Low Friction Regime Research Articles

Osmotic convection-driven instability and cellular eutectic growth in binary systems

Using phase-field theory we demonstrate that osmotic stress may result in intense convection in solidifying eutectic systems. Under isothermal conditions the natural convection is of osmotic origin, and driven by the non-equilibrium composition field. Osmotic forces arise mostly in the interface layer, since large concentration gradients are localized near the triple junctions of the phases. Tuning friction forces at the solid–liquid interface controls the intensity of fluid flow. We have found that convection in the low friction regime significantly affects microstructural pattern formation. Osmotic convection-driven instability of the solid–liquid interface is observed that leads to cellular and dendritic eutectic crystal growth. The mechanism we propose is distinct from diffusive instability that is widely acknowledged as the main cause of cellular and fingerlike patterns.

Load-Induced Transitions in the Lubricity of Adsorbed Poly(l-lysine)-g-dextran as a Function of Polysaccharide Chain Density

Chain-density gradients of poly(l-lysine)-graft-dextran (PLL-g-dex), a synthetic comblike copolymer with a poly(l-lysine) backbone grafted with dextran side chains, were fabricated on an oxidized silicon substrate. The influence of the changing dextran chain density along the gradient on the local coefficient of friction was investigated via colloidal-probe lateral force microscopy. Both in composition and structure, PLL-g-dex shares many similarities with bottlebrush biomolecules present in natural lubricating systems, while having the advantage of being well-characterized in terms of both architecture and adsorption behavior on negatively charged oxide surfaces. The results indicate that the transition of the dextran chain density from the mushroom into the brush regime coincides with a sharp reduction in friction at low loads. Above a critical load, the friction increases by more than an order of magnitude, likely signaling a pressure-induced change in the brush conformation at the contact area and a corresponding change in the mechanism of sliding. The onset of this higher-friction regime is moved to higher loads as the chain density of the film is increased. While in the low-load (and low-friction) regime, increased chain density leads to lower friction, in the high-load (high-friction) regime, increased chain density was found to lead to higher friction.

Barrier crossing dynamics of a charged particle in the presence of a magnetic field: A new turnover phenomenon

In this paper we have investigated the effect of a magnetic field on the barrier crossing rate of a charged particle. At the low friction regime we have observed a new turnover phenomenon for the variation of rate as a function of field strength. Thus although the force due to the magnetic field is not dissipative in nature, it plays a role in the steady state barrier crossing rate similar to that of a dissipative force in the weak damping regime. For appreciable damping strength, the rate monotonically decreases with the increase of field strength. We have demonstrated an interesting resonance effect due to the variation of frequency of the harmonic oscillator associated with the y-component motion at low damping and magnetic field strength.

In Situ Studies of TiC1−x N x Hard Coating Tribology

TiC1−x N x hard coatings present time-dependent tribological behavior with an initial running-in period (500–2000 cycles) marked by an elevated friction coefficient, followed by >10000 cycles with low-friction and wear at room temperature (RT) in ambient air. The mechanisms behind this behavior are not completely understood. Tribological tests performed at RT and at different relative humidity (RH) levels revealed that a minimum value between 15 and 25% RH is needed to trigger the low-friction regime at a sliding speed of 100 mm s−1. By in situ observations of transfer film growth, it could be observed that third body material is formed during this running-in period by plowing of the coating and shearing of the removed material. The appearance and thickening of the transfer film marks the beginning of the steady-state low-friction regime where the velocity is accommodated by interfacial sliding. At this stage in the tribological test, the recorded Raman spectra indicated the presence of C–H bonds in the wear track. Use of in situ analytical tools during wear tests provided insights with respect to tribological phenomena that were not available by conventional, post-mortem analysis methods.

Influences of Film Deposition Condition on Friction of Diamond-Like Carbon Film: A Theoretical Investigation

We theoretically investigated influences of film deposition condition on a friction of diamond-like carbon (DLC) film using our developed molecular dynamics method. The method can deal with chemical reactions on the basis of our original stochastic equation. DLC slab model was firstly constructed, and carbon atoms were deposited onto its surface with various kinetic energies (1, 10 and 30 eV) to mimic physical vapor deposition process. Lower sp3 carbon concentration and density were obtained for the 1 eV case and “subplantation” phenomenon was found for each model. The dynamical friction of the deposited DLC film/iron oxide combination was also simulated. The friction coefficient for the deposited film with kinetic energy of 1 eV was much lower than that of 10 and 30 eV cases due to the friction-induced structural change. The simulations provided us an important insight on DLC film preparation to achieve low friction regime.

Microscopic Friction Studies on Metal Surfaces

Atomically flat and clean metal surfaces exhibit a regime of ultra-low friction at low normal loads. Atomic force microscopy, performed in ultra-high vacuum on Cu(100) and Au(111) surfaces, reveals a clear stick-slip modulation in the lateral force but almost zero dissipation. Significant friction is observed only for higher loads (∼4–6 nN above the pull-off force) together with the onset of wear. We discuss the minor role of thermal activation in the low friction regime and suggest that a compliant metallic neck between tip and surface is formed which brings upon the low, load-independent shear stress.

Anomalous behaviour of the diffusion coefficient in interacting adsorbates

Langevin simulations provide an effective way to study collective effects of Brownian particles immersed in a two-dimensional periodic potential. In this paper, we concentrate essentially on the behaviour of the tracer ( D Tr ) and collective diffusion coefficients ( D C ) as function of friction ( Γ). Our simulations show that in the high friction limit, the two physical quantities D Tr and D C present qualitatively the same behaviour, for both coupled and decoupled substrate potentials. However, for the low friction regime, and especially for the coupled potential case, an anomalous diffusion behaviour is found where D Tr ∼ Γ - σ Tr and D C ∼ Γ - σ C , with σ Tr < σ C < 1 . We also found that in the case of weak dynamical coupling between the adparticles and the substrate, the exponents are not universal and rather depend on the potentials. Moreover, changes in the inter-particle potentials may reverse the behaviour to a normal one.

Towards the use of diamond-like carbon solid lubricant coatings in vacuum and space environments

Owing to the increasing demand in tribological performance for vacuum- and space-related applications, development of new solid lubricant coatings is necessary. Diamond-like carbon (DLC) coatings have been successfully used in many conventional mechanical applications to reduce both friction and wear. The potential use of these new solid lubricants under vacuum becomes then a critical question, which this article will attempt to address. DLC deposition, structure, and properties are first introduced to the reader. The exceptional tribological behaviour of DLC coatings is also discussed, in comparison with other tribological coatings. Attention is focused on the vacuum tribology of DLC films, pointing out the very low friction and wear that may be achieved with these materials. Phenomena accounting for establishment and lifetime of such low-friction regime are proposed. Finally, some open issues concerning vacuum- and space-related applications are discussed.

The lubricity of graphite flake inclusions in sintered polyimides affected by chemical reactions at high temperatures

The internal lubrication of 15 vol% graphite flakes added to polyimide was investigated during sliding at 50–200 N normal loads, 0.3 m/s and 23–260 °C, showing that chemical reactions in the polyimide bulk have an important effect on the sliding efficiency of the graphite. The latter are illustrated by Raman spectroscopy, thermo-analytical measurements and mass spectroscopy. At low temperatures (23–100 °C), transfer consists of pure graphite and mechanical shear prevails. At intermediate temperatures (120–180 °C), transfer consists of coexistent polyimide and graphite. A regime with decreasing friction is related to hydrolysis reactions in the bulk polyimide, lowering the effective water content in the sliding interface. At higher temperatures (180–260 °C), transfer consists of mixed polyimide–graphite. A low friction regime is related to imidisation of the bulk polymer and interfacial water supply, favouring the graphite lubricating properties. The graphite debris morphology occurs as flakes (low temperature) or powders (intermediate temperatures), likely resulting from cleavage between the basal planes or embrittlement across the basal planes.

Thin-film lubrication nano-rheology via molecular dynamics

There are many curious phenomena when very thin lubricant films interact with sliding surfaces. It is difficult to do experiments on these nano-thickness films, and here we describe the use of non-equilibrium molecular dynamics (MD) to investigate friction in alkane lubricant layers. The pronounced increase of viscosity in layers of thickness seven molecules and less enables an increased load capacity to be sustained in such films. We also demonstrate the existence of a newly-discovered low-friction regime.

Unlubricated sliding frictional behaviour of oxide films on plasma nitrocarburised steel

The sliding frictional behaviour of oxide films formed on low alloy steel by the combined plasma nitrocarburising and post oxidation treatment has been investigated. Unlubricated sliding tests of the as-nitrocarburised and nitrocarburised-oxidised specimens showed that the frictional behaviour depends not only on the oxidation treatment conditions, but also on the counterface material and the testing conditions. When sliding against a steel counterface, all the tested specimens exhibited similar frictional behaviour, which is dominated by the material transfer from the counterface to the sliding surface. On the other hand, when sliding against an alumina slider, all the oxidised specimens exhibited a low friction regime. The duration of this low friction regime depends on the treatment and test conditions, with the low temperature oxidised/nitrocarburised specimen being the most durable. The mechanisms associated with the observed frictional characteristics are discussed in terms of material transfer and the structure and mechanical integrity of the films.

The Effect of Surface Roughness on Wear-Life of DLC Coated Silicon Disk in Dry Sliding

Dry sliding wear resistance of DLC coated silicon disk with different surface roughness has been evaluated using a ball-on-disk sliding tester. It was found that the transfer layer formed on steel ball produced a low friction regime and the formation of transfer layer was more active with increasing the substrate surface roughness. The wear life of DLC coating was increased as increasing the real area of contact.

Dissipating the Langevin equation in the presence of an external stochastic potential

In the Langevin formalism, the delicate balance maintained between the fluctuations in the system and their corresponding dissipation may be upset by the presence of a secondary, space-dependent stochastic force, particularly in the low-friction regime. In prior work, the latter was dissipated self-consistently through an additional uniform (mean-field) friction [T. Shepherd and R. Hernandez, J. Chem. Phys. 115, 2430 (2001).] An alternative approach to ensure that equipartition is satisfied relies on the use of a space-dependent friction while ignoring nonlocal correlations. The approach is evaluated with respect to its ability to maintain constant temperature for two simple one-dimensional, stochastic potentials of mean force wherein the friction can be evaluated explicitly when there is no memory in the barriers. The use of a space-dependent friction is capable of providing qualitatively similar results to those obtained previously, but in extreme cases deviations from equipartition may be observed due to the neglect of the memory effects present in the stochastic potentials.

A Phenomenological Model for Surface Diffusion: Diffusive Dynamics across Incoherent Stochastic Aperiodic Potentials

The dynamics of Brownian particles diffusing across a one-dimensional, incoherent stochastic potential of mean force in the Smoluchowski regime has been intensely investigated by several groups. In recent work, we have developed a phenomenological equation of motion that extends this representation throughout the friction regime and, in particular, extends it to the low-friction regime relevant to surface diffusion. Resonant activation is observed throughout; it is manifested by a peak in the transport as a function of the correlation time in the potential fluctuations. The phenomenological equation of motion has now been utilized to probe the dynamics on a variety of one- and two-dimensional surfaces in order to provide a qualitative description of the fundamental factors that govern the surface hopping events of an adsorbate weakly bound to a metal surface. The primary focus is placed on differences that may arise when the substrate is modeled using a one- or two-dimensional potential of mean force, thereafter the effects of spatially coherent or incoherent barrier heights are also addressed. The two-dimensional behavior can be adequately described by the direct product of two separable one-dimensional analogues, as might naïvely be expected, provided the lattice spacing is sufficient to decouple the two degrees of freedom. Coherency between the barriers affects the rates to a smaller degree and is significant only when the barriers are strongly correlated in time.

Controlling directed transport in two-dimensional periodic structures under crossed electric fields

We investigate different mechanisms for the control of directed transport of particles on two-dimensional periodic and symmetric substrates, based on the application of a crossed static and a bi-harmonic (harmonic mixing) field. We focus on inertial systems in the low friction regime, using a prototypical model for atom-surface diffusion, and demonstrate that a proper control of current reversals can be achieved at moderate field strengths by tuning either the static field or changing the relative phase of the harmonic mixing signal, respectively.

Influence of the periodic potential shape on the Fokker–Planck dynamics

The influence of the periodic potential structure on the diffusion mechanism of a Brownian particle is studied using the Fokker–Planck equation. The equation is solved numerically by the matrix continued fraction method in order to calculate relevant correlation functions. In particular, jump length probability, diffusion coefficient and the half-width of the quasi-elastic peak of the dynamical structure factor S( q, ω) are fully studied in a wide range of physical parameters for two forms of periodic potential (bistable and metastable potential). There is some difference between results provided by these two potential models, indicating that dynamical properties are very sensitive to the structure of the periodic potential, especially in the low friction regime.

The response of PACVD TiN coatings to tribological tests with different counterparts

Recently, a low-friction effect with friction coefficients of below 0.2 against ball-bearing steel has been reported for chlorine-containing TiN coatings grown by plasma-assisted chemical vapor deposition (PACVD). This low-friction effect has been attributed to the formation of a chlorine-containing lubricant layer on top of the coating in humid air which can be regarded as a self-adaptation process of the coating to the given tribological situation. Within this study we show that in dry sliding ball-on-disc experiments against different counterparts, the response of the coating to the tribological conditions is determined by the hardness of the counterpart material. For the softest ball material used, i.e. austenitic stainless steel, the friction coefficient drops to the low-friction regime after a running-in distance which is more than 35 times longer compared to that of the hardest counterpart material, i.e. alumina.

Long Jump Diffusion in Low Friction Regime: Effect of the Periodic Potential Structure

The diffusion mechanism of Brownian particles in a periodic bistable and metastable potential is studied using the Fokker-Planck Equation (FPE). The FPE is solved numerically by the Matrix Continued Fraction Method (MCFM). The main objective of this work is to study the effect of the structure of the potential on the diffusion by calculating the escape rate rj (also called jump rate) and the probability distribution of the jump lengths of a Brownian particle subjected to bistable and metastable periodic potentials which can describe realistic physical situations: Jump rate and probability distribution of the jump lengths as function of the friction Γ for low values of the ratio (Δ) of the two barrier heights of the potential are presented. Our numerical results show that the activation of multiple jumps is clear evidence of low-friction diffusion and specialy for low values of Δ with regard to jumps of lengths equal to the period of the potential.

Quantum Kramers equation for energy diffusion and barrier crossing dynamics in the low-friction regime.

Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value, which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders.

Many-particle diffusion in continuum: Influence of a periodic surface potential

We study the diffusion of Brownian particles with a short-range repulsion on a surface with a periodic potential through molecular dynamics simulations and theoretical arguments. We concentrate on the behavior of the tracer and collective diffusion coefficients DT(θ) and DC(θ), respectively, as a function of the surface coverage θ. In the high friction regime we find that both coefficients are well approximated by the Langmuir lattice-gas results for up to θ≈0.7 in the limit of a strongly binding surface potential. In particular, the static compressibility factor within DC(θ) is very accurately given by the Langmuir formula for 0⩽θ⩽1. For higher densities, both DT(θ) and DC(θ)show an intermediate maximum which increases with the strength of the potential amplitude. In the low friction regime we find that long jumps enhance blocking and DT(θ) decreases more rapidly for submonolayer coverages. However, for higher densities DT(θ)/DT(0) is almost independent of friction as long jumps are effectively suppressed by frequent interparticle collisions. We also study the role of memory effects for many-particle diffusion.