Bhushan B. Nanotribology and Nanomechanics: An Introduction

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414 Bharat Bhushan

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measured using an atomic force/friction force microscope, J. Appl. Phys. 88, 4825–

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81. B. Bhushan, G.S. Blackman: Atomic force microscopy of magnetic rigid disks and

sliders and its applications to tribology, ASME J. Tribol. 113, 452–458 (1991)

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85. N.S. Tambe, B. Bhushan: Friction model for the velocity dependence of nanoscale

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86. N.S. Tambe, B. Bhushan: Durability studies of micro/nanoelectromechanical system

materials, coatings, and lubricants at high sliding velocities (up to 10 mm/s) using

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technology applications, Appl. Phys. Lett 86, 061906–1–061906–3 (2005)

8 Nanotribology, Nanomechanics and Materials Characterization 415

94. N.S. Tambe, B. Bhushan: Nanowear mapping: A novel atomic force microscopy based

approach for studying nanoscale wear at high sliding velocities, Tribol. Lett. 20,83–90

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95. S.C. Lim, M.F. Ashby: Wear mechanism maps, Acta Metall. 35, 1–24 (1987)

96. S.C. Lim, M.F. Ashby, J.H. Brunton: Wear-rate transitions and their relationship to

wear mechanisms, Acta Metall. 35, 1343–1348 (1987)

97. B. Bhushan, C. Dandavate: Thin-ﬁlm friction and adhesion studies using atomic force

microscop, J. Appl. Phys. 87, 1201–1210 (2000)

98. B. Bhushan: Adhesion and stiction: Mechanisms, measurement techniques, and meth-

ods for reduction, (invited), J. Vac. Sci. Technol. B 21, 2262–2296 (2003)

99. T. Stifter, O. Marti, B. Bhushan: Theoretical investigation of the distance dependence

of capillary and van der Waals forces in scanning probe microscopy, Phys. Rev. B 62,

13667–13673 (2000)

100. U.D. Schwarz, O. Zwoerner, P. Koester, R. Wiesendanger: Friction Force Spectroscopy

in the Low-load Regime with Well-deﬁned Tips. In: Micro/Nanotribology and Its Ap-

plications, ed. by B. Bhushan (Kluwer Academic, Dordrecht 1997) pp.233–238

101. M. Nosonovsky, B. Bhushan: Stochastic model for metastable wetting of roughness-

induced superhydrophobic surfaces, Microsyst. Technol. 12, 231–237 (2005)

102. M. Nosonovsky, B. Bhushan: Roughness optimization for biomimetic superhydropho-

bic surfaces, Microsyst. Technol. 11, 535–549 (2005)

103. R.N. Wenzel: Resistance of solid surfaces to wetting by water, Indus. Eng. Chem. 28,

988–994 (1936)

104. A. Cassie, S. Baxter: Wetting of porous surfaces, Trans. Faraday Soc. 40, 546–551

(1944)

105. Z. Burton, B. Bhushan: Hydrophobicity, adhesion and friction properties with nanopat-

terned roughness and scale dependence, Nano Lett. 5, 1607–1613 (2005)

106. B. Bhushan, H. Liu, S.M. Hsu: Adhesion and friction studies of silicon and hydropho-

bic and low friction ﬁlms and investigation of scale eﬀects, ASME J. Tribol. 126, 583–

590 (2004)

107. H. Liu, B. Bhushan: Adhesion and friction studies of microelectromechanical

systems/nanoelectromechanical systems materials using a novel microtriboapparatus,

J. Vac. Sci. Technol. A 21, 1528–1538 (2003)

108. B. Bhushan, B.K. Gupta: Handbook of Tribology: Materials, Coatings and Surface

Treatments (McGraw-Hill, New York 1991) reprinted Krieger, Malabar Florida, 1997

109. B. Bhushan, S. Venkatesan: Mechanical and tribological properties of silicon for mi-

cromechanical applications: A Review, Adv. Info. Storage Sys. 5, 211–239 (1993)

110. Anonymous: Properties of Silicon, EMIS Data Reviews Series No. 4. INSPEC, Institu-

tion ofElectrical Engineers, London. See also Anonymous, MEMS Materials Database,

http://www.memsnet.org/material/ (2002)

111. J.E. Field: The properties of natural and synthetic diamond (Academic, London 1992)

112. B. Bhushan: Chemical, mechanical and tribological characterization of ultra-thin and

hard amorphous carbon coatings as thin as 3

nm: Recent developments, Diamond and

lated Materials 8, 1985–2015 (1999)

113. Anonymous: The Industrial Graphite Engineering Handbook (National Carbon Com-

pany, New York 1959)

114. M. Nosonovsky, B. Bhushan: Scale eﬀects in dry friction during multiple-asperity con-

tact, ASME J. Tribol. 127, 37–46 (2005)

115. B. Bhushan, M. Nosonovsky: Comprehensive model for scale eﬀects in friction due to

adhesion and two- and three-body deformation (plowing), Acta Mater. 52, 2461–2474

(2004)

416 Bharat Bhushan

116. B. Bhushan, M. Nosonovsky: Scale eﬀects in dry and wet friction, wear, and interface

temperature, Nanotechnology 15, 749–761 (2004)

117. B. Bhushan, M. Nosonovsky: Scale eﬀects in friction using strain gradient plasticity

and dislocation-assisted sliding (microslip), Acta Mater. 51, 4331–4345 (2003)

118. V.N. Koinkar, B. Bhushan: Scanning and transmission electron microscopies of single-

crystal silicon microworn/machined using atomic force microscopy, J. Mater. Res. 12,

3219–3224 (1997)

119. X. Zhao, B. Bhushan: Material removal mechanism of single-crystal silicon on

nanoscale and at ultralow loads, Wear 223, 66–78 (1998)

120. B. Bhushan, P.S. Mokashi, T. Ma: A new technique to measure Poisson’s ratio of ultra-

thin polymeric ﬁlms using atomic force microscopy, Rev. Sci. Instrum. 74, 1043–1047

(2003)

121. A.V. Kulkarni, B. Bhushan: Nanoscale mechanical property measurements using mod-

iﬁed atomic force microscopy, Thin Solid Films 290-291, 206–210 (1996)

122. A.V. Kulkarni, B. Bhushan: Nano/picoindentation measurements on single-crystal alu-

minum using modiﬁed atomic force microscopy, Mater. Lett. 29, 221–227 (1996)

123. A.V. Kulkarni, B. Bhushan: Nanoindentation measurement of amorphous carbon coat-

ings, J. Mater. Res. 12, 2707–2714 (1997)

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Theory and experiment, Acta Metall. Mater. 42, 475–487 (1994)

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gradient plasticity, J. Mech. Phys. Solids 46, 411–425 (1998)

126. W.B. Li, J.L. Henshall, R.M. Hooper, K.E. Easterling: The mechanism of indentation

creep, Acta Metall. Mater. 39, 3099–3110 (1991)

127. F.P. Bowden, D. Tabor: The Friction and Lubrication of Solids (Clarendon, Oxford

1950)

128. Z. Tao, B. Bhushan: Bonding, degradation, and environmental eﬀects on novel perﬂuo-

ropolyether lubricants, Wear 259, 1352–1361 (2005)

129. H. Liu, B. Bhushan, W. Eck, V. Staedtler: Investigation of the adhesion, friction,

and wear properties of biphenyl thiol self-assembled monolayers by atomic force mi-

croscopy, J. Vac. Sci. Technol. A 19, 1234–1240 (2001)

130. H. Liu, B. Bhushan: Investigation of nanotribological properties of self-assembled

monolayers with alkyl and biphenyl spacer chains, Ultramicroscopy 91, 185–202

(2002)

131. T. Kasai, B. Bhushan, G. Kulik, L. Barbieri, P. Hoﬀman: Nanotribological study of

perﬂuorosilane SAMs for anti-stiction and low wear, J. Vac. Sci. Technol. B 23, 995–

1003 (2005)

132. K.K. Lee, B. Bhushan, D. Hansford: Nanotribological characterization of perﬂuo-

ropolymer thin ﬁlms for biomedical micro/nanoelectrone chemical systems applica-

tions, J. Vac. Sci. Technol. A 23, 804–810 (2005)

133. B. Bhushan, D. Hansford, K.K. Lee: Surface modiﬁcation of silicon and polymethyl-

siloxane surfaces withvapor-phase-deposited ultrathin ﬂuorosilane ﬁlms for biomedical

nanodevices, J. Vac. Sci. Technol. A 24, 1197–1202 (2006)

134. N.S. Tambe, B. Bhushan: Nanotribological characterization of self assembled mono-

layers deposited on silicon and aluminum substrates, Nanotechnology 16,

1549–1558

(2005)

135. Z. Tao, B. Bhushan: Degradation mechanisms and environmental eﬀects on perﬂuo-

ropolyether, self assembled monolayers, and diamondlike carbon ﬁlms, Langmuir 21,

2391–2399 (2005)

Surface Forces and Nanorheology

of Molecularly Thin Films

Marina Ruths and Jacob N. Israelachvili

Summary. In this chapter, we describe the static and dynamic normal forces that occur be-

tween surfaces in vacuum or liquids and the diﬀerent modes of friction that can be observed

between: (i) bare surfaces in contact (dry or interfacial friction), (ii) surfaces separated by

a thin liquid ﬁlm (lubricated friction), and (iii) surfaces coated with organic monolayers

(boundary friction).

Experimental methods suitable for measuring normal surface forces, adhesion and fric-

tion (lateral or shear) forces of diﬀerent magnitude at the molecular level are described. We

explain the molecular origin of van der Waals, electrostatic, solvation and polymer-mediated

interactions, and basic models for the contact mechanics of adhesive and nonadhesive elasti-

cally deforming bodies. The eﬀects of interaction forces, molecular shape, surface structure

and roughness on adhesion and friction are discussed.

Simple models for the contributions of the adhesion force and external load to interfacial

friction are illustrated with experimental data on both unlubricated and lubricated systems, as

measured with the surface forces apparatus. We discuss rate-dependent adhesion (adhesion

hysteresis) and how this is related to friction. Some examples of the transition from wearless

friction to friction with wear are shown.

Lubrication in diﬀerent lubricant thickness regimes is described together with explana-

tions of nanorheological concepts. The occurrence of and transitions between smooth and

stick–slip sliding in various types of dry (unlubricated and solid boundary lubricated) and

liquid lubricated systems are discussed based on recent experimental results and models for

stick–slip involving memory distance and dilatancy.

9.1 Introduction: Types of Surface Forces

In this chapter, we discuss the most important types of surface forces and the rele-

vant equations for the force and friction laws. Several diﬀerent attractive and repul-

siveforces operatebetween surfacesand particles. Some forcesoccur in vacuum,for

example, attractive van der Waals and repulsive hard-core interactions. Other types

of forces can arise only when the interacting surfaces are separated by another con-

densed phase, which is usually a liquid. The most common types of surface forces

and their main characteristics are listed in Table 9.1.

418 Marina Ruths and Jacob N. Israelachvili

Table 9.1. Types of surface forces in vacuum versus in liquid (colloidal forces)

Type of force Subclasses or alternative names Main characteristics

Attractive forces

van der Waals Debye induced dipole force (v & s)

London dispersion force (v & s)

Casimir force (v & s)

Ubiquitous, occurs both in vacuum

and in liquids

Electrostatic Ionic bond (v)

Coulombic force (v & s)

Hydrogen bond (v)

Charge-exchange interaction (v & s)

Acid–base interaction (s)

“Harpooning” interaction (v)

Strong, long-range, arises in polar

solvents; requires surface charging or

charge-separation mechanism

Ion

correlation

van der Waals force of polarizable

ions (s)

Requires mobile charges on surfaces

in a polar solvent

Quantum

mechanical

Covalent bond (v)

Metallic bond (v)

Exchange interaction (v)

Strong, short-range, responsible for

contact binding of crystalline sur-

faces

Solvation Oscillatory force (s)

Depletion force (s)

Mainly entropic in origin, the oscilla-

tory force alternates between attrac-

tion and repulsion

Hydrophobic Attractive hydration force (s) Strong, apparently long-range; origin

not yet understood

Speciﬁc bind-

ing

“Lock-and-key” or complementary

binding (v & s)

Receptor–ligand interaction (s)

Antibody–antigen interaction (s)

Subtle combination of diﬀerent non-

covalent forces giving rise to highly

speciﬁc binding; main recognition

mechanism of biological systems

Repulsive forces

van der Waals van der Waals disjoining pressure (s) Arises only between dissimilar bod-

ies interacting in a medium

Electrostatic Coulombic force (v & s) Arises only for certain constrained

surface charge distributions

Quantum

mechanical

Hard-core or steric repulsion (v)

Born repulsion (v)

Short-range, stabilizing attractive co-

valent and ionic binding forces, ef-

fectively determine molecular size

and shape

Solvation Oscillatory solvation force (s)

Structural force (s)

Hydration force (s)

Monotonically repulsive forces,

believed to arise when solvent

molecules bind strongly to surfaces

Entropic Osmotic repulsion (s)

Double-layer force (s)

Thermal ﬂuctuation force (s)

Steric polymer repulsion (s)

Undulation force (s)

Protrusion force (s)

Due to conﬁnement of molecular or

ionic species; requires mechanism

that keeps trapped species between

the surfaces

9 Surface Forces and Nanorheology of Molecularly Thin Films 419

Table 9.1. (continued)

Type of force Subclasses or alternative names Main characteristics

Dynamic interactions

Non-

equilibrium

Hydrodynamic forces (s)

Viscous forces (s)

Friction forces (v & s)

Lubrication forces (s)

Energy-dissipating forces occurring

during relative motion of surfaces or

bodies

Note: (v) applies only to interactions in vacuum, (s) applies only to interactions in solution

(or to surfaces separated by a liquid), and (v & s) applies to interactions occurring both in

vacuum and in solution

In vacuum, the two main long-rangeinteractions are the attractive van der Waals

and electrostatic (Coulomb) forces. At smaller surface separations (corresponding

to molecular contact at surface separations of D ≈ 0.2nm), additional attractive in-

teractions can be found such as covalentor metallic bondingforces. These attractive

forces are stabilized by the hard-corerepulsion. Together they determine the surface

and interfacial energies of planar surfaces, as well as the strengths of materials and

adhesive junctions. Adhesion forces are often strong enough to elastically or plasti-

cally deform bodies or particles when they come into contact.

In vapors (e.g., atmospheric air containing water and organic molecules), solid

surfaces in, or close to, contact will generally have a surface layer of chemisorbed

or physisorbed molecules, or a capillary condensed liquid bridge between them.

A surface layer usually causes the adhesion to decrease, but in the case of capillary

condensation, the additional Laplace pressure or attractive “capillary” force may

make the adhesion between the surfaces stronger than in an inert gas or vacuum.

When totally immersed in a liquid, the force between particles or surfaces is

completely modiﬁed from that in vacuum or air (vapor). The van der Waals at-

traction is generally reduced, but other forces can now arise that can qualitatively

change both the range and even the sign of the interaction. The attractive force in

such a system can be either stronger or weaker than in the absence of the interven-

ing liquid. For example, the overall attraction can be stronger in the case of two

hydrophobic surfaces separated by water, but weaker for two hydrophilic surfaces.

Depending on the diﬀerent forces that may be operating simultaneously in solution,

the overall force law is not generally monotonically attractive even at long range;

it can be repulsive, or the force can change sign at some ﬁnite surface separation.

In such cases, the potential-energy minimum, which determines the adhesion force

or energy, does not occur at the true molecular contact between the surfaces, but at

some small distance further out.

The forces between surfaces in a liquid medium can be particularly complex at

short range, i.e., at surface separations below a few nanometers or 4–10 molecu-

lar diameters. This is partly because, with increasing conﬁnement, a liquid ceases

to behave as a structureless continuum with bulk properties; instead, the size and

shape of its molecules begin to determine the overall interaction. In addition, the

420 Marina Ruths and Jacob N. Israelachvili

surfaces themselves can no longer be treated as inert and structureless walls (i.e.,

mathematically ﬂat) and their physical and chemical properties at the atomic scale

mustnow be takeninto account. Theforce laws will then dependon whetherthe sur-

faces are amorphous or crystalline (and whether the lattices of crystalline surfaces

are matched or not), rough or smooth, rigid or soft (ﬂuid-like), and hydrophobic or

hydrophilic.

It is also important to distinguish between static (i.e., equilibrium) interactions

and dynamic (i.e., nonequilibrium) forces such as viscous and friction forces. For

example, certain liquid ﬁlms conﬁned between two contacting surfaces may take

a surprisingly long time to equilibrate, as may the surfaces themselves, so that the

short-range and adhesion forces appear to be time-dependent, resulting in “aging”

eﬀects.

9.2 Methods Used to Study Surface Forces

9.2.1 Force Laws

The full force law F(D) between two surfaces, i.e., the force F as a function of

surface separation D, can be measured in a number of ways [2–6]. The simplest

is to move the base of a spring by a known amount, ΔD

. Figure 9.1 illustrates this

method when applied to the interaction of two magnets.However, the method is also

applicable at the microscopic or molecular level, and it forms the basis of all direct

force-measuring apparatuses such as the surface forces apparatus (SFA; [3,7]) and

the atomic force microscope (AFM; [8–10]). If there is a detectable force between

the surfaces, this will cause the force-measuring spring to deﬂect by ΔD

, while the

surface separation changes by ΔD. These three displacements are related by

ΔD

=ΔD

−ΔD . (9.1)

The diﬀerence in force, ΔF, between the initial and ﬁnal separations is given by

ΔF = k

ΔD

, (9.2)

where k

is the spring constant. The equations above provide the basis for measure-

ments of the force diﬀerence between any two surface separations. For example, if

a force-measuring apparatus with a known k

can measure D (and thus ΔD), ΔD

and ΔD

, the force diﬀerence ΔF can be measured between a large initial or refer-

ence separation D, where the force is zero (F = 0), and another separation D−ΔD.

By working one’s way in increasing increments of ΔD =ΔD

−ΔD

, the full force

law F(D) can be constructed over any desired distance regime.

In order to measure an equilibrium force law, it is essential to establish that the

two surfaces have stopped moving before the displacements are measured. When

displacements are measured while two surfaces are still in relative motion, one also

measures a viscous or frictional contribution to the total force. Such dynamic force

9 Surface Forces and Nanorheology of Molecularly Thin Films 421

ΔD

Repulsion

Jump

Slope = k

Jump

Attraction

Force F

Distance D

Base

Fig. 9.1. Schematic attractive force law between two macroscopic objects such as two mag-

nets, or between two microscopic objects such as the van der Waals force between a metal tip

and a surface. On lowering the base supporting the spring, the latter will expand or contract

such that, at any equilibrium separation D, the attractive force balances the elastic spring

restoring force. If the gradient of the attractive force dF/dD exceeds the gradient of the

spring’s restoring force (deﬁned by the spring constant k

), the upper surface will jump from

A into contact at A



(A for “advancing”). On separating the surfaces by raising the base, the

two surfaces will jump apart from R to R



(R for “receding”). The distance R−R



multiplied

by k

gives the adhesion force, i.e., the value of F at the point R (after [1] with permission)

measurements have enabled the viscosities of liquids near surfaces and in thin ﬁlms

to be accurately determined [11–13].

In practice, it is diﬃcult to measure the forces between two perfectly ﬂat sur-

faces, because of the stringent requirement of perfect alignment for making reliable

measurements at distances of a few tenths of a nanometer. It is far easier to measure

the forces between curved surfaces, e.g., two spheres, a sphere and a ﬂat surface, or

two crossed cylinders. Furthermore, the force F(D) measured between two curved

surfaces can be directly related to the energy per unit area E(D) between two ﬂat

surfaces at the same separation, D, by the so-called Derjaguin approximation [14]:

E(D) =

F(D)

2πR

, (9.3)

where R is the radius of the sphere (for a sphere and a ﬂat surface) or the radii of the

cylinders (for two crossed cylinders, cf. Table 9.2).

422 Marina Ruths and Jacob N. Israelachvili

9.2.2 Adhesion Forces

The most direct way to measure the adhesion of two solid surfaces (such as two

spheres or a sphere on a ﬂat) is to suspend one of them on a spring and measure the

adhesion or “pull-oﬀ” force needed to separate the two bodies, using the deﬂection

of the spring. If k

is the stiﬀness of the force-measuring spring and ΔD is the dis-

tance the two surfaces jump apart when they separate, then the adhesion force F

is given by

= F

max

= k

ΔD , (9.4)

where we note that, in liquids, the maximum or minimum in the force may occur

at some nonzero surface separation (see Fig. 9.7). From F

and a known surface

geometry, andassumingthat the surfaceswere everywherein molecularcontact, one

may also calculate the surface or interfacial energy γ. For an elastically deformable

sphere of radius R on a ﬂat surface, or for two crossed cylinders of radius R,we

have [3,15]

γ =

3πR

, (9.5)

while for two spheres of radii R

and R

γ =

3π





, (9.6)

where γ is in units of Jm

−2

(see Sect. 9.5.2).

9.2.3 The SFA and AFM

In a typical force-measuring experiment, at least two of the above displacement pa-

rameters – ΔD

, ΔD,andΔD

– are directly or indirectly measured, and from these

the third displacement and the resulting force law F(D) are deduced using (9.1)

and (9.2) together with a measured value of k

. For example, in SFA experiments,

ΔD

is changed by expanding or contracting a piezoelectric crystal by a known

amount or by moving the base of the spring with sensitive motor-driven mechanical

stages. The resulting change in surface separation ΔD is measured optically, and the

spring deﬂectionΔD

can then be obtained according to (9.1). In AFM experiments,

ΔD

and ΔD

are measured using a combination of piezoelectric, optical, capaci-

tance or magnetic techniques, from which the change in surface separation ΔD is

deduced. Once a force law is established, the geometry of the two surfaces (e.g.,

their radii) must also be known before the results can be compared with theory or

with other experiments.

The SFA (Fig. 9.2) is used for measurements of adhesion and force laws be-

tween two curved molecularly smooth surfaces immersed in liquids or controlled

vapors [3,7,16]. The surface separation is measured by multiple-beam interferom-

etry with an accuracy of ±0.1nm. From the shape of the interference fringes one

9 Surface Forces and Nanorheology of Molecularly Thin Films 423

Fig. 9.2. A surface forces apparatus (SFA) where the intermolecular forces between two

macroscopic, cylindrical surfaces of local radius R can be directly measured as a function

of surface separation over a large distance regime from tenths of a nanometer to microme-

ters. Local or transient surface deformations can be detected optically. Various attachments

for moving one surface laterally with respect to the other have been developed for friction

measurements in diﬀerent regimes of sliding velocity and sliding distance (after [16] with

permission)

also obtains the radius of the surfaces, R, and any surface deformation that arises

during an interaction [17–19]. The resolution in the lateral direction is about 1µm.

The surface separation can be independently controlled to within 0.1nm, and the

force sensitivity is about 10

−8

N. For a typical surface radius of R ≈ 1cm,γ values

can be measured to an accuracy of about 10

−3

mJm

−2

Several diﬀerent materials have been used to form the surfaces in the SFA, in-

cluding mica [20, 21], silica [22], sapphire [23], and polymer sheets [24]. These

materials can also be used as supporting substrates in experiments on the forces

between adsorbed or chemically bound polymer layers [13,25–30], surfactant and

lipid monolayers and bilayers [31–34], and metal and metal oxide layers [35–42].

The range of liquids and vapors that can be used is almost endless, and have thus

far included aqueous solutions, organicliquids and solvents, polymer melts, various

petroleum oils and lubricant liquids, dyes, and liquid crystals.