Bhushan B. Nanotribology and Nanomechanics: An Introduction

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13 Computer Simulations of Nanometer-Scale Indentation and Friction 697

case the stick-slip was over a much longer length scale and may be due to the fact

that the surfaces were not hydrogen-terminated.

Mulliah et al. [210] used MD simulations with bond-order potentials [211] to

model interactions between indenter atoms, EAM potentials [212] to model interac-

tions between substrate atoms, and the Ziegler–Biersack–Littmack potential [213]

to model interactions between indenter and substrate atoms to study the atomic-

scale stick-slip phenomenon of a pyramidal diamond tip interacting with a silver

surface at several sliding rates and vertical support displacements. These simulat-

ions showed that dislocations are related to the stick events emitting a dislocation in

the substrate near the tip. The scratch in the substrate is discrete due to the tip jump-

ing over the surface in the case of small vertical displacements. In contrast, large

displacements of 15Å or more result in a continuous scratch. These simulations

also showed how the dynamic friction coeﬃcient and the static friction coeﬃcient

increase with increasing tip depth. The tip moves continuously through a stick and

slip motion at large depths,whereas it comes to a halt in the case of shallow indents.

Although the sliding rate can change the exact points of stick and slip, the range of

sliding rates over the range of values considered in this study (1.0 to 5.0m/s) has

no inﬂuence on the damage to the substrate, the atomistic stick-slip mechanisms, or

the calculated friction coeﬃcients.

The eﬀect of the way in which the tip is rastered across the surface in MD

simulationswas consideredby Cai and Wang[209,214]using bond-orderpotentials.

In particular, they dragged silicon tips across several silicon surfaces, as illustrated

in Fig. 13.41, in two diﬀerent ways. In the ﬁrst, they moved the tip every MD step

while in the other they advanced the tip every 1000 steps. In both cases, the overall

sliding rate is the same and equals 1.67m/s. In both cases, wear of the tip such as is

illustrated in Fig. 13.41 occurs. However, the mechanisms by which the wear occurs

are found to depend on the approach used, and the latter approach is found to be in

better agreement with experimental data.

In many studies, diamond tips or diamond-decorated tips are used in friction

measurements. Diamond is an attractive material for an FFM tip because of its high

mechanical strength and the belief that such tips are wear-resistant. However, dia-

mond tips that were used to scratch diamond and silicon surfaces and then imaged

showed signiﬁcant wear that increased with the increasing hardness of the tested

material [215,216]. This wear altered the shape of the tip and hence inﬂuenced the

contact area that is used to determine friction coeﬃcients.

In summary, MD simulations provide insight into dry sliding friction and the

sliding of metal tips across clean metal, crystalline ceramics, and layered ceramics

surfaces. Stick-slip friction or wear can occur depending on the sliding conditions.

The good lubricating properties of layered ceramics are observed in the simulations

along with localized ﬂuctuations in atomic-scale friction. Crystalline ceramics, such

as diamond, exhibit relatively low friction and the simulations show how stick-slip

atomic-scale motion changes with the conditions of sliding and the way in which

the simulation is performed.

698 Susan B. Sinnott et al.

Fig. 13.41. Snapshots of

a Si(111) tip interacting with

a Si(001) 2×1 surface. The tip

is rastering along the surface

in the x-direction and starts

oﬀ at a distance of 9 Å from

the surface. After [209] with

the permission of the CCLRC

(2002)

13.4.2 Decorated Surfaces

While dry sliding friction in vacuum assumes that ambient gas particles have no

direct eﬀect on the results, MD simulations show that free particles between two

surfaces in sliding contact inﬂuence friction to a surprisinglylarge degree.These so-

called third-body molecules have been studied extensively by Perry et al. [177,217,

218] using MD simulations with bond-order and LJ potentials. These simulations

focus on the eﬀect of trapped small hydrocarbon molecules on the atomic-scale

friction of two (111) crystal faces of diamond with hydrogen termination. These

molecules might represent hydrocarbon contamination trapped between contacting

surfaces prior to a sliding experiment in dry friction, or hydrocarbon debris formed

during sliding.

In particular, the eﬀects on friction of methane (CH

), ethane (C

), and isobu-

tane (CH

)

CH trappedbetween diamond (111) surfacesin sliding contact were ex-

amined in separate studies (Fig. 13.42). The frictional force for all these systems

generally increases as the load increases, as illustrated in Fig. 13.43. The simulat-

ions predict that the third-body molecules markedly reduce the average frictional

force compared to the results for pristine hydrogen-terminatedsurfaces. This is par-

ticularly true at high loads, where the third-body molecules act as a boundary layer

between the two diamond surfaces. That is, the third-body molecules reduce the in-

teraction of hydrogen atoms on opposing surfaces [218]. This is demonstrated by

examining the vibrational energy excited in the diamond lattice during the sliding

(Fig. 13.44). Signiﬁcant vibrational excitation of the diamond outer layer (C–H) oc-

curs inthe absence ofthe methanemolecules.Thus, the friction isapproximately3.5

13 Computer Simulations of Nanometer-Scale Indentation and Friction 699

a) b) c)

Fig. 13.42a–c. Initial conﬁguration at low load for the diamond plus third-body molecule

systems. These systems are composed of two diamond surfaces, viewed along the [

110] di-

rection, and two methane molecules in (a), one ethane molecule in (b), and one isobutane

molecule in (c). Large white and dark gray spheres represent carbon atoms of the diamond

surfaces and the third-body molecules, respectively. Small gray spheres represent hydrogen

atoms of the lower diamond surface. Hydrogen atoms of the upper diamond surface and the

third-body molecules are both represented by small white spheres. Sliding is achieved by

moving the rigid layers of the upper surface from left to right in the ﬁgure. After [177] with

the permission of the ACS (1997)

times larger when methane is not present. The application of load to the diamond

surfaces causes the normal mode vibrations of the trapped methane molecules to

change. Power spectra calculated from MD simulations [217,218] show that even

under low loads, the peaks in the power spectra are signiﬁcantly broadened. Peaks

in the low-energy region of the spectrum almost disappear with the additional ap-

plication of load.

The size of the methane molecules allows them to be “pushed” in-between hy-

drogen atoms on the diamond surfaces while sliding [218]. However, steric con-

siderations cause the larger ethane and isobutane molecules to change orientation

during sliding. Conformations that lead to increased interactions with the diamond

surfaces increase the average frictional force. Thus, despite the fact that the two dia-

mond surfaces are farther apart when ethane and isobutane are present compared to

when methane is present, the friction is larger because these molecules do not “ﬁt”

nicely into potential energy valleys between hydrogen atoms when sliding.

When similar hydrocarbon molecules (methyl, ethyl, and n-propyl groups) are

chemisorbed to one of the sliding diamond surfaces, instead of trapped between

the surfaces, diﬀerent behavior is observed by Harrison et al. [172,173,208,219].

Simulations show that methyl-termination does not decrease friction signiﬁcantly

but results in frictional forces that are nearly the same as they are for hydrogen-

terminated diamond surfaces [207]. While the methane third-body molecules de-

700 Susan B. Sinnott et al.

Average normal load (nN/atom)

Average frictional force (nN/atom)

0.1

0.2

0.3

0.1

0.2

0.3

0.4

10.25 0.5 0.75

(CH

)

Fig. 13.43. Average frictional force per rigid-layer atom as a function of average normal

load per rigid-layer atom for sliding the upper diamond surface in the [11

2] crystallographic

direction. Data for the methane (CH

)system(open triangles), the ethane (C

)system

(open squares), the isobutane (CH

)

CH system (ﬁlled circles), and diamond surfaces in

the absence of third-body molecules (open circles) are shown in the lower panel. Data for

the methyl-terminated −CH

system (open triangles), the ethyl-terminated (−C

)system

(open squares), the n-propyl-terminated (−C

)system(ﬁlled circles), and diamond sur-

faces in the absence of third-body molecules (open circles)areshownintheupper panel.

Lines have been drawn to aid the eye. After [177] with the permission of the ACS (1997)

crease the frictional force to a greater extent than the chemisorbed methyl groups,

friction as a function of load is comparable for the ethyl-terminated and ethane sys-

tems, with the former giving slightly higher frictional forces. Attaching the hydro-

carbon groups to the diamond surfaces causes them to have less freedom to move

between hydrogen atoms on opposing diamond surfaces during sliding. This gener-

ally increases their repulsive interaction with the diamond counterface.

MD simulations can also provide insight into the rich, nonequilibrium tribo-

chemistry that occurs between surfaces in sliding contact. Harrison and Brenner

examined the tribochemistry that occurs when ethane molecules are trapped be-

tween diamond surfaces in sliding contact, as illustrated in Fig. 13.45 [220]. This

simulation was the ﬁrst to show the atomic-scale mechanisms for the degradation

of lubricant molecules due to friction. The type of debris formed during the sliding

simulation is similar to the types of debris molecules that were observed in macro-

scopic experiments that examined the friction between diamond surfaces [221].

13 Computer Simulations of Nanometer-Scale Indentation and Friction 701

Sliding distance/unit cell

Vibrational energy (K)

500

1000

1500

1000

500

2 4 6

H

Fig. 13.44. Average vibrational energy between the (C–H) bonds of the upper diamond (111)

surface versus sliding distance for hydrogen-terminated diamond (111) surfaces, with (CH

)

and without methane (H), trapped between them. The average normal load is approximately

the same in both simulations and is in the range 0.8–0.85 nN/atom. The average frictional

force on the upper surface is about 3.5 times smaller in the presence of the methane third-body

molecules. After [218] with the permission of Elsevier (1996)

a) c)

b) d)

Fig. 13.45a–d. Snapshots from a molecular dynamics simulation of the sliding of two

hydrogen-terminated diamond (111) surfaces against one another in the [11

2] direction. The

upper surface has two ethyl fragments chemisorbed to it. The simulation shows how sliding

can induce chemistry at the interface. After [220] with the permission of the ACS (1994)

702 Susan B. Sinnott et al.

In the case of sliding metal surfaces, impurity molecules or atoms (both ad-

sorbed and absorbed) on thin metal ﬁlms can be expected to aﬀect the ﬁlm’s proper-

ties. For example, calculations have shown that resistivity changes in the metal are

strongly dependent on the nature of the adsorption bond [222]. When this result is

used to interpret atomic-scale friction results obtained with the QCM, the sliding of

adsorbate structures on metal surfaces are shown to be a combination of electron

excitation and lattice vibrations. Additionally, other interesting quantum eﬀects can

come into play when the adsorbate is very diﬀerent chemically from the surface on

which it is sliding. For instance, the electronic frictional forces acting on small, inert

atoms and molecules, such as C

and Xe, sliding on metal surfaces have been cal-

culated by Persson [223], where the metal surface was approximated by a electron

gas (jellium) model. The calculations showed that the Pauli repulsive and attractive

vander Waals forcesare of similar magnitudes. In addition,the calculated electronic

friction contributions agree well with the values derived from surface resistivity by

Grabhorn et al. [224] and QCM measurements. These studies showed that parallel

friction is mainly due to electronic eﬀects while perpendicular friction is phononic

in nature in this system.

In summary, MD simulations show that the average frictional force decreases

signiﬁcantly in systems with third-body molecules, especially at high loads. Simu-

lations also provide information about the details of tribochemical interactions that

can occur between lubricants and sliding surfaces. Additionally, the eﬀect of the

presence of small molecules on thin metal ﬁlms can inﬂuence ﬁlm properties, such

as resistivity.

13.4.3 Thin Films

As discussed at the beginning of this section, the conversion of the work of sliding

into some other less ordered form is responsible for friction at sliding solid inter-

faces. In the case of adhering systems, the work of sliding may be converted into

damage within the bulk (plastic deformation), while in the case of weakly adhesive

forces, friction can occur through the conversion of work to heat at the interface

that causes no permanent damage to the surface (wearless friction). The latter case,

when it is achieved throughthe presence of lubricatingthin ﬁlms, is the topic of this

section.

There are several types of lubricatingthin ﬁlms, the simplest of which consist of

small moleculesthat are analogousto wear debris that can “roll”between the sliding

surfaces or that represent very short-chain bonded lubricants. These thin ﬁlms were

discussed in the previous subsection. The rest of this subsection will, therefore,

focus on the eﬀects of liquids, larger nanoparticles, self-assembled monolayers and

solid thin ﬁlms on lubrication and friction.

Liquids

Liquids are common lubricants and so they have been studied in great depth at the

macroscale.At the nanoscale,the tribologicalresponseof sphericalliquidmolecules

13 Computer Simulations of Nanometer-Scale Indentation and Friction 703

Fig. 13.46a–c. Thestick/sliptransitionthatoccurs for thinﬁlms of liquid between two sliding

solid surfaces. F is the intrinsic friction and F

is the friction where the liquid is in the

rigid state; F

is the friction where the liquid is in the liquid-like state. After [225] with the

permission of the ACS (1996)

has been well-characterizedexperimentallyusing the SFA and computationally with

MD simulations by Berman et al. [225]. The SFA experiments considered one to

three liquid layers and the stick-slip motion at the interface is found to increase in

a quantized fashion as the number of lubricant layers decrease. When no external

forcesare appliedto thesystem,the slidingstops andthe solid–lubricantinteractions

are strong enough to force the liquid molecules to form a close-packed structure

that is ordered. The transformation of the liquid into this solid-like structure causes

the two surfaces to eﬀectively bond to each other through the lubricant. When the

surfaces startto slide again,lateral shear forces are introducedthat steadily increase,

which causes the molecules in the liquid to undergosmall lateral displacements that

change the ﬁlm thickness. If these shear forces become greater than a critical value,

the ﬁlm disorders in a manner that is analogous to melting. This allows the surfaces

to slide easily past each other in a manner that is still quantized. This sequence of

events is nicely illustrated in Fig. 13.46 and can be reproduced multiple times for

the same system.

Persson et al. [226] used MD simulations with pairwise potentials similar to

those in (13.6) to examine the mechanism by which this sharp transition occurs.

They ﬁnd that in the case of sliding on insulating crystal surfaces, the solid-state

lubricant may be in a “superlubric” state where the friction is negligible. It is clear

from the simulations, however, that any surface defects, even in low concentrations,

will disrupt this state and transform the lubricantback into a ﬂuid. In addition,when

sliding occurs on metallic surfaces above cryogenic temperatures, the electronic

contributions to friction are no longer zero and no superlubric state is possible.

704 Susan B. Sinnott et al.

High applied pressures can force the ﬂuid molecules out from between the two

conﬁning surfaces [227]. The fact that liquid molecules close to a stiﬀ surface are

strongly layered in the direction perpendicular to the surface explains the experi-

mental observation of a (n → n−1) layer transition, where n is number of monolay-

ers, that is observed as the normal load increases [228]. Nucleation theory is used to

calculate the critical pressure and determine the spreading dynamics of the (n−1)

island.

The reactivity of the liquid molecules are also critically important to boundary

layer friction. MD studies by Persson et al. [229] show that inert molecules inter-

act weakly with sliding surfaces. Consequently, as the rate of sliding increases, the

molecular conversion from the solid state to the liquid state occurs in an abrupt

manner. However, when the molecules interact strongly with the surfaces, they un-

dergo a more gradual transition from the solid to the liquid state. Persson et al. [34]

also considered systems where the molecules are attached to one of the surfaces,

which causes the transitions to be abrupt. This is especially true if there are large

separations between the chains.

While the studies discussed so far have focused on spherical liquids, most

widely used liquid lubricants consist of long-chain hydrocarbons.Nonspherical liq-

uid moleculeshavemore diﬃcultyaligning and solidifying. Thisis borneout in MD

simulationsby Thompsonet al. [231] that show that sphericalmoleculeshavehigher

critical velocities than branched molecules. In particular, the simulations show that

when the molecules are branched, the amount of time various parts of the system

spend in the sticking and sliding modes changes with sliding rate. The critical ve-

locity can also depend on the number of liquid layers in the ﬁlm, the structure and

relative orientation of the two sliding surfaces, the applied load and the stiﬀness of

the surfaces.

Additional studies by Landman et al. [230] used MD simulations with bond-

order and EAM potentials coupled with pair-wise potentials similar to (13.6) to

study the sliding of two gold surfaces with pyramidal asperities that have straight

chain C

lubricant molecules trapped between them, as illustrated in Fig. 13.47.

An important aspect of this study is that the sliding rate in the simulations is about

10m/s, which is the same order of magnitude as the scanning speed in a computer

disk. As the asperities approach each other, the hydrocarbon molecules begin to

form layers. This is reﬂected in the oscillations in the frictional force shown in

Fig. 13.48. When the asperities overlap in height and approach each other laterally,

the pressure of the lubricant molecules increases to about 4 GPa which leads to the

deformation of the gold asperities.

Glosli and McClelland [174] modeled the sliding of two ordered monolayers

of alkane chains that are attached to two rigid substrates. This system is shown

schematically in Fig. 13.49. The simulations predicted that energy dissipation oc-

curs by a discontinuous plucking mechanism (sudden release of shear strain) or

a viscous mechanism (continuous collisions of atoms of opposite ﬁlms). The spe-

ciﬁc mechanism that occurs depends on the interfacial interaction strength. In par-

ticular, the “pluck” occurs when mechanicalenergy stored as strain is convertedinto

13 Computer Simulations of Nanometer-Scale Indentation and Friction 705

Fig. 13.47. Stills from a molecular dynamics simulation where Au(111) surfaces with surface

roughness slide over one another while separated by hexadecane molecules. The scanning

velocity is 10 m/s. Layering of the lubricant and asperity deformation occurs as the sliding

continues. The top three rows show the results when the asperity heights are separated by

4.6Å.Thebottom three rows show the results when the asperity heights are separated by

−6.7 Å. After [230] with the permission of the ACS (1996)

thermal energy that leads to low friction forces at low temperatures. On the other

hand, at higher temperatures some of the energy of sliding is dissipated through

phonon excitations, which results in higherfrictional forces. Interestingly, this trend

reverses again at the highest temperatures considered when the molecules move so

much that they slide easily over the surfaces, which decreases the frictional force.

These results are summarized in Figs. 13.50 and 13.51.

706 Susan B. Sinnott et al.

5

t (ps)

(nN)

1000250 500 750

5

(nN)

Fig. 13.48a,b. The lateral

force (F

) and normal force

) from the molecular dy-

namics simulations shown in

Fig. 13.35 as a function of

time. The forces between the

two metal surfaces are shown

by the dashed line. The force

oscillations correspond to

the structural changes of the

lubricant in Fig. 13.35. Af-

ter [230] with the permission

of the ACS (1996)

20.7Å

20.43 Å

Fig. 13.49. Top andside views of the alkane chains attached to surfaces that are sliding against

each other. After [174] with the permission of the APS (1993)

Other studies of sliding surfaces with attached organicchains include MD simu-

lations with LJ potentials by Müser and coworkers, [41,232,233]which considered

friction between polymer “brushes” in sliding contact with one another. In particu-

lar, they considered the eﬀect of sliding rate on the tilting of polymers and the eﬀect

of steady-state sliding versus non-steady-state(“transient”)sliding. The simulations

ﬁnd that shear forces are lower for chains that tilt in a direction that is parallel to the

shear direction. This tilting eﬀect is signiﬁcant for grafted polymers, as illustrated in

Fig. 13.52, and less signiﬁcant for absorbed polymers. This is due to the decrease in

the diﬀerential frictional coeﬃcient for the grafted polymers as well as the increase

in the friction coeﬃcient for absorbed polymers under shear. The tilting is also af-