Bhushan B. Nanotribology and Nanomechanics: An Introduction

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13 Computer Simulations of Nanometer-Scale Indentation and Friction 717

200

Number of water molecules

Friction coefficient

250 300 350 400 450

0.2

0.4

0.6

0.8

1.0

Hydrophilic (OH/CH

)

Hydrophobic (CH

)

Relative humidity

Friction coefficient

20 40 60 80 100

0.2

0.4

0.6

0.8

1.0

Hydrophilic (COOH)

Hydrophobic (CH

)

Fig. 13.63. (a) Friction co-

eﬃcients for hydrophobic

(−CH

) and hydrophilic (50%

mixed −CH

/ −OH) mono-

layers as a function of water

molecules from MD simu-

lations at 300 K (H = 6.0Å),

and (b) scanning force mi-

croscopy measurements of

frictional forces of diﬀerence

surfaces under various rela-

tive humidities. After [248]

with the permission of the

AIP (2005)

separationdistance decreaseas thechain lengthincreases from6 to18 carbon atoms.

However,the friction forces are independentof the chain length and the shear veloc-

ity. The system size is shown to have an eﬀect on the sharpness of the slip transitions

but not on the dynamical events, as shown in Fig. 13.67.

In short, atomic-scale simulations show the relationship between elastic prop-

erties, degree of molecular disorder and friction of self-assembled thin ﬁlms that

illuminates the origin of the properties that are measured experimentally.

Nanoparticles

Nanoparticles are being considered for a wide variety of applications, including as

ﬁllers for nanocomposite materials, novel catalysts or catalytic supports, and com-

ponentsfor nanometer-scaleelectronicdevices[252].They havealso generatedcon-

siderable interest as possible new lubricant materials that have the potential to func-

718 Susan B. Sinnott et al.

è=180°

Chain tilt direction

è=270°

è=90°

è=0°

Fig. 13.64. Schematic illustration of the chain tilt and scan directions on alkanethiol

SAMs/Au(111) in hybrid molecular simulations; θ is the angle between the tip moving di-

rection and the chain tilt direction. The larger spheres represent substrate Au atoms, smaller

spheres sulfur atoms in molecular chains, and zigzag lines molecular chains. After [249] with

the permission of the ACS (2003)

tionas “nanoballbearings”with exceptionallylowfrictioncoeﬃcients.Thenanopar-

ticles of most interest for tribological applications include C

[253–265], carbon

nanotubes [266–273], and MoO

nanoparticles [274,275], among others [276].

The experiments report wide variations in frictional coeﬃcients (for instance,

values of 0.06 to 0.9 have been measured for C

) that may be caused by diﬀer-

ences in the experimental methods used, the thickness of the nanoparticle layer or

island,the atmosphere(argonversus air, levels of humidity)used,and the transfer of

nanoparticles to the FFM tips. As a result, there is much that remains to be clariﬁed

about the tribological behavior of nanoparticle ﬁlms.

In the case of C

, the mechanistic response to applied shear forces has not

been deﬁnitively determined. For example, some experimental studies show evi-

dence of C

molecules rolling against the substrate, each other, or the sliding sur-

faces [253,258,260,263,265]while others hypothesize that the low friction of C

ﬁlms is due in part to blunting of the tip by transfer of fullerene molecules to the

tip apex. Fullerene ﬁlms are found experimentally to have dissipation energies and

shear strengths that are a full order of magnitude lower than the values that are

typical for boundary lubricants [277]. Experimental testing of the frictional proper-

ties of fullerenes reveal low mechanical stability accompanied by progressive wear

and transfer of fullerene materials when they are only physisorbed on a solid sur-

face [278]. Furthermore, measurements with a FFM show that under certain condi-

tions,adsorbedfullereneﬁlmsdeteriorateatpressuresas lowas about0.1GPa[279].

The challenge is therefore to obtain mechanically stable, ordered molecular ﬁlms of

fullerenes ﬁrmly attached to a solid substrate.

13 Computer Simulations of Nanometer-Scale Indentation and Friction 719

Scan direction è (deg)

Frictional force (nN)

0.05

0.1

0.15

0.2

300K

90 180 270 360

Scan direction è (deg)

Frictional force (nN)

0.20

1.0K

90 180 270 360

0.40

0.60

0.80

Fig. 13.65. Frictional force as

a function of scan direction

from hybrid simulations for

SAMs on Au(111)

at (a) 300 K and (b)1.0K.

Frictional force is the small-

est when scanned along the

tilt direction, the largest when

scanned against the tilt di-

rection, and between when

scanned perpendicular to the

tilt direction at both temp-

eratures. After [249] with the

permission of the ACS (2003)

There have been several MD simulation studies to investigate the tribological

properties of fullerenes. A representative study by Legoas et al. [280] investigated

the experimentally observed low-friction system of C

molecules positioned on

highly oriented pyrolytic graphite. The results show that decreasing the van der

Waals interaction between a C

monolayer and graphite sheets, and the charac-

teristic movements of graphite ﬂakes over C

monolayers, explains the measured

ultralow friction of C

molecules and graphite sheets.

Several MD simulation studies have also been carried out on the tribological

properties of carbon nanotubes. For example, simulations by Buldum et al. and

Schall et al. [266, 269] indicate that single-wall carbon nanotubes roll when their

honeycomb lattice is “in registry” with the honeycomb lattice of the graphite. If

this registry is not present, the carbon nanotubes respond to applied forces from

an AFM by sliding. This behavior is nicely summarized in Fig. 13.68. These MD

simulationﬁndingswere simultaneouslyconﬁrmedin experimentalstudiesby Falvo

et al. [268]. Experimental studies of multiwall carbon nanotubes on graphite [272]

show similar evidence of nanotube rolling when the outer tube is pushed.

720 Susan B. Sinnott et al.

a) b) c)

Fig. 13.66. Wireframe images of n = 18 SAMs at ﬁxed separations of (a) d = −5.2Å(low

pressure, under compression only) (b) d = −10.2 Å (high pressure, under compression only)

and (c) d = −10.2 Å (high pressure, under shear). After [251] with the permission of the ACS

(2005)

250

Distance (Å)

Shear stress (MPa)

250

500

142 4 6 8 10 12

250

250

500

250

250

500

250

250

500

Fig. 13.67a–d. Shear stress

as a function of system size

for n = 6 SAMs correspond-

ing to a pressure of 200 MPa

at v = 1.0m/s: (a) 100 chains

per surface, (b) 400 chains

per surface, (c) 1600 chains

per surface, and (d) 16 point

box average of system with

100 chains per surface. Af-

ter [251] with the permission

of the ACS (2002)

The tribological properties of nanotube bundles are important, as it is well-

known that carbonnanotubes agglomeratetogether veryreadily to form bundles and

are often grown in bundle form [252]. An experimental study by Miura et al. [273]

of carbon nanotube bundles being pushed around on a KCl surface with an AFM

13 Computer Simulations of Nanometer-Scale Indentation and Friction 721

Slide

Roll

Slide

Graphite

substrate

Bond order

Lennard-Jones

(612)

(10,10) nanotube

Impulse

In registry  slide

Out of registry  slide-r

oll-slide

Fig. 13.68. Dynamics of a nanotube on a graphite surface. When the nanotube and graphite

plane are out of registry, the nanotube slides as it slows down from an initial impulse (upper

right panel). When the nanotube is oriented such that it is in registry with the graphite, it

slows by a combination of rolling and sliding

tip indicates that bundles of single-wall carbon nanotubes can be induced to roll in

a manner that is similar to the rolling observed for multiwall nanotubes.

MD simulations by Ni et al. [270, 271] considered the responses of horizon-

tally and vertically aligned single-wall carbon nanotubes between two hydrogen-

terminated diamond surfaces, where the top surface is slid relative to the bottom

surface. The movementof the carbon nanotubes in response to the shear forces was

predicted to be simple sliding for both orientations. Interestingly, the simulations do

not predict rolling of the horizontally arranged carbon nanotubes even when they

are aligned with each other in two-layer and three-layer structures. Instead, at low

compressive forces, illustrated in Fig. 13.69, the nanotube bundles slide as a single

unit, and at high compressive forces, also illustrated in Fig. 13.69, the deformed

carbon nanotubes closest to the topmost moving diamond surface start to slide in

a motion reminiscent of the movement of a tank or bulldozer wheel belt. However,

when these moving carbon nanotube atoms would have turned the ﬁrst corner at the

top of the ellipse, they encounter the neighboring nanotube and cannot slide past it.

This causes them to deform even further, form cross-links with one another, and,

in some cases, move in the reverse direction to the sliding motion of the diamond

surface. This causes the large oscillations in the normal and lateral forces plotted in

Fig. 13.69.

The responses of the horizontally arranged carbon nanotubes are substantially

diﬀerent from the responses of the vertically arranged nanotubes at high compres-

sion, as can be seen by comparing Figs. 13.69 and 13.70. The vertical, capped car-

bon nanotubes are quite ﬂexible and bend and buckle in response to applied forces.

As the buckle is forming, the normal force decreases then stabilizes in the buck-

led structure, as illustrated in Fig. 13.70. As the topmost diamond surface slides,

the buckled nanotubes swing around the buckle “neck” which helps dissipate the

applied stresses. For this reason, the magnitudes of the lateral forces are not signiﬁ-

722 Susan B. Sinnott et al.

2.5

200

Displacement (Å)

Force (nN)

100

100

200

300

400

22.50 2.5 5 7.5 10 12.5 15 17.5 20

1 = Normal force

2 = Lateral force

No ompression

Compression 13.7 GPa

a) b)

Fig. 13.69. Top: Snapshots from simulations that examine the sliding of the topmost diamond

surface on horizontally arranged nanotubes at diﬀerent compressions; (a) is at a pressure of ≈

0GPa;(b) is with a pressure of 13.7GPa.Bottom: Plots of the normal and lateral components

of force during sliding of the top diamond’s surface on horizontally arranged nanotubes as

a function of the displacement of the top diamond surface with respect to the diamond surface

on the bottom

cantly diﬀerent for the vertical nanotubes at low and high compression, as indicated

in Fig. 13.70.

When the ratio of the frictional (lateral) force to the normal force is taken to

calculate friction coeﬃcients for these systems, high, nonintuitive values were ob-

tained. As outlined by Ni et al. [270], this is because the actual contact area of the

nanotubesis not proportionalto the sliding force. In the case of the horizontal nano-

tube bundles, the tubes are able to deform and signiﬁcantly change their contact

area with the sliding surface with minimal change in the normal force, as shown in

Fig. 13.69. In the case of the vertical nanotubes, the contact area remains approxi-

mately the same regardless of the initial loading force because of the ﬂexibility of

the nanotubes. This causes the lateral forces to change only slightly with signiﬁcant

changes in the normal force, as shown in Fig. 13.70. This analysis indicates that

care must be taken in calculating friction coeﬃcients for nanotube systems. Recent

experiments by Dickrell et al. [281] show good agreement with these predictions, as

shown in Fig. 13.71.

13 Computer Simulations of Nanometer-Scale Indentation and Friction 723

Displacement (Å)

Force (nN)

100

100

200

300

0 5 10 15 20 25

1 = Normal force

2 = Lateral force

Compression 1.44 GPa

Compression 11.5 GPa

Fig. 13.70. Top: Snapshots

from simulations that exam-

ine the sliding of the topmost

diamond surface on vertically

arranged nanotubes with one

set of capped ends compressed

at a pressure of 11.5GPa.Bot-

tom: Plots of the normal and

lateral components of force

during sliding of the top dia-

mond’s surface on vertically

arranged nanotubes as a func-

tion of the displacement of

the top diamond surface with

respect to the diamond surface

on the bottom

To summarize, this section shows that nanoparticles show some promise as lu-

bricating materials due to their exceptionallylow friction coeﬃcientsin experiments

and simulations. Some nanopaticles show lattice-directed sliding on substrates due

to their unique atomic structures. However, there is much that remains to be done

before the nanometer-scale friction of these materials is well understood.

Solid State

Surfaces are able to slide over eachother at highloads with a minimum of resistance

from friction in the presence of liquid lubricants. Some solid thin ﬁlms can also ful-

ﬁll these functions and, when they do, are termed solid lubricants. Solid lubricants

are generally deﬁned as having friction coeﬃcients of 0.3 or less and low wear.

Bowden and Tabor showed how thin solid ﬁlms can reduce friction as fol-

lows [283]. The total friction force F

is given as

= AF

+ F

, (13.11)

where F

is the plowing term, A is the area of contact and F

is the shear strength of

the interface. If the surfaces are soft, F

will be reduced while the other parameters

will increase. However, if the surfaces under the solid ﬁlm are very stiﬀ, A and F

will decrease thereby decreasing friction. The properties speciﬁc to the ﬁlm will

also have an eﬀect on friction. For instance, if the ﬁlms are less than 1 µmthick,

the surface asperities will be able to break through the ﬁlm to eventually cause wear

between thesurfacesunder normalcircumstances.On the otherhand, if the lubricant

724 Susan B. Sinnott et al.

Fig. 13.71. Coeﬃcient of

friction data versus track

position collected for one

full cycle of reciprocating

sliding for nanotubes that are

vertically and transversely

aligned. After [281]

ﬁlm is too thick, there will be increased plowing and wear that causes the frictional

forces to increase. It is important that the lubricant not delaminate in response to the

frictional forces, so strong bonds between the lubricant and the surface are required

for a solid state lubricant to be eﬀective.

The most common materials used as solid lubricants have layered structures

like graphite or MoS

, that, as discussed above, experience low friction. It is not

necessary for the lubricant ﬁlm to have a layered structure to give low friction. For

example, diamond-like carbon has some of the lowest coeﬃcients of friction meas-

ured and yet does not have a layered structure. Similarly, not all layered structures

are lubricants. For instance, mica gives a relatively high coeﬃcient of friction (> 1).

The atomic-scale tribological behavior that occurs when a hydrogen-terminated

diamond (111) counterface is in sliding contact with amorphous, hydrogen-free,

13 Computer Simulations of Nanometer-Scale Indentation and Friction 725

DLC ﬁlms was examined using MD simulations by Gao et al. [282]. Two ﬁlms,

with approximately the same ratio of sp

–sp

carbon but diﬀerent thicknesses, were

examined. Similar average friction was obtained from both ﬁlms in the load range

examined. A series of tribochemical reactions occur above a critical load that result

in a signiﬁcant restructuringof the ﬁlm, which is analogousto the “run-in” observed

in macroscopic friction experiments, and reduces the friction. The contribution of

adhesion between the counterface and the sample to friction is examinedby varying

the saturation of the counterface. The friction increases when the degree of satura-

tion of the diamond counterface is reduced by randomly removing hydrogen atoms.

Lastly, two potential energy functions that diﬀer only in their long-range forces are

used to examine the contribution of long-range interactions to friction in the same

system (as illustrated in Figs. 13.72 and 13.73).

MD simulations were also recently used by Gao et al. [284] to examine the

eﬀects of the sp

–sp

carbon ratio and surface hydrogen on the mechanical and

tribological properties of amorphous carbon ﬁlms. This work showed that, in addi-

tiontothesp

–sp

ratio of carbon, the three-dimensional structures of the ﬁlms are

a) b)

c) d)

Fig. 13.72a–d. A series of chemical reactions induced by sliding of the counterface over the

thin ﬁlm under an average load of 300 nN. (a) The sliding causes the rupture of a carbon–

hydrogen bond in the counterface. (b) The hydrogen atom is incorporated into the ﬁlm and

forms a bond to a carbon atom in the ﬁlm. (c) A bond is formed between the unsaturated

carbon atoms in the ﬁlm and the carbon that suﬀered the bond rupture in the counterface, and

continued sliding causes this carbon to be transferred into the ﬁlm. (d) The transferred carbon

forms a bond with another carbon in the counterface. The counterface has slid 0.0 (a), 15.9

(b), 26.1 (c), and 30.5Å(d). After [282] with the permission of the ACS (2002)

726 Susan B. Sinnott et al.

600

Load F

(nN)

Friction F

(nN)

100

150

200

250

5004003002001000

90%

100%

80%

Fig. 13.73. Friction curves

for the thin ﬁlm system with

a counterface that is 100%

hydrogen-terminated (open

squares), 90% hydrogen-

terminated (ﬁlled squares),

and 80% hydrogen-terminated

(open circles). After [282]

with the permission of the

ACS (2002)

important when determining the mechanical properties of the ﬁlms. For example,

it is possible to have high sp

-carbon content, which is normally associated with

softer ﬁlms, and large elastic constants. This occurs when sp

-ringlike structures

are oriented perpendicular to the compression direction. The layered nature of the

amorphous ﬁlms examined leads to novel mechanical behavior that inﬂuences the

shape of the friction versus load data, as illustrated in Fig. 13.74. When load is ap-

plied to the ﬁlms, the ﬁlm layer closest to the interface is compressed. This results in

the very low friction of ﬁlms I and II up to approximately 300 nN and the response

of ﬁlms IV and V up to 100 nN. Once the outer ﬁlm layers have been compressed,

additional application of load causes an almost linear increase in friction for ﬁlms I

and II as well as IV and V. Film III has an erratic friction versus load response due

to the early onset of tribochemical reactions between the tip and the ﬁlm.

Load F

(nN)

Friction F

(nN)

100

120

140

160

180

800100 200 300 400 500 600 700

III

Amorphous

carbon films

Fig. 13.74. Average friction

versus load for ﬁve amor-

phous carbon ﬁlms. Films

I–III are hydrogen-free and

contain various ratios of sp

to-sp

carbon. Films IV and V

are both over 90% sp

carbon

and have surface hydrogena-

tion