Theory of friction: Stress domains, relaxation, and creep

On the interdependence of insertion forces, insertion speed, and lubrication: Aspects to consider when testing cochlear implant electrodes

OBJECTIVES

During the insertion of cochlear implant (CI) electrode arrays, forces occur which may cause trauma and poorer hearing outcomes. Unfortunately, research groups investigating factors influencing insertion forces come to contradicting results, especially regarding insertion speed. This study was conducted to investigate the origin of these contradicting results and to determine how different testing conditions influence experimental findings.

METHODS

Repeated, automated insertions with three different FLEX28 CI electrode arrays (MED-EL, Innsbruck, Austria) were performed into a newly developed, anatomically correct and 3D-printed mean scala tympani phantom. The testing protocol for each electrode included variations in insertion speed (v = 0.1-2.0 mm/s) and lubrication (90%, 50%, and 10% liquid soap), resulting in 51 insertions per electrode array and a total of 153 insertions.

RESULTS

The test setup and protocol allowed for repeatable insertions with only minimal change in the morphology of the insertion force profiles per testing condition. Strong but varying dependencies of the maximal insertion forces and work were found regarding both lubrication and speed: work-speed dependency is constant for the 10% lubricant, negative for the 50% lubricant and positive for the 90% lubricant.

CONCLUSION

Our results can explain part of the contradicting results found within previous studies by translating interrelations known from lubricated rubber friction to the field of CI electrode array insertion. We show that the main driver behind measured bulk forces are most likely the generated friction forces, which are strongly dependent on insertion speed and lubrication. The employed test setup allows for conducting repeatable and comparable insertion studies, which can be recapitulated by other centers due to the detailed explanation of the test setup as well as the developed and freely available insertion phantom. This study hence represents another important step toward standardizing CI array insertion testing.

Model of Friction with Plastic Contact Nudging: Amontons-Coulomb Laws, Aging of Static Friction, and Nonmonotonic Stribeck Curves with Finite Quasistatic Limit

We introduce a model of friction between two contacting (stationary or cosliding) rough surfaces, each comprising a random ensemble of polydisperse hemispherical bumps. In the simplest version of the model, the bumps experience on contact with each other only pairwise elastic repulsion and dissipative drag. These minimal ingredients are sufficient to capture a static state of jammed, interlocking contacting bumps, below a critical frictional force that is proportional to the normal load and independent of the apparent contact area, consistent with the Amontons-Coulomb laws of friction. However, they fail to capture two widespread observations: (i) that the dynamic friction coefficient (ratio of frictional to normal force in steady sliding) is a roughly constant or slightly weakening function of the sliding velocity U, at low U, with a nonzero quasistatic limit as U→0 and (ii) that the static friction coefficient (ratio of frictional to normal force needed to initiate sliding) increases ("ages") as a function of the time that surfaces are pressed together in stationary contact, before sliding commences. To remedy these shortcomings, we incorporate a single additional model ingredient: that contacting bumps plastically nudge one another slightly sideways, above a critical contact-contact load. With this additional insight, the model also captures observations (i) and (ii).

Multiscale Post-Seismic Deformation Based on cGNSS Time Series Following the 2015 Lefkas (W. Greece) Mw6.5 Earthquake

In the present work, a multiscale post-seismic relaxation mechanism, based on the existence of a distribution in relaxation time, is presented. Assuming an Arrhenius dependence of the relaxation time with uniform distributed activation energy in a mesoscopic scale, a generic logarithmic-type relaxation in a macroscopic scale results. The model was applied in the case of the strong 2015 Lefkas Mw6.5 (W. Greece) earthquake, where continuous GNSS (cGNSS) time series were recorded in a station located in the near vicinity of the epicentral area. The application of the present approach to the Lefkas event fits the observed displacements implied by a distribution of relaxation times in the range τmin ≈ 3.5 days to τmax ≈ 350 days.

Adhesion and friction between glass and rubber in the dry state and in water: role of contact hydrophobicity

We study the contact mechanics between 3 different tire tread compounds and a smooth glass surface in water. We study both adhesion and sliding friction at low-sliding speeds. For 2 of the compounds the rubber-glass contact in water is hydrophobic and we observe adhesion, and slip-stick sliding friction dynamics. For one compound the contact is hydrophilic, resulting in vanishing adhesion, and steady-state (or smooth) sliding dynamics. We also show the importance of dynamical scrape, both on the macroscopic level and at the asperity level, which reduces the water film thickness between the solids during slip. The experiments show that the fluid is removed much faster from the rubber-glass asperity contact regions for a hydrophobic contact than for a hydrophilic contact. We also study friction on sandblasted glass in water. In this case all the compounds behave similarly and we conclude that no dewetting occur in the asperity contact regions. We propose that this is due to the increased surface roughness which reduces the rubber-glass binding energy.

Atomistic modeling of tribological properties of Pd and Al nanoparticles on a graphene surface

Background: The frictional properties of nanoparticles have been studied to gain insight into the fundamental origin of sliding friction. Results: Using molecular dynamics we investigate frictional properties of aluminum and palladium nanoparticles deposited on a graphene layer. We study the time evolution of the total momentum of the system, the total and potential energies, the temperature, the velocity and position of the center of mass, the dimensions of the nanoparticle, and the friction and substrate forces acting on the particle. We also study how the friction force depends on the nanoparticle-graphene contact area and the temperature. Conclusion: The tribological properties of nanoparticles strongly depend on the materials. The particles move in an irregular (saw-like) manner. The averaged friction force depends nearly linearly on the contact area and non-monotonously on temperature. We observe ordered crystalline domains of atoms at the bottom surface of the metal particles, but the peaks of radial distribution function are blurred indicating that the nanoparticles are amorphous or polycrystalline.

Contact Dependence and Velocity Crossover in Friction between Microscopic Solid/Solid Contacts

Friction at the nanoscale differs markedly from that between surfaces of macroscopic extent. Characteristically, the velocity dependence of friction between apparent solid/solid contacts can strongly deviate from the classically assumed velocity independence. Here, we show that a nondestructive friction between solid tips with radius on the scale of hundreds of nanometers and solid hydrophobic self-assembled monolayers has a strong velocity dependence. Specifically, using laterally oscillating quartz tuning forks, we observe a linear scaling in the velocity at the lowest accessed velocities, typically hundreds of micrometers per second, crossing over into a logarithmic velocity dependence. This crossover is consistent with a general multicontact friction model that includes thermally activated breaking of the contacts at subnanometric elongation. We find as well a strong dependence of the friction on the dimensions of the frictional probe.

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.

Effects of Water on Tribochemical Wear of Silicon Oxide Interface: Molecular Dynamics (MD) Study with Reactive Force Field (ReaxFF)

Molecular dynamics (MD) simulations with the ReaxFF reactive force field were carried out to find the atomistic mechanisms for tribochemical reactions occurring at the sliding interface of fully hydroxylated amorphous silica and oxidized silicon as a function of interfacial water amount. The ReaxFF-MD simulations showed a significant amount of atom transfers across the interface occurs during the sliding. In the absence of water molecules, the interfacial mixing is initiated by dehydroxylation followed by the Si-O-Si bond formation bridging two solid surfaces. In the presence of submonolayer thick water, the dissociation of water molecules can provide additions reaction pathways to form the Si-O-Si bridge bonds and atom transfers across the interface. However, when the amount of interfacial water molecules is large enough to form a full monolayer, the degree of atom transfer is substantially reduced since the silicon atoms at the sliding interface are terminated with hydroxyl groups rather than forming interfacial Si-O-Si bridge bonds. The ReaxFF-MD simulations clearly showed the role of water molecules in atomic scale mechanochemical processes during the sliding and provided physical insights into tribochemical wear processes of silicon oxide surfaces observed experimentally.

Speed of fast and slow rupture fronts along frictional interfaces

The transition from stick to slip at a dry frictional interface occurs through the breaking of microjunctions between the two contacting surfaces. Typically, interactions between junctions through the bulk lead to rupture fronts propagating from weak and/or highly stressed regions, whose junctions break first. Experiments find rupture fronts ranging from quasistatic fronts, via fronts much slower than elastic wave speeds, to fronts faster than the shear wave speed. The mechanisms behind and selection between these fronts are still imperfectly understood. Here we perform simulations in an elastic two-dimensional spring-block model where the frictional interaction between each interfacial block and the substrate arises from a set of junctions modeled explicitly. We find that material slip speed and rupture front speed are proportional across the full range of front speeds we observe. We revisit a mechanism for slow slip in the model and demonstrate that fast slip and fast fronts have a different, inertial origin. We highlight the long transients in front speed even along homogeneous interfaces, and we study how both the local shear to normal stress ratio and the local strength are involved in the selection of front type and front speed. Last, we introduce an experimentally accessible integrated measure of block slip history, the Gini coefficient, and demonstrate that in the model it is a good predictor of the history-dependent local static friction coefficient of the interface. These results will contribute both to building a physically based classification of the various types of fronts and to identifying the important mechanisms involved in the selection of their propagation speed.

General theory of frictional heating with application to rubber friction

The energy dissipation in the contact regions between solids in sliding contact can result in high local temperatures which may strongly effect friction and wear. This is the case for rubber sliding on road surfaces at speeds above 1 mm s(-1). We derive equations which describe the frictional heating for solids with arbitrary thermal properties. The theory is applied to rubber friction on road surfaces and we take into account that the frictional energy is partly produced inside the rubber due to the internal friction of rubber and in a thin (nanometer) interfacial layer at the rubber-road contact region. The heat transfer between the rubber and the road surface is described by a heat transfer coefficient which depends on the sliding speed. Numerical results are presented and compared to experimental data. We find that frictional heating results in a kinetic friction force which depends on the orientation of the sliding block, thus violating one of the two basic Leonardo da Vinci 'laws' of friction.

Muscle activation described with a differential equation model for large ensembles of locally coupled molecular motors

Molecular motors, by turning chemical energy into mechanical work, are responsible for active cellular processes. Often groups of these motors work together to perform their biological role. Motors in an ensemble are coupled and exhibit complex emergent behavior. Although large motor ensembles can be modeled with partial differential equations (PDEs) by assuming that molecules function independently of their neighbors, this assumption is violated when motors are coupled locally. It is therefore unclear how to describe the ensemble behavior of the locally coupled motors responsible for biological processes such as calcium-dependent skeletal muscle activation. Here we develop a theory to describe locally coupled motor ensembles and apply the theory to skeletal muscle activation. The central idea is that a muscle filament can be divided into two phases: an active and an inactive phase. Dynamic changes in the relative size of these phases are described by a set of linear ordinary differential equations (ODEs). As the dynamics of the active phase are described by PDEs, muscle activation is governed by a set of coupled ODEs and PDEs, building on previous PDE models. With comparison to Monte Carlo simulations, we demonstrate that the theory captures the behavior of locally coupled ensembles. The theory also plausibly describes and predicts muscle experiments from molecular to whole muscle scales, suggesting that a micro- to macroscale muscle model is within reach.

Slow slip and the transition from fast to slow fronts in the rupture of frictional interfaces

The failure of the population of microjunctions forming the frictional interface between two solids is central to fields ranging from biomechanics to seismology. This failure is mediated by the propagation along the interface of various types of rupture fronts, covering a wide range of velocities. Among them are the so-called slow fronts, which are recently discovered fronts much slower than the materials' sound speeds. Despite intense modeling activity, the mechanisms underlying slow fronts remain elusive. Here, we introduce a multiscale model capable of reproducing both the transition from fast to slow fronts in a single rupture event and the short-time slip dynamics observed in recent experiments. We identify slow slip immediately following the arrest of a fast front as a phenomenon sufficient for the front to propagate further at a much slower pace. Whether slow fronts are actually observed is controlled both by the interfacial stresses and by the width of the local distribution of forces among microjunctions. Our results show that slow fronts are qualitatively different from faster fronts. Because the transition from fast to slow fronts is potentially as generic as slow slip, we anticipate that it might occur in the wide range of systems in which slow slip has been reported, including seismic faults.

History-dependent friction and slow slip from time-dependent microscopic junction laws studied in a statistical framework

To study how macroscopic friction phenomena originate from microscopic junction laws, we introduce a general statistical framework describing the collective behavior of a large number of individual microjunctions forming a macroscopic frictional interface. Each microjunction can switch in time between two states: a pinned state characterized by a displacement-dependent force and a slipping state characterized by a time-dependent force. Instead of tracking each microjunction individually, the state of the interface is described by two coupled distributions for (i) the stretching of pinned junctions and (ii) the time spent in the slipping state. This framework allows for a whole family of microjunction behavior laws, and we show how it represents an overarching structure for many existing models found in the friction literature. We then use this framework to pinpoint the effects of the time scale that controls the duration of the slipping state. First, we show that the model reproduces a series of friction phenomena already observed experimentally. The macroscopic steady-state friction force is velocity dependent, either monotonic (strengthening or weakening) or nonmonotonic (weakening-strengthening), depending on the microscopic behavior of individual junctions. In addition, slow slip, which has been reported in a wide variety of systems, spontaneously occurs in the model if the friction contribution from junctions in the slipping state is time weakening. Next, we show that the model predicts a nontrivial history dependence of the macroscopic static friction force. In particular, the static friction coefficient at the onset of sliding is shown to increase with increasing deceleration during the final phases of the preceding sliding event. We suggest that this form of history dependence of static friction should be investigated in experiments, and we provide the acceleration range in which this effect is expected to be experimentally observable.

Adhesion: role of bulk viscoelasticity and surface roughness

We study the adhesion between smooth polydimethylsiloxane (PDMS) rubber balls and smooth and rough poly(methyl methacrylate) (PMMA) surfaces, and between smooth silicon nitride balls and smooth PDMS surfaces. From the measured viscoelastic modulus of the PDMS rubber we calculate the viscoelastic contribution to the crack-opening propagation energy γeff(v,T) for a wide range of crack tip velocities v and for several temperatures T. The Johnson-Kendall-Roberts (JKR) contact mechanics theory is used to analyze the ball pull-off force data, and γeff(v,T) is obtained for smooth and rough surfaces. We conclude that γeff(v,T) has contributions of similar magnitude from both the bulk viscoelastic energy dissipation close to the crack tip, and from the bond-breaking process at the crack tip. The pull-off force on the rough surfaces is strongly reduced compared to that of the flat surface, which we attribute mainly to the decrease in the area of contact on the rough surfaces.

Noise-activated dissociation of soft elastic contacts

Adhesive forces are capable of deforming a soft elastic object when it comes in contact with a flat rigid substrate. The contact is in stable equilibrium if the total energy of the system arising from the elastic and surface forces exhibits a minimum at a zero or at a slightly negative load. However, as the system is continually unloaded, the energy barrier decreases and it eventually disappears, thus leading to a ballistic separation of the contact. While this type of contact splitting has received wide recognition, what has not been much appreciated with these types of soft adhesion problems is that rupture of a contact can also occur at any finite sub critical load in the presence of a noise. The soft contact problems are unique in that the noise can be athermal, whereas the metastable and stable states of the thermodynamic potential can arise from the competition of the elastic and the interfacial energies of the system. Analysis based on Kramers' theory and simulations based on Langevin dynamics show that the contact rupture dynamics is amenable to an Eyring's form of a force and noise-induced escape of a particle from a potential well that is generic to various types of colloidal and macromolecular processes. These ideas are useful in understanding the results of a recent experiment involving the noise-activated rolling dynamics of a rigid sphere on a surface, where it is pinned by soft micro-fibrillar contacts.

Chemical origins of frictional aging

Although the basic laws of friction are simple enough to be taught in elementary physics classes and although friction has been widely studied for centuries, in the current state of knowledge it is still not possible to predict a friction force from fundamental principles. One of the highly debated topics in this field is the origin of static friction. For most macroscopic contacts between two solids, static friction will increase logarithmically with time, a phenomenon that is referred to as aging of the interface. One known reason for the logarithmic growth of static friction is the deformation creep in plastic contacts. However, this mechanism cannot explain frictional aging observed in the absence of roughness and plasticity. Here, we discover molecular mechanisms that can lead to a logarithmic increase of friction based purely on interfacial chemistry. Predictions of our model are consistent with published experimental data on the friction of silica.

Surface roughness and dry friction

Persson's multiscale contact mechanics theory combined with a multiscale Brillouin-Prandtl-Tomlinson model is used to show that on the basis of these models "dry friction" [i.e., kinetic friction that remains at exceedingly small velocities (but still above the creep range) close to its value at higher velocities] should almost always occur for self-affine surfaces when the dominant interaction between two surfaces in contact is due to interatomic hard core repulsion, except for extremely smooth surfaces (i.e., surfaces with a Hurst index very close to 1).

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.

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.

Velocity dependence of friction of confined hydrocarbons

We present molecular dynamics friction calculations for confined hydrocarbon "polymer" solids with molecular lengths from 20 to 1400 carbon atoms. Two cases are considered: (a) polymer sliding against a hard substrate and (b) polymer sliding on polymer. We discuss the velocity dependence of the frictional shear stress for both cases. In our simulations, the polymer films are very thin (approximately 3 nm), and the solid walls are connected to a thermostat at a short distance from the polymer slab. Under these circumstances we find that frictional heating effects are not important, and the effective temperature in the polymer film is always close to the thermostat temperature. In the first setup (a), for hydrocarbons with molecular lengths from 60 to 1400 carbon atoms, the shear stresses are nearly independent of molecular length, but for the shortest hydrocarbon C(20)H(42) the frictional shear stress is lower. In all cases the frictional shear stress increases monotonically with the sliding velocity. For polymer sliding on polymer (case b) the friction is much larger, and the velocity dependence is more complex. For hydrocarbons with molecular lengths from 60 to 140 C atoms, the number of monolayers of lubricant increases (abruptly) with increasing sliding velocity (from 6 to 7 layers), leading to a decrease of the friction. Before and after the layering transition, the frictional shear stresses are nearly proportional to the logarithm of sliding velocity. For the longest hydrocarbon (1400 C atoms) the friction shows no dependence on the sliding velocity, and for the shortest hydrocarbon (20 C atoms) the frictional shear stress increases nearly linearly with the sliding velocity.

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.

Binding site models of friction due to the formation and rupture of bonds: state-function formalism, force-velocity relations, response to slip velocity transients, and slip stability

We present a model describing friction due to the thermally activated formation and rupture of molecular bonds between two surfaces, with long molecules on one surface attaching to discrete or continuous binding sites on the other. The physical assumptions underlying this model are formalized using a continuum approximation resulting in a class of master-equation-like partial differential equations that is a generalization of a friction model due to Persson [Phys. Rev. B 51, 13568 (1995)] and is identical to the equations used to describe muscle contraction, first proposed by A. F. Huxley. We examine the properties of this friction model in the continuous binding site limit noting that this model is capable of producing both monotonically increasing and an increasing-decreasing force dependence on slip velocity. When monotonically increasing, the force dependence on velocity is (asymptotically) logarithmic. The model produces a transient increase in friction in response to a sudden velocity increase, whether or not the steady-state friction force is a decreasing or increasing function of steady slip velocity. The model also exhibits both stable steady slip and stick-slip-like oscillatory behavior, in the presence of compliance in the loading machine, even when the steady-state friction force is a decreasing function of steady-state slip velocity.

Rate-dependent frictional adhesion in natural and synthetic gecko setae

Geckos owe their remarkable stickiness to millions of dry, hard setae on their toes. In this study, we discovered that gecko setae stick more strongly the faster they slide, and do not wear out after 30,000 cycles. This is surprising because friction between dry, hard, macroscopic materials typically decreases at the onset of sliding, and as velocity increases, friction continues to decrease because of a reduction in the number of interfacial contacts, due in part to wear. Gecko setae did not exhibit the decrease in adhesion or friction characteristic of a transition from static to kinetic contact mechanics. Instead, friction and adhesion forces increased at the onset of sliding and continued to increase with shear speed from 500 nm s(-1) to 158 mm s(-1). To explain how apparently fluid-like, wear-free dynamic friction and adhesion occur macroscopically in a dry, hard solid, we proposed a model based on a population of nanoscopic stick-slip events. In the model, contact elements are either in static contact or in the process of slipping to a new static contact. If stick-slip events are uncorrelated, the model further predicted that contact forces should increase to a critical velocity (V*) and then decrease at velocities greater than V*. We hypothesized that, like natural gecko setae, but unlike any conventional adhesive, gecko-like synthetic adhesives (GSAs) could adhere while sliding. To test the generality of our results and the validity of our model, we fabricated a GSA using a hard silicone polymer. While sliding, the GSA exhibited steady-state adhesion and velocity dependence similar to that of gecko setae. Observations at the interface indicated that macroscopically smooth sliding of the GSA emerged from randomly occurring stick-slip events in the population of flexible fibrils, confirming our model predictions.

Frictional properties of confined polymers

We present molecular dynamics friction calculations for confined hydrocarbon solids with molecular lengths from 20 to 1400 carbon atoms. Two cases are considered: a) polymer sliding against a hard substrate, and b) polymer sliding on polymer. In the first setup the shear stresses are relatively independent of molecular length. For polymer sliding on polymer the friction is significantly larger, and dependent on the molecular chain length. In both cases, the shear stresses are proportional to the squeezing pressure and finite at zero load, indicating an adhesional contribution to the friction force. The friction decreases when the sliding distance is of the order of the molecular length indicating a strong influence of molecular alignment during run-in. The results of our calculations show good correlation with experimental work.

New dissipation relaxation phenomenon in oscillating solid (4)He

We describe the first observations on the time-dependent dissipation when the drive level of a torsional oscillator containing solid (4)He is abruptly changed. The relaxation of dissipation in solid (4)He shows rich dynamical behavior including exponential and logarithmic time-dependent decays, hysteresis, and memory effects.

Friction dynamics of confined weakly adhering boundary layers

The nanotribological behavior of self-assembled monolayers is investigated. The latter accommodate friction through transient relaxation and dilatancy effects whose kinetics depends on the structure of the confined layers. Thus, the molecular ordering onto the surfaces controls the level and the stability of the friction coefficient. Moreover, the behavior of these systems is theoretically accounted for using a model based on the kinetics of formation and rupture of adhesive bonds between the two shearing surfaces with an additional viscous term.

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.

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.

Logarithmic relaxation due to minimization of interactions in the Burridge-Knopoff model

The time evolution of macroscopic quantities describing the relaxation of complex systems often contains a domain with logarithmic time dependence. This logarithmic behavior at the macroscopic level is often associated with strongly interacting elements at the microscopic level, whose interactions depend significantly on their history. In this paper we show that stress relaxation in the Burridge-Knopoff (BK) model of multicontact friction behaves logarithmically, when the model is in, or close to, the solitary state where the elements move independently. For this regime we present an automaton that allows us to follow the decay of stress relaxation over the entire range where it behaves logarithmically in time. We show that our model can be mapped onto a system of noninteracting elements subject to a uniform distribution of forces, for which logarithmic stress relaxation is derived analytically.

Velocity dependence of friction and hydrogen bonding effects

We show that the friction force varies with the sliding velocity in a manner that depends on the chemical nature of the interface. Surfaces terminated with the hydrogen acceptor and donor moieties capable of forming H-bond networks exhibit a friction that decreases with sliding velocity, a behavior that is opposite to that of surfaces where no such networks can form. We explain the results with a model where the domains of glassy H-bond networks are disrupted at a critical applied stress leading to slippage.

Role of surface roughness in superlubricity

We study the sliding of elastic solids in adhesive contact with flat and rough interfaces. We consider the dependence of the sliding friction on the elastic modulus of the solids. For elastically hard solids with planar surfaces with incommensurate surface structures we observe extremely low friction (superlubricity), which very abruptly increases as the elastic modulus decreases. We show that even a relatively small surface roughness may completely kill the superlubricity state.

Logarithmic chain-exchange kinetics of diblock copolymer micelles

We present a study of equilibrium chain-exchange kinetics of a well-defined model system for starlike polymeric micelles. The results show that the kinetics follows a logarithmic time dependence. The same feature has been confirmed for two other micellar systems. This is in sharp contrast to theoretical predictions and hints towards strongly coupled chain dynamics within the micellar cores induced by geometrical constraints.

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.

Transition to strictly solitary motion in the Burridge-Knopoff model of multicontact friction

We show that, in the continuous 1D Burridge-Knopoff model of multicontact friction, motion occurs via stick-slip sliding on a finite length rather than in avalanches, excluding the occurrence of self-organized criticality. We present strong numerical evidence that a transition from collective to strictly solitary motion occurs at a critical value of the interblock interactions. The solitary motion corresponds to successive stick-slip motion of one block between immobile neighbors, repeated periodically in time. This state persists also with open boundary conditions and moderate temperature.

Friction through dynamical formation and rupture of molecular bonds

We introduce a model for friction in a system of two rigid plates connected by bonds (springs) and experiencing an external drive. The macroscopic frictional properties of the system are shown to be directly related to the rupture and formation dynamics of the microscopic bonds. Different regimes of motion are characterized by different rates of rupture and formation relative to the driving velocity. In particular, the stick-slip regime is shown to correspond to a cooperative rupture of the bonds. Moreover, the notion of static friction is shown to be dependent on the experimental conditions and time scales. The overall behavior can be described in terms of two Deborah numbers.