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Prandtl–Tomlinson-Type Models for Molecular Sliding Friction

Abstract

A model sliding potential, based on Prandtl–Tomlinson type models, is proposed for analyzing the temperature- and velocity-dependences of sliding processes at the interface between a tip and an adsorbed molecular layer. The proposed simple periodic potential has a parabolic form up to a critical distance, corresponding to the onset of detachment, at which point it becomes flat. The simplicity of the model will enable it to be used to analyze complex molecular interfaces, such as molecular films, mechanically induced chemical reactions or biological interfaces such as muscles or transport molecules. A simple analytical model is presented for the resulting velocity- and temperature-dependences of the friction force for the sliding of a compliant atomic force microscopy tip over an array of molecular species adsorbed on a surface, when only considering transitions of the tip in the forward direction (overall sliding direction). The validity of the analysis is tested by using kinetic Monte Carlo (kMC) simulations of the sliding over the molecular potential. This simulation provides excellent agreement with the analytic model, except for some slight differences that arise from the way in which the simulations calculate the lateral force compared to the analytical model. However, significant deviations are found between the kMC simulations and the analytical model when the possibility of both forward and reverse transitions are included, in particular at high sliding velocities and low temperatures. The origin of these effects are discussed in the manuscript, but result in superlubricious behavior, that is, vanishing friction, in particular at low sliding velocities.

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Acknowledgements

We gratefully acknowledge the Civil, Mechanical and Manufacturing Innovation (CMMI) Division of the National Science Foundation under Grant Nos. 1634340 and 2020525 for support of this work. GDK thanks the Fulbright Foundation for support of this work.

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Correspondence to Wilfred T. Tysoe.

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11249_2021_1523_MOESM1_ESM.docx

Supplementary file1 See Supplementary Material for analysis of the P-T Model for a sinusoidal potential, a derivation of Eact (F) for molecular sliding, a derivation of the velocity dependence of sliding, and an analysis of the deviations from the analytical model. (DOCX 1136 kb)

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Manzi, S.J., Carrera, S.E., Furlong, O.J. et al. Prandtl–Tomlinson-Type Models for Molecular Sliding Friction. Tribol Lett 69, 147 (2021). https://doi.org/10.1007/s11249-021-01523-w

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Keywords

  • Prandtl–Tomlinson model
  • Friction
  • Organic surfaces
  • Monte Carlo simulations