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)