NANOFRICTION AN INTRODUCTION E Tosatti SISSAICTPDemocritos TRIESTE Contents

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 = F L/ F N (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 Da. Vinci-Amonton's law explained: FL = t AR = t FN /s = m FN yield stress BOWDEN - TABOR, 1950 s 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 n. N (MEYER)

Na. Cl(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 ~ 2 pn a ~ 0. 6 m/s |Finertial|~ M (2 pn)2 a = 3 x 10 -15 N ~3 x 10 -6 n. N VERY WEAK FORCE --> LINEAR RESPONSE REGIME!

THEORY (a) LINEAR RESPONSE

ZERO EXTERNAL FORCE: 2 D BROWNIAN DIFFUSION <r 2> = 4 Dt y x

WEAK EXTERNAL FORCE: 2 D “DIFFUSIVE” DRIFT

LINEAR RESPONSE THEORY < v > /m = F ---->> “viscous” friction m = mobility EINSTEIN RELATION m=D/ k. BT 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= (E 0/2)cos(2 pxtip/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 K e g=K/ SLIDING PINNED e gc gg g >gc ZERO STATIC FRICTION g <gc FINITE STATIC FRICTION (“PINNING”)

PHONON GAP OF PINNED SLIDER w 2 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 FREE SURFACE

EXAMPLE: “GRAZING” FRICTION SIMULATION Diamond Na. Cl V

Load = 1. 0 n. N T = 1100 K (6 Ang) Zykova-Timan, et al, Nature Materials 6, 231 (2007)

EXAMPLE: “PLOWING” FRICTION WITH WEAR HIGH TEMPERATURE NANOFRICTION, DIAMOND ON Na. Cl(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)

BRAUN, PRL (2006)

WHERE DOES THE ENERGY GO? WEAR + PHONONS IN SIMULATION, 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 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)