Friction in a solid lubricant film

Diffusion coefficient scaling of a free Brownian particle with velocity-dependent damping

An analytical expression for the diffusion coefficient D of a free Brownian particle with velocity-dependent damping γ(v) is derived from the Green-Kubo formula. A special case of damping that decreases monotonically with velocity is considered. At high temperature T, the diffusion coefficient is found to exhibit two scaling types: (i) for a power-law decrease of damping with the particle's kinetic energy, γ(v)∝1/v^{2α}, it scales as D∝T^{α+1}; (ii) for a Gaussian function γ(v), it diverges at temperatures above a critical value T_{c} and behaves as D∝1/sqrt[T_{c}-T] at T slightly below T_{c}. At T>T_{c}, the particle trajectory contains long flight events, which are not observed at T<T_{c} in case (ii) and at all temperatures in case (i).

Hydrodynamic effects on the liquid-hexatic transition of active colloids

We study numerically the role of hydrodynamics in the liquid-hexatic transition of active colloids at intermediate activity, where motility induced phase separation (MIPS) does not occur. We show that in the case of active Brownian particles (ABP), the critical density of the transition decreases upon increasing the particle's mass, enhancing ordering, while self-propulsion has the opposite effect in the activity regime considered. Active hydrodynamic particles (AHP), instead, undergo the liquid-hexatic transition at higher values of packing fraction [Formula: see text] than the corresponding ABP, suggesting that hydrodynamics have the net effect of disordering the system. At increasing densities, close to the hexatic-liquid transition, we found in the case of AHP the appearance of self-sustained organized motion with clusters of particles moving coherently.

Nanoserpents: Graphene Nanoribbon Motion on Two-Dimensional Hexagonal Materials

We demonstrate snake-like motion of graphene nanoribbons atop graphene and hexagonal boron nitride ( h-BN) substrates using fully atomistic nonequilibrium molecular dynamics simulations. The sliding dynamics of the edge-pulled nanoribbons is found to be determined by the interplay between in-plane ribbon elasticity and interfacial lattice mismatch. This results in an unusual dependence of the friction-force on the ribbon's length, exhibiting an initial linear rise that levels-off above a junction-dependent threshold value dictated by the pre-slip stress distribution within the slider. As part of this letter, we present the LAMMPS implementation of the registry-dependent interlayer potentials for graphene, h-BN, and their heterojunctions that were used herein, which provides enhanced performance and accuracy.

Atomic-scale sliding friction on a contaminated surface

Using non-equilibrium molecular dynamic simulations, we investigate the effect of adsorbates on nanoscopic friction. We find that the interplay between different channels of energy dissipation at the frictional interface may lead to non-monotonic dependence of the friction force on the adsorbate surface coverage and to strongly nonlinear variation of friction with normal load (non-Amontons' behavior). Our simulations suggest that the key parameter controlling the variation of friction force with the normal load, surface coverage and temperature is the time-averaged number of adsorbates confined between the tip and the substrate. Three different regimes of temperature dependence of friction in the presence of adsorbates are predicted. Our findings point on new ways to control friction on contaminated surfaces.

Controlled Viscosity in Dense Granular Materials

We experimentally investigate the fluidization of a granular material subject to mechanical vibrations by monitoring the angular velocity of a vane suspended in the medium and driven by an external motor. On increasing the frequency, we observe a reentrant transition, as a jammed system first enters a fluidized state, where the vane rotates with high constant velocity, and then returns to a frictional state, where the vane velocity is much lower. While the fluidization frequency is material independent, the viscosity recovery frequency shows a clear dependence on the material that we rationalize by relating this frequency to the balance between dissipative and inertial forces in the system. Molecular dynamics simulations well reproduce the experimental data, confirming the suggested theoretical picture.

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.

Molecularly thin fluoro-polymeric nanolubricant films: tribology, rheology, morphology, and applications

Molecularly thin perfluoropolyether (PFPE) has been used extensively as a high-performance lubricant in various applications and, more importantly, on carbon overcoats to enhance the reliability and lubrication of micro-/nanoelectro-mechanical systems, where the tribological performance caused by its molecular architecture is a critical issue, as are its physical properties and rheological characteristics. This Highlight addresses recent trends in the development of fluoro-polymeric lubricant films with regard to their tribology, rheology, and physio-chemical properties as they relate to heat-assisted magnetic recording. Nanorheology has been employed to examine the dynamic response of nonfunctional and functional PFPEs, while the viscoelastic properties of nanoscale PFPE films and the relaxation processes as a function of molecular structure and end-group functionality were analyzed experimentally; furthermore, the characteristics of binary blends were reported.

Frictional Properties of Nanojunctions Including Atomically Thin Sheets

Using nonequilibrium molecular dynamics simulations and a coarse-grained description of a system, we have investigated frictional properties of nanojunctions including atomically thin sheets embedded between metal surfaces. We found that the frictional properties of the junctions are determined by the interplay between the lattice mismatch of the contacting surfaces and out-of-plane displacements of the sheet. The simulations provide insight into how and why the frictional characteristics of the nanojunctions are affected by the commensurate-incommensurate transition. We demonstrated that in order to achieve a superlow friction, the graphene sheet should be grown on or transferred to the surface with morphology, which is close to that of the graphene (for instance, Cu), while the second confining surface should be incommensurate with the graphene (e.g., Au). Our results suggest an avenue for controlling nanoscale friction in layered materials and provide insights in the design of heterojunctions for nanomechanical applications.

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.

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.

Tribology of the lubricant quantized sliding state

In the framework of Langevin dynamics, we demonstrate clear evidence of the peculiar quantized sliding state, previously found in a simple one-dimensional boundary lubricated model [A. Vanossi et al., Phys. Rev. Lett. 97, 056101 (2006)], for a substantially less idealized two-dimensional description of a confined multilayer solid lubricant under shear. This dynamical state, marked by a nontrivial "quantized" ratio of the averaged lubricant center-of-mass velocity to the externally imposed sliding speed, is recovered, and shown to be robust against the effects of thermal fluctuations, quenched disorder in the confining substrates, and over a wide range of loading forces. The lubricant softness, setting the width of the propagating solitonic structures, is found to play a major role in promoting in-registry commensurate regions beneficial to this quantized sliding. By evaluating the force instantaneously exerted on the top plate, we find that this quantized sliding represents a dynamical "pinned" state, characterized by significantly low values of the kinetic friction. While the quantized sliding occurs due to solitons being driven gently, the transition to ordinary unpinned sliding regimes can involve lubricant melting due to large shear-induced Joule heating, for example at large speed.

Suppression of friction by mechanical vibrations

Mechanical vibrations are known to affect frictional sliding and the associated stick-slip patterns causing sometimes a drastic reduction of the friction force. This issue is relevant for applications in nanotribology and to understand earthquake triggering by small dynamic perturbations. We study the dynamics of repulsive particles confined between a horizontally driven top plate and a vertically oscillating bottom plate. Our numerical results show a suppression of the high dissipative stick-slip regime in a well-defined range of frequencies that depends on the vibrating amplitude, the normal applied load, the system inertia and the damping constant. We propose a theoretical explanation of the numerical results and derive a phase diagram indicating the region of parameter space where friction is suppressed. Our results allow to define better strategies for the mechanical control of friction.

Spreading of droplets on lubricant-patterned substrates

Droplet spreading behaviors on lubricant-patterned substrates are investigated by using molecular dynamics simulations to explore application potentials in magnetic storage drive systems. Microscopic spreading processes are studied by both potential fields of lubricant-patterned substrates and single molecule movements in lubricant droplets. The potential fields indicate that the wall molecules patterned on the substrates attract the mobile ones in the lubricant droplets. Due to the attraction force, the mobile molecules experience difficulties in diffusing freely along the substrates. The single molecule movements in lubricant droplets demonstrate that during the diffusion process, the mobile molecules encounter, adsorb, encompass, and disengage the wall ones. The spreading behaviors are significantly impacted by the bonded ratio. The potential fields indicate that as the bonded ratio increases, the attractive regions of wall molecules merge to overlap, which indicate combined interactions formed by the adjacent wall molecules.

Crystal Bridges, Tetratic Order, and Elusive Equilibria: The Role of Structure in Lubrication Films

In this paper, we report on molecular dynamics simulation studies of thin dodecane films confined between mica surfaces. On confinement, the film undergoes a surface-mediated transition into a novel phase characterized by tetratic orientational order. The rheology of this ordered film is governed by slip planes and, at low shear rates, stick-slip behavior observable under steady shear rates. Melting of these films was observed either on heating or on exceeding a critical shear rate. Evidence is presented that this tetratic film is not the true equilibrium state; rather, a state characterized by nematic order and very low viscosities is found to be more stable.

Liquid nanodroplets spreading on chemically patterned surfaces

Controlling the spatial distribution of liquid droplets on surfaces via surface energy patterning can be used to deliver material to specified regions via selective liquid/solid wetting. Although studies of the equilibrium shape of liquid droplets on heterogeneous substrates exist, much less is known about the corresponding wetting kinetics. Here we present large-scale atomistic simulations of liquid nanodroplets spreading on chemically patterned surfaces. Results are presented for lines of polymer liquid (droplets) on substrates consisting of alternating strips of wetting (equilibrium contact angle theta0 = 0 degrees) and nonwetting (theta0 approximately 90 degrees) material. Droplet spreading is compared for different wavelength lambda of the pattern and strength of surface interaction on the wetting strips. For small lambda, droplets partially spread on both the wetting and nonwetting regions of the substrate to attain a finite contact angle less than 90 degrees. In this case, the extent of spreading depends on the interaction strength in the wetting regions. A transition is observed such that, for large lambda, the droplet spreads only on the wetting region of the substrate by pulling material from nonwetting regions. In most cases, a precursor film spreads on the wetting portion of the substrate at a rate strongly dependent on the width of the wetting region.

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.

Surface wetting of liquid nanodroplets: droplet-size effects

The spreading of liquid nanodroplets of different initial radii R0 is studied using molecular dynamics simulation. Results for two distinct systems, Pb on Cu(111), which is nonwetting, and a coarse-grained polymer model, which wets the surface, are presented for Pb droplets ranging in size from approximately 55,000 to 220,000 atoms and polymer droplets ranging in size from approximately 200,000 to 780 000 monomers. In both cases, a precursor foot precedes the spreading of the main droplet. This precursor foot spreads as r(2)(f)(t) = 2D(eff)t with an effective diffusion constant that exhibits a droplet-size dependence D(eff) approximately R(1/2)(0). The radius of the main droplet r(b)(t) approximately R(4/5)(0) is in agreement with kinetic models for the cylindrical geometry studied.

Diverse spreading behavior of binary polymer nanodroplets

Molecular dynamics simulations are used to study the spreading of binary polymer nanodroplets in a cylindrical geometry. The polymers, described by the bead-spring model, spread on a flat surface with a surface-coupled Langevin thermostat to mimic the effects of a corrugated surface. Each droplet consists of chains of length 10 or 100 monomers with approximately 350,000 monomers total. The qualitative features of the spreading dynamics are presented for differences in chain length, surface interaction strength, and composition. When the components of the droplet differ only in the surface interaction strength, the more strongly wetting component forms a monolayer film on the surface even when both materials are above or below the wetting transition. In the case where the only difference is the polymer chain length, the monolayer film beneath the droplet is composed of an equal amount of short chain and long chain monomers even when one component (the shorter chain length) is above the wetting transition and the other is not. The fraction of short and long chains in the precursor foot depends on whether both the short and the long chains are in the wetting regime. Diluting the concentration of the strongly wetting component in a mixture with a weakly wetting component decreases the rate of diffusion of the wetting material from the bulk to the surface and limits the spreading rate of the precursor foot, but the bulk spreading rate actually increases when both components are present. This may be due to the strongly wetting material pushing out the weakly wetting material as it moves toward the precursor foot.

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.

Microscopic structure, dynamics, and wear at metal-metal interfaces in sliding contact

The "generic embedded atom model" (GEAM) has been investigated recently [Phys. Rev. E 69, 021509 (2004)]] to analyze the qualitative equilibrium and nonequilibrium properties of bulk metals in both undeformed and shear deformed states. In the present work, a natural extension of the GEAM is proposed and applied to characterize the microscopic structure, dynamics, and wear at clean commensurate metal(A) - metal(A) and metal(A) - metal(B) sliding interfaces. Nonequilibrium molecular dynamics simulation, used as a GEAM solver, reveals that the dynamics of dislocations, crystalline domains, and related flow behaviors (stress tensor, shear moduli) are coupled. The rotation of crystal domains is detected to trigger material mixing at the interface in early stages of sliding. Further, we study the dependence of structural changes in inhomogeneous metal interfaces on the relevant model parameters. A relation is established between shear moduli, effective shear rate, and shear stress across the interface.

Spreading dynamics of polymer nanodroplets in cylindrical geometries

The spreading of one- and two-component polymer nanodroplets is studied using molecular dynamics simulation in a cylindrical geometry. The droplets consist of polymer chains of length 10, 40, and 100 monomers per chain described by the bead-spring model spreading on a flat surface with a surface-coupled Langevin thermostat. Each droplet contains approximately 350,000 monomers. The dynamics of the individual components of each droplet is analyzed and compared to the dynamics of single-component droplets for the spreading rates of the precursor foot and bulk droplet, the time evolution of the contact angle, and the velocity distribution inside the droplet. We derive spreading models for the cylindrical geometry analogous to the kinetic and hydrodynamic models previously developed for the spherical geometry, and show that hydrodynamic behavior is observed at earlier times for the cylindrical geometry. The contact radius is predicted to scale as r(t) approximately t1/5 from the kinetic model and r (t) approximately t1/7 for the hydrodynamic model in the cylindrical geometry.

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.

Structural changes and viscoplastic behavior of a generic embedded-atom model metal in steady shear flow

We study equilibrium and nonequilibrium properties of a simple "generic embedded-atom model" (GEAM) for metals. The model allows to derive simple analytical expressions for several zero-temperature constitutive properties--in overall agreement with real metals. The model metal is then subjected to shear deformation and strong flow via nonequilibrium molecular dynamics simulation in order to discuss the origins of some qualitative properties observed using more specific embedded-atom potentials. The "common neighbor analysis," based on planar graphs is used to obtain information about the transient structures accompanying viscoplastic behavior on an atomic level. In particular, pressure tensor components and plastic yield are investigated and correlated with underlying structural changes. A simple analytical expression for the isotropic pressure at finite temperatures is proposed. A nonequilibrium phase diagram is obtained by semianalytic calculation.

Polymer nanodroplets forming liquid bridges in chemically structured slit pores: A computer simulation

Using a coarse-grained bead-spring model of flexible polymer chains, the structure of a polymeric nanodroplet adsorbed on a chemically decorated flat wall is investigated by means of molecular dynamics simulation. We consider sessile drops on a lyophilic (attractive for the monomers) region of circular shape with radius R(D) while the remaining part of the substrate is lyophobic. The variation of the droplet shape, including its contact angle, with R(D) is studied, and the density profiles across these droplets also are obtained. In addition, the interaction of droplets adsorbed on two walls forming a slit pore with two lyophilic circular regions just opposite of one another is investigated, paying attention to the formation of a liquid bridge between both walls. A central result of our study is the measurement of the force between the two substrate walls at varying wall separation as well as the kinetics of droplet merging. Our results are compared to various phenomenological theories developed for liquid droplets of mesoscopic rather than nanoscopic size.

Spreading dynamics of polymer nanodroplets

The spreading of polymer droplets is studied using molecular dynamics simulations. To study the dynamics of both the precursor foot and the bulk droplet, large hemispherical drops of 200 000 monomers are simulated using a bead-spring model for polymers of chain length 10, 20, and 40 monomers per chain. We compare spreading on flat and atomistic surfaces, chain length effects, and different applications of the Langevin and dissipative particle dynamics thermostats. We find diffusive behavior for the precursor foot and good agreement with the molecular kinetic model of droplet spreading using both flat and atomistic surfaces. Despite the large system size and long simulation time relative to previous simulations, we find that even larger systems are required to observe hydrodynamic behavior in the hemispherical spreading droplet.

Collective stochastic resonance in shear-induced melting of sliding bilayers

The far-from-equilibrium dynamics of two crystalline two-dimensional monolayers driven past each other is studied using Brownian dynamics simulations. While at very high and low driving rates the layers slide past one another retaining their crystalline order, for intermediate range of drives the system alternates irregularly between the crystalline and fluidlike phases. A dynamical phase diagram in the space of interlayer coupling and drive is obtained. A qualitative understanding of this stochastic alternation between the liquidlike and crystalline phases is proposed in terms of a reduced model within which it can be understood as a stochastic resonance for the dynamics of collective order parameter variables. This remarkable example of stochastic resonance in a spatially extended system should be seen in experiments which we propose in the paper.

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.

Kinetic friction and atomistic instabilities in boundary-lubricated systems

The contribution of sliding-induced, atomic-scale instabilities to the kinetic friction force is investigated by molecular dynamics. For this purpose, we derive a relationship between the kinetic friction force F(k) and the nonequilibrium velocity distribution P(v) of the lubricant particles. P(v) typically shows exponential tails, which cannot be described in terms of an effective temperature. It is investigated which parameters control the existence of instabilities and how they affect P(v) and hence F(k). The effects of the interfaces' dimensionality, lubricant coverage, and internal degrees of freedom of lubricant particles on F(k) are studied explicitly. Among other results, we find that the kinetic friction between commensurate surfaces is much more susceptible to changes in (i) lubricant coverage, (ii) sliding velocity, and (iii) bond length of lubricant molecules than incommensurate surfaces.

Transition from stick-slip to smooth sliding: an earthquakelike model

We present a detailed study of an earthquakelike model that exhibits a "transition" from stick-slip motion to smooth sliding at a velocity of the order of those observed in experiments. This contrasts with the many previous microscopic models in which the transition velocity is many orders of magnitude too large. The results show that experimentally observed smooth sliding at the macroscopic scale must correspond to microscopic-scale stick-slip motion.