Nanotribology Lab NC State

m

mg FN

v

Ff = FN W = Ff d

Ff

Nanotribology Part I: Atomic-scale mechanisms

for Friction: Phonons, electrons and quantum

effects, or….

J.Krim, North Carolina State University Work supported by NSF DMR & AFOSR Extreme Friction MURI

• Molecular dynamics simulations of contact

between carbon-based materials: Isolating

the effects of experimental variables. J.

Harrison and co-workers

• Localized thermal activation in atomic

friction: A study using transition state theoy:

Y. Dong and coworkers

• An Atomistic Study of wear and Failure of

Graphene Sheets when used as a solid

lubricant: E. Sandoz-Rosado & coworkers

Nanotribology I – Modeling and Applications

Monday session 1A Room 223

Magnetism

Phonon friction

Superconductivity

The forgotten:

Electrostatic friction

SJ Putterman and coworkers,

PRL2000, Nature 2008

Nf vf

appliedF

Amonton’s Law Viscous Friction

vf friction

mgFgravity

Free Body Diagram Free Body Diagram

Friction force is independent of velocity

for ordinary sliding speeds. – Charles A. Coulomb

gravityF

normalF

frictionf

‘‘De la Resistance Causee dans les Machines,’’

G. Amontons, Mem. del’Academie

Royale A 275–282 1699. A

Macroscopic Friction laws

Leonardo da Vinci

Codex Atlanticus

Codex Arundel

ca. 1500

k = 0.25

Charles-Augustin de Coulomb

Théorie des Machines Simple

1785

Coulomb’s representation of rough surfaces in sliding

contact, published in 1785. While establishing actual area

of contact, macroscopic surface roughness was definitively

ruled out as a fundamental mechanism for friction in the

1970’s by the surface science experiments demonstrating

that films one molecule thick can substantially change

friction, while having minimal impact on surface

roughness. The strength and form of a periodic substrate

potential at atomistic length scales does however have

major impact on friction.

Tomanek’s model of atomic-scale friction, a modern day version of the Coulomb

approach. (Zhong, 1990). (a) Potential energy V(x) of the Pd-graphite system as a

function of surface position x for external forces 3 nN (dots), 6 nN (dashed) and 9

nN (solid) Inset: The adsorption geometry in top view: a possible trajectory of the

Pd layer along x is shown by arrows. (b) Atomic-scale structure of the force along

the surface (dashed) and the friction force (solid line) for fext = 9 nN. (c) Pd

adsorption energy Ead versus adsorption height z above the surface of hexagonal

graphite for sixfold-hollow (H) (solid) and the on-top (T) sites (dashed)

Potential energy U(x,y) versus lateral position for one Mg adatom at

(x,y)=(8.02,8.02 Å) and one missing surface atom at (20.05,20.05 Å)

The scale is in units of the well depth of the gas-Mg atom pair potential

(15 K). (Right) Potential energy V(x,y,z) as a function of normal

distance above the pit (dash-dotted), and above a surface atom in the

unperturbed surface (full curve). The curves are shifted so that their

minima coincide. (Curtarola, 1999)

Update: to ~ 1970

A) Friction not explained by surface roughness

- Coulomb’s attempts unsuccessful

- Ruled out in 1950’s

B) Friction proportional to true contact area:

Ff = S Atrue

S, interfacial shear stress [N/m2]

Recover Amonton’s law:

Atrue FN

for elastic and plastic deformation of

almost all rough surfaces.

Researchers in the field of nanotribology examine micro- and

nano-contacts in well-controlled geometries prepared in advance of

the measurements. Often these contacts have thin films on the

surfaces. Knowledge of physical behaviors at this scale is thought

to be key to understanding how friction works on all length scales.

Nanotribology

Nano: 10-9 meters--molecular scale!

Tribology: The study of friction,

lubrication, and wear.

(a) On an open surface, both solid and

liquid films slides are characterized by

a viscous friction law. (QCM, ``blowoff

experiments)

(b) In a confined geometry(SFA, AFM?),

static friction and stick-slip phenomena

are ever-present and overall friction

levels are substantially higher for

comparable sliding speeds. This may

arise from a mobile particles’ pinning

of counterface materials?

“realistic contact” is a combination of both

(a) and (b)

(a)

(b)

vm

F

s k

Sliding friction geometries spanning atomic (a) to macroscopic (l) configurations. (a) Atomic

vibration, (b) Diffusive motion along a surface, (c) sliding of an adsorbed monolayer along a surface,

(d) monolayer slippage at the interface of a solid and a bulk liquid or gas, (e) electronic contributions

to friction of an adsorbate, (f) - (h) phononic models of frictional sliding, (i) disordered submonolayer

coverages of confined layers, (j) confined layers at full monolayer coverages, (k) single-asperity

contact and (l) multi-aserity contact. Ref. J. Krim, in preparation for Advance in Physics

Theoretical schematic of atomic scale friction geometries

Experimental probes of atomic scale friction geometries

“Spreading Diffusion and its Relation to Sliding Friction in Molecularly Thin Adsorbed Films”, A. Widom

and J. Krim, 49, 4154-4156, (1994); “Sliding friction measurements of molecularly thin ethanol and

pentanol films: How friction and spreading impact lubricity”, B.P. Miller and J. Krim, J. Low. Temp. Phys.,

157 Special issue on Wetting, Spreading, and Filling, (Nov. 2009); Pisov, S, Tosatti, E, Tartaglino, U,

Vanossi, A (2007), “Gold Clusters Sliding on Graphite: A Possible Quartz Crystal Microbalance

Experiment?” J. Phys. Condens. Matt. 19, 303015.

Submonolayer islands of physisorbed materials are generally

more mobile than individual particles, since they are

less commensurate with the substrate.

=DimN/kBt T

sD

Projections of atoms from the bottom and top surfaces into the plane

of the walls. In (A)–(C) the two walls have the same structure and

lattice constant, but the topwall has been rotated by 0, 11.6 or 90

degrees, respectively. In (D) the walls are aligned, but the lattice

constant of the topwall has been reduced by 12/13. Atoms can only

achieve perfect commensurability in case (A) (from (He, 1999)

Impact of physisorbed films on macroscale friction

How thin of an adsorbed layer or fraction of a layer can provide

lubrication?

When do adsorbed films increase friction?

“Friction, Force Chains and Falling Fruit ”,

Krim and R.P. Behringer,

Physics Today, 62, pp. 66-67 (Sept. 2009)

Theoretical and experimental challenges:

Where does the heat go?

Does the model thermostat address it correctly?

Do chemical reactions or melting occur?

What if the tip and substrate at not at the same temperature?

What is the temperature and velocity dependence?

Phonons

• The “good” friction……

The Tomlinson model was published by Prandtl! Figures 7-9 from Prandtl

(1928) depicting the mechanical analog of his model. A sliding piece G is

attached to a point tracer Z. The upper end of the sliding piece is attached to

a cord that is run over rollers and whose opposite end is attached to a mass

M connected to two springs. For particular combinations of mass and spring

strengths there are multiple equilibrium points that result in abrupt jumps

followed by mechanical vibration of the mass. The upper curves show the

path traced out by the tracer (Z) in the forward and backward direction.

(Prandtl, 1928)

(a-e) Detail of motion of one atom in the Independent

Oscillator, or Tomlinson model. When an atom moves to a

position where the barrier between two minima (b-d) has

disappeared (e), it is set into vibration and the energy is

dissipated as a phonon. (From Xu, 2007)

Numerical solutions and hybrid approaches for increasingly complex

models of phonon friction have become routine, increasing the ability to

both predict and control friction. Left: Figure 2 from (Xu, 2007) Right:

Crystalline solid such as that modeled by Sokoloff. (Sokoloff, 1990)

Diamond

Coated Tip

Direction of

motion Friction

Quadrant

Photodiode

Sample Stage

Sample

Diode To Cryostat

Thermal

Braid

Scan

tube

AFM data is also treated within a phononic friction model

Tomlinson Independent Oscillator model routinely used to interpret

AFM data (figure courtesy of P. Taborek) , which results in a prediction of thermolubricty

AFM probes of phononic friction: Cannara et al.

?

Cannara et al Science 2007 W.S. Zeng et al, Infrared Physics, vol. 33, pp459 (1992)

vm

F

We measure frequency and amplitude

change of the QCM.

Frequency shift is proportional to

mass uptake:

2

2 tf

q q

tfvf

The amplitude is related to the quality

factor: 1 1Q A

Sometime f can be reduced if there

is extreme slippage:

21 ( )mass

film

ff

We then calculate a slip time:

1 4 fQ

(Krim and Widom, PRB, v. 38, n.17, 1988)

Quartz Crystal Microbalance (QCM)

(QCM): Well described by phononic and electronic wear free

dissipative mechanisms: focus on phonons.

Atoms vibrate as they slide: more phonons modes and

higher phonon frequency with increasing temperature.

More phonon modes with higher coverage.

Surface commensurability determines dissipation levels.

Schematic of the Frenkel-Kontorova (left) and Frekel-

Kontorova-Tomlinson (right) models. These are more

applicable to adsorbed layers and extended interfaces.

QCM confirmations of phononic friction

Solid-liquid

Transition in

a Kr/Au layer

Krim, PRL 1991

Monolayer to

Bilayer in Xe/Ag

Daly, PRL 1996

Slip time versus

substrate potential

corrugation

Coffey, PRL 2006

Is temperature the same as vibration? Krim, Yu and Behringer,

PAGEOPH V.168 in press (Dec.1, 2011)

Fmmm m

Fmmm m

Schematic sketch of a model setup: Courtesy of M. Urbakh, See for example O.M. Braun, I. Barel and M. Urbakh, PRL, 2009. Friction has a peak like

enhancement at low temperature, associated with variable atomic slip lengths and vibration..

Unvibrated solid

Unvibrated “macroscopic monolayer: Solid substrate”

Top: The variation of the friction force

between the inner and outer tubes versus the

temperature for (4, 4)/(9, 9) DWCNTs with

tube lengths of 20 layers and 12 layers of

carbon atoms, respectively. The energy scale in

the LJ potential is ε = 2ε0. As temperature

increases, the thermal jump probability

saturates and the friction force becomes

insensitive to temperature. (From Chen, 2009)

Left: (a) Sliding velocity of the friction force

Fx under various normal loads for bare Al

surfaces under different normal forces. (b)

semi-logarithm plots of friction force versus

sliding velocity for different degrees of

hydroxylation. As the sliding velocity increases,

a crossover from a thermal activation to

viscous damping type behavior is observed.

(From Wei, 2009)

Electronic Friction

• Here’s where it starts to get bad, and

then perhaps ugly.

Electronic contributions to friction

• When an adsorbed layer slides, conduction electrons in the metal substrate are scattered into the surface, exciting electron-hole pairs*. This as a surface effect: It changes gradually at the superconducting transition.

• Resistive dissipation of image charges in the metal substrate, a bulk effect, which changes abruptly at the superconducting transition.

See: B.N.J. Persson, Sliding Friction, Physical Principles and Applications,

Springer Verlag, 1998.

Nanotribology Lab

Excited

Electron

Ohmic Loss

(Left) Slip time and shear stress s versus temperature for

nitrogen sliding on Pb(111), above and below the Pb

superconducting transition at Tc=7.2K. (Dayo, 1998b) (Right)

Friction coefficient versus temperature for a sharp cantilever tip

vibration at 5.3 kHz in close (but not contacting) proximity to a

Nb surface above and below the Nb superconducting transition at

9.2K. (Kisiel, 2011) Phononic contributions are sufficiently small

in both geometries to allow conduction electron contributions to

be detected.

both

Probing the electronic component of friction

Bruch’s theory would predict the effect to be

weaker for He than Nitrogen or Oxygen, Is it?

Electronic effects are observed in both QCM

Superconductivity-dependent Friction

A. Dayo, Alnasrallah, and Krim, PRL (1998); M. Highland

and J. Krim, PRL (2006) Superconductivity dependent

friction for nitrogen, helium and water on Pb(111)

B

Nitrogen

Helium

H2O

Normal state Pb(111) Superconducting Pb

FrictionNormal >Friction Superconducting

Unexpected observation (This could get ugly) Highland and Krim, PRL 2006, compared to Bruch 2000

Nanotribology Lab

• The changing magnetic field alters

the Frictional force.

– Diamagnetic and paramagnetic

films display different behavior – Lijnis Nelemans, High Field Magnet Laboratory,

Radboud University Nijmegen

No Magnet Cycled Magnet field

present

N2/Pb

(107s-1)

He/Pb

(107s-1)

O2/Pb

(para)

N2/Pb

(107s-1)

He/Pb

(107s-1)

O2/Pb

ηsc 2.5 0.51 Drop in

friction

0.084 0.065 Pinned

Layer ηn 5.1 1.3 0.714 1.14

Diamagnetic frog

ElectroStatics • The “forgotten” friction…

When opposing surfaces have like charges,

the friction decreases due to mutual

electrostatic repulsion. (Raviv, 2003,

Sokoloff, 2008) This occurs for example

when charged polymers are anchored to both

surfaces of a Surface Forces Apparatus.

But for nanoasperity contacts the friction

increases due to contact electrification

effects….

Park, JY, Qi, YB, Ogletree, DF, et al. (2007), “Influence of Carrier Density on the Friction Properties of Silicon Pn Junctions,” Phys. Rev. B 76

(6), 064108. Ogletree, DF, Park, JY, Salmeron, M, Thiel, PA (2006), “Electronic Control of Friction in Silicon pn Junctions,” Science 313 (5784),

pp. 186.

Electronic contributions to friction are commonly reported in

AFM experiments, particularly by M. Salmeron & coworkers

The surface vibrational modes in YBCO can

be finely tuned: Also a semiconducting

layer can be formed through oxygen

depletion in vacuum. This enhances

electrostatic friction. YBCO is thus an ideal

candidate for studies of the temperature

dependence of atomic scale friction

mechanisms.

Temperature dependence of friction in YBCO: a perfect test bed

Cannara et al Science 2007 W.S. Zeng et al, Infrared Physics, vol. 33, pp459 (1992)

Preparation and properties of YBa2Cu3O7−ı/Ag self-lubricating composites Qiaodang Ding, Changsheng Li, Lirong Dong, MinluWang, Yi Peng, Xuehua Yan, Wear 265 (2008) 1136–1141

• A: Friction coefficient of: (a) YBCO–steel and (b) steel–steel as function as temperature: load = 16N and sliding speed = 1.574 m/min.

• B: Friction coefficient as function of Ag content and sliding velocity at room temperature, load = 0.98N for Ag

• C

Steel/YBCO

Steel/YBCOAg

Superconductivity-dependent friction reported at the Macroscopic

scale: Is this a boundary layer effect??

: 75% YBCO 25% AgNO3

composite: samples were

derived from both Ag and

AgNO3 crystals

Steel/Steel

Consistent with prior reports,[1] magnetic force microscopy

can detect superconductivity through the repulsive effects

levitation in the superconducting regime. Altfeder and Krim,

JAP, in press (2012)

[1] H.J. Hug et al., Physica B, 194-196 (1994)

Superconductivity dependent friction in YBCO?? Repeat with AFM in

very controlled conditions

Lateral friction force versus applied load for an iron-coated AFM tip

on YBCO,

Altfeder and Krim, submitted

Superconductivity dependent friction in YBCO?? Repeat with AFM in

very controlled conditions

TC

T (K)

fric

tio

n c

oef

fici

en

t Levitation

Force

( nN

)

Superconductivity dependent friction in YBCO: Magnetic levitation

does not correlate with friction; neither do phononic effects, neither do

contact heating effects!

Electrostatic effects remain as strong contenders.

Nanotribology Lab NC State

m

mg FN

v

Ff = FN W = Ff d

Ff

Nanotribology Part I: Atomic-scale mechanisms

for Friction: Phonons, electrons and quantum

effects, or…. Much work remains…

Stay tuned for part II…….

J.Krim, North Carolina State University