Driven Frenkel-Kontorova model. I. Uniform sliding states and dynamical domains of different particle densities

Strunz, Torsten; Elmer, Franz-Josef

doi:10.1103/physreve.58.1601

Cited by 82 publications

(90 citation statements)

References 29 publications

(103 reference statements)

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“…This shows a strong dependence on the misorientation angle . This anisotropic behavior agrees well with the analytic theories, [2][3][4][5] which conclude that there is no static friction on most clean incommensurate interfaces. Because we used a supercell with periodic boundary condition in our simulation, there is a long-range ordering of the interface which could account for the small but nonzero static friction for the 30°and 45°cases, and for the dramatic differences between these two cases.…”

Section: Comparison With Experimental Resultssupporting

confidence: 87%

“…Analytic theories indicate that static friction vanishes at most clean, incommensurate crystal interfaces due to the lack of periodicity, but it is quite large when clean surfaces are commensurate, when the surfaces deform elastically, and the interactions between the surfaces are weak. [2][3][4][5] These analytic models focus on such intrinsic factors as the interactions between constituent atoms, while ignoring such complicating factors as surface roughness, fracture, plastic deformation, and contaminants.…”

Section: Introductionmentioning

confidence: 99%

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Friction anisotropy at Ni(100)/(100) interfaces: Molecular dynamics studies

Qi¹,

Cheng²,

Çağın

et al. 2002

Phys. Rev. B

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The friction of surfaces moving relative to each other must derive from the atomic interaction at interfaces. However, recent experiments bring into question the fundamental understanding of this phenomenon. The analytic theories predict that most perfect clean incommensurate interfaces would produce no static friction, whereas commensurate aligned surfaces would have very high friction. In contrast recent experiments show that the static friction coefficient between clean but 45°misoriented Ni͑001͒ surfaces is only a factor of 4 smaller than for the aligned surfaces ( ϳ0°) and clearly does not vanish ͑ is defined as the rotation angle between the relative crystallographic orientations of two parallel surfaces͒. To understand this friction anisotropy and the difference between analytic theory and experiment, we carried out a series of nonequilibrium molecular dynamics simulations at 300 K for sliding of Ni͑001͒/Ni͑001͒ interfaces under a constant shear force. Our molecular dynamics calculations on interfaces with the top layer roughed ͑and rms roughness of 0.8 Å͒ lead to the static frictional coefficients in good agreement with the corresponding experimental data. On the other hand, perfect smooth surfaces ͑rms roughness of 0 Å͒ lead to a factor of 34 -330 decreasing of static friction coefficients for misaligned surfaces, a result more consistent with the analytic theories. This shows that the major source of the discrepancy is that small amounts of roughness dramatically increase the friction on incommensurate surfaces, so that misaligned directions are comparable to aligned directions.

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Section: Comparison With Experimental Resultssupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Friction anisotropy at Ni(100)/(100) interfaces: Molecular dynamics studies

Qi¹,

Cheng²,

Çağın

et al. 2002

Phys. Rev. B

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show abstract

“…For chains shorter than the critical length, N cr , using a perturbation theory we can expand particles velocities, ̇ , in terms of the small parameter = / , as ̇ = ̇ + ̇ + ( ), where ̇ = is the exact solution for = 0. Then, it is straightforward to find [22] that…”

mentioning

confidence: 99%

Critical Length Limiting Superlow Friction

Benassi

Vanossi

et al. 2015

Phys. Rev. Lett.

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Since the demonstration of super-low friction (superlubricity) in graphite at nanoscale, one of the main challenges in the field of nano-and micro-mechanics was to scale this phenomenon up. A key question to be addressed is to what extent superlubricity could persist, and what mechanisms could lead to its failure. Here, using an edge-driven Frenkel-Kontorova model, we establish a connection between the critical length above which superlubricity disappears and both intrinsic material properties and experimental parameters. A striking boost in dissipated energy with chain length emerges abruptly due to a high-friction stick-slip mechanism caused by deformation of the slider leading to a local commensuration with the substrate lattice. We derived a parameter-free analytical model for the critical length that is in excellent agreement with our numerical simulations.Our results provide a new perspective on friction and nano-manipulation and can serve as a theoretical basis for designing nano-devices with super-low friction, such as carbon nanotubes.

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“…A procedure to find such stationary state have been developed in reference 57 . Nevertheless such technique can not be applied directly in our case due to the presence of the thermal noise.…”

Section: Theoretical Discussionmentioning

confidence: 99%

Single-file mobility of water-like fluid in a generalized Frenkel-Kontorova model

Ternes

Mendoza-Coto

Salcedo

2017

The Journal of Chemical Physics

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In this work we used a generalized Frenkel-Kontorova model to study the mobility of water molecules inside carbon nanotubes with small radius at low temperatures.Our simulations show that the mobility of the confined water decreases monotonically increasing the amplitude of the substrate potential at fixed commensurations. On the other hand, the mobility of the water molecules shows a non-monotonic behavior when varying the commensuration. This result indicates that the mobility of the confined fluid presents different behavior regimes depending on the amplitude of the water-nanotube interaction. In order to understand qualitatively these results, we study analytically the driven Frenkel-Kontorova model at finite temperatures.This analysis allows us to obtain the curves of the mobility versus commensurations, at fixed substrate potentials. Such curves shows the existence of three regimes of mobility behavior as a function of the commensuration ratio. Additionally, our study indicates a nontrivial and strong dependence of the mobility with a quantity that can be interpreted as an effective amplitude of the substrate potential, depending on the bare amplitude of the substrate potential, the commensuration ratio and temperature.

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Driven Frenkel-Kontorova model. I. Uniform sliding states and dynamical domains of different particle densities

Cited by 82 publications

References 29 publications

Friction anisotropy at Ni(100)/(100) interfaces: Molecular dynamics studies

Friction anisotropy at Ni(100)/(100) interfaces: Molecular dynamics studies

Critical Length Limiting Superlow Friction

Single-file mobility of water-like fluid in a generalized Frenkel-Kontorova model

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