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 NANOFRICTIONFN 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
( )

6. COULOMB EULER 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
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

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. MACRO-MESOSCOPIC NANO
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 N nN
(MEYER)

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

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

18. QCM Frequency n= 107 Hz Amplitude a = 100 Angstrom
Velocity v ~ 2pn a ~ 0.6 m/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. F~ log v F~ v “COULOMB”! STIFF SOFT SMOOTH SLIDING STICK-SLIP SLIDING
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. e FRENKEL-KONTOROVA MODEL (1938) K
O.M.BRAUN, YU.S.KIVSHAR, The Frenkel Kontorova Model:
Concepts, Methods, Applications, Springer (2004)

28. e e THE AUBRY TRANSITION K g = K / gg
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 SLIDERw2
g > gc
g < gc q q

30. (c) NANOFRICTION SIMULATIONS
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. Zykova-Timan, et al, Nature Materials 6, 231 (2007)
Load = 1.0 nN
T = 1100 K
(6 Ang)
Zykova-Timan, et al, Nature Materials 6, 231 (2007)

36. EXAMPLE: “PLOWING” FRICTION WITH WEAR
HIGH TEMPERATURE NANOFRICTION, DIAMOND ON NaCl(100)
Zykova-Timan, Ceresoli, Tosatti, Nature Materials 6, 231 (2007)

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

38. HIGH T FRICTIONAL DROP: 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, (2006)

41. BRAUN, PRL (2006)

42. Temp.(K) t (fs) 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. THE END 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. Materials 6, 231 (2007)
Squeezout Simulation: TARTAGLINO, SIVEBAEK, PERSSON,
TOSATTI, J. Chem Phys 125, (2006)
Nanoscale Rolling Simulation: O.M. BRAUN, PRL (2006)