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.

Electric-field frictional effects in confined zwitterionic molecules.

We theoretically explore the effect of a transverse electric field on the frictional response of a bi-layer of packed zwitterionic molecules. The dipole-moment reorientation promoted by the electric field can lead to either stick-slip or smooth sliding dynamics, with average shear stress values varying over a wide range. A structure-property relation is revealed by investigating the array of molecules and their mutual orientation and interlocking. Moreover, the thermal friction enhancement previously observed in these molecules is shown to be suppressed by the electric field, recovering the expected thermolubricity at large-enough fields. The same holds for other basic tribological quantities, such as the external load, which can influence friction in opposite ways depending on the strength of the applied electric field. Our findings open a route for the reversible control of friction forces via electric polarization of the sliding surface.

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.

Understanding the rheology of nanocontacts.

Mechanical stiffness, as opposed to softness, is a fundamental property of solids. Its persistence or rheological evolution in vibrating solid-solid nanocontacts is important in physics, materials science and technology. A puzzling apparent liquefaction under oscillatory strain, totally unexpected at room temperature, was suggested by recent experiments on solid gold nano-junctions. Here we show theoretically that realistically simulated nanocontacts actually remain crystalline even under large oscillatory strains. Tensile and compressive slips, respectively of "necking" and "bellying" types, do take place, but recover reversibly even during fast oscillatory cycles. We also show that, counterintuitively, the residual stress remains tensile after both slips, driving the averaged stiffness from positive to negative, thus superficially mimicking a liquid's. Unlike a liquid, however, rheological softening occurs by stick-slip, predicting largely frequency independent stiffness with violent noise in stress and conductance, properties compatible with experiments. The baffling large amplitude rheology of gold nanocontacts and its consequences should apply, with different parameters, to many other metals.

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.

Thermal Friction Enhancement in Zwitterionic Monolayers.

We introduce a model for zwitterionic monolayers and investigate its tribological response to changes in applied load, sliding velocity, and temperature by means of molecular-dynamics simulations. The proposed model exhibits different regimes of motion depending on temperature and sliding velocity. We find a remarkable increase of friction with temperature, which we attribute to the formation and rupture of transient bonds between individual molecules of opposite sliding layers, triggered by the out-of-plane thermal fluctuations of the molecules' orientations. To highlight the effect of the molecular charges, we compare these results with analogous simulations for the charge-free system. These findings are expected to be relevant to nanoscale rheology and tribology experiments of locally-charged lubricated systems such as, e.g., experiments performed on zwitterionic monolayers, phospholipid micelles, or confined polymeric brushes in a surface force apparatus.

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.

Amplitude nanofriction spectroscopy.

Atomic scale friction, an indispensable element of nanotechnology, requires a direct access to, under actual growing shear stress, its successive live phases: from static pinning, to depinning and transient evolution, eventually ushering in steady state kinetic friction. Standard tip-based atomic force microscopy generally addresses the steady state, but the prior intermediate steps are much less explored. Here we present an experimental and simulation approach, where an oscillatory shear force of increasing amplitude leads to a one-shot investigation of all these successive aspects. Demonstration with controlled gold nanocontacts sliding on graphite uncovers phenomena that bridge the gap between initial depinning and large speed sliding, of potential relevance for atomic scale time and magnitude dependent rheology.

Structural lubricity in soft and hard matter systems.

Over the recent decades there has been tremendous progress in understanding and controlling friction between surfaces in relative motion. However the complex nature of the involved processes has forced most of this work to be of rather empirical nature. Two very distinctive physical systems, hard two-dimensional layered materials and soft microscopic systems, such as optically or topographically trapped colloids, have recently opened novel rationally designed lines of research in the field of tribology, leading to a number of new discoveries. Here, we provide an overview of these emerging directions of research, and discuss how the interplay between hard and soft matter promotes our understanding of frictional phenomena.

Pile-up transmission and reflection of topological defects at grain boundaries in colloidal crystals.

Crystalline solids typically contain large amounts of defects such as dislocations and interstitials. How they travel across grain boundaries (GBs) under external stress is crucial to understand the mechanical properties of polycrystalline materials. Here, we experimentally and theoretically investigate with single-particle resolution how the atomic structure of GBs affects the dynamics of interstitial defects driven across monolayer colloidal polycrystals. Owing to the complex inherent GB structure, we observe a rich dynamical behavior of defects near GBs. Below a critical driving force defects cannot cross GBs, resulting in their accumulation near these locations. Under certain conditions, defects are reflected at GBs, leading to their enrichment at specific regions within polycrystals. The channeling of defects within samples of specifically-designed GB structures opens up the possibility to design novel materials that are able to confine the spread of damage to certain regions.

Detachment Dynamics of Graphene Nanoribbons on Gold.

Metal-surface physisorbed graphene nanoribbons (GNRs) constitute mobile nanocontacts whose interest is simultaneously mechanical, electronic, and tribological. Previous work showed that GNRs adsorbed on Au(111) generally slide smoothly and superlubrically owing to the incommensurability of their structures. We address here the nanomechanics of detachment, as realized when one end is picked up and lifted by an AFM cantilever. AFM nanomanipulations and molecular-dynamics (MD) simulations identify two successive regimes, characterized by (i) a progressively increasing local bending, accompanied by the smooth sliding of the adhered part, followed by (ii) a stick-slip dynamics involving sudden bending relaxation associated with intermittent jumps of the remaining adhered GNR segment and tail end. AFM measurements of the vertical force exhibit oscillations which, compared with MD simulations, can be associated with the successive detachment of individual GNR unit cells of length 0.42 nm. Extra modulations within one single period are caused by steplike advancements of the still-physisorbed part of the GNR. The sliding of the incommensurate moiré pattern that accompanies the GNR lifting generally yields an additional long-period oscillation: while almost undetectable when the GNR is aligned in the standard "R30" orientation on Au(111), we predict that such feature should become prominent in the alternative rotated "R0" orientation on the same surface, or on a different surface, such as perhaps Ag(111).

Recent highlights in nanoscale and mesoscale friction.

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.

Velocity dependence of sliding friction on a crystalline surface.

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

Smallest Archimedean Screw: Facet Dynamics and Friction in Multiwalled Nanotubes.

We identify a new material phenomenon, where minute mechanical manipulations induce pronounced global structural reconfigurations in faceted multiwalled nanotubes. This behavior has strong implications on the tribological properties of these systems and may be the key to understand the enhanced interwall friction recently measured for boron-nitride nanotubes with respect to their carbon counterparts. Notably, the fast rotation of helical facets in these systems upon coaxial sliding may serve as a nanoscale Archimedean screw for directional transport of physisorbed molecules.

Graphene on h-BN: to align or not to align?

The contact strength, adhesion and friction, between graphene and an incommensurate crystalline substrate such as h-BN depends on their relative alignment angle θ. The well-established Novaco-McTague (NM) theory predicts for a monolayer graphene on a hard bulk h-BN crystal face a small spontaneous misalignment, here θNM ≃ 0.45 degrees which if realized would be relevant to a host of electronic properties besides the mechanical ones. Because experimental equilibrium is hard to achieve, we inquire theoretically about alignment or misalignment by simulations based on dependable state-of-the-art interatomic force fields. Surprisingly at first, we find compelling evidence for θ = 0, i.e., full energy-driven alignment in the equilibrium state of graphene on h-BN. Two factors drive this deviation from the NM theory. First, graphene is not flat, developing on h-BN a long-wavelength out-of-plane corrugation. Second, h-BN is not hard, releasing its contact stress by planar contractions/expansions that accompany the interface moiré structure. Repeated simulations by artificially forcing graphene to keep flat, and h-BN to keep rigid, indeed yield an equilibrium misalignment similar to θNM as expected. Subsequent sliding simulations show that friction of graphene on h-BN, small and essentially independent of misalignments in the artificial frozen state, strongly increases in the more realistic corrugated, strain-modulated, aligned state.

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.

Slider thickness promotes lubricity: from 2D islands to 3D clusters.

The sliding of three-dimensional clusters and two-dimensional islands adsorbed on crystal surfaces represents an important test case to understand friction. Even for the same material, monoatomic islands and thick clusters will not as a rule exhibit the same friction, but specific differences have not been explored. Through realistic molecular dynamics simulations of the static friction of gold on graphite, an experimentally relevant system, we uncover as a function of gold thickness a progressive drop of static friction from monolayer islands, that are easily pinned, towards clusters, that slide more readily. The main ingredient contributing to this thickness-induced lubricity appears to be the increased effective rigidity of the atomic contact, acting to reduce the cluster interdigitation with the substrate. A second element which plays a role is the lateral contact size, which can accommodate the solitons typical of the incommensurate interface only above a critical contact diameter, which is larger for monolayer islands than for thick clusters. The two effects concur to make clusters more lubric than islands, and large sizes more lubric than smaller ones. These conclusions are expected to be of broader applicability in diverse nanotribological systems, where the role played by static, and dynamic, friction is generally quite important.

Subharmonic Shapiro steps of sliding colloidal monolayers in optical lattices.

We investigate theoretically the possibility to observe dynamical mode locking, in the form of Shapiro steps, when a time-periodic potential or force modulation is applied to a two-dimensional (2D) lattice of colloidal particles that are dragged by an external force over an optically generated periodic potential. Here we present realistic molecular dynamics simulations of a 2D experimental setup, where the colloid sliding is realized through the motion of soliton lines between locally commensurate patches or domains, and where the Shapiro steps are predicted and analyzed. Interestingly, the jump between one step and the next is seen to correspond to a fixed number of colloids jumping from one patch to the next, across the soliton line boundary, during each ac cycle. In addition to ordinary 'integer' steps, coinciding here with the synchronous rigid advancement of the whole colloid monolayer, our main prediction is the existence of additional smaller 'subharmonic' steps due to localized solitonic regions of incommensurate layers executing synchronized slips, while the majority of the colloids remains pinned to a potential minimum. The current availability and wide parameter tunability of colloid monolayers makes these predictions potentially easy to access in an experimentally rich 2D geometrical configuration.