![Schematic view of the interaction between chemically passivated solids. Part (a) shows a snapshot of a simulation. Part (b) represents the coupling of a surface atom to its neighbors (reflected by the harmonic springs) and to the substrate (reflected by the sinusoidal line). The parabola indicates the maximum curvature of the atom- substrate potential, which corresponds to the curvature κ of the substrate potential in the PT model. Part (c) describes the scaling procedure for a one-dimensional elastic chain. From Ref. [26].](https://www.researchgate.net/profile/Martin-Mueser/publication/281702059/figure/fig1/AS:293964613337088@1447098033039/Schematic-view-of-the-interaction-between-chemically-passivated-solids-Part-a-shows-a_Q320.jpg)
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Theoretical Studies of Superlubricity
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Analytical models and computer simulations clearly point to the possibility of identifying superlubricity for many pairs of materials. Chemical passivation and smoothness of the interfaces are some of the most important components of superlubricity. The absence/saturation of dangling bonds on the contact regions between solids as well as the property of some materials to form layered structures appears to be other necessary conditions to achieve ultralow friction. Systems similar to diamond, such as carbon obtained using hydrogen treatment, are currently the best candidates to show superlubricity. They have very smooth and nonreactive interfaces. In theory, the dangling bonds in these types of systems could be terminated with atoms larger than hydrogen such as fluorine making the surfaces even smoother. However, the fluorinated layers may rub off easily, thereby resulting in the formation of debris, which could ultimately increase friction.
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... Therefore, if the expressions (16) and (17) turn out to be valid at extremely high loads, then the friction coefficient at high loads should be quite small. However, such an effect has nothing to do with a change in the friction mechanism, as is observed, for example, when establishing a superlubricity mode with a negligible friction coefficient [40]. In (16) and (17), the nature of the friction coefficient reduction is related to the contact geometry during the indentation of a spherical (parabolic) indenter. ...
... Biomimetics 2024, 9, x FOR PEER REVIEW 6 of 25 example, when establishing a superlubricity mode with a negligible friction coefficient [40]. In (16) and (17), the nature of the friction coefficient reduction is related to the contact geometry during the indentation of a spherical (parabolic) indenter. ...
The quasi-static regime of friction between a rigid steel indenter and a soft elastomer with high adhesion is studied experimentally. An analysis of the formally calculated dependencies of a friction coefficient on an external load (normal force) shows that the friction coefficient monotonically decreases with an increase in the load, following a power law relationship. Over the entire range of contact loads, a friction mode is realized in which constant shear stresses are maintained in the tangential contact, which corresponds to the “adhesive” friction mode. In this mode, Amonton’s law is inapplicable, and the friction coefficient loses its original meaning. Some classical works, which show the existence of a transition between “adhesive” and “normal” friction, were analyzed. It is shown that, in fact, there is no such transition. A computer simulation of the indentation process was carried out within the framework of the boundary element method, which confirmed the experimental results.
... Here, especially the sublinear contact-area dependence of friction has been recognized as a unique fingerprint of structural lubricity, which reflects the underlying physical mechanism of collective force cancellations of slider atoms moving on the potential energy surface of the substrate. These cancellation effects become more and more effective, when the particle size increases, ultimately leading to a sublinear relation between friction and contact area described by , with F the friction force, A the contact area, and γ < 1 the scaling exponent [66][67][68]. The initial friction decreases with time (as described by the time constants) until a stationary friction level is reached. ...
... A first experimental verification of this effect has been provided by UHV nanomanipulation experiments of gold and antimony nanoparticles on highly oriented pyrolithic graphite (HOPG) [46], where the precise value of γ was found to depend sensitively on the crystallinity of the particles. As predicted theoretically [66,67], γ = 0.5 was found for the case of amorphous Sb nanoparticles, whereas crystalline gold nanoparticles can be described by an effective scaling exponent of approximately half this value. This difference can be understood simply by considering how force cancellation effects become less effective for amorphous interfaces with irregular positioning of slider atoms [46]. ...
Friction is the oldest branch of non-equilibrium condensed matter physics and, at the same time, the least established at the fundamental level. A full understanding and control of friction is increasingly recognized to involve all relevant size and time scales. We review here some recent advances on the research focusing of nano- and mesoscale tribology phenomena. These advances are currently pursued in a multifaceted approach starting from the fundamental atomic-scale friction and mechanical control of specific single-asperity combinations, e.g., nanoclusters on layered materials, then scaling up to the meso/microscale of extended, occasionally lubricated, interfaces and driven trapped optical systems, and eventually up to the macroscale. Currently, this "hot" research field is leading to new technological advances in the area of engineering and materials science.
... For amorphous surfaces, Müser [15] predicted that 1/ 2 f A and this prediction was supported by molecular dynamics simulations [16] and experiments [17]. For crystalline surfaces, de Wijn [18] studied the issue theoretically and focused on an application in heterogeneous surfaces: the sliding of gold nanoparticles on the surface of grapheme, and five different relationships were predicted: 0 1 /2 1 , , , A A A when the shape of contact area was regular, and 1/ 4 3/ 4 1 , , , A A A when the shape was irregular. ...
Relationship between contact size (A) and static friction (f) has been studied for rigid crystalline systems. We built a series of systems with two identical surfaces but different orientations and investigated the effects of the size and shape of the contact area on static friction. In these systems, there are numerous nontrivial commensurate contacts. Our results confirmed that the relationship between A and f was determined by both commensurability and shape of the contact. For commensurate contacts, f ∝ A independent of the shape. For incommensurate contacts, generally f ∝ A0 for regular shapes or f ∝ A1/4 for irregular shapes; however, in very few cases of regular shapes, f ∝ A1/2. Moreover, in above systems, commensurability of a contact can be easily changed by a perturbation of the misfit angle. Therefore, if the perturbation caused by the lateral force and the deformation of the surface are considered (as is the case in real systems), further research is necessary.
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.
Hydration lubrication has long been invoked to account for the ultralow sliding friction between charged surfaces in aqueous environments, but still not well understood at molecular-level. Herein, we explored the lubrication effect of hydrated halogen anions on positively charged surface at the atomic scale by using three-dimensional atomic force microscopy and friction force microscopy. Atomically resolved three-dimensional imaging revealed that the anion layer was topped by a few hydration layers. The mechanical properties of the hydration layers were found mainly dependent on the concentration of electrolyte solutions and independent of the species of hydrated anions. Atomic-scale friction experiments showed that the hydration friction coefficient and friction dissipation at low concentrations were orders of magnitude lower than that at high concentrations and in pure water. Superlubricity can be achieved in low concentration electrolyte solution. These results indicated that the changes of electrolyte solution concentrations led to different adsorption state of anions on the positively charged surface which gave rise to the difference of the friction behaviors. The findings in this study reveal the role of hydrated anions in hydration lubrication and provide deep insights into the origins of hydration lubrication.
Two-dimensional heterostructures are excellent platforms to realize twist-angle-independent ultra-low friction due to their weak interlayer van der Waals interactions and natural lattice mismatch. However, for finite-size interfaces, the effect of domain edges on the friction process remains unclear. Here we report the superlubricity phenomenon and the edge-pinning effect at MoS2/graphite and MoS2/hexagonal boron nitride van der Waals heterostructure interfaces. We found that the friction coefficients of these heterostructures are below 10−6. Molecular dynamics simulations corroborate the experiments, which highlights the contribution of edges and interface steps to friction forces. Our experiments and simulations provide more information on the sliding mechanism of finite low-dimensional structures, which is vital to understand the friction process of laminar solid lubricants. MoS2/graphite and MoS2/h-BN interfaces are shown to have ultra-low friction coefficients, whereas edges and interface steps mainly contribute to the friction force.
Controlling, and in many cases minimizing, friction is a goal that has long been pursued in history. From the classic Amontons–Coulomb law to the recent nanoscale experiments, the steady-state friction is found to be an inherent property of a sliding interface, which typically cannot be altered on demand. In this work, we show that the friction on a graphene sheet can be tuned reversibly by simple mechanical straining. In particular, by applying a tensile strain (up to 0.60%), we are able to achieve a superlubric state (coefficient of friction nearly 0.001) on a suspended graphene. Our atomistic simulations together with atomically resolved friction images reveal that the in-plane strain effectively modulates the flexibility of graphene. Consequently, the local pinning capability of the contact interface is changed, resulting in the unusual strain-dependent frictional behavior. This work demonstrates that the deformability of atomic-scale structures can provide an additional channel of regulating the friction of contact interfaces involving configurationally flexible materials.
Friction at the nanoscale revealed rich load-dependent behaviors which depart strongly from the long-standing Amontons law. While the electrostatic repulsion induced friction collapse for rare gas sliding over metallic surfaces in the high-load regime was found by Righi et al. (Phys. Rev. Lett. 2007, 99, 176101), the picture of the significant role of attraction on frictional properties has not emerged yet. In this work, frictional motion of Xe/Cu(111), Xe/Pd(111) and Ar/Cu(111) are studied through van der Waals corrected density functional calculations. An attraction-induced zero friction, which is a signal of superlubricity, is found for the sliding systems. The superlubric state results from the disappearance of potential corrugation along the favored sliding path as consequence of potential crossing in the attractive regime when the interfacial pressure approaches to critical-value. The finding of attraction-driven drop of friction, together with the repulsion-induced collapse in high-load regime, which breaks down the classic Amontons’ law, provides a distinct approach for the realization of inherent superlubricity in some adsorbate/substrate interfaces.
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Kinetic friction during dry sliding along atomistic-scale Al(001)∕Al(001) and α-Al2O3(0001)∕α-Al2O3(0001) interfaces has been investigated using molecular dynamics (MD) with recently developed Reactive Force Fields (ReaxFF). It is of interest to determine if kinetic friction variations predicted with MD follow the macroscopic-scale friction laws known as Coulomb’s law (for dry sliding) and Stokes’ friction law (for lubricated sliding) over a wide range of sliding velocities. The effects of interfacial commensuration and roughness on kinetic friction have been studied. It is found that kinetic friction during sliding at commensurate α-Al2O3(0001)∕α-Al2O3(0001) interfaces exceeds that due to sliding at an incommensurate α-Al2O3(0001)∕α-Al2O3(0001) interface. For both interfaces, kinetic friction at lower sliding velocities deviates minimally from Coulombic friction, whereas at higher sliding velocities, kinetic friction follows a viscous behavior with sliding damped by thermal phonons. For atomically smooth Al(001)∕Al(001), only viscous friction is observed. Surface roughness tends to increase kinetic friction, and adhesive transfer causes kinetic friction to increase more rapidly at higher sliding velocities.
The scaling of friction with the contact size A and (in)commensurabilty of nanoscopic and mesoscopic crystals on a regular substrate are investigated analytically for triangular nanocrystals on hexagonal substrates. The crystals are assumed to be stiff, but not completely rigid. Commensurate and incommensurate configurations are identified systematically. It is shown that three distinct friction branches coexist, an incommensurate one that does not scale with the contact size (A0) and two commensurate ones which scale differently (with A1/2 and A) and are associated with various combinations of commensurate and incommensurate lattice parameters and orientations. This coexistence is a direct consequence of the two-dimensional nature of the contact layer, and such multiplicity exists in all geometries consisting of regular lattices. To demonstrate this, the procedure is repeated for rectangular geometry. The scaling of irregularly shaped crystals is also considered, and again three branches are found (A1/4,A3/4,A). Based on the scaling properties, a quantity is defined which can be used to classify commensurability in infinite as well as finite contacts. Finally, the consequences for friction experiments on gold nanocrystals on graphite are discussed.
Analytic results and experiments in ultrahigh vacuum indicate that the static friction between two clean crystalline surfaces
should almost always vanish, yet macroscopic objects always exhibit static friction. A simple and general explanation for
the prevalence of static friction is proposed. “Third bodies,” such as small hydrocarbon molecules, adsorb on any surface
exposed to air and can arrange to lock two contacting surfaces together. The resulting static friction is consistent with
experimental behavior, including Amontons' laws.
An overview of the dynamics of one of the fundamental models of low-dimensional nonlinear physics, the Frenkel–Kontorova (FK) model, is presented. In its simplest form, the FK model describes the motion of a chain of interacting particles (“atoms”) subjected to an external on-site periodic potential. Physically important generalizations of the FK model are discussed including nonsinusoidal on-site potentials and anharmonic (e.g., nonconvex, Kac–Baker, power-law) interactions between the particles. The results are summarized for the one-dimensional dynamics of kinks – topological excitations, including the kink diffusion and effects of disorder, and also for nonlinear localized modes, discrete breathers. A special attention is paid to the numerous applications of the FK model in the problems of low-dimensional solid state physics.
The classical molecular dynamics simulations presented here examine the periodicities associated with the sliding of a diamond counterface across a monolayer of hydrocarbon chains that are covalently bound to a diamond substrate. Periodicities observed in a number of system quantities are a result of the tight packing of the monolayer and the commensurate structure of the diamond counterface. The packing and commensurability of the system force synchronized motion of the chains during sliding contact. This implies that the size of the simulations for this special case can be reduced so that the simulations can be conducted with sliding speeds and time durations that may bridge the gap between theory and experiment.
Dynamics in friction is studied from an atomistic point of view. Friction is formulated as a problem of whether or not a given kinetic energy for the translational motion dissipates into the kinetic energies for the internal motions during sliding. From the study of the Frenkel-Kontorova model with kinetic energy terms, it is found that two different regimes appear in the parameter space specifying the model: the superlubricity and the friction regimes. The friction exactly vanishes in the superlubric regime and appears in the friction regime. The conditions for the superlubricity to occur are described. It is emphasized that a high dimensionality in the friction system is a key to understanding the physics of superlubricity. For high dimensional systems, superlubricity is a generic phenomenon, appearing for a wide class of (strong or weak) adhesion such as the metallic bonding and the van der Waals interaction. The results are discussed in comparison with those obtained by assuming the case where the upper surface slides quasi-statically against the lower surface.
An elastic block on a substrate experiences a random pinning potential which breaks the lattice at the block–substrate interface into “correlated volumes” (cells of size ξ) that behave elastically independent and are pinned individually. We calculate the elastic coherence length ξ and discuss its relevance for sliding friction and earthquake dynamics.
Molecular dynamic calculations of pullout in multiwall carbon nanotubes (CNTs) demonstrate that inner walls with fractured ends have pullout forces ∼3−4 times larger than those for capped ends, due to deformation of the fractured end, quantitatively accounting for experiments. Under pressure, Amonton’s law applies to an area of contact at the fractured end, with μ=0.13–0.33. Defects in the CNT walls affect the force, suggesting a mechanism for the observed stick-slip behavior and an increase of pullout force with decreasing embedded length. The results have implications for CNT composite strength and toughness.