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  • Open Access

Thermally Activated Contact Strengthening Explains Nonmonotonic Temperature and Velocity Dependence of Atomic Friction

Mykhaylo Evstigneev* and Peter Reimann

  • Universität Bielefeld, Fakultät für Physik, 33615 Bielefeld, Germany

  • *mykhaylo@physik.uni-bielefeld.de
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Phys. Rev. X 3, 041020 – Published 26 November, 2013

DOI: https://doi.org/10.1103/PhysRevX.3.041020

Abstract

While the well-established Prandtl-Tomlinson (PT) model of atomic friction predicts that the friction force decreases with temperature and grows with velocity, several recent experiments reported that a nonmonotonic temperature dependence and a decreasing velocity dependence may also occur. We propose a minimal extension of the PT model, incorporating the possibility of thermally activated contact strengthening and providing one common framework to quantitatively explain all those “anomalous” experimental findings, as well as the previously known “normal” (PT-like) behavior.

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We encounter friction in our everyday life. Such friction involves interactions between large numbers of asperities on the two rough surfaces in contact. To understand the nature of this extremely complex process, atomic friction experiments focus on the interaction of a single asperity, for example, the tip of an atomic force microscope (AFM), with an atomically flat surface. The generally accepted model of atomic friction relies on this picture: In the course of its motion, the AFM tip, assisted by thermal noise, performs interstitial jumps from one surface lattice site to the next, overcoming energy barriers between the sites. The prediction is then that the time-averaged friction should decrease monotonically with temperature and grow logarithmically with velocity when the tip is pulled sufficiently fast. Surprisingly, recent measurements have countered that prediction: At low temperatures, the friction force developed a peak at a particular temperature, and in one experiment, this peak was preceded by a minimum. Besides, at some temperatures, the friction force actually decreased with velocity. A single theoretical model that provides consistent rationalizations of all these experimental data does not yet appear to exist. In this theoretical paper, we propose such a theory.

Our theory extends the standard model of atomic friction by postulating the notion of contact “aging”: The tip-substrate contact is dynamical in nature and becomes stronger with time through formation of new tip-substrate bonds. Another concept is the assumption that this contact-strengthening process is thermally activated and thus occurs faster at elevated temperatures. This minimal quantitative theory generically predicts a minimum and a maximum of friction as a function of temperature. Friction force as a function of velocity is shown to logarithmically grow at slow and fast pulling, but to develop a decreasing branch at those velocities where the time for the tip to travel one lattice constant becomes comparable to the aging time scale. These predictions are in good quantitative agreement with the experimental results.

We hope that our findings will stimulate further research in the growing field of nanotribology.

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Phys. Rev. X 3, 041020– Published 26 November, 2013
  • Received 3 September 2013
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This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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