Bhushan B. Nanotribology and Nanomechanics: An Introduction

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13 Computer Simulations of Nanometer-Scale Indentation and Friction 707

2

Shear stress ô/ô

/å

= 0.1

1

34234234

/å

= 1.0

2

T = 20K

T = 100K T = 300K

Displacement (D/a)

Heat flow Q/Q

1.0

/å

= 0.1

/å

= 1.0

0.5

h) i)

0.25 0.5 0.75 0.25 0.5 0.75 0.25 0.5 0.75

1

0.1

0.2

0.3

Fig. 13.50a–j. Data from molecular dynamics simulations of the sliding of the surfaces shown

in Fig. 13.32. (a)–(f) The shear stress and (g)–(j) the heat ﬂow as a function of sliding for

normal and reduced interfacial strengths. The plots show how the calculated values change

with system temperature. After [174] with the permission of the APS (1993)

Velocity v/v

Friction <ô >/ô

0.5

1.0

1.5

0.01 0.02 0.03 0.04 0.05 0.06

T = 300K

T = 200K

Fig. 13.51. A plot of calcu-

lated values of the average

interfacial shear stress as

a function of the velocity of

sliding of the two surfaces

shown in Fig. 13.33. Af-

ter [174] with the permission

of the APS (1993)

708 Susan B. Sinnott et al.

fected by the rate of sliding and is much larger at high sliding rates than small rates,

as indicated in Fig. 13.52. The simulations further show that the inclination angle

of the chains decreases much more slowly than the shear stress, and the shear stress

maximum is more pronounced if there is hysteresis in the chain orientations.

Typical friction loops for tips that are functionalized and sliding against surfaces

that are functionalized in the same manner as illustrated in Fig. 13.25 are shown in

Fig. 13.53. The friction force between the OH/OH pairs is signiﬁcantly larger than

the friction force between the CH

/CH

pairs. This is due to the formation and

breaking of hydrogen bonds during the shearing for the OH/OH pairs. The mean

forces vs. load forces for the OH/OH and CH

/CH

pairs given in Fig. 13.54 are

reduced by the tip radius.

MD simulations by Manias et al. considered the shearing of entangled oligomer

chains that are attached to sliding surfaces, as illustrated in Fig. 13.55 [234]. They

ﬁnd that slip takes place within the ﬁlm and that this occurs through changes in the

chain conformations. Increased viscosity is predicted at the ﬁlm–surface interface

Fig. 13.52. Snapshots of sliding walls with attached polymers in a solvent. Right-hand ﬁgure

illustrates the sliding process at low sliding rates while the left-hand ﬁgure illustrates the

sliding process at high sliding rates. After [41] with the permission of the CCLR (2002)

10

X displacement (Å)

Friction force (nN)

5101520

5

OH/OH

/CH

Fig. 13.53. Typical friction

loops for the systems shown

in Fig. 13.25 for CH

/CH

and OH/OH pairs under

a contact load of 0.2nN.Af-

ter [160] with the permission

of the ACS (2002)

13 Computer Simulations of Nanometer-Scale Indentation and Friction 709

compared to the middle of the ﬁlm, which results in a range of viscosities across the

ﬁlm as one moves away from the points of sliding contact.

To summarize this section, experiments and MD simulations show similar

stick/slip transitions that occur for thin ﬁlms of liquid between two sliding solid

surfaces. Frictional properties are found to depend to a signiﬁcant degree on molec-

ular shape, whether the molecules are grafted on the surfaces or merely absorbed

on them, and the degree of tilting in the case of molecular chains. In the case of

long-chain molecules, temperature is found to aﬀect the frictional force because the

Load force F

/R (nN/nm)

Friction force F

/R (nN/nm)

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

/CH

(á = 0.045)

OH/OH (á = 2.4)

Fig. 13.54. Friction force

versus contact load from the

systems shown in Fig. 13.25

for CH

/CH

and OH/OH.

After [160] with the permis-

sion of the ACS (2002)

Equilibrium (no flow) Under shear flow

Wall affinity 1.0kT

Wall affinity 2.0kT

Fig. 13.55. Changes in the conformation of adsorbed hydrocarbon chains on weakly (top)

and strongly (bottom) physisorbing surfaces at equilibrium and under shear. After [234] with

the permission of the ACS (1996)

710 Susan B. Sinnott et al.

mechanical energy stored in long-chains can be converted into thermal energy by

friction.

Self-Assembled Structures

There have been numerous experimental studies of friction on SAMs on solid sur-

faceswith AFM and FFM.The experimentalresults revealrelationshipsamongelas-

tic compliance, topography and friction on thin LB ﬁlms [235]. For example, they

have detected diﬀerences in the adhesive interactions between the microscope tips

and CH

and CF

end groups[106]. Fluorocarbon domains generally exhibit higher

friction than the hydrocarbon ﬁlms, which the authors attribute to the lower elastic-

ity modulusof the ﬂuorocarbonﬁlms thatresults in a largercontact area betweenthe

tip and the sample [235–237]. Perry and coworkers examined the friction of alka-

nethiols terminated with −CF

and −CH

[238]. The lattice constants for both ﬁlms

are similar and the ﬁlms are well-ordered. The friction of the SAMs with chains that

are terminated with ﬂuorine end groups is larger than the friction of the SAMs with

chains that are terminated with hydrogen end groups. However, the pull-oﬀ force

is similar in both systems, which implies that these end groups have similar contact

areas. The authors speculate that the larger −CF

groups interact more stronglywith

adjacent chains than the −CH

-terminated chains. Therefore, the ﬂuorinated chains

have more modes of energy dissipation within the plane of the monolayer and, thus,

have larger friction.

Molecular disorder of the alkyl chains at the surface can also aﬀect the fric-

tional properties of self-assembled ﬁlms if the layers are not packed too closely

together [240]. Indentation can induce disorder in the chains that then compress as

the tip continues to press against them. If the tip presses hard enough, the ﬁlm hard-

ens as a result of the repulsive forces between the chains. However, if the chains are

tilted, they bend or deform when the tip pushes on them in a mostly elastic fashion

that produces long lubrication lifetimes. At low contact loads of about 10

−8

N, wear

usually occurs at defect sites, such as steps. Wear can also occur if there are strong

adhesive forces between the ﬁlm and the surface [241].

The friction of model SAMs composed of alkane chains was examined us-

ing MD simulations with bond-order and LJ potentials by Mikulski and Harri-

son [239, 242]. These simulations show that periodicities observed in a number of

system quantities are the result of the synchronized motion of the chains when they

are in sliding contact with the diamond counterface. The tight packing of the mo-

nolayer and commensurability of the counterface are both needed to achieve syn-

chronized motion when sliding in the direction of chain tilt. The tightly packed

monolayer is composed of alkane chains attached to diamond (111) in the (2×2) ar-

rangementand the loosely packedsystem has approximately30% fewer chains. The

average friction at lowloads is similar in boththe tightly and looselypacked systems

at low loads. Increasing the load, however, causes the tightly packed monolayer to

have signiﬁcantly lower friction than the loosely packed monolayer (Fig. 13.56).

While the movement of chains is somewhat restricted in both systems, the tightly

packed monolayer under high loads is more constrained with respect to the move-

13 Computer Simulations of Nanometer-Scale Indentation and Friction 711

100

Load (nN)

Friction (nN)

200 300 400 500 600 700 800 900 1000

Tight packing

Loose packing

Fig. 13.56. Friction as a func-

tion of load when a hydrogen-

terminated counterface is

in sliding contact with C

alkane monolayers. Af-

ter [239] with the permission

of the ACS (2001)

ment of individual chains than the loosely packed monolayer, as illustrated in

Fig. 13.57. Therefore, sliding initiates larger bond-length ﬂuctuations in the loosely

packed system, which ultimately lead to more energy dissipation via vibration and,

thus, higher friction. Thus, the eﬃcient packing of the chains is responsible for the

lower friction observed for tightly packed monolayers under high loads.

Several AFM experiments have examined the friction of SAMs composed of

chains of mixed lengths [243]. For example, the friction of SAMs composed of

Fig. 13.57. Snapshots of tightly packed C

alkane monolayers on the left, and loosely packed

monolayers on the right under a load of about 500 nN. The chains in both systems are ar-

ranged in a (2×2) arrangement on diamond (111). The loosely packed system has 30% of

the chains randomly removed. The sliding direction is from left to right. After [239] with the

permission of the ACS (2001)

712 Susan B. Sinnott et al.

spiroalkanedithiols was examined by Perry and coworkers [244]. The eﬀects of

crystalline order at the sliding interface were examined by systematically shortening

some of the chains. The resulting increase in disorder at the sliding interface causes

an increase in friction.

The link between friction and disorder in monolayers composed of n-alkane

chains was recently examined using MD simulations by Harrison and cowork-

ers [245]. The tribological behavior of monolayers of 14 carbon atom-containing

alkane chains, or pure monolayers, was compared to monolayers that randomly

combine equal amounts of 12 and 16 carbon-atom chains, or mixed monolayers.

Pure monolayers consistently show lower friction than mixed monolayers when

sliding under repulsive (positive) loads in the direction of chain tilt. These MD

simulations reproduce trends observed in AFM experiments of mixed-length alka-

nethiols [243] and spiroalkanedithiols on Au [246].

Because the force on individual atoms is known as a function of time in MD

simulations, it is possible to calculate the contact forces between individual mono-

layer chain groups and the tip, where contact force is deﬁned as the force between

the tip and a −CH

or a −CH

- group in the alkane chains. The distribution of

contact forces between individual monolayer chain groups and the tip are shown

in Fig. 13.58. It is clear from these contact force data that the magnitude, or scale

of the forces, is similar in both the pure and the mixed monolayers. In addition, it

is also apparent that the pure and mixed monolayers resist tip motion in the same

way. That is, the shape of the histograms in the positive force intervals is similar.

In contrast, the contact forces “pushing” the tip along diﬀer in the two monolayers.

The pure monolayers exhibit a high level of symmetry between resisting and push-

ing forces. Because the net friction is the sum of the resisting and pushing forces,

the symmetry in these distributions of the pure monolayers results in a lower net

friction than the mixed monolayers. Thus, the ordered, densely packed nature of

the pure monolayers allows the energy stored when the monolayer is resisting tip

motion (positive forces) to be regained eﬃciently when the monolayer “pushes” on

the tip (negative forces). The distribution of negative contact forces in the mixed

monolayers is diﬀerent from the distribution of the positive forces. For this reason,

mechanical energyis not eﬃciently channeled back into the mixed monolayeras the

tip passes over the chains and, as a result, the friction is higher. The range of motion

of the chains is monitored by computing the deviation in a chain group’s position

compared to its starting position, as illustrated in Fig. 13.59. It is clear from analyz-

ing these data that the increased range of motion is linked to large contact forces.

The increased range of motion of the protruding tails in the mixed system prevents

the eﬃcient recovery of energy during sliding (negative contact force distribution)

and allows for the dissipation of energy.

The pure monolayers exhibit marked friction anisotropy. The contact force dis-

tribution changes dramatically as a resultof the change in sliding direction, resulting

in an increase in friction (Fig. 13.58). Sliding in the direction perpendicular to chain

tilt can cause both types of monolayers to transition to a state where the chains are

13 Computer Simulations of Nanometer-Scale Indentation and Friction 713

0.8

Force interval (nN)

Net force (nN)

0.4 0 0.4 0.8

Pre-transition

Post-transition

0.4

0.4

0.8

0.8

Pure SAM

Mixed-SAM

0.4

0.4

0.8

Pure SAM

Fig. 13.58. Thedistribution of contact forces along the sliding direction (friction force). Inthe

upper panel, the forces for the mixed and pure system sliding in the direction of chain tilt are

shown. The forces for the pure system sliding in the transverse direction to the chain tilt are

shown in the lower panel. Positive force intervals correspond to chain groups that resist tip

motion while negative intervals correspond to chain groups that “push” the tip in the sliding

direction. Forces from four runs with independent starting conﬁgurations are binned for all

sets of data

4

Sliding distance (Å)

Deviation (Å)

1020304050607080

Mixed SAM

4

Pure SAM

Fig. 13.59. Trajectories of individual chain groups that generate the largest contact forces

when sliding in the direction of chain tilt for both the pure and mixed monolayer systems.

The deviation is deﬁned as the change in position along the sliding direction relative to the

chain group’s starting position. (The positions are averaged over 2000 simulation steps)

714 Susan B. Sinnott et al.

primarily tilted along the sliding direction. This transition is accompanied by a large

change in the distribution of contact forces and a reduction in friction.

Recently, the response of monolayers composed of alkyne chains, which con-

tain diacetylene moieties, to compression and shear [247] was examined using MD

simulations. These are the only simulations to date that show that compression and

shear canresult in cross-linking,or polymerization,between chains. Theverticalpo-

sitioningof the diacetylenemoieties within the alkynechains (spacer length)and the

sliding direction both have an inﬂuence on the pattern of cross-linking and friction.

Compression and shear cause irregular polymerization patterns to be formed among

a) b)

Fig. 13.60. (a) Perpendicular-, (b) tilted-, and (c) end-chain monolayer systems after com-

pression to 200 nN and pull-back of the hydrogen-terminated tip. Large, dark spheres in the

hydrocarbon monolayers represent cross-linked atoms with sp

hybridization. Dark, small

spheres represent hydrogen atoms that are initially on the hydrogen-terminated amorphous

carbon tip. After [247] with the permission of the ACS (2004)

13 Computer Simulations of Nanometer-Scale Indentation and Friction 715

the carbon backbones, as illustrated in Fig. 13.60. When diacetylene moieties are

located at the ends of the chains closest to the tip, chemical reactions between the

chains of the monolayer and the amorphous carbon tip occur causing the friction to

increase 100 times, as indicated in Fig. 13.61. The friction between the amorphous

carbon tip and all of the diacetylene-containing chains is larger than the friction be-

tween a hydrogen-terminated diamond counterface and tightly packed monolayers

composed of n-alkane chains [239]. This is attributed to the disorder at the interface

caused by the irregular counterface.

Zhang et al. [248] used MD simulations to study the eﬀect of conﬁned wa-

ter between alkyl monolayers terminated with −CH

(hydrophobic) and −OH (hy-

drophilic) groups on Si(111), as illustrated in Fig. 13.62. For the hydrophobic

molecules, the friction coeﬃcient is almost constant independent of the number of

water molecules. For the hydrophilic molecules, the friction coeﬃcient decreases

rapidly with an increase in the number of water molecules, as shown in Fig. 13.63.

These results are in good agreement with surface force microscopy (SFM) experi-

mental results. Zhang et al. [249] also studied the friction of alkanethiol SAMs on

gold using hybrid molecular simulations at the same time scales as are used in AFM

and FFM experiments. Various quantities were varied in the simulations, includ-

ing chain length, terminal group, scan direction and scan velocity. The simulations

showed that the frictional force decreases as the chain length increases and is small-

est when scanned along the tilt direction. They also predicted a maximum friction

coeﬃcient for hydrophobic −CH

-terminated SAMs and low friction coeﬃcients

for hydrophilic −OH-terminated SAMs as the scan velocity increases. The simulat-

Average load (nN)

Average friction (nN)

180

100

150

200

250

30 60 90 120 150

Average friction (nN) end-chains only

Perperdicular-chains

Tilied-chains

End-chains

Fig. 13.61. Average friction on the tip as a function of load for the monolayer systems shown

in Fig. 13.60. The scale for the average friction in the end-chain system is shown on the

right-hand side of the ﬁgure. After [247] with the permission of the ACS (2004)

716 Susan B. Sinnott et al.

Fig. 13.62a–d. Snapshots of

hydrophilic monolayers and

conﬁned water molecules

from MD simulations at

300 K. The tilt direction of

monolayers on the top plate

changed after t = 10.0ps.Af-

ter [248] with the permission

of the AIP (2005)

ions further predicted a saturated constant value at high scan rates for both surfaces.

These results are summarized in Figs. 13.64 and 13.65.

The work of Chandross et al. [250,251] illustrates the eﬀects of chain length

on friction and stick-slip behavior between two ordered SAMs consisting of alkyl-

silane chains over a range of shear rates at various separation distances or pressure,

as illustrated in Fig. 13.66. The adhesion forces between the two SAMs at the same