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NANOFRICTION-- AN INTRODUCTION
E. Tosatti
SISSA/ICTP/Democritos
TRIESTE
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
FRICTION
NANOFRICTION
FN
FL
(MEYER)
(BRAUN)
FRICTION COEFFICIENT:
General Refs:
m = FL/ FN
(usually~0.1-1)
B.N.J. PERSSON, Sliding Friction, Springer (2000);
J.KRIM, Surf. Sci. 500, 741 (2002)
RELEVANCE
-- FRICTION: energy conservation; machine wear; ...
-- NANOFRICTION: basic understanding; nanotechnology.
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)
COULOMB
3. Friction independent of velocity
4. Friction tied to roughness
EULER
5. Static vs. dynamic friction
STATIC vs DYNAMIC FRICTION
SLIDING
VELOCITY
Fk= Fr
Fs= Fd APPLIED
FORCE
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
Rodrigues et al.
(2000)
Au
NANOCONTACTS
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)
-- .....
6. Stick-slip motion vs smooth sliding
low velocity &/or soft system
high velocity &/or stiff system
SOME EXPERIMENTAL NANOFRICTION
METHODS
SOME EXPERIMENTAL TECHNIQUES
MACRO-MESOSCOPIC
Tabor, Winterton, Israelachvili (~1975)
NANO
Binnig, Quate, Gerber (1986)
FRICTION
NANOFRICTION
(MEYER)
HEINI ROHRER
GERD BINNIG
AFM INSTRUMENTS
Measure FL , F N
Typical F N 1-100 nN
(MEYER)
NaCl(100)
(MEYER et al)
-- “ATOMIC” STICK-SLIP MOTION OF TIP
-- ENCLOSED AREA IN (F, x) PLANE EQUALS
DISSIPATED FRICTIONAL ENERGY
QCM
(QUARTZ CRYSTAL MICROBALANCE)
a
2
Slip time t:
t: = d (Q-1)/dw
KRIM, WIDOM, PRB 38, 12184 (1986)
Frequency n= 107 Hz
QCM
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!
THEORY
(a)
LINEAR RESPONSE
ZERO EXTERNAL FORCE: 2D BROWNIAN DIFFUSION
<r2> = 4 Dt
y
x
WEAK EXTERNAL FORCE: 2D “DIFFUSIVE” DRIFT
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
THEORY
(b) SIMPLE (“MINIMALISTIC” ) FRICTION
AND NANOFRICTION MODELS
PRANDTL-TOMLINSON MODEL (1928)
v
keff
H= (E0/2)cos(2pxtip/a) + (keff/2)(xtip-x)2+damping
LARGE K
SMALL E
SMOOTH
SLIDING
F~ v
STIFF
SOFT
LARGE E
SMALL K
STICK-SLIP
SLIDING
F~ log v
“COULOMB”!
SASAKI, KOBAYASHI, TSUKADA, PRB 54 ,2138 (1996)
STICK-SLIP
FRENKEL-KONTOROVA MODEL (1938)
K
e
O.M.BRAUN, YU.S.KIVSHAR, The Frenkel Kontorova Model:
Concepts, Methods, Applications, Springer (2004)
THE AUBRY TRANSITION
INCOMMENSURATE: a c / a b = IRRATIONAL
Fstatic
SLIDING
K
e
PINNED
g=K/
e
gc gg
g >gc ZERO STATIC FRICTION
g <gc FINITE STATIC FRICTION (“PINNING”)
PHONON GAP OF PINNED SLIDER
w2
g > gc
g < gc
q
q
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
MOLECULAR DYNAMICS SIMULATIONS
NEWTON
TOT (FREE) EN.
LANGEVIN
THERMAL NOISE
- gvi(t)+ hi(t)
EMPIRICAL INTERPARTICLE FORCES
(EXAMPLE: LENNARD-JONES PAIR POTENTIAL)
SLAB GEOMETRY
FREE SURFACE
PBC
PBC
FREE SURFACE
EXAMPLE: “GRAZING” FRICTION SIMULATION
Diamond
NaCl
V
Load = 1.0 nN
T = 1100 K
(6 Ang)
Zykova-Timan, et al, Nature Materials 6, 231 (2007)
EXAMPLE: “PLOWING” FRICTION WITH WEAR
QuickTime™ and a
YUV420 codec decompressor
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QuickTime™ and a
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HIGH TEMPERATURE NANOFRICTION, DIAMOND ON NaCl(100)
Zykova-Timan, Ceresoli, Tosatti, Nature Materials 6, 231 (2007)
PLOWING FRICTION FORCES
v = 50 m/s
T=1100 K
Normal force
6 Angstrom penetration
HIGH T FRICTIONAL DROP: SKATING
“SKATING”
TIP IN LOCAL
LIQUID CLOUD
v = 50 m/s
FURROW
CLOSES UP
BEHIND TIP
SIMULATED LUBRICATION
(BRAUN)
SQUEEZOUT
TARTAGLINO, SIVEBAEK, PERSSON, TOSATTI, J. Chem Phys 125, 014704 (2006)
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BRAUN, PRL (2006)
WHERE DOES THE ENERGY GO? WEAR + PHONONS
IN SIMULATION, THE THERMOSTATING METHOD MAY
INFLUENCE AND FALSIFY THE REAL PHONON FRICTION
Temp.(K)
t (fs)
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
SOME REFERENCES
General :
B.N.J. PERSSON, Sliding Friction, Springer (2000);
J.KRIM, Surf. Sci. 500, 741 (2002)
Stic-slip in PrandtlTomlinson 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, 014704 (2006)
Nanoscale Rolling Simulation: O.M. BRAUN, PRL (2006)