Friction: From Atoms to Earthquakes

Friction: From Atoms to Earthquakes Sponsored by: National Science Foundation Collaborators: S. Hyun, L. Pei, J. F. Molinari,N. Bernstein, J. Harrison, B. Luan,G. He, M. H. Müser, L. Wenning Rough Surface ContactAtomic EffectsFriction Space Telescope Science Institute, 1/30/07

Friction and Every Day Life  Allows us to walk and drive Holds nails, screws, bolts, bricks, … in place Holds fabric and knots together Gives adhesives their strength Determines how things feel, texture of food  Wastes energy  ~20% in car engine Produces wear  abrades material destroys lubricants Economic cost of poor friction controlmore than 6% of GNP > $400 billion/year

Typical measurement of friction  Load v F Static friction Fs minimum force needed to initiate sliding. Kinetic friction Fk(v)  force to keep sliding at velocity v. Typically, Fk(v) varies only as log(v) and Fs>Fk(v) at low v Amontons’ Laws (1699):  Friction  load  constant =F/Load. Friction force independent of the apparentcontact area Aapp. But: Amontons coated all surfaces with pork fat Friction at zero and negative loads  Aapp Friction depends on history Nice to have data to show with green text

N F  WhyFriction Load, Independent of Apparent Area? Geometric explanation (Amontons,Parents,Euler,Coulomb) Surfaces are rough  Friction = force to lift up ramp formed by bottom surface  F=N tan  =tan  Problems:  Most surfaces can’t mesh, A/A0 small (Müser, Wenning, Robbins, PRL 86, 1295 (2001)) Roughening can reduce  (hard disks)  Monolayer of grease changes  not roughness  Once over peak, load favors sliding  kinetic friction=0 Static friction  Force to escape metastable stateHow can two surfaces always lock together?Kinetic friction  Energy dissipation as slideWhy is this correlated to static friction? Why does T matter?

Surfaces Often Rough on Many Scales  Self-Affine Height variation Dh over length ℓ Dh ℓH H<1Average slope Dh / ℓ ℓH-1  diverges as scale ℓ decreases  goes to zero as ℓ increases(J. Greenwood) H=0.5

Examples, with H=0.8(www.phys.ntnu.no) Picture of Mount Everest 10x10mm AFM image of clay Crack in a plexiglass block Fractured and polished surfaces self-affine over large range of scales Polished wood, granite, lucite H~0.6 Simple way of parameterizing large range of roughness scalesFind similar results for non-fractal experimental surfaces

Complex Contact Morphology – Area  Load Experimental contact area – Dieterich & Kilgore

Constant mean pressure in contact ‹ p ›=N/A at low N Controlled by rms local slope, D, not total roughness Elastic: /E’=D/kE’=E/(1-n2) =effective modulus =rms surface slope k(H,) from1.8 to 2.2Analytic predictions: Bush et al., k=(2p)1/2≈2.5 Persson k=(8/p)1/2≈1.6 Plastic: ‹p›≠ 3sy 3sy=single-asperity hardness Area  load N for nonadhesive contact Plastic E’/≡AE’/N Elastic

Complex Morphology Varies with Constitutive Law Power law distribution of connected areas ac: P(ac)  ac-t Connected regions are fractal ac rDfInconsistent with overlap model → Ideal Elastic Perfectly Plastic Overlap Modelt >2, Df=1.6 t≈ 2, Df=1.8 t=(2-H/2), Df=2Spread evenly Near highest peak All results for same surface, 0.015% in contact.

Geometrical Interlocking: F=N tan q Unlikely to mesh, F goes up as smooth Kinetic friction vanishes Elastic Metastability: Intersurface interaction too weak Mixing or Cold-Welding Hard to observe in sims. even with clean, unpassivated surfaces in vacuum Plastic Deformation (plowing) Load and roughness dependentHigh loads, sharp tips Mobile third bodies → “glassy state”hydrocarbons, wear debris, gouge, … Glass seen in Surface Force Apparatus,Robust friction, Mech. on many scales Friction Mechanisms in Contacts

Why is friction often proportional to load? • Not just Areal Load and FAreal since Areal varies with parameters like D that have weaker effect on m • Friction between clean surfaces very sensitive to local structure, surface orientation, … but measured m is not • Assume friction from yield stress s of molecular contacts Glassy systems: s rises linearly with pressure p If: Fs=Areal s(p) with s=0+p (Briscoe) • Then: Fs=Areal 0 +  Load s= Fs/Load =  + 0/Constant  if =Load/ Areal=const.or0 << (Independent of distribution of pressure)Friction at zero or negative load with adhesion, as observed •  Adsorbed layers give s=0+P with small t0 anda nearly independent of factors not controlled in experiment

Wall Geometries b) 8.2º a) 0º d) dtop/dbot=13/12 c)90º

Find:s > 0 for incommensurate walls with adsorbed film All incommensurate walls (b-d) give same ss independent of sliding direction: x, y, etc. s = 0 +  P up to P > 1GPa (-3~ 40MPa) quartermonolayer

Effect of Potential  indep. of coverage, chain length (n6), w or rc  increases with d/w  “rougher” surface default:ew=1sw=1 d=1.2 -3  40MPa

Geometric Explanation If pressure high enough  hard sphere limitRepulsive force balances pressure F ~P/c ~ 48 (w /w )(w /r)13 where c=coverage  r ~ w (c w /P w )1/13 Effective hard-sphere radius: insensitive to c, w , P almost linear in w Surface of closest approach depends on d/sw a  maximum slope as in geometric model  larger d/ w, steeper slope, bigger a w w d Analytic theory: Müser, Wenning, Robbins PRL 86, 1295, ‘01

Airborne hydrocarbon films can explain Amontons’ laws  Adsorbed layers (even diffusing) lock surfaces together producing a static friction consistent with macro experiments s=0+P for P up to ~1GPa    of order 0.1 crystal:  0.03 to 0.2, amorphous larger 0 small compared to typical P 0 < 10MPa s  independent of uncontrolled experimental parameters sliding direction  wall orientation thickness of adsorbed film (coverage) chain length n=1 to 6 (~C20H42 and smaller) a primarily depends on relative size of wall atoms and adsorbed molecules in this simple modelG. He, M. H. Muser and M. O. Robbins, Science 284, 1650 (1999); Phys. Rev. B64, 035413 (2001).

Friction: From Atoms to Earthquakes