Kinetic Monte Carlo theory of sliding friction

Furlong, Octavio Javier; Manzi, Sergio Javier; Pereyra, V.; Bustos, V.

doi:10.1103/physrevb.80.153408

Cited by 29 publications

(43 citation statements)

References 15 publications

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“…However, if we instead consider β as a fitting parameter, V = 1 β (F c − F) 3/2 provides an adequate description of the barrier variation over a large range of forces. This issue was also recently identified by Furlong et al [21] when fitting a friction versus velocity curve to Monte Carlo simulations. They too found that equation (1) was applicable when used with a semi-empirical value of β = , where C eff is an effective stiffness.…”

Section: Corrugation Potential Shapesupporting

confidence: 59%

“…It is worth noting that a linear form of the energy barrier V = 1 β (F c −F) was first proposed in the pioneering work of Gnecco et al [1], followed by Sang et al, who showed the sub-linear three-halves law to be more rigorous [2]. Although it is not easy to differentiate the sub-linear from the linear relationship under current experimental conditions [20], we expect that (1)) with β given by Riedo et al [3] (dotted line), reported by Furlong et al [21] (dashed line), and fitted to the analytical equation using the numerical data (solid line).…”

Section: Corrugation Potential Shapementioning

confidence: 64%

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Thermal activation in atomic friction: revisiting the theoretical analysis

Dong

Pérez

Gao

et al. 2012

J. Phys.: Condens. Matter

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The effect of thermal activation on atomic-scale friction is often described in the framework of the Prandtl-Tomlinson model. Accurate use of this model relies on parameters that describe the shape of the corrugation potential β and the transition attempt frequency f 0 . We show that the commonly used form of β for a sinusoidal corrugation potential can lead to underestimation of friction, and that the attempt frequency is not, as is usually assumed, a constant value, but rather varies as the energy landscape evolves. We partially resolve these issues by demonstrating that numerical results can be captured by a model with a fitted β and using harmonic transition state theory to develop a variable form of the attempt frequency. We incorporate these developments into a more accurate and generally applicable expression relating friction to temperature and velocity. Finally, by using a master equation approach, we verify the improved analytical model is accurate in its expected regime of validity.

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Section: Corrugation Potential Shapesupporting

confidence: 59%

Section: Corrugation Potential Shapementioning

confidence: 64%

Thermal activation in atomic friction: revisiting the theoretical analysis

Dong

Pérez

Gao

et al. 2012

J. Phys.: Condens. Matter

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“…The solution of the thermally activated, modified Prandtl model for AFM friction has been discussed in detail elsewhere [9,21,39,41,[43][44][45][46] and is briefly summarised here. The probability p(t) that the tip surmounts the barrier is calculated following Prandtl for a forward jump from:…”

Section: Velocity and Temperature Dependence For A Compliant Contactmentioning

confidence: 99%

On the Commonality Between Theoretical Models for Fluid and Solid Friction, Wear and Tribochemistry

2015

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Tribology is concerned with the influence of mechanically applied forces on interfacial phenomena that accompany and control sliding. A wide range of models has been developed to describe these phenomena, which include frictional dissipation, wear and tribochemical reactions. This paper shows that these apparently disparate models are based on the same fundamental concept that an externally applied force accelerates the rate of thermal transition of atoms or molecules across energy barriers present in solid and liquid materials, thereby promoting flow, slip or bond cleavage. Such ''stress-assisted'' effects and the associated thermal activation concepts were developed independently and in different forms by Prandtl (Z Angew Math Mech 8:85, 1928) and Eyring (J Chem Phys 4(4): [283][284][285][286][287][288][289][290][291] 1936). These two works have underpinned subsequent theories of dry friction, boundary lubrication, EHD rheology, tribochemistry and nanoscale wear modelling. This paper first reviews the historical development of the concepts, focussing in particular on the models of Prandtl and Eyring and how they have subsequently been used and adapted by others. The two approaches are then compared and contrasted, noting that although superficially similar, they contain quite different assumptions and constraints. First, the Prandtl model assumes that the force is exerted through a compliant spring, while constant force sliding is assumed by Eyring. Second, different approximations are made in the two models to describe the change in energy barrier with external force. Prandtl explores the asymptotic behaviour of the energy barrier as the applied force become sufficiently high to reduce it to zero, while Eyring assumes that the energy barrier is reduced by an amount equal to the external work carried out on the system. The theoretical underpinnings of these differences are discussed along with the implications of compliant coupling and constant force sliding on the velocity and temperature dependence of the friction forces for the two models.

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“…The transition between different patterns can be induced by many physical factors, such as temperature [13][14][15], sliding velocity [16][17][18] and so on. And Monte Carlo theory was also exploited to rectify the semi-empirical analytical solution of Tomlinson model [19,20]. Meanwhile in order to improve the level of details, molecular dynamics (MD) simulation and molecular statics (MS) calculation were utilized to explore the effect of atomistic properties on friction [21].…”

Section: Introductionmentioning

confidence: 99%