Tribology a short review (pdf 0.42 Mb) on my understanding of friction may be found here: 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

• 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

• 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 a mesoscopic scale

  • 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

  • Stick-slip kinetics

    • Motion equation

    • Elastic instability

    • Slip details

    • Interacting contacts

    • Discussion

  • Concerted slips

  • Complete set of equations

  • Conclusion

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

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

• 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 December 6, 2010 by Oleg Braun