Tribology a short review (pdf 0.42 Mb) on my understanding of friction may be found here in Russian / English

Outline: the questions of interest

• How to model the friction, and when one can use simple models like the FK model?

• How the frictional force depends on model parameters, e.g.,

  • on the parameters of interaction?

  • on the geometry of the contact?

  • on the lubricant structure (solid / amorphous / liquid)?

  • on the thickness of the lubricant film?

  • on the shape of lubricant molecules?

  • on temperature?

• How the kinetic frictional force depends on the driving velocity v?

  • what is a minimally possible  v  for smooth sliding?

  • what is a maximally possible driving velocity?

  • where the energy losses occur, and what is the mechanism of losses?

  • does the lubricant is heated / melted during sliding?

• What is a mechanism of stick-slip motion, what is a mechanism of the transition from smooth sliding to stick-slip, and are the microscopic and macroscopic mechanisms of stick-slip the same?

• When the friction is minimal / maximal?

Content

• Introduction

  • Why friction is important

  • Hydrodynamic and boundary lubrication

  • Experimental technique

  • Results and laws for solid-on-solid friction

  • Important notes

  • Macroscopic theory

  • Stick-slip motion and smooth sliding

    • Phenomenological theory

  • Low-dimensional models

• Nanotribology

  • MD model

    • A microscopic model

    • Why Langevin equations?

    • External damping

    • Stochastic equations

    • Motion equations

    • Parameters of the model

    • Units

  • Simulation results

    • Soft and hard lubricants

      • Constant-force algorithm: hysteresis

      • Spring algorithm: stick-slip

      • Melting of the confined film

    • Soft lubricant: melting/freezing

      • Two sliding regimes

      • Onset of sliding (short)

      • Very thin lubricant films

    • Hard lubricant

      • Perfect sliding

      • Energy losses

      • Melting

      • Role of temperature

      • Stick-slip to smooth sliding transition

      • Phenomenology of kinetic friction

    • Role of substrate geometry

      • Curved surface

      • Stepped surface

      • Rotated surface

    • Conclusion

  • Onset of sliding (soft lubricant)

    • N_l=1

    • N_l=2

    • N_l=3

    • N_l=5

    • Size scaling of f_s

  • Self-ordering of the lubricant

    • Introduction

    • Some examples

      • Hard lubricant, N_l=1

      • Hard lubricant, N_l=3

      • Curved substrate

    • Dependence on V_ll

    • Conclusion  

  • Role of lubricant molecule shape

    • Introduction

    • Model and technique

    • Totally- vs head-glued molecules

    • Conclusion

  • Microscopic rolling friction

    • Introduction

    • Model

    • Results

    • Cogwheel model

    • Conclusion

• Minimal sliding velocity

  • Hysteresis

    • Soft lubricant

    • Hard lubricant

  • The simplest model

  • One-dimensional model

    • Simulation results

    • A finite slab

  • Analytics

    • Green-function technique

    • One-dimensional model

    • Three-dimensional model

  • Conclusion

• Earthquake-like model

  • The problem

  • Earthquake-like model

  • Minimal model

  • Simulation

    • A typical dependence

    • Details of the transition

    • Avalanche sizes

  • Estimation

    • Avalanche size at “smooth” sliding

    • Avalanche at stick-slip

  • Conclusion

• Friction on mesoscopic scale

  • Overview

  • Master equation approach

  • Some examples:

    • Steplike distribution

    • Rectangular distribution

    • Singular case

    • Two delta-functions

    • Friction loop

  • Generalizations

    • Delay in contact formation

    • Aging of junctions

    • Role of temperature

  • Distribution of thresholds

    • Rough surfaces

    • Dry contact

    • Lubricated surfaces

  • Kinetic friction: f_k(v)

    • Introduction

    • Steady-state

    • Nonzero T

    • Aging of contacts

    • Delay in contact formation

    • A link with experiments

    • Conclusion

  • Stick-slip kinetics

    • Motion equation

    • Elastic instability

    • Slip details

    • Interacting contacts

    • Discussion

  • Stick-slip vs smooth sliding

  • Elastic slider

    • Interaction between contacts

    • Nearby contacts: MF approach

    • Macrocontacts (λ-contacts)

  • Collective effects

    • Elastic screening

    • Self-healing crack as a solitary wave

    • Crack propagation length (onset of sliding)

  • Conclusion

Our main publications on the topic (pdf files may be found here; see also a short review in Russian / English):

• O.M. Braun, M. Peyrard, D.V. Stryzheus, and E. Tosatti, Tribology Letters 48 (2012) 11 "Collective effects at frictional interfaces"

• O.M. Braun, Tribology Letters 39 (2010) 283-293 "Bridging the gap between the atomic-scale and macroscopic modeling of friction"

• O.M. Braun and A.G. Naumovets, Surf. Sci. Reports 60 (2006) 79-158 "Nanotribology: Microscopic mechanisms of friction"

• O.M. Braun, Europhys. Lett. 109 (2015) 48004 "Stick-slip vs. smooth sliding in the multicontact interface"
• O.M. Braun and J. Scheibert, Tribology Letters 56 (2014) 553 "Propagation length of self-healing slip pulses at the onset of sliding: A toy model"
• O.M. Braun, Nicola Manini, and Erio Tosatti, Phys. Rev. Lett. 110 (2013) 085503 "Size scaling of static friction"
• O.M. Braun and M. Peyrard, Phys. Rev. E 85 (2012) 026111 "Crack in the frictional interface as a solitary wave"
• S.M. Rubinstein, I. Barel, Z. Reches, O.M. Braun, M. Urbakh, and J. Fineberg, Pure and Applied Geophysics 168 (2011) 2151-2166 "Slip sequences in laboratory experiments resulting from inhomogeneous shear as analogs of earthquakes associated with a fault edge"
• O.M. Braun and E. Tosatti, Philosophical Magazine 91 (2011) 3253-3275 "Kinetics and dynamics of frictional stick-slip in mesoscopic boundary lubrication"
• O.M. Braun and M. Peyrard, Phys. Rev. E 83 (2011) 046129 "Dependence of kinetic friction on velocity: Master equation approach"
• Nicola Manini and O.M. Braun, Phys. Lett. A 375 (2011) 2946-2951 "Crystalline misfit-angle implications for solid sliding"
• O.M. Braun and Nicola Manini, Phys. Rev. E 83 (2011) 021601 "Dependence of boundary lubrication on the misfit angle between the sliding surfaces"
• O.M. Braun and M. Peyrard, Phys. Rev. E 82 (2010) 036117 "Master equation approach to friction at the mesoscale"
• O.M. Braun and E. Tosatti, Europhys. Lett. 88 (2009) 48003 "Kinetics of stick-slip friction in boundary lubrication"
• O.M. Braun, I. Barel, and M. Urbakh, Phys. Rev. Lett. 103 (2009) 194301 "Dynamics of transition from static to kinetic friction"

• O.M. Braun and E. Tosatti, Phil. Mag. Lett. 88 (2008) 509 "Rack-and-pinion effects in molecular rolling friction"

• O.M. Braun and E. Tosatti, J. Phys.: Condens. Matter 20 (2008) 354007 (2008) 509 "Molecular rolling friction: the cogwheel model"

• O.M. Braun, Phys. Scr. 78 (2008) 015802 "Phenomenological theory of kinetic friction for the solid lubricant film"

• O.M. Braun and M. Peyrard, Phys. Rev. Lett. 100 (2008) 125501 "Modeling friction on a mesoscale: Master equation for the earthquakelike model"

• M. Paliy, O.M. Braun, and S. Consta, Tribology Letters 23 (2006) 7 "The friction properties of an ultrathin confined water film"

• O.M. Braun, M. Peyrard, V. Bortolani, A. Franchini, and A. Vanossi, Phys. Rev. E 72 (2005) 056116 "Transition from smooth sliding to stick-slip motion in a single frictional contact"

• O.M. Braun, Phys. Rev. Lett. 95 (2005) 126104 "Simple model of microscopic rolling friction"

• O.M. Braun, M. Paliy, and S. Consta, Phys. Rev. Lett. 92 (2004) 256103 "Ordering of a thin lubricant film due to sliding"

• O.M. Braun and M. Peyrard, Phys. Rev. E 68 (2003) 011506 "Dynamics and melting of a thin confined film"

• O.M. Braun and J. Röder, Phys. Rev. Lett. 88 (2002) 096102 "Transition from stick-slip to smooth sliding: An earthquakelike model"

• O.M. Braun and M. Peyrard, Phys. Rev. E 63 (2001) 046110 "Friction in a solid lubricant film"

• O.M. Braun, A. R. Bishop, and J. Röder, Phys. Rev. Lett. 82 (1999) 3097 "Multistep locked-to-sliding transition in a thin lubricant film"

• O.M. Braun, Thierry Dauxois, and M. Peyrard, Phys. Rev. B 56 (1997) 4987 "Friction in a thin commensurate contact"

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Last updated on March 25, 2018 by Oleg Braun