NANOFRICTION-- AN INTRODUCTION E. Tosatti

1. NANOFRICTION-- AN INTRODUCTION E. Tosatti SISSA/ICTP/Democritos TRIESTE

2. Contents 1. Friction. Generalities, history. 2. “Stick-slip” versus smooth sliding; friction mechanisms. 3. Nanofriction: experimental methods. AFM, QCM, SFA… 4. Nanofriction: theory . a). Linear response b). Nonlinear friction in simple models: Prandtl-Tomlinson, Frenkel-Kontorova c). Simulated nanofriction: Molecular Dynamics--applications

3. FRICTION NANOFRICTION FN FL (MEYER) (BRAUN) FRICTION COEFFICIENT: m = FL/ FN (usually~0.1-1) General Refs: B.N.J. PERSSON, Sliding Friction, Springer (2000); J.KRIM, Surf. Sci. 500, 741 (2002)

4. RELEVANCE -- FRICTION: energy conservation; machine wear; ... -- NANOFRICTION: basic understanding; nanotechnology.

5. HISTORY LEONARDO DA VINCI 1. Friction is independent of the geometrical contact area 2. Friction is proportional to normal load AMONTONS Guillaume Amontons (1663-1705)

6. COULOMB 3. Friction independent of velocity 4. Friction tied to roughness EULER 5. Static vs. dynamic friction

7. STATIC vs DYNAMIC FRICTION SLIDING VELOCITY Fs= Fd Fk= Fr APPLIED FORCE

8. WHY FRICTION IS INDEP. OF AREA, AND PROPORT. TO LOAD Philip Bowden 1903-1968 Real contact surface AR= FN/s << A DaVinci-Amonton's law explained: FL = t AR = t FN /s = m FN yield stress BOWDEN - TABOR, 1950s David Tabor 1913-2005

9. Rodrigues et al. (2000) Au NANOCONTACTS

10. MORE GENERAL SLIDING FRICTION MECHANISMS -- Entanglement of asperities, plastic deformation, wear (commonest macroscopic friction mechanism) -- Viscous friction (fluid interfaces, acquaplaning) -- Phonon dissipation, elastic deformation (flat solid interfaces) -- Bulk viscoelastic dissipation (e.g., car tyres) -- Electronic friction (metals, still being established) -- Vacuum friction (more speculative) -- .....

11. 6. Stick-slip motion vs smooth sliding low velocity &/or soft system high velocity &/or stiff system

12. SOME EXPERIMENTAL NANOFRICTION METHODS

13. SOME EXPERIMENTAL TECHNIQUES MACRO-MESOSCOPIC NANO Tabor, Winterton, Israelachvili (~1975) Binnig, Quate, Gerber (1986)

14. FRICTION NANOFRICTION (MEYER) GERD BINNIG HEINI ROHRER

15. AFM INSTRUMENTS Measure FL , F N Typical F N1-100 nN (MEYER)

16. NaCl(100) (MEYER et al) -- “ATOMIC” STICK-SLIP MOTION OF TIP -- ENCLOSED AREA IN (F, x) PLANE EQUALS DISSIPATED FRICTIONAL ENERGY

17. QCM (QUARTZ CRYSTAL MICROBALANCE) a Slip timet: 2 t: = d (Q-1)/dw KRIM, WIDOM, PRB 38, 12184 (1986)

18. QCM Frequency n= 107 Hz Amplitude a = 100 Angstrom Velocity v ~ 2pna ~ 0.6m/s |Finertial|~ M (2pn)2 a = 3 x 10-15N ~3 x 10-6nN VERY WEAK FORCE --> LINEAR RESPONSE REGIME!

19. THEORY (a) LINEAR RESPONSE

20. ZERO EXTERNAL FORCE: 2D BROWNIAN DIFFUSION <r2> = 4 Dt y x

21. WEAK EXTERNAL FORCE: 2D “DIFFUSIVE” DRIFT

22. LINEAR RESPONSE THEORY < v > /m =F ---->> “viscous” friction m = mobility EINSTEIN RELATION m=D/ kBT D = S (w=0) S (w) = F.T. { <v(t) - v(0)>} VIVISCOUS FRICTION GOOD FOR FLUIDS, BUT NOT FOR SOLIDS: VIOLATES “OBEY” COULOMB’S LAW, F DEPENDENT ON VELOCITY

23. THEORY (b) SIMPLE (“MINIMALISTIC” ) FRICTION AND NANOFRICTION MODELS

24. PRANDTL-TOMLINSON MODEL (1928) v keff H= (E0/2)cos(2pxtip/a) + (keff/2)(xtip-x)2+damping

25. STIFF SOFT LARGE K SMALL E LARGE E SMALL K SMOOTH SLIDING STICK-SLIP SLIDING F~ log v “COULOMB”! F~ v SASAKI, KOBAYASHI, TSUKADA, PRB 54 ,2138 (1996)

26. STICK-SLIP

27. FRENKEL-KONTOROVA MODEL (1938) K e O.M.BRAUN, YU.S.KIVSHAR, The Frenkel Kontorova Model: Concepts, Methods, Applications, Springer (2004)

28. THE AUBRY TRANSITION INCOMMENSURATE: a c / a b = IRRATIONAL Fstatic SLIDING K e PINNED e g = K / gc gg g >gc ZERO STATIC FRICTION g <gc FINITE STATIC FRICTION (“PINNING”)

29. PHONON GAP OF PINNED SLIDER w2 g > gc g < gc q q

30. THEORY (c) NANOFRICTION SIMULATIONS -- NEWTONIAN or LANGEVIN DYNAMICS -- FROM MODELS TO REALISTIC MOLECULAR DYNAMICS (MD) -- MD: EMPIRICAL AND AB INITIO FORCES -- VARIETY OF SYSTEMS, APPLICATIONS

31. MOLECULAR DYNAMICS SIMULATIONS NEWTON TOT (FREE) EN. LANGEVIN THERMAL NOISE + - gvi(t)+ hi(t)

32. EMPIRICAL INTERPARTICLE FORCES (EXAMPLE: LENNARD-JONES PAIR POTENTIAL)

33. SLAB GEOMETRY FREE SURFACE PBC PBC FREE SURFACE

34. EXAMPLE: “GRAZING” FRICTION SIMULATION Diamond V NaCl

35. Load = 1.0 nN T = 1100 K (6 Ang) Zykova-Timan, et al, Nature Materials6, 231 (2007)

36. EXAMPLE: “PLOWING” FRICTION WITH WEAR HIGH TEMPERATURE NANOFRICTION, DIAMOND ON NaCl(100) Zykova-Timan, Ceresoli, Tosatti, Nature Materials6, 231 (2007)

37. PLOWING FRICTION FORCES v = 50 m/s T=1100 K Normal force 6 Angstrom penetration

38. HIGH T FRICTIONAL DROP: SKATING “SKATING” TIP IN LOCAL LIQUID CLOUD FURROW CLOSES UP BEHIND TIP v = 50 m/s

39. SIMULATED LUBRICATION (BRAUN)

40. SQUEEZOUT TARTAGLINO, SIVEBAEK, PERSSON, TOSATTI, J. Chem Phys 125, 014704 (2006)

41. BRAUN, PRL (2006)

42. WHERE DOES THE ENERGY GO? WEAR + PHONONS IN SIMULATION, THE THERMOSTATING METHOD MAY INFLUENCE AND FALSIFY THE REAL PHONON FRICTION Temp.(K) t (fs)

43. SUMMARY FRICTION OFFERS MUCH MORE INTEREST AT NANOSCALE SIMPLE MODELS DEMONSTRATE STICK-SLIP, PINNING TRANSITION SIMULATIONS EXTREMELY USEFUL AND PREDICTIVE IN NANOFRICTION DISPOSAL OF DISSIPATED PHONON ENERGY NEEDS SPECIAL ATTENTION THE END

44. SOME REFERENCES General : B.N.J. PERSSON, Sliding Friction, Springer (2000); J.KRIM, Surf. Sci. 500, 741 (2002) Stic-slip in Prandtl- Tomlinson Model:SASAKI, KOBAYASHI, TSUKADA, PRB 54 ,2138 (1996) Frenkel-Kontorova Model: O.M.BRAUN, YU.S.KIVSHAR, The Frenkel Kontorova Model: Concepts, Methods, Applications, Springer (2004) Nanofriction Simulation: Zykova-Timan et al, Nat. Materials6, 231 (2007) Squeezout Simulation: TARTAGLINO, SIVEBAEK, PERSSON, TOSATTI, J. Chem Phys 125, 014704 (2006) Nanoscale Rolling Simulation: O.M. BRAUN, PRL (2006)