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A Molecular-Scale Analysis of Pressure-Dependent Sliding Shear Stresses

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Abstract

Stress-modified activated processes are analyzed using a model first proposed by Evans and Polanyi that uses transition-state theory to calculate the effect of some perturbation, described by an intensive variable, \(I\), on the reaction rate. They suggested that the rate constant depended primarily on the equilibrium between the transition state and the reactant, which, in turn, depends on the effect of the perturbation \(I\) on the Gibbs free energy, \(G=U-TS+IC\), where \(C\) is a variable conjugate to \(I\). For example, in the case of a hydrostatic pressure \(P\), the conjugate variable is the volume, \(-V\). This allows a pressure-dependent rate to be calculated from the equilibrium constant between the reactant and transition state. Advantages to this approach are that the analysis is independent of the pathway between the two states and can simultaneously include the effect of multiple perturbations. These ideas are applied to the Prandtl–Tomlinson model, which analyses the force-induced transition rate over a surface energy barrier. The Evans–Polanyi analysis is independent of the shape of the sliding potential and merely requires the locations of the initial and transition states. It also allows the effects of both normal and shear stresses to be analyzed to identify the molecular origins of the well-known pressure-dependent shear stress: \(\tau ={\tau }_{0}+{\mu }_{L}P\), where \({\tau }_{0}\) is a pressure-independent stress. The analysis reveals that \({\mu }_{L}\) depends on the molecular corrugation of the potential and that \({\tau }_{0}\) is velocity dependent, in accord with an empirical equation proposed by Briscoe and Evans.

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Acknowledgements

We gratefully acknowledge the Civil, Mechanical and Manufacturing Innovation (CMMI) Division of the National Science Foundation under Grant Number 2020525 for support of this work. This work was also supported by the French Agency for Ecological Transition (ADEME) through the IMOTEP project. WTT thanks Drs. J. P. Bonavia, B. P. Buggy and C. K. Rokkas without whom this work would not have been possible.

Funding

This study was supported by National Science Foundation (Grant No. CMMI2020525), French Agency for Ecological Transition (ADEME) (Grant No. IMOTEP).

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  1. Department of Chemistry and Biochemistry, University of Wisconsin-Milwaukee, Milwaukee, WI, 53211, USA

    Nicholas Hopper & Wilfred T. Tysoe

  2. Laboratoire de Tribologie et Dynamique des Systèmes, CNRS UMR5513, Ecole Centrale de Lyon, 69134, Ecully Cedex, France

    François Sidoroff, Juliette Cayer-Barrioz & Denis Mazuyer

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Hopper, N., Sidoroff, F., Cayer-Barrioz, J. et al. A Molecular-Scale Analysis of Pressure-Dependent Sliding Shear Stresses. Tribol Lett 71, 121 (2023). https://doi.org/10.1007/s11249-023-01791-8

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