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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
FRICTION COEFFICIENT: = FL/ FN (usually~0.1-1)
General Refs: B.N.J. PERSSON, Sliding Friction, Springer (2000); J.KRIM, Surf. Sci. 500, 741 (2002)
(MEYER) (BRAUN)
FL
FN
RELEVANCE
-- FRICTION: energy conservation; machine wear; ...
-- NANOFRICTION: basic understanding; nanotechnology.
1. Friction is independent of the geometrical contact area2. Friction is proportional to normal load
Guillaume Amontons(1663-1705)
HISTORY LEONARDO DA VINCI
AMONTONS
COULOMB
3. Friction independent of velocity4. Friction tied to roughness
EULER
5. Static vs. dynamic friction
STATIC vs DYNAMIC FRICTION
APPLIED FORCE
SLIDINGVELOCITY
Fs= FdFk= Fr
Philip Bowden 1903-1968
David Tabor1913-2005
Real contact surface AR= FN/<< A DaVinci-Amonton's law explained:
FL = AR = FN / = FN yield stress
BOWDEN - TABOR, 1950s
WHY FRICTION IS INDEP. OF AREA, AND PROPORT. TO LOAD
Rodrigues et al.(2000)
AuNANOCONTACTS
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
MACRO-MESOSCOPIC NANO
Tabor, Winterton, Israelachvili (~1975)
Binnig, Quate, Gerber (1986)
SOME EXPERIMENTAL TECHNIQUES
FRICTION NANOFRICTION
(MEYER)
HEINI ROHRER GERD BINNIG
(MEYER)
Measure FL , F N
Typical F N 1-100 nN
AFM INSTRUMENTS
NaCl(100)
-- “ATOMIC” STICK-SLIP MOTION OF TIP
-- ENCLOSED AREA IN (F, x) PLANE EQUALS DISSIPATED FRICTIONAL ENERGY
(MEYER et al)
QCM (QUARTZ CRYSTAL MICROBALANCE)
a
Slip time 2 = d (Q-1)/d
KRIM, WIDOM, PRB 38, 12184 (1986)
QCMFrequency = 107 Hz
Amplitudea = 100 Angstrom
Velocity v ~ 2 a ~ 0.6 m/s
|Finertial|~ M (2)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
x
y
WEAK EXTERNAL FORCE: 2D “DIFFUSIVE” DRIFT
= mobility
EINSTEIN RELATION
=D/ kBT
D = S (=0)
S () = F.T. { <v(t) - v(0)>}
< v > /F ---->> “viscous” friction
LINEAR RESPONSE THEORY
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)
H= (E0/2)cos(2xtip/a) + (keff/2)(xtip-x)2+damping
keff
v
SMOOTH SLIDING
STICK-SLIP SLIDING
STIFF SOFT
SASAKI, KOBAYASHI, TSUKADA, PRB 54 ,2138 (1996)
F~ v F~ log v “COULOMB”!
LARGE KSMALL E
LARGE ESMALL K
STICK-SLIP
FRENKEL-KONTOROVA MODEL (1938)
K
O.M.BRAUN, YU.S.KIVSHAR, The Frenkel Kontorova Model: Concepts, Methods, Applications, Springer (2004)
THE AUBRY TRANSITION
K
INCOMMENSURATE: a c / a b = IRRATIONAL
g >gc ZERO STATIC FRICTION g <gc FINITE STATIC FRICTION (“PINNING”)
g = K /
Fstatic
gggc
SLIDING
PINNED
PHONON GAP OF PINNED SLIDER
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
vi(t)+ i(t)
NEWTON TOT (FREE) EN. LANGEVIN THERMAL NOISE
EMPIRICAL INTERPARTICLE FORCES
(EXAMPLE: LENNARD-JONES PAIR POTENTIAL)
PBC PBC
FREE SURFACE
SLAB GEOMETRY
FREE SURFACE
NaClDiamond V
EXAMPLE: “GRAZING” FRICTION SIMULATION
(6 Ang)
T = 1100 K
Load = 1.0 nN
Zykova-Timan, et al, Nature Materials 6, 231 (2007)
HIGH TEMPERATURE NANOFRICTION, DIAMOND ON NaCl(100) HIGH TEMPERATURE NANOFRICTION, DIAMOND ON NaCl(100)
Zykova-Timan, Ceresoli, Tosatti, Nature Materials 6, 231 (2007)
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EXAMPLE: “PLOWING” FRICTION WITH WEAR
T=1100 K
6 Angstrom penetration
v = 50 m/s
PLOWING FRICTION FORCES
Normal force
“SKATING”
v = 50 m/s
HIGH T FRICTIONAL DROP: SKATING
TIP IN LOCALLIQUID CLOUD
FURROWCLOSES UPBEHIND TIP
SIMULATED LUBRICATION
(BRAUN)
SQUEEZOUT
TARTAGLINO, SIVEBAEK, PERSSON, TOSATTI, J. Chem Phys 125, 014704 (2006)
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BRAUN, PRL (2006)
Temp.(K)
t (fs)
WHERE DOES THE ENERGY GO? WEAR + PHONONS IN SIMULATION, THE THERMOSTATING METHOD MAY INFLUENCE AND FALSIFY THE REAL PHONON FRICTION
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
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, 014704 (2006)
Nanoscale Rolling Simulation: O.M. BRAUN, PRL (2006)