Prandtl-Tomlinson Model: A Simple Model Which Made History

Popov, Valentin L.; Gray, J. A. T.

doi:10.1007/978-3-642-39905-3_10

Cited by 19 publications

(22 citation statements)

References 29 publications

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“…Here, we use the definition of EDR W shown in Eq. (12) for the comparison with the experimental force curves. For simplicity, the lateral force is approximated by a perfect sawtooth curve.…”

Section: Analytical Formulation Of Edrmentioning

confidence: 99%

“…In this paper, the energy transition and dissipation under stick-slip friction are quantitatively examined using the Prandtl-Tomlinson (PT) model [10][11][12]. Factors influencing the energy dissipation, such as the stiffness, potential-energy corrugation, damping coefficient, sliding velocity, and temperature of the system, are systematically investigated.…”

Section: Introductionmentioning

confidence: 99%

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Energy dissipation of atomic-scale friction based on one-dimensional Prandtl-Tomlinson model

Wang

et al. 2015

Friction

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Abstract:The energy transition and dissipation of atomic-scale friction are investigated using the one-dimensional Prandtl-Tomlinson model. A systematic study of the factors influencing the energy dissipation is conducted, indicating that the energy that accumulated during the stick stage does not always dissipate completely during stick-slip motion. We adopt the energy-dissipation ratio (EDR) to describe the relationship between the energy dissipated permanently in the system and the conservative reversible energy that can be reintroduced to the driving system after the slip process. The EDR can change continuously from 100% to 0, covering the stick-slip, intermediate, and smooth-sliding regimes, depending on various factors such as the stiffness, potential-energy corrugation, damping coefficient, sliding velocity, and the temperature of the system. Among these, the parameter η, which depends on both the surface potential and the lateral stiffness, is proven in this paper to have the most significant impact on the EDR. According to η-T phase diagrams of the EDR, the smooth-sliding superlubricity and thermolubricity are found to be unified with regard to the energy dissipation and transition. An analytical formulation for the EDR that can be used to quantitatively predict the amount of energy dissipation is derived from a lateral-force curve.

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Section: Analytical Formulation Of Edrmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Energy dissipation of atomic-scale friction based on one-dimensional Prandtl-Tomlinson model

Wang

et al. 2015

Friction

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“…Thus, after overcoming the static friction the body will continue to move with a smaller force than the static friction force (see p. 155 in Ref. ) and

true〈 v true(t true) true〉 \to v_{0}

. A conceptually similar mechanism of realizing the kinetic and static friction regime in NEMD is through Eq.…”

Section: Equations Of Motion and Friction Coefficientmentioning

confidence: 98%

“…The second term on the right hand side of the equation acts as a time dependent driving force which causes the particle to move with an average velocity over time equal to

v_{0}

. Equation can be related to the well known Prandtl–Tomlinson friction model, in which a point mass is pulled along the surface by a spring of stiffness,

κ

, attached to a platform moving with velocity,

v_{0}

m \ddot{x} = - F_{0} s i n true(x true) + κ true(v_{0} t - x true) - η \dot{x},

where

η

is a velocity damping coefficient. As the spring constant decreases the spring force (the second term on the right hand side of Eq.…”

Section: Equations Of Motion and Friction Coefficientmentioning

confidence: 99%

“…As the spring constant decreases the spring force (the second term on the right hand side of Eq. ) changes less over time, and in a certain ‘softness’ limit can be treated as a constant,

F

. Equation can then be simplified to

m \ddot{x} = - F_{0} s i n true(x true) + F - η \dot{x},

from which it follows that,

F - η \dot{x} = γ v_{0} - γ \dot{x}

on comparing Eqs.…”

Section: Equations Of Motion and Friction Coefficientmentioning

confidence: 99%

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Non‐Equilibrium Phase Behavior of Confined Molecular Films at Low Shear Rates

Maćkowiak

Heyes

Pieprzyk

et al. 2017

Physica Status Solidi (b)

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In a recent publication [Maćkowiak et al., J. Chem. Phys. 145, 164704 (2016)] the results of Non‐Equilibrium Molecular Dynamics (NEMD) simulations of confined sheared Lennard‐Jones molecular films have been presented. The present work builds on that study by focusing on the low wall speed (shear rate) regime. Maps are given of the steady‐state structures and corresponding friction coefficients in the region where a transition from static to kinetic friction is observed. The boundary between static and kinetic friction regions is determined as a function of wall speed and applied pressure, which is located for wall speeds up to about 0.8 m s−1. It was found that stick‐slip behavior extends to pressures as high as 1000 MPa. The NEMD equations of motion are shown to be consistent with the Prandtl–Tomlinson model in the ‘soft spring’ limit, which leads to a new expression for the friction coefficient. This study provides new details and insights into the nature of anomalous friction behavior in the so‐called Plug‐Slip part of the nonquilibrium phase diagram regime.

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A dynamic and tribological simulation of a monolayer graphene sheet for a carbon atom‐graphene contact

Palaiologos

Grigoriadis

Zavos

et al. 2018

Lubrication Science

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This study focuses on the dynamic and tribological characterisation of a single‐layer graphene sheet (SLGS). A 10 × 10 nm graphene model is developed, which is modally analysed for both zigzag and armchair lattices, thus enabling the examination of chirality effect on the SLGS' eigenfrequencies. The tribological analysis consists of the same SLGS model and a carbon atom simulating the graphene tip. The carbon atom is set to move on multiple paths to examine the importance of the path's position over the sheet. The friction forces applied on the tip during its movement can be calculated. The carbon atom tip is interlinked with the graphene atoms via the Lennard‐Jones model, characterising the real contact area. Spring elements mimic the interatomic forces, while beam and mass elements simulate the graphene's C─C covalent bonds and atoms, respectively, on a finite element simulation verified by the Prandtl‐Tomlinson model. It is perceived a strong stick‐slip effect on the friction force's areal pattern, which can be verified by the Prandtl‐Tomlinson theory of the atomic scale friction. It also became clear the effect of chirality, on graphene's tribological behaviour, after the differences in the calculated friction forces. Finally, an increase in the coefficient of friction analogous to the increase of the vertical load, due to graphene's deformation, is determined, while in the zigzag lattice, the coefficient of friction appears to be significantly lower that the armchair one.

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Prandtl-Tomlinson Model: A Simple Model Which Made History

Cited by 19 publications

References 29 publications

Energy dissipation of atomic-scale friction based on one-dimensional Prandtl-Tomlinson model

Energy dissipation of atomic-scale friction based on one-dimensional Prandtl-Tomlinson model

Non‐Equilibrium Phase Behavior of Confined Molecular Films at Low Shear Rates

A dynamic and tribological simulation of a monolayer graphene sheet for a carbon atom‐graphene contact

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