Bhushan B. Nanotribology and Nanomechanics: An Introduction

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13 Computer Simulations of Nanometer-Scale Indentation and Friction 677



[101



[0001]

[013



[101



Fig. 13.15. Snapshots of the

silicon nitride (a) surface,

(b) slide parallel to the edges

of the indenter, and (c) slide

across the indenter diago-

nal. The left-hand side shows

the surface when it is fully

loaded, while the right-hand

side shows the surface after

the tip has been withdrawn.

After [148] with the permis-

sion of the AIOP (2003)

6700

Potential energy (eV)

6600

6500

6400

6300

6200

Fig. 13.16. Potential energy as a function of rigid-layer separation generated from an MD

simulation of an elastic (nonadhesive) indentation of a hydrogen-terminated diamond (111)

surface using a hydrogen-terminated, sp

-hybridized tip. After [149] with the permission of

Elsevier (1992)

retracted. Not surprisingly, when the surface is bare and not terminated with hydro-

gen atoms, the repulsive interactions between the tip and the surface are minimized

and the tip indents the substrate without twisting [149]. Because carbon–carbon

678 Susan B. Sinnott et al.

Fig. 13.17. Illustration of

atoms in the MD simulat-

ion of the indentation of

a hydrogen-terminated dia-

mond (111) substrate with

a hydrogen-terminated, sp

hybridized tip at selected time

intervals. The ﬁgure illustrates

the tip–substrate system as the

tip was being withdrawn from

the sample. Large and small

spheres represent carbon and

hydrogen atoms, respectively.

After [149] with the permis-

sion of Elsevier (1992)

bonds are formed between the tip and the ﬁrst layer of the substrate, the indentation

is ordered (the surface is not disrupted as much by interacting with the tip) and the

eventual fracture of the tip during retraction results in minimal damage to the sub-

strate. The concerted fracture of all bonds in the tip gives rise to a single maximum

in the potential versus distance curve at large distances.

Harrison et al. [152,153] and Garg et al. [151,154] considered the indentation

of hydrogen-terminated diamond and graphene surfaces with AFM tips of carbon

nanotubes and nanotube bundles using MD simulations and bond-order potentials.

Tips consisting of both single-wall nanotubes and multiwall nanotubes were con-

sidered. The simulations predicted that nanotubes do not plastically deform during

tip crashes on these surfaces. Rather, they elastically deform, buckle, and slip as

shown in Fig. 13.18. However, as is the case for diamond tips indenting reactive di-

amond surfaces discussed above, strong adhesion can occur between the nanotube

and the surface that destroys the nanotube in the case of highly reactive surfaces, as

illustrated in Fig. 13.19.

To summarize, MD simulations reveal the properties of ceramic tips and sur-

faces with covalent or ceramic bonding that are most importantfor nanometer-scale

indentation. They predict that brittle fracture of the tip can occur that is sometimes

13 Computer Simulations of Nanometer-Scale Indentation and Friction 679

Fig. 13.18. Snapshots of the indentation of a single-wall nanotube (left-hand image)and

a bundle of nanotubes (right-hand image) on hydrogen-terminated diamond (111)

Fig. 13.19. Snapshot of

a single-wall carbon nano-

tube as it is withdrawn fol-

lowing indentation on a bare

diamond (111) surface. Af-

ter [151] with the permission

of APS (1999)

accompanied by strong adhesion with the surface. They also reveal the conditions

under which neither the tip nor the surface is aﬀected by the nanoindentation pro-

cess. The insight gained from these simulations helps in the interpretation of ex-

perimental data, and it also reveals the nanometer-scale mechanisms by which, for

example, tip buckling and permanent modiﬁcation of the surface occur.

680 Susan B. Sinnott et al.

13.3.2 Thin Films

In many instances, surfaces are covered with thin ﬁlms that can range in thickness

from a few atomic layers to several µm. These ﬁlms are more likely to have proper-

ties that diﬀer from the properties of bulk materials of similar composition, and the

likelihood of this increases as the ﬁlm thickness decreases. Nanoindentation is one

of the best approaches to determining the properties of these ﬁlms. Consequently,

numerous computational simulations of this process have been carried out.

For example, MD simulations have been used to study the indentation of metal

surfaces covered with liquid n-hexadecane ﬁlms, as illustrated in Fig. 13.20. As

the metal tip touches the ﬁlm, some of the molecules from the surface transfer to

the tip and this causes the ﬁlm to “swell”. As the tip continues to push against

the surface, the hydrocarbon ﬁlm wets the side of the tip. The simulations show

how the hydrocarbon ﬁlm passivates the surface and prevents the strong attractive

interactions discussed above for clean metal surfaces and tips from occurring.

In a series of MD simulations, Tupper and Brenner modeled the compression

of a thiol self-assembled monolayer (SAM) on a rigid gold surface using both

Fig. 13.20a–e. Cutaways of the side view from molecular dynamics simulations of a Ni tip

indenting a Au (001) surface covered with a hexadecane ﬁlm. In (e) only the metal atoms are

shown. Note how the hexadecane is forced out from between the metal surfaces. After [110]

with the permission of Elsevier (1995)

13 Computer Simulations of Nanometer-Scale Indentation and Friction 681

a smooth compressing surface [155] and a compressing surface with an asper-

ity [156]. These simulations showed that compression with the smooth surface pro-

duced a compression-induced structural change that led to a change in slope of the

simulated force versus compression curve. This transition is reversible and involves

a change in the ordered arrangement of the sulfur head groups on the gold surface.

A similar change in slope seemed to be present in the experimental indentation

curves of Houston and coworkers [157], but was not discussed by the authors. The

simulations with the asperity showed that the asperity is able to penetrate the tail

groups of the SAM, as illustrated in Fig. 13.21, before an appreciable load is appar-

ent on the compressing surface. This result indicates that it is possible to image the

head groups of a thiol self-assembled monolayer that are adsorbed onto the surface

of a gold substrate using STM, and consequently ordered images of these systems

may not be indicative of the arrangement of the tail groups.

Zhang et al. [158] used a hybrid MD simulation approach, where a dynamic

element model for the AFM cantilever was merged with a MD relaxation approach

for the rest of the system, to study the frictional properties of alkanethiol SAMs

on gold. They investigated the eﬀect of several variables like chain length, terminal

group, scan direction, and scan velocity. Their results show that friction forces de-

crease as the chain length of the SAMs increase. In the case of shorter chains such

Fig. 13.21. Snapshots illus-

trating the compression of

a self-assembled thiol ﬁlm

on gold for a smooth surface

(top) and a surface contain-

ing an asperity (bottom). The

asperity can penetrate and

disorder the ﬁlm tail groups

before appreciable load oc-

curs

682 Susan B. Sinnott et al.

as C

, the SAMs near the tip can be deformed by indentation, as illustrated in

Fig. 13.22. This behavior is predicted to be the cause of higher friction that occurs

for the short-length chains.

Harrison and coworkers have used classical MD simulations [153,159] to ex-

amine the indentation of monolayers composed of linear hydrocarbon chains that

are chemically bound (or anchored) to a diamond substrate. Both ﬂexible and rigid

single-wall,capped nanotubeswere usedas tips.The simulationsshowedthat inden-

tation causes the ordering of the monolayer to be disrupted regardless of the type of

tip used. Indentation results in the formationof gauche defects within the monolayer

and, for deep indents, results in the pinning of selected hydrocarbon chains beneath

the tube. Flexible nanotubes tilt slightly as they begin to indent the softer mono-

layers. This small distortion is due to the fact that nanotubes are stiﬀ along their

axial direction and more ﬂexible in the transverse direction. In contrast, when the

nanotubesencounter the hard diamondsubstrate, after “pushing”through the mono-

layer, they buckle. This process is illustrated in Fig. 13.23 and the force curves are

shown in Fig. 13.24. The buckling of the nanotube was previously observed when

single-wall, capped nanotubes were brought into contact with hydrogen-terminated

diamond (111) surfaces [151,152]. In the absence of the monolayer, the nanotube

tips encounter the hard substrate in an almost vertical position. This interaction with

the diamond substrate causes the cap of the nanotubes to be “pushed” inside the

nanotube (they invert). Increasing the load on the nanotubes causes the walls of the

tube to buckle. Both the cap inversion and the buckling are reversible processes.

That is, when the load on the tube is removed, it recovers its original shape.

Fig. 13.22. (a)Sideand

(b) top views of the ﬁnal

conﬁguration of a C

self-assembled monolayer on

Au (111) under a high normal

load of 1.2 nN at 300 K. The

tip is not shown in (b)for

clarity. After [158] with the

permission of the ACS (2003)

13 Computer Simulations of Nanometer-Scale Indentation and Friction 683

Fig. 13.23a–c. Snapshots

from the simulation of the in-

teraction of a ﬂexible single-

walled carbon nanotube with

a monolayer of C

chains

on diamond. The loads are

(a)19.8nN,(b)41.2nN,and

the permission of the ACS

(2003)

684 Susan B. Sinnott et al.

10

Indent time (ps)

(nN)

305 10 15 20 25

Fig. 13.24. The load on

the upper two layers of the

ﬂexible carbon nanotube in-

denter shown in Fig. 13.23

as a function of indentation

time for the nanoindentation

of the indicated hydrocarbon

monolayes on diamond. Af-

ter [159] with the permission

of the ACS (1999)

Deep indents of the hydrocarbon monolayers using rigid nanotubes result in

rupture of chemical bonds. The simulations also show that the number of gauche

defects generated by the indentation is a linear function of penetration depth and

equal for C

and C

monolayers. Thus, it is the tip that governs the number of

gauche defects generated.

Leng and Jiang[160]investigatedthe eﬀect of using tips coated with SAMs con-

taining hydrophobicmethyl (CH

) or hydrophilichydroxyl (OH) terminal groups to

nanoindent gold surfaces that also are covered with SAMs with the identical termi-

nal groups as the tip. Figure 13.25 contains snapshots for the indentation process

predicted to occur for terminal OH/OH interactions during compression and the

pull-oﬀ. The adhesion force of OH/OH pairs is calculated to be about four times

larger than that of CH

/CH

pairs, as shown in Fig. 13.26. This is due to the forma-

tion of hydrogen bonding between OH/OH pairs. This interaction is also expected

to increase the frictional force between monolayers with OH terminations.

Related MD simulations by Mate predict that the end groups on polymer lubri-

cants have a signiﬁcant inﬂuence on the lubrication properties of polymers [161].

For instance, ﬂuorinated end groups are predicted to be less reactive than regular

alcohol end groups. When ﬂuorinated ﬁlms are indented, the normal force becomes

Compression

Pull-off

Fig. 13.25. Snapshots from the OH/OH pair interaction during (a) compression and (b) pull-

oﬀ. After [160] with permission of the ACS (2002)

13 Computer Simulations of Nanometer-Scale Indentation and Friction 685

Fig. 13.26. Top: The force versus distance curve (indentation part only) for unbonded per-

ﬂuoropolyether on Si (100). The unreactive end groups were from a 10 Å-thick ﬁlm; the

reactive alcohol end groups were from a 30 Å-thick ﬁlm. The negative forces represent at-

tractive interactions between the tip and the surface. Bottom: Measured plots of friction and

load forces of the tip as it slides over the sample with the alcohol end groups. After [161]

with the permission of the APS (1992)

more attractive as the distance between the tip and ﬁlm decreases until the hard wall

limit is reached and the interactions become repulsive. In contrast, when AFM tips

indent hydrogenated ﬁlms, the forces become increasingly repulsive as the distance

between them decreases, as shown in Fig. 13.27 and Fig. 13.28. This predicted be-

havior is due to the compression of the end group beneath the tip. For the lubricant

molecules to be squeezed out from between the tip and the surface, the hydrogen

686 Susan B. Sinnott et al.

20

(Å)

100

120

1200 20406080100

OH OH

CH

OH/OH

20

5

(Å)

(nN)

1200 20406080100

/CH

4

3

2

1

Fig. 13.27. (a) Force–

distance curves and (b) tip

position (z

) versus sup-

port position (z

)forthe

OH/OH contact pair and the

/CH

contact pair. Af-

ter [160] with the permission

of the ACS (2002)

bonding between the two must ﬁrst be broken and this increases the force needed to

indent the system. As a result, a major eﬀect of the presence of alcohol end groups

is to dramatically increase the load that a liquid lubricant can support before failure

(solid–solid contact) occurs.

When atomically sharp tips are used to indent solid-state thin ﬁlms where there

is a large mismatch in the mechanical properties of the ﬁlm and the substrate, it

is diﬃcult to determine the true contact area between the tip and the surface dur-

ing nanoindentation. In the case of soft ﬁlms on hard substrates, pile-up can occur

around the tip that eﬀectively increases the contact area. In contrast, with hard ﬁlms

on soft substrates, “sink-in” is experienced around the tip that decreases the true

contact area.

A class of coatings that has received much attention is diamond-like amorphous

carbon (DLC) coatings. DLC coatings are almost as hard as crystalline diamond

and may have very low friction coeﬃcients (< 0.01) depending upon the growth

conditions [162–165]. They have therefore generated much interest in the tribologi-

cal community and there have been several MD simulation studies to determine the