Onset of sliding friction in incommensurate systems

Friction on incommensurate substrates: Role of anharmonicity and defects

We present molecular dynamics simulations of one- and two-dimensional bead-spring models sliding on incommensurate substrates after an initial kick, in the case where the coupling to the underlying substrate is weak, i.e., energy can dissipate only into the internal degrees of freedom of the sliding object, but not into the substrate below. We investigate how sliding friction is affected by structural defects and interaction anharmonicity. In their absence, we confirm earlier findings, namely, that at special resonance sliding velocities, friction is maximal. When sliding off-resonance, partially thermalized states are possible, whereby only a small number of vibrational modes becomes excited, but whose kinetic energies are already Maxwell-Boltzmann distributed. Anharmonicity and defects typically destroy partial thermalization and instead lead to full thermalization, implying much higher friction. For sliders with periodic boundaries, thermalization begins with vibrational modes whose spatial modulation is compatible with the incommensurate lattice. For a disk-shaped slider, modes corresponding to modulations compatible with the slider radius are initially the most dominant. By tuning the mechanical properties of the slider's edge, this effect can be controlled, resulting in significant changes in the sliding distance covered.

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.

Sliding states of a soft-colloid cluster crystal: Cluster versus single-particle hopping

We study a two-dimensional model for interacting colloidal particles which displays spontaneous clustering. Within this model we investigate the competition between the pinning to a periodic corrugation potential and a sideways constant pulling force which would promote a sliding state. For a few sample particle densities and amplitudes of the periodic corrugation potential we investigate the depinning from the statically pinned to the dynamically sliding regime. This sliding state exhibits the competition between a dynamics where entire clusters are pulled from a minimum to the next and a dynamics where single colloids or smaller groups leave a cluster and move across the corrugation energy barrier to join the next cluster downstream in the force direction. Both kinds of sliding states can occur either coherently across the entire sample or asynchronously: the two regimes result in different average mobilities. Finite temperature tends to destroy separate sliding regimes, generating a smoother dependence of the mobility on the driving force.

Dependence of the sliding distance of a one-dimensional atom chain on initial velocity

In our daily lives, a body with a high initial velocity sliding freely on a rough surface moves a longer distance than that with a low initial velocity. However, such a phenomenon may not occur in the microscopic world. The dynamical behavior of a one-dimensional atom chain (1DAC) sliding on a substrate is investigated in this study by using a modified Frenkel–Kontorova model, in which the vibration of atoms on the substrate is considered. The dependence of sliding distance on initial velocity is examined. Result shows that although sliding distance is proportional to the initial value for most velocities, such a linear relation does not exist in some special velocities. This phenomenon is explained by a theoretical analysis of phonon excitation. The physical process is divided into three stages. The first stage is a superlubric sliding process with small amplitude of the vibrication of the atoms. The single-mode phonon is excited in the second stage. In the third stage, the system exhibits instability because of multiple-mode phonon excitations. In addition, the dependence of the coupling strength between 1DAC and the substrate is investigated. The findings are helpful in understanding the energy dissipation mechanism of friction.

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.

Pinned-to-sliding transition and structural crossovers for helically confined charges

We explore the nonequilibrium dissipative dynamics of a system of identical charged particles trapped on a closed helix. The particles are subject to an external force accelerating them along the underlying structure. The effective interactions between the charges induce a coupling of the center of mass to the relative motion which in turn gives rise to a pinned-to-sliding transition with increasing magnitude of the external force. In the sliding regime we observe an Ohmic behavior signified by a constant mobility. Within the same regime a structural transition of the helical particle chain takes place with increasing the helix radius leading to a global change of the crystalline arrangement. The resulting crystal is characterized by the existence of multiple defects whose number increases with the helix radius.

Emergent friction in two-dimensional Frenkel-Kontorova models

Simple models for friction are typically one-dimensional, but real interfaces are two-dimensional. We investigate the effects of the second dimension on static and dynamic friction by using the Frenkel-Kontorova (FK) model. We study the two most straightforward extensions of the FK model to two dimensions and simulate both the static and dynamic properties. We show that the behavior of the static friction is robust and remains similar in two dimensions for physically reasonable parameter values. The dynamic friction, however, is strongly influenced by the second dimension and the accompanying additional dynamics and parameters introduced into the models. We discuss our results in terms of the thermal equilibration and phonon dispersion relations of the lattices, establishing a physically realistic and suitable two-dimensional extension of the FK model. We find that the presence of additional dissipation channels can increase the friction and produces significantly different temperature dependence when compared to the one-dimensional case. We also briefly study the anisotropy of the dynamic friction and show highly nontrivial effects, including that the friction anisotropy can lead to motion in different directions depending on the value of the initial velocity.

Critical length limiting superlow friction

Since the demonstration of superlow friction (superlubricity) in graphite at nanoscale, one of the main challenges in the field of nano- and micromechanics was to scale this phenomenon up. A key question to be addressed is to what extent superlubricity could persist, and what mechanisms could lead to its failure. Here, using an edge-driven Frenkel-Kontorova model, we establish a connection between the critical length above which superlubricity disappears and both intrinsic material properties and experimental parameters. A striking boost in dissipated energy with chain length emerges abruptly due to a high-friction stick-slip mechanism caused by deformation of the slider leading to a local commensuration with the substrate lattice. We derived a parameter-free analytical model for the critical length that is in excellent agreement with our numerical simulations. Our results provide a new perspective on friction and nanomanipulation and can serve as a theoretical basis for designing nanodevices with superlow friction, such as carbon nanotubes.

The effect of temperature and velocity on superlubricity

We study the effects of temperature and sliding velocity on superlubricity in numerical simulations of the Frenkel-Kontorova model. We show that resonant excitations of the phonons in an incommensurate sliding body lead to an effective friction and to thermal equilibrium with energy distributed over the internal degrees of freedom. For finite temperature, the effective friction can be described well in terms of a viscous damping force, with a damping coefficient that emerges naturally from the microscopic dynamics. This damping coefficient is a non-monotonic function of the sliding velocity which peaks around resonant velocities and increases with temperature. At low velocities, it remains finite and nonzero, indicating the preservation of superlubricity in the zero-velocity limit. Finally, we propose experimental systems in which our results could be verified.

Stability of superlubric sliding on graphite

Recent atomic force microscope (AFM) experiments have shown that the low-friction sliding of incommensurate graphite flakes on graphite can be destroyed by torque-induced rotations. Here we theoretically investigate the stability of superlubric sliding against rotations of the flake. We find that the occurrence of superlubric motion critically depends on the physical parameters and on the experimental conditions: particular scan lines, thermal fluctuations, and high loading forces can destroy the stability of superlubric orbits. We find that the optimal conditions to achieve superlubric sliding are given by large flakes, low temperature, and low loads, as well as scanning velocities higher than those used in AFM experiments.

Trans-phonon effects in ultra-fast nanodevices

We report a novel phenomenon in carbon nanotube based ultra-fast mechanical devices, the trans-phonon effect, which resembles the transonic effects in aerodynamics. It is caused by dissipative resonance of nanotube phonons similar to the radial breathing mode, and subsequent drastic surge of the dragging force on the sliding tube, and multiple phonon barriers are encountered as the intertube sliding velocity reaches critical values. It is found that the trans-phonon effects can be tuned by applying geometric constraints or varying chirality combinations of the nanotubes.

Quantum phase transition in the Frenkel-Kontorova chain: from pinned instanton glass to sliding phonon gas

We study analytically and numerically the one-dimensional quantum Frenkel-Kontorova chain in the regime where the classical model is located in the pinned phase characterized by the gaped phonon excitations and devil's staircase. By extensive quantum Monte Carlo simulations, we show that for the effective Planck constant Planck smaller than the critical value Planck(c) the quantum chain is in the pinned instanton glass phase. In this phase, the elementary excitations have two branches: phonons, separated from zero energy by a finite gap, and instantons that have an exponentially small excitation energy. At Planck = Planck(c) the quantum phase transition takes place and for Planck > Planck(c) the pinned instanton glass is transformed into the sliding phonon gas with gapless phonon excitations. This transition is accompanied by the divergence of the spatial correlation length and appearance of sliding modes at Planck > Planck(c).

Kink nucleation in the two-dimensional Frenkel-Kontorova model

A computer simulation of thermofluctuation nucleation of kinks on dislocations and their dynamics is carried out in the framework of the two-dimensional Frenkel-Kontorova model. It is shown that at relatively low temperatures and applied stresses the kinks can appear as a result of developing instability of phonon modes localized in the vicinity of the dislocation. The transition from this mechanism to the ordinary thermofluctuation kink nucleation with temperature increase can reveal itself in the peculiarities of yield stress temperature dependence.

Fractal spin glass properties of low energy configurations in the Frenkel-Kontorova chain

We study, numerically and analytically, the classical one-dimensional Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon gap. Our results show the existence of exponentially many static equilibrium configurations that are exponentially close to the energy of the ground state. The energies of these configurations form a fractal quasidegenerate band structure that is described on the basis of elementary excitations. Contrary to the ground state, the configurations inside these bands are disordered.

Breakdown of a conservation law in incommensurate systems

We show that invariance properties of the Lagrangian of an incommensurate system, as described by the Frenkel-Kontorova model, imply the existence of a generalized angular momentum that is an integral of motion if the system remains floating. The behavior of this quantity can therefore monitor the character of the system as floating (when it is conserved) or locked (when it is not). We find that, during the dynamics, the nonlinear couplings of our model cause parametric phonon excitations that lead to the appearance of Umklapp terms and to a sudden deviation of the generalized momentum from a constant value, signaling a dynamical transition from a floating to a pinned state. We point out that this transition is related but does not coincide with the onset of sliding friction, which can take place when the system is still floating.