(NANO)FRICTIONSOME THEORETICAL SURPRISES

Erio Tosatti

SISSAICTPINFM/CNR (Democritos)

SLONANO, Ljubljana, 10 October 2007

1. Dynamical pinning/depinning of a model solid lubricant between incommensurate sliders A. VANOSSI, G.E. SANTORO, N. MANINI, G. DIVITINI, E.T., PRL 97, 056101 (2006); PRL, to appear Oct/Nov 2007

2. High temperature nanofriction: skating vs. grazing T. ZYKOVA-TIMAN, D. CERESOLI, E.T., Nature Mat., 6,231 (2007)

3. Negative differential friction in sliding CNTs X.H.ZHANG, U. TARTAGLINO, G.E.SANTORO, E..T., Surf. Science 601, 3693 (2007)

4. Why do tyres skid on wet roads? B.N.J. PERSSON, U. TARTAGLINO, O. ALBOHR, E.T., Nature Mat. 3, 882 (2004); Phys. Rev. B 71, 035428 (2005).

DIENWIEBEL et al,PRL (2004)1. MOVING MOIRE' PATTERNS AROUND

Lubricated FrictionVextTop crystalBottom crystalSolidLubricantVL= ? Macroscopic expectation: VL=Vext/2 At nanoscale: How substrate/lubricant periodicities and hardness of lubricant influence VL? A. VANOSSI, G.E. SANTORO, N. MANINI, G. DIVITINI, E.T., PRL 97, 056101 (2006); PRL, to appear Oct/Nov 2007

Harmonic Chain Among Two Periodic Sliding Substrates [4]We study the dissipative dynamics of a 1D chain of harmonically interacting atoms, subject two sinusoidal potentials, sliding one relative to the other with constant velocity VextTo model the lubricated sliding of two hard surfaces, we consider a generalized FK system with three inherent lengths: the periods of the bottom and top substrates, and the period of the confined lubricant structure.[4] See also, O.M. Braun, A. Vanossi, and E. Tosatti, Phys. Rev. Lett. 95, 026102 (2005).

[5] M.G. Rozman, M. Urbakh, and J. Klafter, Phys. Rev. Lett. 77, 683 (1996); Europhys. Lett. 39, 183 (1997); V. Zaloj, M. Urbakh, and J. Klafter, Phys. Rev. Lett. 81, 1227 (1998);

The system dynamics is described by: xi (i = 1,,N) coordinates of the N chain particles of mass m Vext is the driving external velocity for Top substrate K harmonic inter-particle interaction, with equilibrium spacing a0 a+, a- spatial periods of Bottom (+) and Top (-) substrates F+, F- force amplitudes for Bottom (+) and Top (-) substrates phenomenological viscous damping [6] (chosen in the underdamped regime)[6] J. Rder et al., Physica D 142, 306 (2000); J. Rder et al., Phys. Rev. B 57, 2759 (1998). The equations are integrated using a fourth-order Runge-Kutta. Initial condition: After relaxing an evenly spaced configuration, the top substrate begins to move at the constant velocity Vext.ExternalDrivingDissipation

Length ratios: commensurability1) Golden mean2) Spiral meana-a0a++++==--

Lubricant sliding velocity: surprise!Vext= 0.1 Large non-trivial plateaus w=Vcm/Vext1/2 only for large KVcm/Vext= 11/r+ universal (independent of F+, F-, )Chain can slide backward!r-=r+2(r-=2>1) wK = chain stiffness

Animations: kinks

Animations: anti-kinks

Animations: the Golden Mean

MOIRE' PATTERNS: THEY ARE THE REAL OBJECTS THAT CAN BE DRAGGED!

EXTPTS: AFM? OPTICAL LATTICES?

Free PowerPoint Template from www.brainybetty.com*T. ZYKOVA-TIMAN, D. CERESOLI, E.T., Nature Mat., 6,231 (2007)

Ice skating

Free PowerPoint Template from www.brainybetty.com*

Tomagnini et al, Surf. Sci. 287, 1041 (1993)PP

TRY A NONMELTING SURFACE:

NaCl(100)

SURFACE NONMELTING

T= Tm + 50 K

Ice skating

Need

WEARLESS, GRAZING FRICTION1. CONTACT SURFACE GENTLY, FORCE F

z(0-1 nN)2.SLIDING v (50 m/s)3. MEASURE FORCE Fx

CHAIKIN et al

3.Negative Differential Friction in sliding carbon nanotubes

X.H.ZHANG, U. TARTAGLINO, G.E.SANTORO, E..T., Surf. Science 601, 3693 (2007)

SLIDING OF COAXIAL NANOTUBES

FRICTION PEAKS vs SPEED ...

...DUE TO INNER TUBETERMINATIONS

n=v/aa=2.46 ATangney et al:Breathing modeINNER TUBE TERMINATIONS EXCITE OUTER TUBE VIBRATIONAL MODE dwtube(k)/dk = v = wa/2p

SOME OUTSTANDING ISSUES

1. WHAT ABOUT FRICTION FROM NANOTUBE BODY RATHER THAN FROM TERMINATIONS? IS CORRUGATION WELL DESCRIBED?

2. APPLY FORCE TO GET SLIDING VELOCITY, NOT THE OPPOSITE...

SimulationsForce pulling the inner tubep.b.cp.b.cthermostat T=T0 coupled to outer tube onlyInteratomic model forces

a) Intra-tube (strong)Tersoff-Brenner potentialb) Inter-tube (weak)Kolmogorov Crespi potential (KDP0)clamped outer nanotube: no shift, no rotation A.N. Kolmogorov and V.H. Crespi: Registry dependent interlayer potential for graphitic systems [PRB 71 (2005) 235415]

Choice of nanotube pairsCommensurate(5,5)-(10,10)Incommensurate(11,2)-(12,12)r=3.41 R=6.80 r=4.76 R=8.15

VELOCITY PLATEAUS, JUMPS!!

(5,5)-(10,10) T = 50 KFRICTIONAL PEAKS

FORCE DRIVES VELOCITY, NOT THE OPPOSITE....

IVIVS-SHAPEDN-SHAPEDForceVelEx.: GUNN EFFECTOSCILLATOR (GaAs)Ex.: GASDISCHARGE

plateaujump PLATEAUS AND JUMPS DUE TO NEGATIVE DIFFERENTIAL FRICTION

(5,5)-(10,10) T = 50 KNO TERMINATIONS, NO BREATHING MODE: WHY FRICTIONAL PEAKS AND JUMPS?

n=v/aa=2.46 A FRICTIONAL PEAKS AND JUMPS DUE TOEXCITATION OF PSEUDOROTATIONAL MODES

l=5 pseudorotational mode above 710 m/s

CONCLUSIONS-- BULK NANOTUBE FRICTION IMPORTANT

-- WHEN APPLY FORCE AND NOT VELOCITY...

-- ..FIND VELOCITY PLATEAUS AND JUMPS

-- S-SHAPED NEGATIVE DIFFERENTIAL FRICTION

-- UNDERLYING MECHANISM IS NONLINEAR EXCITATION OF OUTER TUBE PSEUDOROTATIONAL MODES

X.H.ZHANG, U. TARTAGLINO,G.E.SANTORO, E..T., Surf. Science 601, 3693 (2007)

1. Dynamical pinning/depinning of a model solid lubricant between incommensurate sliders A. VANOSSI, G.E. SANTORO, N. MANINI, G. DIVITINI, E.T., PRL 97, 056101 (2006); PRL, to appear Oct/Nov 2007

2. High temperature nanofriction: skating vs. grazing T. ZYKOVA-TIMAN, D. CERESOLI, E.T., Nature Mat., 6,231 (2007)

3. Negative differential friction in sliding CNTs X.H.ZHANG, U. TARTAGLINO, G.E.SANTORO, E..T., Surf. Science 601, 3693 (2007)

4. Why do tyres skid on wet roads? B.N.J. PERSSON, U. TARTAGLINO, O. ALBOHR, E.T., Nature Mat. 3, 882 (2004); Phys. Rev. B 71, 035428 (2005).

PART 4.

WHY DO TYRES SKID ON WET ROADS? B.N.J. PERSSON, U. TARTAGLINO, O. ALBOHR, E.T., Nature Mat.3, 882 (2004); Phys. Rev. B 71, 035428 (2005);

B.N.J. PERSSON et al J. Phys.,Cond. Mat. 17 (2005) R1-R62

POWER IS NOTHING WITHOUT CONTROL

Aquaplaning: irrelevant below 60 Km/h

mu/slip=(v -wR)/v

EXPERIMENTAL

m = m + msurf bulkGROSCH 1963RUBBER FRICTION LARGELY BULK

BULK RUBBERRESPONSE FUNCTION(schem.)

E(w) = rubber complex response functionB.N.J. PERSSON (2001, 2002)

Figure of C(q)

FRICTION,FLASH TEMPERATURE,AND CONTACT AREAPERSSON 2006slip

ENTER WATER...RUBBER MAY SEALPUDDLES!

Dry and wet

SUMMARY-- INCOMMENSURATE SLIDING FULL OF SURPRISES

-- HIGH TEMPERATURE EFFECTS ON FRICTION CAN BE OPPOSITE: DROP FOR WEAR (AS IN SKATING), PEAK FOR GRAZING (AS IN TYPE 2 SUPERCONDUCTORS) -- TYRE ON WET ROAD: WATER SMOOTHEN OUT ROUGHNESS, REDUCE BULK DISSIPATION

PBC

Nanotube Corrugation(5,5)-(10,10)(11,2)-(12,12)Translational barrier: 0.23 meV/atRotational barrier: 1.12 meV/atTranslational barrier: 0.022 meV/atRotational barrier: 0.025 meV/atNONCHIRALCHIRAL

Computational techniqueClassical molecular dynamics.Rigid-ion interatomic potentials (BMH-Fumi-Tosi).Long range Coulomb interaction 3-dim. Ewald sum.slab geometry 40 of vacuum.Largest simulation: 8200 atoms.Born-Meyer-Huggins potential:

Conclusions (Part 1)Generalized FK for lubricated frictionRemarkable plateaus of asymmetric sliding of the lubricant, robust, universal Solitons are the key for this universality Can lead to backward motion of the lubricant film Implications on real systems?A. VANOSSI, G.E. SANTORO, N. MANINI, G. DIVITINI, E.T., to appear on PRL (2006)

INNER (5,5) TUBE VELOCITY POWER SPECTRUML=5 FREQ.~ WASHBOARDREVOLVER PSEUDOROTATION~ v~800 m/sec

Appendix

Carbon nanotubesX.H. Zhang, U. Tartaglino, E. Tosatti (unpub)