NANOFRICTION-- AN INTRODUCTION

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NANOFRICTION-- AN INTRODUCTION
E. Tosatti
SISSA/ICTP/Democritos
TRIESTE
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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
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FRICTION NANOFRICTION
FN
FL
(MEYER)
(BRAUN)
FRICTION COEFFICIENT m FL/ FN
(usually0.1-1) General Refs B.N.J.
PERSSON, Sliding Friction, Springer (2000)
J.KRIM, Surf. Sci. 500,
741 (2002)
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RELEVANCE
-- FRICTION energy conservation machine wear
... -- NANOFRICTION basic understanding
nanotechnology.
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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)
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COULOMB
3. Friction independent of velocity 4. Friction
tied to roughness
EULER
5. Static vs. dynamic friction
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STATIC vs DYNAMIC FRICTION
SLIDING VELOCITY
Fs Fd
Fk Fr
APPLIED FORCE
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WHY FRICTION IS INDEP. OF AREA, AND PROPORT. TO
LOAD
Philip Bowden 1903-1968
Real contact surface AR FN/s ltlt A
DaVinci-Amonton's law explained FL t
AR t FN /s m FN
yield stress
BOWDEN - TABOR, 1950s
David Tabor 1913-2005
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Rodrigues et al. (2000)
Au
NANOCONTACTS
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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) -- .....
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6. Stick-slip motion vs smooth sliding
low velocity /or soft system high velocity
/or stiff system
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SOME EXPERIMENTAL NANOFRICTION
METHODS
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SOME EXPERIMENTAL TECHNIQUES
MACRO-MESOSCOPIC NANO

Tabor, Winterton, Israelachvili (1975)
Binnig, Quate, Gerber (1986)
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FRICTION NANOFRICTION
(MEYER)
GERD BINNIG
HEINI ROHRER
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AFM INSTRUMENTS
Measure FL , F N Typical F N 1-100 nN
(MEYER)
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NaCl(100)
(MEYER et al)
-- ATOMIC STICK-SLIP MOTION OF TIP -- ENCLOSED
AREA IN (F, x) PLANE EQUALS DISSIPATED
FRICTIONAL ENERGY
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QCM
(QUARTZ CRYSTAL MICROBALANCE)
a
Slip time t 2 t d (Q-1)/dw
KRIM, WIDOM, PRB 38, 12184 (1986)
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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 --gt LINEAR RESPONSE
REGIME!
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THEORY (a)
LINEAR RESPONSE
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ZERO EXTERNAL FORCE 2D BROWNIAN DIFFUSION
ltr2gt 4 Dt
y
x
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WEAK EXTERNAL FORCE 2D DIFFUSIVE DRIFT
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LINEAR RESPONSE THEORY
lt v gt /m F ----gtgt viscous friction
m mobility EINSTEIN
RELATION mD/ kBT D S (w0)
S (w) F.T. ltv(t) - v(0)gt
VIVISCOUS FRICTION GOOD FOR FLUIDS, BUT NOT FOR
SOLIDS VIOLATES OBEY COULOMBS LAW, F
DEPENDENT ON VELOCITY
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THEORY (b) SIMPLE
(MINIMALISTIC ) FRICTION




AND NANOFRICTION MODELS
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PRANDTL-TOMLINSON MODEL (1928)
v
keff
H (E0/2)cos(2pxtip/a) (keff/2)(xtip-x)2da
mping
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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)
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STICK-SLIP
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FRENKEL-KONTOROVA MODEL (1938)
K
e
O.M.BRAUN, YU.S.KIVSHAR, The Frenkel Kontorova
Model Concepts, Methods, Applications,
Springer (2004)
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THE AUBRY TRANSITION
INCOMMENSURATE a c / a b IRRATIONAL
Fstatic
SLIDING
K
e
PINNED
e
g K /
gg
gc
g gtgc ZERO STATIC FRICTION g ltgc
FINITE STATIC FRICTION (PINNING)
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PHONON GAP OF PINNED SLIDER
w2
g gt gc
g lt gc
q
q
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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
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MOLECULAR DYNAMICS SIMULATIONS
NEWTON TOT (FREE) EN. LANGEVIN
THERMAL NOISE


- gvi(t) hi(t)
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EMPIRICAL INTERPARTICLE FORCES (EXAMPLE
LENNARD-JONES PAIR POTENTIAL)
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SLAB GEOMETRY
FREE SURFACE
PBC
PBC
FREE SURFACE
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EXAMPLE GRAZING FRICTION SIMULATION
Diamond
V
NaCl
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Load 1.0 nN
T 1100 K
(6 Ang)
Zykova-Timan, et al, Nature
Materials 6, 231 (2007)
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EXAMPLE PLOWING FRICTION WITH WEAR
HIGH TEMPERATURE NANOFRICTION, DIAMOND ON
NaCl(100)
Zykova-Timan, Ceresoli, Tosatti, Nature Materials
6, 231 (2007)
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SIMULATED LUBRICATION
(BRAUN)
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SQUEEZOUT
TARTAGLINO, SIVEBAEK, PERSSON, TOSATTI, J. Chem
Phys 125, 014704 (2006)
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BRAUN, PRL (2006)
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WHERE DOES THE ENERGY GO? WEAR PHONONS IN
SIMULATION, THE THERMOSTATING METHOD MAY
INFLUENCE AND FALSIFY THE REAL PHONON FRICTION
Temp.(K)
t (fs)
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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
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SOME
REFERENCES General B.N.J. PERSSON,
Sliding Friction, Springer (2000)
J.KRIM, Surf. Sci. 500, 741
(2002) Stic-slip in Prandtl- Tomlinson
ModelSASAKI, 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)