Structural lubricity in soft and hard matter systems

Abstract

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.

Fig. 1. Systems and length scales of nano/micro tribology: from single-asperity atomic contacts to microscopic sliding interfaces.

The multifaceted discipline of tribology starts, at the shortest scale, by the investigation, via proximal-probe techniques, of a single atomistically small contact as that realized, e.g., between a sharp atomic force microscope tip, or a deposited molecule (reprinted (adapted) with permission from ref. . Copyright (2016) American Chemical Society), and an underlying reference substrate. Entering into the nanoscale range of tens-of-nanometer extended adsorbates, such as AFM-manipulated graphitic ribbons (reprinted (adapted) with permission from ref. . Copyright (2018) American Chemical Society) and metallic clusters, or rare-gas islands sheared by a quartz-crystal microbalance, interface geometry and incommensurability features rule the frictional response. With unprecedented real-time resolution processed at the single-particle level, the novel experimental mesoscale techniques of driven trapped cold ions and colloids have recently made crucial systematic inroads in the physics of frictional phenomena. State-of-the-art technology and fabrication procedures, especially in the realm of 2D layered materials (e.g., graphitic tubes and mesas), have nowadays offered tribology the chance to investigate atomistically well-characterized mechanical contacts up to the millimeter range and beyond. With the exponential boost of computer power in the last decades, numerical modeling and atomistic simulations are jointly advancing our theoretical understanding across all these length scales.

Fig. 2. Geometrical configurations at crystalline interfaces.

Mating identical surfaces with the same lattice spacing (red and blue) may give rise to both a commensurate interfaces when aligned and b incommensurate ones when orientationally misaligned at a misfit generic angle. c Structural incommensurability may also emerge when dealing with crystalline lattice-mismatched surfaces (red and green). The overall geometrical features of the contacting interface are captured in terms of the superstructure of the moire’ interference pattern.

Fig. 3. 2D materials as building blocks for clean and atomically flat mechanical junctions.

a Examples of 2D materials used in the construction of layered van der Waals structures (adapted from ref. ). b, c Homogeneous—graphene on graphite—and heterogeneous—graphene on hexagonal boron nitride—interface junctions, respectively, characterized by weakly coupled and extremely stiff atomic layers, and thus exploited for mechanical and tribological applications. While structural lubricity requires an angular misalignment for the homogeneous contact (b), the hybrid junction (c), thanks to the intrinsic lattice incommensurability, ensures superlubric sliding^– independently of the surface relative orientation.

Fig. 4. Strain distribution and static friction of a uniformly driven versus edge-driven 2D FK model.

a–c Colored maps showing the local average distance δ_loc between nearest-neighbor particles in a 2D FK model of an incommensurate (overdense) circular island subjected to a periodic square-symmetry substrate potential, 10.1103/PhysRevMaterials.2.046001. Expressed in units of the underlying periodicity, values of δ_loc = 1 (white color) indicate local commensuration to the substrate. The three panels compare the local strain distribution in the island at rest (a), and under the action of an external force, below the static friction threshold, applying a uniform driving (b) or pulling at the leading edge of the cluster (c). d Static friction force as a function of the contact area, i.e., the number of particles in the island, evaluated for uniform driving (black) and pulling at the leading edge. Due to the particle overdensity of the island with respect to the substrate minima arrangement, the edge pulling procedure favors the formation of locally strained commensurate regions, enhancing static friction.

Fig. 5. Experimental confirmation of the Aubry transition in atomic and colloidal systems.

a Sketch of an experimental setup with two interacting chains of laser-cooled YB positive ions inside a linear trap which is created by four quadrupole electrodes. The two laser beams are used for the illumination of the ions and for performing vibrational spectroscopy. The ions are imaged onto an electron multiplying CCD camera. b Illustration of an extended two-dimensional micron-sized colloidal monolayer consisting of several thousand particles which are interacting with an optical substrate potential created by three interfering laser beams. Variation of the corrugation amplitude of the substrate potential is achieved by changes in the laser intensity. Both experiments confirm the existence of a transition from a superlubric to a pinned state in agreement with theoretical predictions.

Fig. 6. Aubry transition in 1D and 2D systems.

a, b Schematic view of a 1D system of elastically interacting particles subjected to an incommensurate periodic substrate. a When the substrate corrugation amplitude U₀ is below a critical value U_c, particles are found at any displacement relative to substrate minima which results in a superlubric state. b When U₀ > U_c particles become localized near the potential minima. This leads to a continuous Aubry transition from a superlubric to a pinned state. c Static friction force versus substrate corrugation obtained from experiments (solid symbols) and simulations (open symbols) of a 2D colloidal system; the shaded area shows the coexistence region, across which the Aubry transition takes place. Measured colloidal particle configurations for increasing substrate potential: d U₀ < U_c, e U₀ ≈ U_c, and f U₀ > U_c. The color code corresponds to the local misfit angle θ of the particles relative to the substrate. g–i Misfit angle-distribution for increasing substrate potential indicating the coexistence between a suberlubric and a pinned state in agreement with numerical simulations predicting a first-order Aubry transition in 2D^,.

Fig. 7. Directional and orientational locking of clusters driven across periodic surfaces.

a Mesoscopic colloidal cluster whose direction of motion (green arrow) substantially deviates from that of the driving force (white arrow) due to the interaction with the underlying periodic substrate potential. In addition to the direction of motion the orientation of the cluster becomes locked during the sliding process. Particles are colored corresponding to their displacement relative to the nearest substrate potential well. b AFM-manipulated crystalline gold nanoparticles on molybdenum disulfide also displaying a pronounced deviation between the direction of translation (blue arrow) versus external forcing (red arrow), 10.1103/PhysRevB.98.165417.