Friction and nonlinear dynamics.

The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.

Aftershocks in a frictional earthquake model.

Inspired by spring-block models, we elaborate a "minimal" physical model of earthquakes which reproduces two main empirical seismological laws, the Gutenberg-Richter law and the Omori aftershock law. Our point is to demonstrate that the simultaneous incorporation of aging of contacts in the sliding interface and of elasticity of the sliding plates constitutes the minimal ingredients to account for both laws within the same frictional model.

Size scaling of static friction.

Sliding friction across a thin soft lubricant film typically occurs by stick slip, the lubricant fully solidifying at stick, yielding and flowing at slip. The static friction force per unit area preceding slip is known from molecular dynamics (MD) simulations to decrease with increasing contact area. That makes the large-size fate of stick slip unclear and unknown; its possible vanishing is important as it would herald smooth sliding with a dramatic drop of kinetic friction at large size. Here we formulate a scaling law of the static friction force, which for a soft lubricant is predicted to decrease as f(m)+Δf/A(γ) for increasing contact area A, with γ>0. Our main finding is that the value of f(m), controlling the survival of stick slip at large size, can be evaluated by simulations of comparably small size. MD simulations of soft lubricant sliding are presented, which verify this theory.

Crack in the frictional interface as a solitary wave.

We introduce and investigate a multiscale model for the propagation of rupture fronts in friction. Taking advantage of the correlation length for the motion of individual contacts in elastic theory, we introduce collective contacts which can be characterized by a master equation approach. The problem of the dynamics of a chain of those effective contacts under stress is studied. We show that it can be reduced to an analog of the Frenkel-Kontorova model. In some limits this allows us to derive analytical solutions for kinks describing the rupture fronts. Numerical simulations are used to study more complex cases.

Dependence of kinetic friction on velocity: master equation approach.

We investigate the velocity dependence of kinetic friction with a model that makes minimal assumptions on the actual mechanism of friction so that it can be applied at many scales, provided the system involves multicontact friction. Using a recently developed master equation approach, we investigate the influence of two concurrent processes. First, at a nonzero temperature, thermal fluctuations allow an activated breaking of contacts that are still below the threshold. As a result, the friction force monotonically increases with velocity. Second, the aging of contacts leads to a decrease of the friction force with velocity. Aging effects include two aspects: the delay in contact formation and aging of a contact itself, i.e., the change of its characteristics with the duration of stationary contact. All these processes are considered simultaneously with the master equation approach, giving a complete dependence of the kinetic friction force on the driving velocity and system temperature, provided the interface parameters are known.

Dependence of boundary lubrication on the misfit angle between the sliding surfaces.

Using molecular dynamics based on Langevin equations with a coordinate- and velocity-dependent damping coefficient, we study the frictional properties of a thin layer of "soft" lubricant (where the interaction within the lubricant is weaker than the lubricant-substrate interaction) confined between two solids. At low driving velocities the system demonstrates stick-slip motion. The lubricant may or may not be melted during sliding, thus exhibiting either the "liquid sliding" (LS) or the "layer over layer sliding" (LoLS) regimes. The LoLS regime mainly operates at low sliding velocities. We investigate the dependence of friction properties on the misfit angle between the sliding surfaces and calculate the distribution of static frictional thresholds for a contact of polycrystalline surfaces.

Master equation approach to friction at the mesoscale.

At the mesoscale friction occurs through the breaking and formation of local contacts. This is often described by the earthquakelike model which requires numerical studies. We show that this phenomenon can also be described by a master equation, which can be solved analytically in some cases and provides an efficient numerical solution for more general cases. We examine the effect of temperature and aging of the contacts and discuss the statistical properties of the contacts for different situations of friction and their implications, particularly regarding the existence of stick-slip.

Dynamics of transition from static to kinetic friction.

We propose a model for a description of dynamics of cracklike processes that occur at the interface between two blocks prior to the onset of frictional motion. We find that the onset of sliding is preceded by well-defined detachment fronts initiated at the slider trailing edge and extended across the slider over limited lengths smaller than the overall length of the slider. Three different types of detachment fronts may play a role in the onset of sliding: (i) Rayleigh (surface sound) fronts, (ii) slow detachment fronts, and (iii) fast fronts. The important consequence of the precursor dynamics is that before the transition to overall sliding occurs, the initially uniform, unstressed slider is already transformed into a highly nonuniform, stressed state. Our model allows us to explain experimental observations and predicts the effect of material properties on the dynamics of the transition to sliding.

Modeling friction on a mesoscale: master equation for the earthquakelike model.

The earthquakelike model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach naturally describes stick-slip and smooth-sliding regimes of tribological systems within a framework which separates the calculation of the friction force from the studies of the properties of the contacts.

Transition from smooth sliding to stick-slip motion in a single frictional contact.

We show that the transition from smooth sliding to stick-slip motion in a single planar frictional junction always takes place at an atomic-scale relative velocity of the substrates.

Simple model of microscopic rolling friction.

Rolling friction at a microscopic scale is studied with the help of a simple two-dimensional model. Molecular dynamics simulations show that rolling of spherical lubricant molecules exists only for concentrations lower than the concentration of a close-packed layer. At concentrations higher than a critical one due to jamming of lubricant molecules the rolling of nearest neighboring molecules is hindered. An optimal concentration exists which provides the minimum of kinetic friction. Methods for avoiding jamming and increasing the range of operation of rolling mechanism of friction are discussed.

Incommensurability of a confined system under shear.

We study a chain of harmonically interacting atoms confined between two sinusoidal substrate potentials, when the top substrate is driven through an attached spring with a constant velocity. This system is characterized by three inherent length scales and closely related to physical situations with confined lubricant films. We show that, contrary to the standard Frenkel-Kontorova model, the most favorable sliding regime is achieved by choosing chain-substrate incommensurabilities belonging to the class of cubic irrational numbers (e.g., the spiral mean). At large chain stiffness, the well known golden mean incommensurability reveals a very regular time-periodic dynamics with always higher kinetic friction values with respect to the spiral mean case.

Two-dimensional two-state lattice-gas model.

We propose a two-dimensional lattice-gas (2D LG) model where atoms may be in two different states: the immobile state, in which they jump as usual in the LG model, and the running state, in which the atoms always jump in the driving direction. The model demonstrates a typical behavior of "traffic-jam" models: the system splits into domains of immobile atoms (jams) and running atoms. We considered four variants of the 2D LG model, namely the multilane and truly 2D models, each with "passive" and "active" atomic jumps. The model has the steady state with a power law distribution of jam sizes characterized by a universal exponent 3/2. The phase diagram of the model shows that the mobility of the 2D system is lower than the mobility of the 1D model due to the spreading of jams in the direction transverse to the driving direction.

Clustering of atoms in a model with multiple thermostats.

We propose a model for a one-dimensional chain of interacting particles in an external periodic potential. In this model the particles have a complex structure treated in a mean-field fashion: particle collisions are inelastic and also each particle is considered as having its own thermostat. We derived the Fokker-Planck equation for this model and demonstrated that the model has a truly equilibrium ground state. When an external dc force is applied to the atoms, the model exhibits a hysteresis even at high temperatures due to the clustering of atoms with the same velocity. Another effect of clustering is phase separation in the steady state when the system splits into regions of immobile atoms ("traffic jams") and regions of running atoms.

Dynamic phases in the two-dimensional underdamped driven Frenkel-Kontorova model.

We study the nonlinear dc response of a two-dimensional underdamped system of interacting atoms subject to an isotropic periodic external potential with triangular symmetry. When driving force increases, the system transfers from a disorder locked state to an ordered sliding state corresponding to a moving crystal. By varying the values of the effective elastic constant, damping, and temperature, we found different scenarios and intermediate phases during the ordering transition. For a soft atomic layer, the system passes through a plastic-channel regime that appears as a steady-state regime at higher values of the damping coefficient. For high values of the effective elastic constant, when the atomic layer is stiff, the intermediate plastic phase corresponds to a traffic-jam regime with immobile islands in the sea of running atoms. At a high driving of the stiff layer, a solitonlike elastic flow of atoms has been observed.

Ordering of a thin lubricant film due to sliding.

A thin lubricant film confined between two substrates in moving contact is studied using Langevin molecular dynamics with the coordinate- and velocity-dependent damping coefficient. It is shown that an optimal choice of the interaction within the lubricant can lead to minimal kinetic friction as well as to low critical velocity of the stick-slip to smooth-sliding transition. The strength of this interaction should be high enough (relative to the strength of the interaction of lubricant atoms with the substrates) so that the lubricant remains in a solid state during sliding. At the same time, the strength of the interaction should not be too high, in order to allow annealing of defects in the lubricant at slips.

Stimulated diffusion of an adsorbed dimer.

The mobility and the diffusivity of a dimer (two atoms coupled by an elastic spring) in a periodic substrate potential under the action of the dc and ac external forces are studied. It is shown that the dimer diffusivity may be strongly enhanced due to driving.

Dynamics and melting of a thin confined film.

Molecular dynamics is used to investigate the melting of a thin lubricant film confined between two crystalline surfaces. The dynamics of the film is significantly affected by the substrate, both in the solid and in the molten phases. The solid phase, able to sustain shear stress, shows, however, large diffusional motions of the atoms. The melting temperature depends strongly on the confinement. A phenomenological microscopic theory, based on the Lindemann criterion, is proposed to explain this effect.

Driven kinks in the anharmonic Frenkel-Kontorova model.

Multiple and supersonic topological excitations (kinks) driven by an external dc force in the Frenkel-Kontorova model (a chain of atoms subjected to a periodic substrate potential) with the exponential interatomic interaction are studied with the help of numerical simulation. The simulation results are interpreted in terms of dynamics of two limiting cases, the exactly integrable sine-Gordon equation and the Toda chain. The stability of driven kinks and scenarios of their destruction are described for a wide range of model parameters.

Role of long jumps in surface diffusion.

We analyze a probability of atomic jumps for more than one lattice spacing in activated surface diffusion. First, we studied a role of coupling between the x and y degrees of freedom for the diffusion in a two-dimensional substrate potential. Simulation results show that in the underdamped limit the average jump length scales with the damping coefficient eta as proportional, variant eta(-sigma(lambda)) with 1/2