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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
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
“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?
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.
Recommended