Bhushan B. Handbook of Micro/Nano Tribology, Second Edition

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diamond surfaces was also changed by altering the relative surface alignment (changing the space available

to the third-body molecule) and the load (changing the distance between the diamond surfaces).

Despite the fact that the ethane and isobutane molecules forced the opposing diamond surfaces to be

farther apart than the methane molecules (Figure 11.42), the friction was larger with ethane and isobutane

molecules present because the molecules interacted more with the diamond surfaces while sliding.

It is interesting to note that the presence of the trapped methane molecules lowered the frictional force

more than the presence of the chemisorbed methyl groups (Figure 11.42). Because the methyl groups

were chemically bonded to the diamond surface, their interaction with the opposing diamond surface

was greater because the chemisorbed molecules could not “avoid” the interaction with the hydrogen

atoms on the diamond surfaces. However, the frictional force data were not dramatically different for

the methane and methyl-terminated systems when analyzed as a function of interface separation. In fact,

in the region between 1.5 and 2.0 Å, the curves overlap (Figure 11.42). The marked difference in frictional

force when measured as a function of normal load arose from the higher load required to bring the

methane system to the same interface separation as the methyl-terminated system.

11.5.3 Tribochemistry

A number of interesting phenomena result when two bodies are placed in sliding contact. One such

phenomenon involves the formation of nascent particles via the wear of the contacting surfaces or via

chemical reactions. Chemical reactions can occur between wear particles or between wear particles and

contamination present on the contacting surfaces. (These reactions can lead to the formation of a distinct

layer between the contacting surfaces, known as a transfer layer.) This interaction of chemistry and sliding

is known as tribochemistry and can have profound effects on the friction between the contacting surfaces.

Experimental characterization of tribochemical reactions (Singer, 1991; Fischer, 1992) using traditional

analysis methods such as optical microscopy, electron microscopy, cathodoluminescence, and infrared

spectroscopy (Wilks and Wilks, 1979; Feng and Field, 1991; Tabor and Field, 1992) has proved difﬁcult

because, depending upon the geometry and materials, these techniques are usually restricted to exami-

nation of the contact region subsequent to sliding. This limitation has historically led to a lack of

FIGURE 11.44 Frictional force as a function of sliding distance divided by unit cell length for three ethane system

(Figure 11.40b) simulations. The average normal load and frictional force were 0.12 and 0.013 nN/atom (lower

panel), 0.64 and 0.090 nN/atom (middle panel), and 0.63 and 0.11 nN/atom (upper panel). The sliding direction is

the [11

–

2] crystallographic direction. (Data from Perry, M. D. and Harrison, J. A. (1997), J. Phys. Chem. 101,

1364–1373. With permission.)

information regarding the mechanisms of tribochemical reactions. Indeed, even new atomic-scale prox-

imal probe techniques, such as AFMs (Binnig et al., 1986) and FFMs, have yet to characterize speciﬁc,

atomic-scale, tribochemical reaction mechanisms. The need for experiments that can probe the interface

between sliding bodies as sliding progresses has been recognized (Singer, 1992). Recent experiments have

attempted to probe the contact region as the sliding progresses. Hiller (1995) has used methods based

on optical light scattering to detect particle sizes during sliding. More recent experiments have used

ultraviolet Raman spectroscopy to monitor the formation of amorphous carbon when a steel ball is in

sliding contact with a sapphire window in the presence of a polyperﬂuorinated ether lubricant (Cheong

and Stair, 1997). Preliminary results have shown that the measured amount of amorphous carbon during

sliding differs from the amount measured after sliding.

The recent experiments of Cheong and Stair (1997) underscore the need to monitor reactants and the

formation of intermediates as the sliding progresses. Because the precise positions of all atoms are known

as a function of time, MD simulations are uniquely suited to this task. Indeed, Harrison and Brenner

(1994) reported tribochemical reaction sequences that occurred when two diamond surfaces were placed

in sliding contact. These simulations provided the ﬁrst glimpse into the rich, nonequilibrium tribochem-

istry that is possible in covalently bonded systems.

The MD simulations were carried out as described in Section 11.5.1 using the hydrogen-terminated,

ethyl-terminated (Figure 11.47), and methyl-terminated diamond systems. The temperature of the system

FIGURE 11.45 Sample starting conﬁgurations for two isob-

utane system sliding simulations. The “arrow” in (a) and the

“sled” orientations in (b). For clarity, the carbon atoms of the

upper diamond surface (Figure 11.40) are not shown and the

color coding is as in Figure 11.40. The system is viewed along

the [111] direction, the [11

–

2] direction is from left to right, and

the [1

–

10] direction is from bottom to top. (From Perry, M. D.

and Harrison, J. A. (1997), J. Phys. Chem. 101, 1364–1373. With

permission.)

was maintained at 70 K using a thermostat (Berendsen et al., 1984) and the average normal force (load)

on the systems was ≈ 1.3 nN/atom or ≈ 23 GPa. This pressure was well below the pressure that causes

plastic deformation of diamond on the macroscopic scale (100 GPa). In addition, this pressure is com-

parable to the pressures (up to 20 GPa) achieved in AFM experiments and in macroscopic friction

experiments on diamond in which wear was observed (Germann et al., 1993).

For both the hydrogen-terminated and the methyl-terminated surfaces examined, sliding did not result

in any chemical reactions at the loads examined (Harrison et al., 1992b, 1993c). In contrast, when the

ethyl groups were present, the simulations revealed a number of possible tribochemical reactions. For

FIGURE 11.46 Frictional force as a function of sliding dis-

tance divided by unit cell length for two isobutane system sim-

ulations initially in the arrow orientation (Figure 11.45a). The

average normal load and frictional force were 0.59 and

0.13 nN/atom (lower panel) and 0.59 and 0.080 nN/atom

(upper panel). The sliding direction was the [11

–

2] crystallo-

graphic direction. (Data from Perry, M. D. and Harrison, J. A.

(1997), J. Phys. Chem. 101, 1364–1373.)

FIGURE 11.47 Typical starting conﬁguration for the system with two chemisorbed ethyl (–CH

) groups at the

interface. Large white and dark spheres represent carbon atoms and small white and dark spheres represent hydrogen

atoms. The system is viewed along the [1

–

10] direction in (a) and the [111] direction in (b). Box in (a) denotes region

of interface illustrated in Figure 11.48. In (b) the carbon atoms of the upper lattice are not shown for clarity. (From

Harrison, J. A. and Brenner, D. W. (1994), J. Am. Chem. Soc. 116, 10399–10402. With permission.)*

* Color reproduction follows page 16

instance, in one simulation, sliding in the [11

–

2] crystallographic direction resulted in the shearing of a

hydrogen atom from the tail portion (–CH

) of each ethyl group. Thus, radicals on each ethyl group

along with free hydrogen atoms were formed. The free hydrogen atoms became trapped at the sliding

interface. One of these free hydrogen atoms abstracted a hydrogen atom from the lower diamond surface

to form a hydrogen molecule, H

(Figure 11.48c). This molecule did not undergo any further reaction

during the 20-ps simulation. (The simulation geometry kept the free atoms trapped at the interface for

the duration of the simulation. However, if the geometry was different, e.g., a tip and a surface, it would

have been possible for an atom to escape the interface region during the sliding.)*

Further sliding of the upper surface caused one of the radical-containing ethyl groups to pass over the

radical site on the lower surface created by the abstraction of hydrogen to form H

. These two radicals

combined to form a carbon–carbon bond. As a result, the upper and lower diamond surfaces became

chemically joined by a D

–CH

–D

linkage (green entity in Figure 11.48b). (Here, D

and D

represent

the upper and lower diamond surfaces, respectively.) The upper and lower diamond surfaces remained

bound until the shear stress was large enough to sever the carbon–carbon bonds connecting the two

surfaces. The carbon–carbon bonds to the upper and lower surfaces broke almost simultaneously, creating

an ethylene molecule, CH

(Figure 11.48c) and leaving radical sites on both the upper and lower

surfaces. The planar ethylene molecule remained trapped at the interface for the remainder of the

FIGURE 11.48 Simulation conﬁgurations at different times for

sliding the upper diamond surface (in Figure 11.47) in the [11

–

direction with the same color coding as in Figure 11.47. The system

is shown after hydrogen atoms have been sheared from the ends of

both ethyl groups in (a). These free hydrogen atoms are colored dark

to help distinguish them from bound atoms. Adhesion of the two

diamond surfaces occurred in (b) via the formation of a carbon–car-

bon bond from the ethyl group at the right to the lower diamond

surface. A hydrogen molecule is visible at the left of the ﬁgure. The

system is shown after the adhesive bonds between the surfaces have

broken in (c). The resulting ethylene and hydrogen molecules are

visible at the left and center of the panel, respectively. At the end of

the simulation the ethylene and hydrogen molecules were still

present at the interface (d). Hydrogen atoms that originated from

the ethyl groups became chemically bound to the upper (at the left)

and lower (at the right) diamond surfaces. One of the ethyl groups

abstracted two hydrogen atoms from the lower diamond surface.

(From Harrison, J. A. and Brenner, D. W. (1994), J. Am. Chem. Soc.

116, 10399–10402. With permission.)*

* Color reproduction follows page 16.

simulation (Figure 11.48d). The nascent radical site on the lower surface was ﬁlled via the addition of a

free hydrogen atom that originated from the tail of the second ethyl group (Figure 11.48d).

Note that the sequence of reactions differed for the two ethyl groups within the same simulation.

Subsequent to shearing of the hydrogen atom from the second ethyl group, the ethyl radical abstracted

a hydrogen atom from the lower surface (Figure 11.48c) forming a fully saturated ethyl group on the

upper surface and a radical on the lower surface. Another hydrogen atom was “worn” from the tail of

the ethyl group upon continued sliding. The nascent hydrogen atom became trapped at the interface and

eventually added to the radical site on the upper surface created by the shearing of the D

–CH

–D

connection (Figure 11.48d). Eventually, the radical-containing ethyl group abstracted a second hydrogen

atom from the lower surface to become saturated (Figure 11.48d). This group did not undergo any

additional reactions by the end of the 30-ps simulation. Each of these observations was consistent with

conclusions inferred (but not directly measured) from experimental studies of the friction and wear of

diamond surfaces.

The tribochemistry of the ethyl-terminated diamond surfaces was also shown to be anisotropic. For

instance, sliding the upper surface of the same system described above in the [1

–

10] direction caused tail

of one ethyl group to become lodged between several lower-surface hydrogen atoms. Because one end

of the molecule was “ﬁxed,” continued sliding resulted in the breakage of the C–C bond of the ethyl

group. Although the simulation evidence has too few of these rare events to allow a quantitative conclu-

sion, these different reaction mechanisms imply different wear rates for each direction, consistent with

the experimental observation that wear rates depend on the direction of abrasion (Wilks and Wilks, 1979;

Feng and Field, 1991).

11.6 Summary

In this chapter, we have tried to present a relatively complete discussion of the contribution that MD

and related simulations are making in the area of nanotribology. Based on the examples discussed above,

it is clear that these approaches are providing new and exciting insights into friction, wear, and related

processes at the atomic scale that could not have been obtained in any other way. Furthermore, the

synergy between these simulations and new and exciting experimental techniques such as the SFA and

AFM is producing a revolution in our understanding of the origin of friction at its most fundamental

atomic level.

In the section on indentation, examples were discussed that illustrated many of the unexpected

phenomena that are being characterized using MD simulations. These include atomic-scale jumps to

contact in both metallic and ionically bonded systems that deform either tip or substrate depending on

surface energies; the inﬂuence of very thin hydrocarbon ﬁlms on inhibiting this jump to contact; and

the indentation-induced disordering of covalently bonded silicon and diamond substrates. Furthermore,

these results are closely related to experimental observations, often providing clear explanations for results

such as hysteresis in loads during indentation and pull back.

The section on thin liquid ﬁlms discussed the deviations of liquid ﬁlm behavior from bulk ﬂuids,

again using speciﬁc examples from the literature. From this discussion it is clear that many of the ideas

regarding liquid lubrication based on macroscopic experimental observations may not be valid for liquids

as small as a few atomic layers across. Indeed, liquid ﬁlms on this scale may not be good lubricants at

all, forcing us to reevaluate how friction and wear can be controlled in soon-to-be-developed nanometer-

scale machines. The answers to these and related questions may come from the types of studies discussed

in the ﬁnal section on solid bodies in contact. These simulations are beginning to provide the kind of

knowledge needed to tailor new solid interfaces with desired atomic-scale friction and wear properties.

Finally, we note that simulations of the type discussed in this chapter have really just begun to make

substantial contributions to the ﬁeld of tribology. We fully expect that the range of processes and systems

that can be characterized with this method to grow as more realistic and sophisticated models are

developed and implemented on increasingly powerful computers. These, in turn, will continue to make

important contributions to current and future technologies.

Acknowledgments

This work was supported by the U.S. Ofﬁce of Naval Research under contracts #N00014-97-WR-20019

(USNA) and #N00014-95-1-270 (NCSU). David W. Brenner is supported by a National Science Foun-

dation Early Career Development Grant. The authors would like to thank Richard J. Colton, Susan B.

Sinnott, Irwin L. Singer, and Carter T. White for many helpful discussions and Mark O. Robbins, Jonathan

G. Harris, Richard J. Colton, Joan E. Curry, James F. Belak, and Gary M. McClelland for providing ﬁgures

from their work. Judith A. Harrison would also like to thank John Foerster and Jeanette Walsh for technical

assistance.

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