Bhushan B. Nanotribology and Nanomechanics: An Introduction

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970 Bharat Bhushan and Huiwen Liu

The schematic (bottom) in Fig. 18.8 shows relative size and sources of menis-

cus. The native oxide layer (SiO

) on the top of Si(100) wafer exhibits hydrophilic

properties, and some water molecules can be adsorbed on this surface. The con-

densed water will form a meniscus as the tip approaches the sample surface. In the

case of a sphere (such as a single-asperity AFM tip) in contact with a ﬂat surface,

the attractive Laplace force (F

) caused by capillary is:

= 2πRγ

(cosθ

+ cosθ

) , (18.2)

where R is the radius of the sphere, γ

is the surface tension of the liquid against

air, θ

and θ

are the contact angles between liquid and ﬂat and spherical surfaces,

respectively [2,3,40]. As the surface tension value of Z-15 (24dyn/cm) is smaller

than that of water (72 dyn/cm), the larger adhesive force in Z-15 cannot only be

caused by the Z-15 meniscus. The nonpolarized Z-15 liquid does not have complete

coverage and strong bonding with Si(100). In the ambient environment, the con-

densed water molecules will permeate through the liquid Z-15 lubricant ﬁlm and

compete with the lubricant molecules present on the substrate. The interaction of

the liquid lubricant with the substrate is weakened, and a boundary layer of the liq-

uid lubricant forms puddles [20,34]. This dewetting allows water molecules to be

adsorbed on the Si(100) surface as aggregates along with Z-15 molecules. And both

of them can form meniscus while the tip approaches the surface. In addition, as the

Z-15 ﬁlm is pretty soft compared to the solid Si(100) surface, penetration of the tip

in the ﬁlm occurs while pushing the tip down. This leads to a large area of the tip

involved to form the meniscus at the tip–liquid (water aggregates along with Z-15)

interface. These two factors of the liquid-like Z-15 ﬁlm result in higher adhesive

force. It should also be noted that Z-15 has a higher viscosity compared to that of

water. Therefore, Z-15 ﬁlm provides higher resistance to sliding motion and results

in a larger coeﬃcient of friction. In the case of Z-DOL(BW) ﬁlm, both of the active

groups of Z-DOL molecules are strongly bonded on Si(100) substrate through the

thermal and washing treatment. Thus, the Z-DOL(BW) ﬁlm has relatively low free

surface energy and cannot be displaced readily by water molecules or readily ad-

sorb water molecules. Thus, the use of Z-DOL(BW) can reduce the adhesive force.

We further believe that the bonded Z-DOL molecules can be orientated under stress

(behaving as a soft polymer solid), which facilitates sliding and reduces coeﬃcient

of friction.

Thesestudies suggest that, if the lubricant ﬁlms exist as liquid-like,such as Z-15

ﬁlms, they easily form meniscus (by themselves and the adsorbed water molecules),

and thus have higher adhesive force and higher friction force. Whereas, if the lubri-

cant ﬁlm exists in solid-likephase, such as Z-DOL(BW) ﬁlms,they are hydrophobic

with low adhesion and friction.

In order to study the uniformity of lubricant ﬁlm and its inﬂuence on friction

and adhesion, friction force mapping and adhesive force mapping of PFPE have

been carried out by Koinkar and Bhushan [34] and Bhushan and Dandavate [36],

respectively. Figure 18.9 shows gray scale plots of surface topography and friction

force images obtained simultaneously for unbonded Demnum-type PFPE lubricant

18 Nanoscale Boundary Lubrication Studies 971

Friction force

5.00

2.50

0 2.50 5.00 0 2.50 5.00

Surface topography

0 1.3 2.5 nm 0 4.0 8.0 nm

Fig. 18.9. Gray scale plots

of the surface topography

and friction force obtained

simultaneously for unbonded

2.3-nm-thick Demnum-type

PFPE lubricant ﬁlm on sili-

con [20]

ﬁlm on silicon [34].The friction force plot shows well-distinguished low- and high-

friction regions corresponding roughly to high- and low-surface-height regions in

the topography image (thick- and thin-lubricant regions). A uniformly lubricated

sample does not show such a variation in friction. Figure18.10 shows the gray scale

plots of the adhesive force distribution for silicon samples coated uniformly and

nonuniformlywith Z-DOL lubricant. It can be clearly seen that there exists a region

that has an adhesive force distinctly diﬀerent from the other region for the nonuni-

formly coated sample. This implies that the liquid ﬁlm thickness is nonuniform,

giving rise to a diﬀerence in the meniscus forces.

Adhesive force

3.5 nm uniform Z-DOL/ Si(100)

30μm

20 nN

2 – 10 nm nonuniform Z-DOL/ Si(100)

30μm

030μm

Adhesive force

30μm

Fig. 18.10. Gray scale plots of the adhesive force distribution of a uniformly coated,

3.5-nm-thick unbonded Z-DOL ﬁlm on silicon and 3–10 nm-thick unbonded Z-DOL ﬁlm

on silicon that was deliberately coated nonuniformly by vibrating the sample during the coat-

ing process [36]

972 Bharat Bhushan and Huiwen Liu

18.4.2 Rest Time Eﬀect

It is well known that, in the computer rigid disk drive, the stiction force increases

rapidly with an increase in rest time between the head and magnetic-medium

disk [10,11]. Considering that the stiction and friction are two of the major issues

that lead to the failure of computer rigid disk drives and MEMS, it is very important

to ﬁnd out if the rest time eﬀect also exists on the nanoscale. First, the rest time

eﬀect on the friction force, adhesive force, and coeﬃcient of Si(100) sliding against

70 nN, 2μm/s, 22°C, RH 45–55%

Friction force (nN)

Time (s)

Adhesive force (nN)

Coefficient of friction

From friction force plot

Si(100)

0.15

0.10

0.05

1,000

100

1,000

100

10,0001,000100

10 100,000

10,0001,000100

100,000

10,0001,000100

100,000

Fig. 18.11. (a) Rest time eﬀect on friction force, adhesive force, and coeﬃcient of friction of

Si(100).

18 Nanoscale Boundary Lubrication Studies 973

tip was studied, Fig. 18.11a [21]. It was found that the friction and adhesive

forces logarithmically increase up to a certain equilibrium time after which they

remain constant. Figure 18.11a also shows that the rest time does not aﬀect the co-

eﬃcient of friction. These results suggest that the rest time can result in the growth

of the meniscus, which causes a higher adhesive force, and in turn, a higher friction

force. But in the whole testing range the friction mechanisms do not change with

70 nN, 2μm/s,

22°C, RH 45 –55%

Friction force (nN)

Adhesive force (nN)

Coefficient of friction

From friction force plot

t =0s

t = 180 s

Z-DOL(BW)Z-15Si(100)

0.15

0.10

0.05

200

150

100

Fig. 18.11. (b) Summary of the rest time eﬀect on friction force, adhesive force, and coeﬃ-

cient of friction of Si(100), 2.8-nm-thick Z-15 ﬁlm, and 2.3-nm-thick Z-DOL(BW) ﬁlm. All

of the measurements were carried out at 70 nN, 2 µm/s, and in ambient air [21]

974 Bharat Bhushan and Huiwen Liu

the rest time. Similar studies were also performed on Z-15 and Z-DOL(BW) ﬁlms.

The results are summarized in Fig. 18.11b [21]. It is seen that a similar time eﬀect

has been observed on Z-15 ﬁlm, but not on Z-DOL(BW) ﬁlm.

AnAFMtipincontactwithaﬂatsamplesurfacecanbetreatedasasingle-asperity

contact. Therefore, a Si

tip in contact with Si(100) or Z-15/Si(100)can be mod-

eled as a sphere in contact with a ﬂat surface covered by a layer of liquid (adsorbed

water and/orliquidlubricant),Fig.18.12a.Meniscusformsaroundthecontactingas-

perity and growswith time until equilibrium occurs [41]. The meniscus force, which

is the product of meniscus pressure and meniscus area, depends on the ﬂow of li-

quid phase toward the contact zone. The ﬂow of the liquid toward the contact zone

is governed by the capillary pressure P

, which draws liquid into the meniscus, and

the disjoining pressure Π, which tends to draw the liquid away from the meniscus.

Based on the Young and Laplace equation, the capillary pressure, P

,is:

= 2Kγ, (18.3)

where 2K is the mean meniscus curvature (= K

+ K

,whereK

and K

are the cur-

vatures of the meniscus in the contact plane and perpendicular to the contact plane)

and γ is the surface tension of the liquid. Mate and Novotny [6] have shown that the

disjoining pressure decreases rapidly with increasing liquid ﬁlm thickness in a man-

ner consistent with a strong van der Waals attraction. The disjoining pressure, Π,

for these liquid ﬁlms can be expressed as:

Π =

6πh

, (18.4)

where A is the Hamaker constant and h is the liquid ﬁlm thickness. The driving

forces that cause the lubricant ﬂow that results in an increase in the meniscus force

are the disjoining pressure gradient, due to a gradient in ﬁlm thickness, and the

capillary pressure gradient, due to the curved liquid–air interface. The driving pres-

sure, P, can then be written as:

P = −2Kγ −Π. (18.5)

Asperity

Sample surface



Fig. 18.12. (a) Schematic of a single asperity in contact with a smooth ﬂat surface in the

presence of a continuous liquid ﬁlm when φ is large

18 Nanoscale Boundary Lubrication Studies 975

15.7

15.6

15.5

15.4

15.3

15.2

Meniscus force (μN)

Rest time (s)

= 250 μm

η = 0.25 Pa s

= 3 nm

R = 250 μm

= 1 nm

η = 0.001 Pa s

0.05

0.25

R =50μm

= 1 nm

η = 0.25 Pa s

Meniscus force (μN)

Rest time (s)

Meniscus force (

μN)

Rest time (s)

Fig. 18.12. (b) Results of the

single-asperity model. Eﬀect

of viscosity of the liquid,

radius of the asperity, and

ﬁlm thickness is studied with

respect to the time-dependent

meniscus force [41]

976 Bharat Bhushan and Huiwen Liu

Based on these three basic relationships, the following diﬀerential equation has

been derived by Chilamakuri and Bhushan [41], which can describe the meniscus at

time t:

2πx

⎛

⎜

⎝

D+

−h

⎞

⎟

⎠

2πh

3η

(1+ cosθ)

D+ a−h

−

3ηh

cotα,

(18.6)

where η is the viscosity of the liquid and a is given as

a = R(1−cosφ) ∼

Rφ

∼

. (18.7)

The diﬀerential equation (18.4) was solved numerically using Newton’s iteration

method. The meniscus force at any time t less than the equilibrium time is propor-

tional to the meniscus area and meniscus pressure (2Kγ), and it is given by

(t) = 2πRγ(1+ cosθ)



)







, (18.8)

where (x

)

is the value of x

at the equilibrium time



)



= 2R

⎡

⎢

⎣

−6πh

γ(1+ cosθ)

+ (h

−D)

⎤

⎥

⎦

. (18.9)

This modeling work (at the microscale) showed that the meniscus force initially

increases logarithmically with the rest time up to a certain equilibrium time, after

which it remains constant. Equilibrium time decreases with an increase in liquid

ﬁlm thickness, a decrease in viscosity, and a decrease in the tip radius, Fig. 18.12b.

This early numerical modeling work and the data at the nanoscale in Fig. 18.11aare

in good agreement.

18.4.3 Velocity Eﬀect

To investigate the velocity eﬀect on friction and adhesion, the relationshipsbetween

friction force and normal load for Si(100), Z-15, and Z-DOL(BW) at diﬀerent ve-

locities were measured, Fig. 18.13 [21]. Based on these data, the adhesive force and

coeﬃcient of friction values can be calculated by (18.1). The variation of friction

force, adhesive force, and coeﬃcient of friction of Si(100), Z-15, and Z-DOL(BW)

as a function of velocity are summarized in Fig. 18.14. This indicates that, for sili-

con wafer, the friction force decreases logarithmically with increasing velocity. For

Z-15,the frictionforce decreaseswith increasingvelocity up to 10µm/s, afterwhich

it remains almost constant. The velocity has a much smaller eﬀect on the friction

force of Z-DOL(BW); it reduced slightly only at very high velocity. Figure 18.14

18 Nanoscale Boundary Lubrication Studies 977

0 100755025

120 μm/s0.4 2 8 20 40

0 100755025

22°C, RH 45 – 55%

Friction force (nN)

Z-15

Si(100)

Z-DOL(BW)

Normal load (nN)

Fig. 18.13. Friction forces versus normal load data of Si(100), 2.8-nm-thick Z-15 ﬁlm, and

2.3-nm-thick Z-DOL(BW) ﬁlm at various velocities in ambient air [21]

978 Bharat Bhushan and Huiwen Liu

125

100

0.15

0.10

0.05

1 1,000100100.1

70 nN, 22°C, RH 45 – 55%

Friction force (nN)

Si(100)

Z-DOL(BW)

Z-15

Velocity (μm/s)

From friction force plot

Adhesive force (nN)

Si(100)

Z-DOL(BW)

Z-15

Coefficient of friction

Si(100)

Z-DOL(BW)

Z-15

Z-DOL(BW)

Si(100)

Increasing velocity

0.4

μm/s

240 μm/s

Si(OH)

Z-15

Z-DOL

Fig. 18.14. The inﬂuence of velocity

on the friction force, adhesive force,

and coeﬃcient of friction of Si(100),

2.8-nm-thick Z-15 ﬁlm, and 2.3-nm-thick

Z-DOL(BW) ﬁlm at 70 nN, in ambi-

ent air. The schematic (right)showsthe

change of surface composition (by tribo-

chemical reaction) and change of menis-

cus with increasing velocity [21]

also indicates that the adhesive force of Si(100) is increased when the velocity is

higher than 10µm/s. The adhesive force of Z-15 is reduced dramatically with a ve-

locity increase up to 20 µm/s, after which it is reduced slightly; the adhesive force

of Z-DOL(BW) also decreases at high velocity. In the testing range of velocity, only

the coeﬃcient of friction of Si(100) decreases with velocity, but the coeﬃcients

of friction of Z-15 and Z-DOL(BW) almost remain constant. This implies that the

friction mechanisms of Z-15 and Z-DOL(BW) do not change with the variation of

velocity.

The mechanisms of the eﬀect of velocity on the adhesion and friction are ex-

plained based on the schematics shown in Fig. 18.14 (right). For Si(100), tribo-

chemical reaction plays a major role. Although at high velocity the meniscus is

18 Nanoscale Boundary Lubrication Studies 979

broken and does not have enough time to rebuild, the contact stresses and high ve-

locity lead to tribochemicalreactions of the Si(100)wafer andSi

tip, whichhave

native oxide (SiO

) layers with water molecules. The following reactions occur:

SiO

+ 2H

O → Si(OH)

(18.10)

+ 16H

O →3Si(OH)

+ 4NH

OH . (18.11)

The Si(OH)

is removed and continuously replenished during sliding. The Si(OH)

layer between the tip and Si(100) surface is known to be of low shear strength and

causes a decrease in friction force and coeﬃcient of friction in the lateral direc-

tion [42–46]. The chemical bonds of Si

−

OH between the tip and Si(100) surface

induce large adhesive force in the normal direction. For Z-15 ﬁlm, at high velocity

the meniscus formed by condensed water and Z-15 molecules is broken and does

not have enough time to rebuild. Therefore, the adhesive force and, consequently,

friction force is reduced. For Z-DOL(BW) ﬁlm, the surface can adsorb few water

molecules in ambient condition, and at high velocity these molecules are displaced,

which is responsible for a slight decrease in friction force and adhesive force. Even

in the high-velocity range, the friction mechanisms for Z-15 and Z-DOL(BW) ﬁlms

are still shearing of the viscous liquid and molecular orientation, respectively. Thus

the coeﬃcients of friction of Z-15 and Z-DOL(BW) do not change with velocity.

Koinkar and Bhushan [20,34] have suggested that, in the case of samples with

mobileﬁlms,such ascondensedwaterand Z-15ﬁlms,alignmentof liquidmolecules

(shear thinning) is responsible for the drop in friction force with an increase in

scanning velocity. This could be another reason for the decrease in friction force

with velocity for Si(100) and Z-15 ﬁlm in this study.

18.4.4 Relative Humidity and Temperature Eﬀect

The inﬂuence of relative humidity on friction and adhesion was studied in an envi-

ronmentally controlled chamber. The friction force was measured by making meas-

urements at increasing relative humidity, the results are presented in Fig. 18.15 [21].

These shows that, for Si(100) and Z-15 ﬁlm, the friction force increases with a rel-

ative humidity increase up to RH 45%, and then it shows a slight decrease with

a further increase in relative humidity. Z-DOL(BW) has a smaller friction force than

Si(100) and Z-15 in the whole testing range, and its friction force shows a relatively

apparent increase when the relative humidity is higher than RH 45%. For Si(100),

Z-15, and Z-DOL(BW), adhesive forces increase with relative humidity. And their

coeﬃcients of friction increase with relative humidity up to RH 45%, after which

they decrease with further increases of the relative humidity. It is also observed that

the humidity eﬀect on Si(100) really depends on the history of the Si(100) sample.

As the surface of Si(100) wafer readily adsorbs water in air, without any pretreat-

ment the Si(100) used in our study almost reaches its saturated stage of adsorbing

water and is responsible for a smaller eﬀect with increasing relative humidity. How-

ever, once the Si(100) wafer was thermally treated by baking at 150

◦

Cfor1h,

a bigger eﬀect was observed.