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

Подождите немного. Документ загружается.

velocity proﬁles became curved (Figure 11.23b). Increasing the wall–ﬂuid interaction strength further

(Figure 11.23c) caused the ﬁrst two liquid layers to become locked to the solid wall.

For unequal wall and ﬂuid densities, the ﬂow BC changed dramatically. At the smallest wall–ﬂuid

interaction strengths examined, the velocity proﬁle was linear; however, the no-slip BC was not present.

The magnitude of the liquid velocity at the wall was less than the wall velocity; therefore, slip occurred

(i.e., |V

|U < 1) (Figure 11.23a). The magnitude of this slip decreased as the strength of the wall–ﬂuid

interaction increased. For an intermediate value of wall–ﬂuid interaction strength (ε

/ε = 1.8), the ﬁrst

ﬂuid layer was partially locked to the solid wall. Sufﬁciently large values of wall-ﬂuid interaction strength

(ε

/ε = 15) led to the locking of the second ﬂuid layer to the wall.

Using a simulation geometry similar to Figure 11.18b, Thompson and Robbins (1990a) examined the

origin of stick-slip motion when an LJ liquid is sheared between two solid walls using MD. Instead of

two solids in contact moving smoothly, the solids may alternatively stick and then slip past one another,

this is known as stick-slip motion. Simulation details are described above (Thompson and Robbins,

1990b), except that the walls in this case were composed of fcc solids with (111) surfaces and the density

of the wall atoms was usually equal to the density of the ﬂuid atoms. The wall separation usually

corresponded to a few layers (i.e., 2σ). To mimic boundary-layer lubrication experiments, the simulations

were performed at constant load by varying the distance between the walls.

The upper wall was coupled through a spring to a stage that advanced at constant velocity. Initially,

the force on the spring was zero when the upper wall was at rest. As the stage moved forward, the spring

stretched and the forced increased. When the ﬁlm was in a liquid state, the upper wall accelerated until

the force applied by the spring balanced the viscous dissipation. When the ﬁlm was crystalline in nature,

stick-slip behavior was observed (Figure 11.24). Initially, the ﬁlm responded elastically, the wall remained

stationary, and the forced increased linearly (Figure 11.24a). When the force exerted by the spring

exceeded the yield stress of the ﬁlm, the ﬁlm melted and the tip wall began to slide. The wall accelerated

to catch up with the stage, decreasing the force and creating the sawtooth pattern indicative of stick-slip

motion. The stick-slip behavior was dependent on the velocity of the stage, with the degree of stick-slip

increasing as the velocity decreased. Analysis of the two dimensional structure factor during the course

of the simulation conﬁrmed the existence of the solid–liquid phase transition as the ﬁlm proceeded from

static to sliding states (Figure 11.24c).

FIGURE 11.24 Force per unit area f, wall displacement

, and the Debye Waller factor e

–2W

= 0.6 for a

solid) as a function of time t during stick-slip motion for

a wall velocity of 0.1. The simulation contained 288 wall

atoms and 144 ﬂuid atoms. The walls were fcc solids with

(111) surfaces, and the shear direction was (100). All

quantities have been normalized using the appropriate

variables so that they are dimensionless. (From Thomp-

son, P. A. and Robbins, M. O. (1990). Science 250,

792–794. With permission.)

While simulations with spherical molecules were successful in explaining some experimental phenom-

ena, they were unable to reproduce other features of the experimental data. For instance, the calculated

relaxation times and viscosities remained near bulk ﬂuid values until the ﬁlms crystallized. Experimen-

tally, these quantities typically increase many orders of magnitude before a yield stress is observed

(Israelachvili et al., 1988; Van Alsten and Granick, 1988). With this in mind, Thompson et al. (1992)

repeated their earlier shearing simulations (Thompson and Robbins, 1990b) using freely jointed, linear-

chain molecules instead of spherical molecules.

The behavior of the viscosity of the ﬁlms as a function of shear rate was examined for ﬁlms of different

thicknesses. The relationship between ﬁlm viscosity and shear rate was examined (Figure 11.25). The

response of ﬁlms that were six to eight molecular diameters m

thick was approximately the same as it

is for bulk systems. When the thickness of the ﬁlm was reduced, the viscosity of the ﬁlm increased

dramatically, particularly at low shear rates, consistent with the aforementioned experimental observations.

The structure of liquids conﬁned to smooth pores was compared with the structure of liquids in

irregularly shaped pores by Curry et al. (1994) using grand canonical Monte Carlo and microcanonical

MD methods. Both the conﬁning pore walls were comprised of rigid atoms ﬁxed in a (100) fcc arrange-

ment. One wall was atomically ﬂat and the other was scored with regularly spaced rectilinear grooves

(i.e., corrugated) (Figure 11.26). The structure of the conﬁned ﬁlm as a function of groove dimension

and frequency was examined. In each case, the behavior of the ﬁlm was studied as the registry α was

systematically varied at ﬁxed temperature, chemical potential, and pore width.

When the groove was ﬁve lattice constants wide and the walls of the corrugated pore were in registry

(α = 0.0) the one-layer liquid in the narrow region of the pore was in equilibrium with the two-layer

liquid in the wide region of the pore. Snapshots of the MD simulation taken together with the broad

peaks in the density proﬁle conﬁrmed this conclusion (Figure 11.27). Changing the registry of the pore

walls signiﬁcantly affected the structure of the liquid. It was clear from examination of the density proﬁles

that increasing the registry to α = 0.325 caused the liquid in the narrow region of the pore to begin to

separate into two layers, while the liquid in the wide region of the pore remained unaffected. At α = 0.4,

the liquid in the narrow portion of the pore had solidiﬁed into two distinct layers while there were still

two liquid layers in the wide region of the pore. Thus, the conﬁned ﬁlm consisted of parallel, rectilinear

liquid-ﬁlled nanocapillaries separated by solid strips. Increasing the registry to α = 0.5 (exactly out of

registry) caused the entire ﬁlm to solidify and resulted in sharp peaks in the density proﬁle.

The structural character within the ﬁlm was ascertained from examination of the in-plane pair-

correlation function g

(2)

(Figure 11.27). For registries corresponding to α = 0.0 and α = 0.325, the

conﬁgurations were disordered or liquid-like as evidenced by the lack of structure in g

(2)

. The in-plane

pair correlation functions calculated when α = 0.4 clearly showed a different degree of transverse order

in the narrow portion of the pore than in the wide region of the pore. This supported the conclusion

that nanocapillaries had formed. When the registry was increased to α = 0.5 the in-plane pair correlation

functions for both regions of the pore were identical and very structured, indicating total solidiﬁcation

of the ﬁlm.

FIGURE 11.25 Dependence of time-averaged liquid viscosity

µ (µ = fh/v, where f is the mean frictional force per unit area,

h is the wall separation, and v is the sliding velocity) on the

shear rate γ (γ = v/h). The variable P

⊥

represents the pressure

on the walls and m

corresponds to the number of ﬂuid layers.

The dashed line has a slope of –

⅔. (From Thompson, P. A.

et al. (1992), Phys. Rev. Lett. 68, 3448–3451. With permission.)

Plots of the stress in the ﬁlm, T*

, as a function of α also yielded insights into the sequence of phase

transitions experienced by the ﬁlm (Figure 11.28). When α = 0.5 the corrugated-pore ﬁlm consisted of

two solid layers in the narrow region and three in the wide region. In comparison, the pore with no

groove contained two solid layers. Because the surfaces are symmetrically arranged when α = 0.5, the

shear stress was equal to zero. Pushing the walls into registry (i.e., decreasing α) caused the shear stress

to increase rapidly. Because the corrugated-pore ﬁlm was, on average, thicker than the ﬁlm in the

atomically ﬂat pore, the shear stress was less for the corrugated-pore ﬁlm (Schoen et al., 1994). The shear

stress in the ungrooved pore rose rapidly with increasing α and then dropped precipitously when α fell

below 0.33. This sharp drop was due to abrupt melting and the concomitant loss of nearly an entire layer

of the ﬁlm. The result was a one-layer liquid ﬁlm that continued to support substantial shear stresses

FIGURE 11.26 Schematic representation of a corrugated slit pore. The walls consist of atoms rigidly ﬁxed in the

(100) plane of the fcc lattice. The lattice constant corresponds to l (l = 1.5985σ), the cell dimensions are deﬁned by

and s

, the separation of the walls is h in the narrow regions and h + h

in the wide regions, and α determines the

alignment of the walls. When α = 0 the walls are in registry. The origin of the coordinate system lies at the intersection

of the vectors labeled x, y, and z. (From Curry, J. B. et al. (1994). J. Chem. Phys. 101, 10824–10832. With permission.)

FIGURE 11.27 Local density proﬁles ρ

)

(z) in (A), snapshots looking down the y-axis of the pore ﬂuid for various registries in (B), and in-plane pair

correlation functions g

(2)

in (C). The dotted and solid lines correspond to the functions calculated separately in the narrow and wide regions of the pore. In

the snapshots black and gray shaded spheres correspond to alternating rows of the fcc lattice and unshaded spheres correspond to ﬁlm atoms. Starred variables

are reported in reduced units, that is, z

= z/σ and ρ

= ρ × σ

. (From Curry, J. B. et al. (1994), J. Chem. Phys. 101, 10824–10832. With permission.)

down to α = 0.30. In contrast, the corrugated-pore ﬁlm did not all melt at once as α was varied. First,

when α = 0.45 the solid in the wide region of the pore melted and almost an entire layer of liquid exited

the wide region of the pore. This was accompanied by a drop in the shear stress of the ﬁlm (Figure 11.28).

The shear stress decreased approximately linearly with decreasing α until approximately equal to 0.35.

Beyond this point the solid in the narrow region of the pore melted and one layer of liquid exited the

pore; consequently, the shear stress decreased signiﬁcantly. Because the ﬁlm in the narrow region of the

pore melted gradually, the shear stress in the region of α = 0.35 was rounded (Figure 11.28). The melting

of the ﬁlm in the narrow region of the pore began at the interface between the narrow and wide regions

and progressed toward the middle of the narrow region with increasing α.

Finally, the range of registry values where the solid (narrow region of pore) and liquid (wide region

of pore) coexist was shown to increase with increasing groove width. In the limit of very large groove

width, the ﬂuid in the wide region of the pore acted like an ungrooved or smooth pore.

Curry and Cushman (1995a,b) also used the grand canonical Monte Carlo method to study binary

mixtures of LJ atoms conﬁned to a corrugated pore that were in thermodynamic equilibrium with their

bulk-phase counterpart. The geometry of the corrugated pore was the same as it was in a previous work

(Curry et al., 1994) (Figure 11.26). The ﬂuid and wall atoms were spherical, nonpolar, LJ atoms charac-

terized by diameters σ

and interaction energies ε

, where i represents the type of atom. The cutoff distance

for the shifted force LJ potential used in this work depended on σ

, where σ

= ½(σ

+ σ

). Thus, the

cutoff distance varied depending on the identity of the atoms. The values of σ for the two different-sized

atoms (large and small) were chosen so that the mixture resembled a mixture of octamethyltetracyclosi-

loxane and cyclohexane because this mixture has been used in SFA experiments. Two different pores

were examined: one with the walls composed of large atoms and one with the walls composed of small

atoms. For each pore, two binary mixtures were examined, with either 86% of 15% large atoms. Thus,

four combinations of wall size and ﬂuid atom mixture were studied.

When the wall atoms were large and the bulk ﬂuid was composed of 86% large atoms, the small atoms

were nearly eliminated from both regions of the pore (Figure 11.29) when the walls were in registry (α =

0.0). The pore width was such that one solid-like fcc layer of large atoms ﬁt into the narrow region of

the corrugated pore while the wide region accommodated two solid-like fcc layers of large atoms. Altering

the alignment of the pore walls gradually liqueﬁed the ﬁlm in both regions of the pore, as evidenced by

the broadening of the local density proﬁles and the reduced structure in the in-plane pair-correlation

functions. In addition, as the ﬁlm melted a signiﬁcant number of small atoms were able to enter both

the narrow and the wide regions of the pore. This effect was most marked when the walls were totally

out of alignment (α = 0.5). The reason for this is that the alignment of the wall atoms effectively decreased

the pore width. This had the effect of excluding large atoms from discrete regions of the pore.

Decreasing the percentage of large atoms (15%) in the bulk dramatically affected the behavior of the

mixture in the pore. For example, when α = 0.0, small atoms were no longer excluded from the pore.

Indeed, in the wide region of the pore a two-layer, liquid-like ﬁlm composed of small and large atoms

was formed. The liquid-like nature of the ﬁlm was conﬁrmed using both the density proﬁles (Figure 11.30)

and the in-plane pair-correlation function. This ﬁlm was only slightly affected by changing the registry

FIGURE 11.28 Shear stress T

in the x-direction vs.

registry for the ungrooved slit pore (open squares) with

= 2.3 and for the corrugated pore shown in

Figure 11.27 (ﬁlled circles) with h

= 2.3 in the narrow

region. Starred variables are reported in reduced units,

that is, T

= T

× σ

/ε. (From Curry, J. B. et al. (1994),

J. Chem. Phys. 101, 10824–10832. With permission.)

of the walls. In the narrow region of the pore, the large atoms formed a one-layer solid and the number

of large atoms participating in the structure was small compared with the number of small atoms.

Decreasing the registry of the surfaces (increasing α) caused the large atoms to be driven from the narrow

region of the pore and resulted in the formation of a two-layer small-atom solid. Examination of the in-

plane correlation function conﬁrmed the existence of the two-layer solid at α = 0.5.

When the wall atoms were small and the mixture was composed of 86% large atoms, the narrow and

the wide regions of the pore contained a one-layer and two-layer liquid, respectively (Figure 11.31). In

the narrow region of the pore the one-layer liquid was composed mostly of large atoms, and changing

the registry of the pore walls had very little effect. In contrast, the two-layer liquid in the wide region of

the pore was composed of both large and small atoms. Altering the registry of the pore walls drove the

small atoms from the wide region of the pore and caused the ﬁlm to solidify. The two-layer solid in the

wide region was in equilibrium with the one-layer liquid in the narrow region. This freezing in the wide

region while the narrow region remained liquid was not observed in the other cases considered. Indeed,

if the component that froze was the same size as the wall atoms, the atoms in the wide region of the pore

froze only after the atoms in the narrow region were frozen (i.e., after nanocapillaries were formed).

Last, decreasing the percentage of large atoms in the mixture while keeping the size of the wall atoms

small resulted in liquid-like structures, composed of large and small atoms, in both the wide and narrow

regions of the pore. Altering the registry of the walls had little effect on the liquid in the wide region of

FIGURE 11.29 Local density proﬁles ρ

(1)

for large atoms (ﬁlled circles) and small atoms (open circles) calculated

separately for the narrow (left) and wide (right) regions of the pore at various registries α. (The variable z is deﬁned

in Figure 11.27.) The bulk ﬂuid contained 86% large atoms and the period of the corrugation s

(Figure 11.26) was

10l, where l is the lattice constant. The value of l used in these simulations was 1.5985σ

, where σ

corresponds to

the diameter of the wall atoms and was equal to the diameter of the large ﬂuid species. The variables s

and s

(Figure 11.27) were both set to 5l. (From Curry J. E. and Cushman, J. H. (1995a), J. Chem. Phys. 103, 2132–2189.)

the pore. In contrast, the small atoms, which possessed a one-layer liquidlike structure in the narrow

region of the pore, developed a two-layer structure as the registry was changed.

The corrugated-pore studies of Curry and co-workers (Curry et al., 1994; Curry and Cushman,

1995a,b) provided unique insight into the behavior of mixed LJ liquids conﬁned between nonuniform

surfaces. The behavior of liquids between nonuniform surfaces under shear was also investigated by Gao

et al. (1995) using MD simulations. In that work, Gao et al. (1995) conﬁned hexadecane (n–C

)

between two Au substrates with exposed (111) faces. Topographical nonuniformities (or asperities) were

modeled by ﬂat-topped pyramidal Au structures of height h

from the underlying Au surface. The

asperities had a ﬁnite length in the sliding direction and an inﬁnite length in the direction perpendicular

to sliding. In this respect, they were very similar to the corrugated slit pore geometry of Curry et al.

(1994). The interactions between Au atoms were modeled by EAM (Foiles et al., 1986), the alkane

molecules were modeled by the united-atom model, and the interactions between the molecular segments

and gold atoms were modeled by an LJ potential.

Sliding was performed by moving the opposing Au surfaces in opposite directions so that the relative

sliding speed was 10 m/s. the simulations typically lasted 1.2 ns and were carried out at 350 K. Three

simulation geometries were examined. The ﬁrst consisted of 422 hexadecane molecules with the separa-

tion between asperity tops held at 17.5 Å. The second, “near-overlap,” case consisted of 243 hexadecane

molecules with the relative separation between asperity tops set to 4.6 Å. The third, “overlap,” case

consisted of 201 ﬂuid molecules with a relative separation between asperity tops of –6.7 Å. (It should be

noted that the height of the asperities was 9.3 Å in geometries one and two. In the third geometry the

FIGURE 11.30 Local density proﬁles ρ

(1)

for large atoms (ﬁlled circles) and small atoms (open circles) calculated

separately for the narrow (left) and wide (right) regions of the pore at various registries α. The bulk ﬂuid contained

15% large atoms and all other pore parameters were the same as in Figure 11.29. (From Curry, J. E. and Cushman,

J. H. (1995a), J. Chem. Phys. 103, 2132–2139.)

asperities were larger at 14 Å.) Prior to the start of the sliding simulations, each system was equilibrated

with the asperities well separated in the horizontal direction such that steady-state ﬂow was established.

From an examination of the atomic and molecular conﬁgurations recorded as a function of time

during the shearing process, Gao et al. (1995) were able to elucidate two main patterns for all three

simulation geometries. First, there was an evolution of layered liquid structures in the region between

the colliding asperities. In particular, for large transverse separations of the asperities, layering of the

liquid in the interasperity region was initially absent and developed dynamically as the asperities

approached each other. Furthermore, the number of layers in the interasperity region evolved in each

case in a quantized manner as successive layers were squeezed out as the asperities drew near. Finally,

severe deformation of the asperities resulted for the near-overlapping and overlapping asperity height

cases.

This interasperity layering phenomenon was also apparent from examination of the time variation of

the shear ( f

) and normal ( f

) forces. For example, for the near-overlap case, plots of both f

and f

vs.

time had oscillatory patterns prior to the collision between asperities. This oscillatory behavior of the

forces was reminiscent of solvation-force oscillations observed between smooth solid surfaces under

equilibrium conditions.

Gao et al. (1995) also commented on the crucial importance of the dynamic mechanical response of

the substrate (and the asperities) in determining the evolution and properties of the sheared systems.

FIGURE 11.31 Local density proﬁles ρ

(1)

for large atoms (ﬁlled circles) and small atoms (open circles) calculated

separately for the narrow (left) and wide (right) regions of the pore at various registries α. The bulk ﬂuid contained

86% large atoms and the period of the corrugation s

(Figure 11.26) was 14l, where l is the lattice constant. The value

of l equaled 1.5985σ

, where σ

corresponds to the diameter of the wall atoms and was equal to the diameter of the

small ﬂuid species. The parameters s

and s

(Figure 11.26) were both set to 7l. (From Curry, J. E. and Cushman,

J. H. (1995a), J. Chem. Phys. 103, 2132–2139.)

When the asperities were separated vertically by large distances (the ﬁrst simulation geometry), the shear

ﬂow was accompanied by a structuring of the liquid with no distortions of the metal surfaces. In contrast,

for the overlapping and near-overlapping cases, shearing resulted in pressurization of the liquid in the

interasperity region, accompanied by a signiﬁcant increase in effective viscosity. This resulted in plastic

deformations of the gold asperities.

It is clear, based on the discussion in this section, that ﬂuids conﬁned to areas of atomic-scale

dimensions do not necessarily behave like liquids on the macroscopic scale. In fact, depending on the

condition, they may often behave more like solids in terms of structure and ﬂow. This presents a new

set of concerns for lubricating moving parts at the nanometer scale. However, with the aid of simulations

like the ones mentioned here, plus experimental studies using techniques such as the SFA, general

properties of nanometer-scale ﬂuids are being characterized effectively with profound precision. This, in

turn, will allow scientists and engineers to design new materials and interfaces that will have speciﬁc

interactions with conﬁned lubricants, effectively controlling friction (and wear) at the atomic scale.

11.5 Friction

Friction at sliding solid interfaces results from the conversion of the work of sliding into some other,

less-ordered, form. For strongly adhering systems, the work of sliding may be converted into damage

within the bulk. As adhesive forces are decreased between the solid surfaces, the conversion of work

changes to mechanical damage at or near the surface, leading to, for example, the formation of wear

debris and transfer ﬁlms (Singer, 1991; Singer et al., 1991). For still weaker adhesive forces, friction can

occur through the conversion of work to heat at the interface with no permanent damage to the surface.

The latter regime is the topic of this section.

While the thermodynamic principles of the conversion of work to heat are well known, many of the

detailed mechanisms at sliding interfaces are just beginning to be understood. This understanding is the

by-product of new scientiﬁc instrumentation, such as the SFA and the AFM, analytic theories, and

simulations. A detailed understanding of these processes is important for producing interfaces with

speciﬁc friction (and wear) properties.

Atomic-scale friction has been investigated using MD simulations for systems composed of a variety

of materials, in a number of geometries. For instance, the atomic-scale friction and wear of diamond

surfaces, both atomically ﬂat and rough, was examined using MD by Harrison et al. (1992c, 1993a,b,c).

In addition, atomic-scale friction between monolayers composed of alkane chains bound to rigid sub-

strates (Glosli and McClelland, 1993), between perﬂuorocarboxylic acid and hydrocarboxylic LB mono-

layers (Koike and Yoneya, 1996), between contacting Cu surfaces (Hammerberg et al., 1995; Sorensen

et al., 1996), between a silicon tip and a silicon substrate (Landman et al., 1989a,b), and between con-

tacting diamond surfaces in the presence of third-body molecules (Perry and Harrison, 1997) have all

been examined using MD simulations.

Molecular dynamics simulations have also provided the ﬁrst insights into tribochemical reactions that

might occur when two diamond surfaces are in sliding contact (Harrison and Brenner, 1994).

11.5.1 Solid Lubrication

Harrison et al. (1992c, 1993a,b,c) examined the atomic-scale phenomena that occurred when two (111)

diamond surfaces were placed in sliding contact. The effects of crystallographic sliding direction, tem-

perature, sliding speed, applied normal load, and nature of the surface on atomic-scale friction were

examined. The frictional properties of hydrogen-terminated diamond surfaces were compared with the

frictional properties of alkyl-terminated diamond surfaces to elucidate the effects of surface condition

on atomic-scale friction. The alkyl-terminated systems were composed of two diamond lattices, conﬁg-

ured so that their (111) surfaces were in contact (Figures 11.32a to d). One eighth of the hydrogen atoms

on the upper surfaces were then randomly replaced with methyl (Figure 11.32b), ethyl (Figure 11.32c),

or n-propyl (Figure 11.32d) groups.

In these simulations, the vertical separation of the atoms in the two outermost layers of the lattices

were held constant. The molecular dynamics friction simulations were carried out by moving the atoms

in the rigid layers of the upper surface at a constant velocity (usually 100 m/s) in the chosen crystallo-

graphic sliding direction. (Similar results were obtained with sliding speeds of 50 m/s.) Both the [1

–

10]

and the [11

–

2] crystallographic directions were examined. (These correspond to moving the upper surface

in Figure 11.32 in the page, or from left to right, respectively.) The remaining atoms were allowed to

dynamically evolve in time according to classical equations of motion. The forces governing their motion

were derived from the Brenner potential (Brenner, 1990). The temperature of the systems was maintained

at 300 K by applying a thermostat (Berendsen et al., 1984) to the middle ﬁve layers of each lattice. The

simulations were performed at average normal loads varying between 0 to 15 GPa. These pressures are

well within the range of pressures that can be achieved experimentally using an AFM (Germann et al.,

1993).

A constant value for the relative distance between the rigid layers in the top and bottom slabs was

maintained during these simulations, and this distance was used to deﬁne the separation between the

two slabs.

The average frictional forces for sliding in the [11

–

2] crystallographic direction were calculated as a

function of load for the systems shown in Figure 11.32. For an individual sliding simulation, the frictional

force was taken to be the sum of the forces in the sliding direction on the rigid-layer atoms, normalized

by the number of rigid-layer atoms and averaged over the simulation. Because the relative lateral place-

ment of the opposing diamond surfaces affects the frictional force, frictional force (and normal force)

data were also averaged over simulations whose starting conﬁgurations differed in lateral registry of the

upper surface. (For precise details, see Harrison et al., 1993c and Perry and Harrison, 1997.)

The frictional force was found to increase with normal load in all cases, usually in an approximately

linear manner (Figure 11.33). This result is entirely reasonable, and was found to originate from the

detailed atomic-scale sliding mechanisms and the associated pathways of energy dissipation. For instance,

FIGURE 11.32 Illustration of atoms of a number of diamond-containing systems viewed along the [1

–

10] crystal-

lographic direction at the start of MD simulations. The (111) faces of two hydrogen-terminated, diamond lattices

are in contact in (a). Two of the upper-surface hydrogen atoms have been replaced by methyl groups in (b), ethyl

groups in (c), and n-propyl groups in (d). Sliding was achieved by moving the top two (rigid) layers of the upper

surfaces in the [11

–

2] crystallographic (right to left in the ﬁgure). Large spheres represent carbon atoms and small

spheres represent hydrogen atoms. (From Harrison, J. A. et al. (1993), Mater. Res. Soc. Bull. 18, 50–53. With permission.)