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Molecular dissipation phenomena of nanoscopic friction in the heterogeneous relaxation regime of a glass former.

Nanoscale sliding friction involving a polystyrene melt near its glass transition temperature Tg (373 K) exhibited dissipation phenomena that provide insight into the underlying molecular relaxation processes. A dissipative length scale that shows significant parallelism with the size of cooperatively rearranging regions (CRRs) could be experimentally deduced from friction-velocity isotherms, combined with dielectric loss analysis. Upon cooling to approximately 10 K above Tg, the dissipation length Xd grew from a segmental scale of approximately 3 A to 2.1 nm, following a power-law relationship with the reduced temperature Xd approximately TR-phi. The resulting phi=1.89+/-0.08 is consistent with growth predictions for the length scale of CRRs in the heterogeneous regime of fragile glass formers. Deviations from the power-law behavior closer to Tg suggest that long-range processes, e.g., the normal mode or ultraslow Fischer modes, may couple with the alpha relaxation, leading to energy dissipation in domains of tens of nanometers.

Journal Article↗

The non-Markovian quantum master equation in the collective-mode representation: application to barrier crossing in the intermediate friction regime.

The calculation of chemical reaction rates in the condensed phase is a central preoccupation of theoretical chemistry. At low temperatures, quantum-mechanical effects can be significant and even dominant; yet quantum calculations of rate constants are extremely challenging, requiring theories and methods capable of describing quantum evolution in the presence of dissipation. In this paper we present a new approach based on the use of a non-Markovian quantum master equation (NM-QME). As opposed to other approximate quantum methods, the quantum dynamics of the system coordinate is treated exactly; hence there is no loss of accuracy at low temperatures. However, because of the perturbative nature of the NM-QME it breaks down for dimensionless frictions larger than about 0.1. We show that by augmenting the system coordinate with a collective mode of the bath, the regime of validity of the non-Markovian master equation can be extended significantly, up to dimensionless frictions of 0.5 over the entire temperature range. In the energy representation, the scaling goes as the number of levels in the relevant energy range to the third power. This scaling is not prohibitive even for chemical systems with many levels; hence we believe that the current method will find a useful place alongside the existing techniques for calculating quantum condensed-phase rate constants.

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Electro-osmosis at inhomogeneous charged surfaces: hydrodynamic versus electric friction.

Electrokinetic methods are efficient in probing the electrostatic surface properties of charged systems. However, anomalies observed in experiments indicate that the classical electrokinetic theory should be reconsidered. Using Green's function methods and hydrodynamic simulations, we investigate electro-osmosis driven by electric-field-induced ion motion near a charged planar substrate with smooth or rough boundary. First, a reformulation of electro-osmotic theory for planar charged surfaces employing Green's functions shows that the Helmholtz-Smoluchowski (HS) relation between electrostatic potential and solvent velocity is exact for smooth surfaces, even in the presence of ion correlations. Deviations from HS theory are caused by combined hydrodynamic and electric surface friction, as our hydrodynamic simulations of ions at smooth and corrugated charged surfaces in lateral electric fields demonstrate. Within the simulations, hydrodynamic interactions are treated in the continuum limit and the presence of a no-slip boundary condition at the surface is taken into account. While electrofriction is relevant in highly charged system and/or for multivalent ions, hydrodynamic friction is dominant in systems with moderate surface charge density and/or low ionic valency. We also derive the effective electrokinetic surface charge from the electro-osmotic solvent profiles, which is substantially reduced when compared with the bare value and shows qualitative agreement with the experimental tendency.

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Liquid friction on charged surfaces: from hydrodynamic slippage to electrokinetics.

Hydrodynamic behavior at the vicinity of a confining wall is closely related to the friction properties of the liquid/solid interface. Here we consider, using molecular dynamics simulations, the electric contribution to friction for charged surfaces, and the induced modification of the hydrodynamic boundary condition at the confining boundary. The consequences of liquid slippage for electrokinetic phenomena, through the coupling between hydrodynamics and electrostatics within the electric double layer, are explored. Strong amplification of electro-osmotic effects is revealed, and the nontrivial effect of surface charge is discussed. This work allows us to reconsider existing experimental data, concerning zeta potentials of hydrophobic surfaces and suggests the possibility to generate "giant" electro-osmotic and electrophoretic effects, with direct applications in microfluidics.

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Friction traced to the single atom.

Friction is caused by dissipative lateral forces that act between macroscopic objects. An improved understanding of friction is therefore expected from measurements of dissipative lateral forces acting between individual atoms. Here we establish atomic resolution of both conservative and dissipative forces by lateral force microscopy, presenting the resolution of atomic defects. The interaction between a single-tip atom that is oscillated parallel to an Si(111)-(7 x 7) surface is measured. A dissipation energy of up to 4 eV per oscillation cycle is found. The dissipation is explained by a "plucking action of one atom on to the other" as described by G. A. Tomlinson in 1929 [Tomlinson, G. A. (1929) Phil. Mag. 7, 905-939].

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Effect of floor conditions upon frictional characteristics of squash court shoes.

Vertical (FN) and horizontal (FH) forces were recorded while four vertically-loaded court shoes were dragged horizontally across six types of floor surface. Variation in coefficient of limiting friction (FH/FN) between floor surfaces was greater than that between shoes. Squash strokes were also performed on the same surfaces during which FH/FN was calculated. Slips occurred on some surfaces either at heel contact or upon attainment of full-sole contact. It is concluded that the coefficient of limiting friction obtained during full-sole contact with the floor is a suitable means of distinguishing between tractional qualities of shoes. Alternatively, this measure is an inadequate predictor of the likelihood of slips in the game of squash racquets. Dusty floor conditions produce poor traction as does a damp sealed floor. As sweat droplets are unavoidable in the game, floors sealed with urethane represent a significant hazard. Bare, clean, wooden flooring which can absorb moisture represents a better surface than a sealed floor from the point of view of traction.

Biophysical Phenomena↗

A comparison of physiological responses to rowing on friction-loaded and air-braked ergometers.

The physiological responses of 10 trained rowers to a progressive incremental rowing protocol to exhaustion were investigated on Gjessing, Rowperfect fixed-mechanism and Rowperfect free-mechanism rowing ergometers. Heart rate, oxygen uptake (VO2), ventilation (VE) and blood lactate were determined at matched power values for each ergometer. The mean power and heart rate at the lactate anaerobic threshold were determined by graphical interpolation of data for each ergometer. Analysis of variance and linear regression showed differing responses at matched power and an approximate 40-50 W difference in power at the lactate anaerobic threshold when comparing the friction-loaded Gjessing with the air-braked Rowperfect fixed and Rowperfect free ergometers (P<0.01). No significant differences were noted when comparing the air-braked Rowperfect fixed and Rowperfect free ergometers. However, comparisons of VO2, VE and blood lactate at given heart rates and of heart rate at the lactate anaerobic threshold showed no significant differences between ergometers. Our results indicate similar physiological profiles for all ergometers tested when compared at equivalent heart rates, but differences when compared at matched power. A direct comparison of the data from Gjessing (friction-loaded) with Rowperfect fixed and Rowperfect free (air-braked) ergometers would therefore require a correction factor for inter-ergometer variation in displayed power data.

Adult↗

Practical management of iliotibial band friction syndrome in runners.

This article outlines the practical management of iliotibial band friction syndrome (ITBFS) in running athletes. ITBFS is the most common cause of lateral knee pain in runners and is related to repetitive friction of the iliotibial band sliding over the lateral femoral epicondyle. Runners predisposed to this injury are typically in a phase of over training and often have underlying weakness of the hip abductor muscles. The diagnosis of ITBFS is clinical and is based on a thorough patient history and physical exam. In the acute phase, treatment includes activity modification, ice, nonsteroidal anti-inflammatory medication, and corticosteroid injection in cases of severe pain or swelling. During the subacute phase emphasis is on stretching of the iliotibial band and soft tissue therapy for any myofascial restrictions. The recovery phase focuses on a series of exercises to improve hip abductor strength and integrated movement patterns. The final return to running phase is begun with an every other day program, starting with easy sprints and avoidance of hill training with a gradual increase in frequency and intensity. In rare refractory cases that do not respond to conservative treatment, surgery can be considered.

Cumulative Trauma Disorders↗

Friction and noise-induced coherent structures in boundary lubrication

We examine the effect of stick-slip boundary conditions on the friction generated by a molecularly thin layer of a liquid lubricant separating two plates. For one-dimensional compressible flows, noise-induced coherent dissipative structures on a micron scale are generated due to cooperation between the external drive and the thermal noise. As a function of the thermal noise these structures show a peak in their amplitudes similar to stochastic resonance. At low velocities a reduction in friction with increasing thermal noise is observed.

Journal Article↗

Self-oscillations in ring Toda chains with negative friction.

We study here the different modes of self-oscillations in ring Toda chains with Rayleigh-type negative friction. Assuming that at small friction the shape of self-oscillations is close to one of the known Toda solitonlike solutions we use analytical methods in combination with numerical ones for study of the self-oscillations. We calculate explicitly for a Toda chain consisting of N elements the N+1 different modes of self-oscillations. Among them two modes correspond to left and right rotations of the chain as a whole with a constant velocity Each of the other N-1 modes represents a combination of solitonlike oscillations and a rotation with a velocity depending on the mode number. Only for the mode corresponding to antiphase oscillations of the chain neighboring elements (such oscillations are possible for an even N) the constant component of the velocity is equal to zero.

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Role of nanoscopic liquid bridges in static friction.

Interpretations of recent experiments on the effects of humidity on friction hypothesize that liquid-water bridges can span nanoscopic gaps at the interface between the sliding surfaces. By means of a lattice-gas model the mechanisms by which such bridges may engender static friction at a single ideal nanoscopic contact were studied. The model contact consists of a simple (spherically symmetric) fluid constrained between two plane-parallel substrates decorated with weakly and strongly attractive stripes that alternate periodically in one transverse direction. In analogy with the experiments the shear yield stress (yield strength) tau(s) of the contact was computed as a function of the chemical potential mu of the fluid (the analog of humidity). The influence of other thermodynamic state variables, such as temperature and distance between the substrates, and of the relative strength of the stripes on the yield-strength curves (i.e., tau(s) versus mu) was explored. Some intriguing correlations between experiment and theory are observed.

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Direct measurements of colloidal friction coefficients.

The time-independent hydrodynamic forces operating between two hard spheres were studied as a function of the interparticle separation r. Two colloids were positioned a distance r apart using a dual-beam optical tweezer similar to that described by Meiners and Quake [Phys. Rev. Lett. 82, 2211 (1999)]. Brownian fluctuations in the positions of the two spheres were followed by recording the intensity of forward scattered laser light. The two particles move cooperatively as a result of hydrodynamic forces. The strength of the correlation increased strongly with decreasing separation r. We show that the temporal and spatial correlations in the particle displacements are determined by the distance dependence of the pair friction tensor xi. The distance and geometry dependence of the measured friction tensor is found to be in excellent agreement with the predictions of low-Reynolds number calculations.

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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.

Journal Article↗

Friction and second-order phase transitions.

A microscopic model is studied numerically to describe wearless dry friction without thermal fluctuations between atomically flat contact interfaces. The analysis is based on a double-chain model with a Lennard-Jones interaction between the chains which are the respective upper flexible monolayers of the rigid bulk systems. Whereas below a critical interaction strength epsilon(c) the system exhibits a frictionless state, it offers static friction above epsilon(c) . Introducing an appropriate order parameter function we demonstrate the analogy of the critical behavior to a phase transition of second order. The order parameter is related to a hull function describing uniquely the incommensurate ground state of the model. The breakdown of analyticity of the hull function is identified with the phase transition. Critical exponents are calculated and the validity of finite-size scaling is displayed.

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Effect of friction in a toy model of granular compaction.

A toy model of granular compaction which includes some resistance due to granular arches is proposed. In this model, the solid/solid friction of contacting grains is a key parameter and a slipping threshold omega(c) is defined. Realistic compaction behaviors have been obtained. Two regimes separated by a critical point omega*(c) of the slipping threshold have been emphasized: (i) a slow compaction with lots of paralyzed regions and (ii) an inverse logarithmic dynamics with a power-law scaling of grain mobility. Below the critical point omega*(c) , the physical properties of this frozen system become independent of omega(c) . Above the critical point omega*(c) --i.e., for low friction values--the packing properties behave as described by the classical Janssen theory for silos.

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Friction versus texture at the approach of a granular avalanche.

We perform an analysis of the granular texture of a granular bed close to stability limit. Our analysis is based on a unique criterion of friction mobilization in a simulated two-dimensional packing. In this way, we recover the bimodal character of granular texture and the coexistence of weak and strong phases in the sense of distinct contacts populations. Moreover, we show the existence of a well-defined subset of contacts within the weak contact network. These contacts are characterized by their important friction and form a highly coherent population in terms of fabric. They play an antagonistic role with respect to force chains. Thus, we are able to discriminate between incoherent contacts and coherent contacts in the weak phase and to specify the role that the latter plays in the destabilization process.

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Quantum lubrication: suppression of friction in a first-principles four-stroke heat engine.

A quantum model of a heat engine resembling the Otto cycle is employed to explore strategies to suppress frictional losses. These losses are caused by the inability of the engine's working medium to follow adiabatically the change in the Hamiltonian during the expansion and compression stages. By adding external noise to the engine frictional losses can be suppressed.

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Correlation between charge transfer and stick-slip friction at a metal-insulator interface

Techniques have been developed that facilitate the measurement and imaging of the charge exchanged between metal-insulator surfaces in relative motion. In the regime where the forces of friction lead to stick-slip motion, we find that the charge transfer accompanying the slip events is proportional to the force jumps and is bunched at the stick locations. The constant of proportionality is measured in electron volts per angstrom and has a small variance over a large range of slip sizes, suggesting that in these experiments macroscopic friction originates from and scales to the intrinsic electronic interactions that form between metal and insulator surfaces.

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