physical properties of twisted van der Waals materials. Unfortunately, precise characterization of the stacked interfaces remains a great challenge as they are buried internally. With conductive atomic force microscopy, we show that the moiré superlattice structure formed at the embedded interfaces of small-angle twisted multilayer graphene (tMLG) can noticeably regulate surface conductivity even when the twisted interfaces are 10 atomic layers beneath the surface. Assisted by molecular dynamics (MD) simulations, a theoretical model is proposed to correlate surface conductivity with the sequential stacking state of the graphene layers of tMLG. The theoretical model is then employed to extract the complex structure of a tMLG sample with crystalline defects. Probing and visualizing the internal stacking structures of twisted layered materials is essential for understanding their unique physical properties, and our work offers a powerful tool for this via simple surface conductivity mapping.

Stiffness and Atomic-Scale Friction in Superlubricant MoS2 Bilayers

Molecular dynamics simulations, performed with chemically accurate ab initio machine-learning force fields, are used to demonstrate that layer stiffness has profound effects on the superlubricant state of two-dimensional van der Waals heterostructures. We engineer bilayers of different rigidity but identical interlayer sliding energy surface and show that a 2-fold increase in the intralayer stiffness reduces the friction by a factor of ∼6. Two sliding regimes as a function of the sliding velocity are found. At a low velocity, the heat generated by the motion is efficiently exchanged between the layers and the friction is independent of the layer order. In contrast, at a high velocity, the friction heat flux cannot be exchanged fast enough and a buildup of significant temperature gradients between the layers is observed. In this situation, the temperature profile depends on whether the slider is softer than the substrate.

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.

Interlayer Registry Dictates Interfacial 2D Material Ferroelectricity

We discover that the complex ferroelectric response of layered materials toward interlayer sliding is fully dictated by the interlayer lattice registry. Importantly, the entire sliding polarization landscape of two-dimensional (2D) layered material interfaces is fully described via a simple and intuitive geometric measure, termed the polarization registry index (PRI), that quantifies the degree of interlayer commensurability. Beyond the understanding of the fundamental origin of 2D ferroelectricity, the developed tool also provides highly efficient characterization and rationalization of existing experimental and computational evidence of 2D interfacial ferroelectricity, as well as the prediction of emergent controllable polarization in new noncentrosymmetric layered systems.

Interfacial friction of vdW heterostructures affected by in-plane strain

Interfacial properties of van der Waals (vdW) heterostructures dominate the durability and function of their booming practical and potential applications such as opoelectronic devices, superconductors and even pandemics research. However, the strain engineering modulates of interlayer friction of vdW heterostructures consisting of two distinct materials are still unclear, which hinders the applications of vdW heterostructures, as well as the design of solid lubricant and robust superlubricity. In the present paper, a molecular model between a hexagonal graphene flake and a rectangular SLMoS₂sheet is established, and the influence of biaxial and uniaxial strain on interlayer friction is explored by molecular dynamics. It is found that the interlayer friction is insensitive to applied strains. Strong robustness of superlubricity between distinct layers is owed to the structure's intrinsic incommensurate characteristics and the existence of Moiré pattern. In engineering practice, it is of potential importance to introduce two distinct 2D materials at the sliding contact interface to reduce the interfacial friction of the contact pair and serve as ideal solid lubricants. Our research provides a further basis to explore the nanotribology and strain engineering of 2D materials and vdW heterostructures.

Structural lubricity of physisorbed gold clusters on graphite and its breakdown: Role of boundary conditions and contact lines

The sliding motion of gold slabs adsorbed on a graphite substrate is simulated using molecular dynamics. The central quantity of interest is the mean lateral force, that is, the kinetic friction rather than the maximum lateral forces, which correlates with the static friction. For most setups, we find Stokesian damping to resist sliding. However, velocity-insensitive (Coulomb) friction is observed for finite-width slabs sliding parallel to the armchair direction if the bottom-most layer of the three graphite layers is kept at zero stress rather than at zero displacement. Although the resulting kinetic friction remains much below the noise produced by the erratic fluctuations of (conservative) forces typical for structurally lubric contacts, the nature of the instabilities leading to Coulomb friction could be characterized as quasi-discontinuous dynamics of the Moiré patterns formed by the normal displacements near a propagating contact line. It appears that the interaction of graphite with the second gold layer is responsible for the symmetry break occurring at the interface when a contact line moves parallel to the armchair rather than to the zigzag direction.

Edge State Quantum Interference in Twisted Graphitic Interfaces

Zigzag edges in graphitic systems exhibit localized electronic states that drastically affect their properties. Here, room-temperature charge transport experiments across a single graphitic interface are reported, in which the interlayer current is confined to the contact edges. It is shown that the current exhibits pronounced oscillations of up to ≈40 µA with a dominant period of ≈5 Å with respect to lateral displacement that do not directly correspond to typical graphene lattice spacing. The origin of these features is computationally rationalized as quantum mechanical interference of localized edge states showing significant amplitude and interlayer coupling variations as a function of the interface stacking configuration. Such interference effects may therefore dominate the transport properties of low-dimensional graphitic interfaces.

Interlayer Registry Index of Layered Transition Metal Dichalcogenides

Inspired by the fascinating electronic properties of twisted transition metal dichalcogenides, we extend the registry index approach to quantify the interlayer commensurability of homogeneous and heterogeneous interfaces of MoS₂, WS₂, MoSe₂, and WSe₂. The developed geometric measure provides quantitative information about their sliding energy landscape with vast mechanical and tribological implications. Furthermore, the registry index is highly suitable for characterizing surface reconstruction in twisted transition metal dichalcogenide interfaces that dictates their intricate electronic and ferroelectric properties. The simple and intuitive nature of the registry index marks it as a powerful computational tool for studying the fascinating physical phenomena demonstrated by these materials.

A heat and force locating sensor with nanoscale precision: a knitted graphene sheet

Fast and accurately locating the heating or force bearing points is essential to the maintenance and diagnosis of nano/micro-electromechanical systems. Here, a knitted graphene sheet (KGS), prepared by knitting graphene nanoribbons, is proposed as a heat or force sensor to locate the spot with nanoscale precision under thermal or mechanical loadings. The heat flux transport among the ribbons in the KGS is more difficult than in the ribbon due to the weaker van der Waals interactions among ribbons, so the heat energy can be restricted in the directly loaded ribbons over a period of time. Molecular dynamics results demonstrate that the KGS can efficiently locate and evaluate the spots and sizes of heat/force sources with high accuracy dependent on the width of the ribbons in the KGS. Our research provides a new detection approach and sheds light on designing and assembling KGS-based nanosensors for locating thermal and mechanical loads.

Synergistic lubrication performance by incommensurately stacked ZnO-decorated reduced graphene oxide/MoS2 heterostructure

Incommensurate stacking between two different types of two-dimensional layered materials furnished the weak interfacial interaction due to the mismatch of their lattice structure, which can be harnessed for development of new generation lubricant additives. Herein, a facile approach is presented to synthesize the ZnO-decorated reduced graphene oxide/MoS₂ (Gr-MS-Zn) nanosheets. The Fourier transform infrared, X-ray photoelectron spectroscopic, Raman, and transmission electron microscopic analyses confirmed the preparation of Gr-MS-Zn heterostructure. The MoS₂ nanosheets having 3-7 molecular lamellae are thoroughly distributed over the graphene skeleton via weak interfacial interaction. The curved and bent structure of MoS₂ nanosheets grown over the graphene lamellae subsidized the cohesive interaction and furnished the stable dispersion of Gr-MS-Zn in the fully formulated engine oil. The minute dose of Gr-MS-Zn as a nano-additive to engine oil significantly enhanced the tribological performance between the steel-steel tribopair by decreasing the friction (37%) and the wear volume (87%). The microscopic and spectroscopic analyses revealed the formation of a Gr-MS-Zn-based surface protective tribo thin film of low shear strength. The enhanced tribo performance is collectively attributed to (a) uninterrupted supply of ultrathin Gr-MS-Zn nanosheets to tribo-interfaces, (b) stable dispersion of Gr-MS-Zn, and (c) the significantly low shear strength, arising from weak interfacial interaction between the incommensurately stacked graphene and MoS₂ nanosheets.

Nanomaterials application in greenhouse structures, crop processing machinery, packaging materials and agro-biomass conversion

The discovery of nanomaterials has flagged off crucial research and innovations in science and engineering. Its unique properties and diverse applications present it as the material for the future. The aim of this study is to presents the relative applications of nanomaterial in some aspects of agriculture production. The study discussed nanotechnology applicability in climate control and photosynthesis in the greenhouse farming, hydroponic systems, solar drying, fabrication of crop processing machine components, oxygen scavengers in crop packaging, and micro-organism stimulant in anaerobic digestion for agro biomass conversion. Some highlights from the review revealed that Nanotechnology can be applied to increase water surface area to volume ratio and heat transfer in the air moving into a greenhouse farming. Water cluster can be changed when treated with nanoparticles through ultraviolet absorption spectrum and nuclear magnetic resonance (NMR) spectroscopy resulting in lower micelles to manipulate water delivery in green house farming. Nano-fluids or Nano-composites can be used to recombine the reactive parts of thermal storage materials after broken at elevated temperature to recover the stored heat for drying purpose during the off-sunshine periods in solar drying of crops. Nanomaterials can be a source of electroluminescence light in hydroponic system and act as coatings and surface hardener in crop processing machinery for post-harvest machines. The reviewed work showed that nanotechnologies has good prospect in adding value in agricultural production in the aspects discussed.

Structural Superlubricity Based on Crystalline Materials

Herein, structural superlubricity, a fascinating phenomenon where the friction is ultralow due to the lateral interaction cancellation resulted from incommensurate contact crystalline surfaces, is reviewed. Various kinds of nano- and microscale materials such as 2D materials, metals, and compounds are used for the fabrication. For homogeneous frictional pairs, superlow friction forces exist in most relative orientations with incommensurate configuration. Heterojunctions bear no resemblance to homogeneous contact, since the lattice constants are naturally mismatched which leads to a robust structural superlubricity with any orientation of the two different surfaces. A discussion on the perspectives of this field is also provided to meet the existing challenges and chart the future.

Tribo-Induced Interfacial Material Transfer of an Atomic Force Microscopy Probe Assisting Superlubricity in a WS2/Graphene Heterojunction

Robust superlubricity of 2D materials could be obtained by transferring graphene on the tip surface for the formation of interlayer friction of heterojunction, owing to the availability of stable interfacial incommensurate contact. Nevertheless, the material transfer mechanisms assisting superlubricity via atomic force microscopy (AFM) probe are still hardly comprehended. In this work, we reported a superlow friction coefficient (0.003) of the WS₂/graphene heterojunction governed by graphene flake-transferred AFM tips and achieved a superlubricity state of velocity independence. Both low adhesion of the heterojunction and excellent wear-resistance for tip were also observed, which were attributed to the extremely low interface interaction during the incommensurate contact. The in-depth investigation on the frictional contact zones of probes was performed through high-resolution transmission electron microscopy. The observations emphasize the prevailing mechanisms of tribo-induced interfacial material transfer when AFM probes scan on the surface of 2D materials. The evolution of the superlubricity state principally depends on the establishment of interfacial nanostructures in the self-adaptive running-in period, by different contact mechanics and tribo-reconstructing pathways. These results stimulate a technical route to develop superlubricious tribopairs of 2D materials and guide a promising perspective in the engineering system.

Effect of Ambient Chemistry on Friction at the Basal Plane of Graphite

Graphite is widely used as a solid lubricant due to its layered structure, which enables ultralow friction. However, the lubricity of graphite is affected by ambient conditions and previous studies have shown a sharp contrast between frictional behavior in vacuum or dry environments compared to humid air. Here, we studied the effect of organic gaseous species in the environment, specifically comparing the adsorption of phenol and pentanol vapor. Atomic force microscopy experiments and reactive molecular dynamics simulations showed that friction was larger with phenol than with pentanol. The simulation results were analyzed to test multiple hypotheses to explain the friction difference, and it was found that mechanically driven chemical bonding between the tip and phenol molecules plays a critical role. Bonding increases the number of phenol molecules in the contact, which increases the adhesion as well as the number of atoms in registry with the topmost graphene layer acting as a pinning site to resist sliding. The findings of this research provide insight into how the chemistry of the operating environment can affect the frictional behavior of graphite and layered materials more generally.

Structural superlubricity and ultralow friction across the length scales

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

Nanoserpents: Graphene Nanoribbon Motion on Two-Dimensional Hexagonal Materials

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

Interlayer Friction and Superlubricity in Single-Crystalline Contact Enabled by Two-Dimensional Flake-Wrapped Atomic Force Microscope Tips

Interlayer friction between the atomic planes of 2D materials and heterostructures is a promising probe of the physics in their interlayer couplings and superlubricity. However, it is still challenging to measure the interlayer friction between well-defined 2D layers. We propose an approach of thermally assisted mechanical exfoliation and transfer to fabricate various 2D flake-wrapped atomic force microscopy (AFM) tips and to directly measure the interlayer friction between 2D flakes in single-crystalline contact. First, superlubricity between different 2D flakes and layered bulk materials is achieved with a friction coefficient as low as 10^-4. The rotation angle dependence of superlubricity is observed for friction between graphite layers, whereas it is not observed between graphite and h-BN because of the incommensurate contact of the mismatched lattices. Second, the interlayer lateral force map between ReS₂ layers is measured with atomic resolution, showing hexagonal patterns, as further verified by theoretical simulations. The tribological system constructed here offers an experimental platform to study interlayer couplings and friction between 2D flakes and layered bulk materials.

Friction fluctuations of gold nanoparticles in the superlubric regime

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

On the lubricity of transition metal dichalcogenides: an ab initio study

Owing to specific characteristics engendered by their lamellar structures, transition metal dichalcogenides are posited as being some of the best dry lubricants available. Herein, we report a density functional investigation into the sliding properties and associated phenomena of these materials. Calculated potential energy and charge transfer profiles are used to highlight the dependence of shear strength on chemical composition and bilayer orientation (sliding direction). Furthermore, our calculations underscore the intrinsic relationship between incommensurate crystals and the oft-touted superlubric behaviour of molybdenum disulfide.

Robust microscale superlubricity under high contact pressure enabled by graphene-coated microsphere

Superlubricity of graphite and graphene has aroused increasing interest in recent years. Yet how to obtain a long-lasting superlubricity between graphene layers, under high applied normal load in ambient atmosphere still remains a challenge but is highly desirable. Here, we report a direct measurement of sliding friction between graphene and graphene, and graphene and hexagonal boron nitride (h-BN) under high contact pressures by employing graphene-coated microsphere (GMS) probe prepared by metal-catalyst-free chemical vapour deposition. The exceptionally low and robust friction coefficient of 0.003 is accomplished under local asperity contact pressure up to 1 GPa, at arbitrary relative surface rotation angles, which is insensitive to relative humidity up to 51% RH. This ultralow friction is attributed to the sustainable overall incommensurability due to the multi-asperity contact covered with randomly oriented graphene nanograins. This realization of microscale superlubricity can be extended to the sliding between a variety of two-dimensional (2D) layers.

Multiwalled nanotube faceting unravelled

Nanotubes show great promise for miniaturizing advanced technologies. Their exceptional physical properties are intimately related to their morphological and crystal structure. Circumferential faceting of multiwalled nanotubes reinforces their mechanical strength and alters their tribological and electronic properties. Here, the nature of this important phenomenon is fully rationalized in terms of interlayer registry patterns. Regardless of the nanotube identity (that is, diameter, chirality, chemical composition), faceting requires the matching of the chiral angles of adjacent layers. Above a critical diameter that corresponds well with experimental results, achiral multiwalled nanotubes display evenly spaced extended axial facets whose number equals the interlayer difference in circumferential unit cells. Elongated helical facets, commonly observed in experiment, appear in nanotubes that exhibit small interlayer chiral angle mismatch. When the wall chiralities are uncorrelated, faceting is suppressed and outer layer corrugation, which is induced by the Moiré superlattice, is obtained in agreement with experiments. Finally, we offer an explanation for the higher incidence of faceting in multiwalled boron nitride nanotubes with respect to their carbon-based counterparts.

Frictional Properties of Nanojunctions Including Atomically Thin Sheets

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

Monte Carlo simulations of the static friction between two grafted polymer brushes

A configurational bias Monte Carlo method has been developed to calculate the static friction between two grafted polymer brushes.

Sliding mechanisms in multilayered hexagonal boron nitride and graphene: the effects of directionality, thickness, and sliding constraints

The interlayer sliding potential of multilayered hexagonal boron nitride (h-BN) and graphene is investigated using density-functional theory including many-body van der Waals (vdW) interactions. We find that interlayer sliding constraints can be employed to tune the contribution of electrostatic interactions and dispersive forces to the sliding energy profile, ultimately leading to different sliding pathways in these two materials. In this context, vdW interactions are found to contribute more to the interlayer sliding potential of polar h-BN than they do in nonpolar graphene. In particular, the binding energy, the interlayer distance, and the friction force are found to depend sensitively on the number of layers. By comparing with the experimental findings, we identify sliding pathways which rationalize the observed reduced friction for thicker multilayers and provide quantitative explanation for the anisotropy of the friction force.

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

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