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Tambe2008NanoscaleFrictionandWear.pdf
Downloaded from rsta.royalsocietypublishing.org on October 25, 2012
Nanoscale friction and wear maps
Nikhil S Tambe and Bharat Bhushan
Phil. Trans. R. Soc. A 2008 366, 1405-1424
doi: 10.1098/rsta.2007.2165
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Phil. Trans. R. Soc. A (2008) 366, 1405–1424
doi:10.1098/rsta.2007.2165
Published online 20 December 2007
Nanoscale friction and wear maps
B Y N IKHIL S. T AMBE 1, *
AND
B HARAT B HUSHAN 2
1
GE Global Research, John F. Welch Technology Center, Plot no. 122, EPIP
Phase 2, Hoodi Village, Whitefield Road, Bangalore 560 066, India
2
Nanotribology Laboratory of Information Storage and MEMS/NEMS, The
Ohio State University, 201 West 19th Avenue, Columbus, OH 43210-1142, USA
Friction and wear are part and parcel of all walks of life, and for interfaces that are in close
or near contact, tribology and mechanics are supremely important. They can critically
influence the efficient functioning of devices and components. Nanoscale friction force follows
a complex nonlinear dependence on multiple, often interdependent, interfacial and material
properties. Various studies indicate that nanoscale devices may behave in ways that cannot
be predicted from their larger counterparts. Nanoscale friction and wear mapping can help
identify some ‘sweet spots’ that would give ultralow friction and near-zero wear. Mapping
nanoscale friction and wear as a function of operating conditions and interface properties is a
valuable tool and has the potential to impact the very way in which we design and select
materials for nanotechnology applications.
Keywords: nanoscale friction; nanoscale wear; nanotribology; mechanism map
1. Introduction
Nanotechnology, defined literally as any technology performed on a nanoscale
that has applications in the real world (Feynman 1960), has spurred the
development of innovative micro/nanosystems with the discovery of novel
materials, processes and phenomena on the micro/nanoscale and led to the rapid
advancement of micro/nanoelectromechanical systems (MEMS/NEMS) and
their various biological and biomedical applications (BioMEMS). Recent years
have seen a multitude of new emerging applications in this field. Commercial
applications such as the microfluidic devices that can manipulate tiny amounts of
fluids, ‘lab-on-chip’ sensors used for drug delivery, accelerometers used for
automobile air bag deployment, and digital micromirror devices used in
hi-definition TVs and video projectors in homes and theatres are just the tip
of the iceberg (Bhushan 2007a). In fact, these MEMS/NEMS are now believed to
be the next logical step in the ‘silicon revolution’. Visionaries and leading
scientists and researchers, presenting at the National Nanotechnology Initiative
Workshop on Nanotechnology in Space Exploration held in Palo Alto, CA (USA)
in August 2004, have slated the emerging field of nanotechnology to be the next
disruptive technology that will have a major impact on the next one to three
* Author for correspondence ([email protected]).
One contribution of 8 to a Theme Issue ‘Nanotribology, nanomechanics and applications to
nanotechnology I’.
1405
This journal is q 2007 The Royal Society
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1406
N. S. Tambe and B. Bhushan
decades. It is estimated that the annual global impact of products where
nanotechnology will play a key role will exceed US$1 trillion by 2015 and would
require approximately 2 million nanotechnology workers (Roco 2003).
Despite the increasing popularity and technological advances in nanotechnology
applications, the severe tribological (friction and wear) problems tend to undermine
their performance and reliability. In fact, several studies have shown that the
tribology and mechanics of these devices are the limiting factors to the imminent
broad-based impact of nanotechnology on our everyday lives (Maboudian &
Howe 1997; Bhushan 1998, 2003, 2007a,b). Miniaturization and the subsequent
development of devices for nanotechnology applications require better tribological
performance of the system components and a fundamental understanding of the basic
phenomena underlying friction, wear and lubrication on the micro- and nanoscale
(Bhushan 1997, 1998, 1999a,b, 2001, 2007a,b). The components used in the micro/
nanostructures are very light (of the order of a few micrograms) and operate under
very light loads (of the order of a few micrograms to a few milligrams). Moving
from the macro- to nanoscale, the surface area-to-volume ratio increases
considerably and becomes a cause of serious concern from the tribological point of
view. On the nanoscale, surface forces, such as friction, adhesion, meniscus forces,
viscous drag and surface tension, which are proportional to area, significantly
increase and can limit the life and reliability of nanotechnology applications.
2. Measurement technique
The emergence of the new field of nanotribology, which pertains to the experimental
and theoretical investigations of interfacial processes occurring during adhesion,
friction, wear and thin film lubrication of sliding surfaces on the scales ranging from
the atomic and molecular scale to the microscale, and its associated techniques
(Bhushan 1999a) have provided a viable means of addressing the tribological issues
on the nanoscale. Nanotribological investigations can be performed using the surface
force apparatus that was pioneered by David Tabor, R. H. S. Winterton and Jacob
Israelachvili in the early 1970s at Cambridge University, and the atomic force
microscope (AFM) that was developed by Binnig et al. (1986). These instruments
have already provided valuable insights into the behaviour of materials on the
nanoscale (Bhushan et al. 1995; Bhushan 1999a, 2007a).
For studying surface interaction on the micro/nanoscale, the sharp tip of an
AFM is ideally suited and has been successfully employed by a number of
researchers for studying friction and wear properties of various materials,
coatings and lubricants (Mate et al. 1987; Ruan & Bhushan 1994; Koinkar &
Bhushan 1996; Bennewitz et al. 2001; Bhushan & Liu 2001; Liu & Bhushan 2003;
Tambe & Bhushan 2004, 2005a–i; Tambe 2005; Gnecco et al. 2007; Tao &
Bhushan 2007). Contrary to the classical friction laws postulated by Amontons
(1699) and Coulomb (1785) centuries ago, nanoscale friction force is found to be
strongly dependent on the normal load and sliding velocity. Many materials,
coatings and lubricants that have wide applications show reversals in friction
behaviour corresponding to the transitions between friction mechanisms
(Bowden & Tabor 1950, 1964; Singer & Pollock 1992; Bhushan 1999b; Tambe
2005; Tambe & Bhushan 2005b,f,i; Gnecco et al. 2007; Tao & Bhushan 2007).
Recently, Tambe & Bhushan (2005a) and Tao & Bhushan (2006) developed new
Phil. Trans. R. Soc. A (2008)
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Nanoscale friction and wear maps
1407
tip sliding direction
1 µm
Figure 1. SEM image of wear mark and debris for Si(100) produced at a normal load of 40 mN and
one scan cycle (Bhushan 2007a).
AFM-based techniques for studying the effect of sliding velocity on nanoscale
friction behaviour for velocities from a few mm sK1 to hundreds of mm sK1. This
has enabled friction investigations to be conducted in velocity ranges that are of
scientific as well as engineering significance.
The AFM can be used to investigate how surface materials can be moved
or removed on the nanoscale, for example, in scratching and wear (Bhushan 1999a,
2005), where these things are undesirable and nanofabrication/nanomachining,
where they are desirable (Bhushan 2007a). A ‘continuous microscratch’ technique
developed for an AFM by Sundararajan & Bhushan (2001) gave a direct
dependence of the scratch/wear depth on the applied normal load and has been
used for understanding critical loads for ‘visible’ wear damage (Sundararajan &
Bhushan 2001; Liu & Bhushan 2002; Tambe & Bhushan 2005g). Figure 1 shows a
typical scanning electron microscopic image of such a wear mark and the associated
wear particles. The mechanism of material removal during nanoscale wear under
ultralow loads was studied by Koinkar & Bhushan (1997) and Zhao & Bhushan
(1998) using both a scanning electron microscope and a transmission electron
microscope (TEM). They reported an increase in the number and size of cuttingtype particles with the normal load, thereby suggesting nanoscale wear by plastic
deformation. They undertook a systematic study to analyse wear debris and
concluded based on the evidence they found from the TEM images and the
diffraction patterns that the strain fields arising inside the wear mark with no
applied stress, the ribbon-like wear debris observed outside the wear mark, an
absence of phase transformation (amorphization) and the existence of dislocation
arrays all pointed to a process wherein the material was being removed by a cutting
action via plastic deformation and with a small contribution from elastic fracture.
To understand the wear mechanisms on the nanoscale, Bhushan et al. (1994)
studied the evolution of wear using an AFM. They observed that wear evolution was
not uniform, but was initiated at the sites of nanoscratches where the surface defects
(with high surface energy) acted as initiation sites for wear. Wear precursors
(precursors to measurable wear) were studied by making surface potential
measurements (DeVecchio & Bhushan 1998; Bhushan & Goldade 2000a,b). The
Phil. Trans. R. Soc. A (2008)
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1408
N. S. Tambe and B. Bhushan
(a)
(i)
(ii)
1 µN
9 µN
10 µm
0
10 µm
100 nm
(b) (i)
0
200 mV
(ii)
5 µm
0
25 nm
5 µm
0
150 mV
Figure 2. (a) (i) Surface height and (ii) surface potential maps of wear regions generated at 1 and
9 mN on a single-crystal aluminium sample showing bright contrast in the surface potential mapping
on the worn region. (b) Close-up scan of upper (low load) wear region (DeVecchio & Bhushan 1998).
contact potential difference, or simply the surface potential between two surfaces,
depends on a variety of parameters such as electronic work function, adsorption and
oxide layers. The surface potential map of an interface gives a measure of changes in
the work function, which is sensitive to both physical and chemical conditions of the
surfaces, including structural and chemical changes. Before the material is actually
removed in a wear process, the surface experiences stresses that result in surface and
subsurface changes of structure and/or chemistry. These can cause changes in the
measured potential of a surface. An AFM tip allows mapping of the surface potential
with nanoscale resolution. Surface height and change in the surface potential maps of
a polished single-crystal aluminium (100) sample abraded using a diamond tip at
loads of 1 and 9 mN are shown in figure 2a. (Note that the sign of the change in the
surface potential is reversed here from that in DeVecchio & Bhushan (1998).) It is
evident that both the abraded regions show a large potential contrast (approx.
0.17 V) with respect to the non-abraded area. The black region in the lower
Phil. Trans. R. Soc. A (2008)
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1409
Nanoscale friction and wear maps
wear mark
AFM tip
direction of
motion of tip
direction
of motion
of sample
sample mounted on
high-velocity piezo stage
Figure 3. Novel nanowear mapping technique, achieved by controlled movement of the AFM tip while the
sample is sliding perpendicular to the direction of the AFM tip movement (Tambe & Bhushan 2005h).
right-hand part of the topography scan shows a step that was created during the
polishing phase. There is no potential contrast between the high region and the low
region of the sample, indicating that the technique is independent of surface height.
Figure 2b shows a close-up scan of the upper (low load) wear region shown in figure 2a.
Note that while there is no detectable change in the surface topography, there is,
nonetheless, a large change in the potential of the surface in the worn region. Indeed,
the wear mark in figure 2b might not have been visible at all in the topography map,
were it not for the noted absence of wear debris generated nearby and then swept
off during the low load scan. Thus, even in the case of zero wear (no measurable
deformation of the surface using the AFM), there can be a significant change in the
surface potential inside the wear mark, which is useful for the study of wear
precursors. It is believed that the removal of the thin contaminant layer including the
natural oxide layer gives rise to the initial change in the surface potential. The
structural changes, which precede the generation of wear debris and/or measurable
wear scars, occur under ultralow loads in the top few nanometres of the sample and
are primarily responsible for the subsequent changes in the surface potential.
One way of exploring the broader wear patterns is to construct wear mechanism
maps (Tabor 1983) that summarize the data and models for wear, thereby showing
not only how the mechanisms interface but also allowing the dominant mechanisms
for any given set of conditions to be identified. On the macroscale, the approach
followed by various researchers to map wear involves running a multitude of
experiments that measure the wear rate at a given normal load (or normal pressure)
and a relative sliding velocity and then plotting wear maps based on the failure data
or the rate of removal of material during wear (Bowden & Tabor 1950, 1964; Singer &
Pollock 1992; Bhushan 1999b). Lim & Ashby (1987) constructed wear maps using
empirical data as well as theoretical analysis. They demonstrated the utility of the
wear mechanism mapping method as a way of classifying and ordering wear data and
of showing the relationships between competing wear mechanisms.
A novel AFM-based technique was developed by Tambe & Bhushan (2005h)
to generate wear maps on the nanoscale by varying the sliding velocity, the
number of sliding cycles and the normal load. For generating nanoscale wear
maps, a raster scanning mode was used. The sample was oscillated using the
piezo stage and simultaneously the AFM tip was dragged perpendicular to
the direction of motion of the sample (figure 3). The sample oscillation frequency
Phil. Trans. R. Soc. A (2008)
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1410
N. S. Tambe and B. Bhushan
(scan speed), the AFM tip velocity and the normal load were controlled to
achieve appropriate relative sliding velocities, normal loads and a specific
number of sliding cycles. The relative sliding velocity was varied by changing the
scan speed, while the number of sliding cycles was varied by varying the rate of
movement of the AFM tip (i.e. the velocity of the AFM tip while sliding
perpendicular to the direction of motion of the sample; this varying rate of
movement results in the AFM tip residing for different time intervals on the
sample surface and thereby the number of sliding cycles obtained at each location
on the sample surface is different).
For studying the effect of increasing normal load and increasing number of sliding
cycles at constant sliding velocity, the AFM tip was programmed to make
controlled movements at desired normal loads and velocities. This controlled
motion of the AFM tip was achieved using custom software code written in
NANOSCRIPT1 (Anon. 1999). To achieve varying sliding velocities across the scan
area, the input voltage pulse for the piezo stage was slightly modified. In normal
operation, a triangular time-varying voltage pulse is provided to the piezo stage to
achieve scanning operation and to obtain a constant sliding velocity. For the wear
mapping experiments, a parabolic voltage pulse was used as an input to drive the
piezo. This resulted in a steady increase in the sliding velocity across the scan area.
The synchronized and controlled movement of the AFM tip and the sample is a
novel approach for obtaining nanoscale wear maps and helps generate a visual
representation of the sample surface wear as a function of sliding velocity, applied
normal load and number of sliding cycles (Tambe & Bhushan 2005h). Using this
approach, a wear map can be generated in one single experiment, as against the
rather cumbersome approach where the researchers conduct multiple experiments
at different normal loads, sliding velocities and for different number of sliding cycles
and then generate a contour map for the sample wear based on individual data
points obtained from each experiment.
3. Nanoscale friction maps and mechanisms
Most of the analytical models developed for explaining nanoscale friction
behaviour have remained limited in their focus and have left investigators shorthanded when trying to explain friction behaviour scaling multiple regimes.
Nanoscale friction maps provide fundamental insights into friction behaviour.
They help identify and classify the dominant friction mechanisms, as well as
determine the critical operating parameters that influence transitions between
different mechanisms (Tambe & Bhushan 2005i). Figure 4 shows the nanoscale
friction maps obtained by varying the normal load and the sliding velocity
(details of the samples used are given in table 1). The contours represent
constant friction force lines and are marked by the value of the friction force in
nN. Horizontal contour lines indicate the velocity-independent nature of the
friction force. This behaviour is found at high velocities for highly oriented
pyrolytic graphite (HOPG), at moderately high velocities for Al and at low
velocities for polymethylmethacrylate (PMMA). Studies on the nanoscale
friction force dependence on velocity (Riedo et al. 2003; Gnecco et al. 2007)
indicate that friction force becomes constant relative to sliding velocity when the
1
NANOSCRIPT is a trademark of Veeco Metrology.
Phil. Trans. R. Soc. A (2008)
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1411
Nanoscale friction and wear maps
normal load (nN)
(a) (i)
50
16
14
30
8 12
10
4
6
(ii)
50
40
30
10
20
8 6
normal load (nN)
40
30
16
0.13 0.10
12
80
60
11.0
7.0
9.5
20 5.0 8.0
4.0
10
103
10
102
–1
velocity (µm s )
(b)
40
20
8
0.04
(v)
100
12.3
3.0
0.15
10
(iv)
50
0.20
0.07
0.04
(iii)
24
8.0
2.0
32
120
6.2
80
40
3.4
102
1.01.5
(vi)
160
5.2
4.3
3.4
2.5
2.5
10
velocity (µm s–1)
103
(i)
(ii)
(iii)
(iv)
(v)
(vi)
28
24
20
16
12 8
10
103
–1
velocity (µm s )
102
Figure 4. (a) Contour maps showing friction force dependence on a range of normal loads and
sliding velocities for different samples at 208C and 50% RH (contours are lines with constant
friction force in nN). (i) Si(100), (ii) HOPG, (iii) diamond-like carbon, (iv) Al, (v) PMMA,
(vi) polydimethylsiloxane. (b) The summary of characteristic contour patterns and their
significance (note that the normal load is the ordinate and the velocity is the abscissa). (i)
Horizontal contour lines, velocity independence of friction force; (ii) vertical contour lines, normal
load independence of friction force; (iii) parallel contour lines with a negative slope, atomic scale
stick–slip contribution to friction force; (iv) parallel contour lines with a positive slope, stick–slip
and meniscus contribution to friction force; (v) concentric contour lines, phase transformation,
localized melting; (vi) sudden change in the direction of contour lines, change in the dominating
friction mechanism ( Tambe & Bhushan 2005f ).
atomic scale stick–slip occurring at low sliding velocities loses its dominance. A
constant friction force with respect to sliding velocity would appear as horizontal
contour on a friction map and is the reason, for example, for the horizontal
contours observed for HOPG at high velocities. Vertical contour lines indicate a
normal load independence of friction force. In all the samples studied, this
behaviour is not observed, although the steep contour lines for Si(100), HOPG
and Al indicate that there is a very small normal load dependence on friction at
low velocities. For all practical instances, it would be impossible to find a
material that shows normal load independence of friction force.
Some other characteristic contours are those with slanting lines (with either a
positive or negative slope). These friction contours arise from the microscale
stick–slip-related contributions or from the formation of meniscus bridges by
Phil. Trans. R. Soc. A (2008)
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1412
N. S. Tambe and B. Bhushan
Table 1. Specimen description/preparation details.
material
details
Si(100)
HOPG
DLC
Al
Wafer World, Inc. (West Palm Beach, FL, USA)
highly oriented pyrolytic graphite (freshly cleaved before experiments)
filtered cathodic arc deposition on Si(100) substrate, 10 nm thick film
250 nm thick Al alloy film on Si substrate (film consists of an alloy with more than
90% Al and traces of Ti and Si)
10% by weight of PMMA dissolved in an organic solvent (anisole) is spin coated
on a glass substrate, 1–2 mm thick film
mixture of a translucent base in a curing agent (10 : 1 ratio) is vacuum dried
and cured for 48 h at room temperature
PMMA
PDMS
preferential condensation of liquid films at the sliding interface, particularly for
hydrophilic interfaces. Stick–slip can originate from the atomic scale stick–slip
leading to an increase in friction force with velocity (Riedo et al. 2003; Gnecco et al.
2007) and thus appearing as slanted contours with a positive slope. HOPG,
diamond-like carbon (DLC) and Al showed this behaviour. Stick–slip originating as
a result of some other mechanisms can result in a decrease in friction force with
an increase in sliding velocity (Ruths & Israelachvili 2007). This behaviour would
result in slanted contours with a negative slope on the friction map such as that seen
for PMMA at high sliding velocities and for polydimethylsiloxane (PDMS). The
friction force arising from meniscus contributions, found for the hydrophilic surfaces
such as Si(100), results in the drop in friction force with an increase in sliding
velocity. A minimum threshold equilibrium time is necessary for the formation of
stable meniscus bridges at contacting and near-contacting asperities for a sliding
interface (Bouquet et al. 1998; Tambe & Bhushan 2005b). With increasing velocity,
fewer meniscus bridges build up at the interface, and thus the overall contribution
to friction force drops with an increase in velocity. This behaviour would manifest
itself in the form of slanted contour lines with a negative slope on the friction map.
Contour maps can also consist of concentric contour lines suggesting a peak
friction force for a particular critical normal load–sliding velocity combination.
Any change in the normal load or the sliding velocity around this critical value
would result in a decrease in the friction force. This kind of behaviour typically
would imply localized melting at the contact zone or a phase transformation by
the formation of a low friction phase at the interface. Localized melting would
arise from very high frictional energy dissipation and is expected particularly in
the case of polymer materials. PMMA appeared to show concentric lines at
moderately high velocities; however for the given range of normal load and
sliding velocity, the experimental evidence is not sufficient to support this
hypothesis. Phase transformation has been known to occur for DLC resulting in a
low friction graphite-like layer by an sp3 to sp2 phase transition (Grill 1997;
Tambe & Bhushan 2005e). The sharp Si3N4 tip used in the AFM studies
(30–50 nm radius) gives rise to contact pressures in the range of 1.8–3.8 GPa for
DLC films corresponding to the normal loads of 10–100 nN (assuming Hertzian
contact analysis for single-asperity elastic contact), and Voevodin et al. (1996)
have reported the formation of debris with polycrystalline graphite-like structure
for contact pressures in the range of 0.8–1.1 GPa.
Phil. Trans. R. Soc. A (2008)
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1413
Nanoscale friction and wear maps
Table 2. Young’s modulus (E ) and measured values of coefficient of friction. (All measurements
were performed using Si3N4 AFM tips of nominal radius 30–50 nm in controlled environment of
20G28C and 50% RH.)
material E (GPa)
reference
r.m.s.
coefficient roughness
of friction (nm)
diamond 1140
Field (1992)
0.05
2.3
SiC
395
0.02
0.89
DLC
Si(111)
280
188
Sundararajan &
Bhushan (1998)
Bhushan (1999d )
Anon. (1988)
0.03
0.04
0.14
0.14
Polysilicon
Si(100)
Al alloy
film
Au(111)
167
0.04
0.86
130
91
Sundararajan &
Bhushan (1998)
Anon. (1988)
Wei et al. (2004)
0.05
0.06
0.14
1.6
77
Anon. (2004)a
0.035
0.37
SiO2
73
0.05
0.14
HOPG
PMMA
PDMS
Bhushan & Gupta
(1997)
Field (1992)
9–15
0.008
7.7
0.07
0.36–0.87 MPa Livermore & Voldman 0.1
(2004)
reference
Bhushan & Kulkarni
(1996)
Sundararajan &
Bhushan (1998)
Bhushan & Kulkarni
(1996)
Sundararajan &
Bhushan (1998)
Bhushan & Liu
(2001)
Bhushan & Kulkarni
(1996)
0.09
0.98
a
http://www.matweb.com.
Another interesting facet in the friction maps is the region where the contour
lines change direction. This implies a change in the dominant friction
mechanism, which can be abrupt as seen for Si(100) and Al or gradual as for
DLC and PDMS. Generally speaking, the contours for each material are
characteristic of the friction behaviour exhibited by that particular material.
There are some features that can be classified as universal irrespective of the
material though. Each characteristic contour suggests a specific friction
mechanism. Based on the specific arrangement of contour lines, the dominant
friction mechanisms can be identified. In figure 4b, the most commonly observed
features in the contours (or the characteristic contours) as found from the study
are summarized and the significance of each is stated. It is evident that different
mechanisms are dominant for different operating conditions and the factors that
influence them include not only the normal load and the sliding velocity but also
other factors such as the operating environment (humidity and temperature),
surface roughness and mechanical properties of the interface.
The interdependence between friction and material properties on the
nanoscale is of significant interest for selecting materials that would be ideal
from the tribology point of view, i.e. materials with low friction and adhesion.
Scientific studies indicate that mechanical properties can strongly affect the
tribological performance (Bhushan 1999b). Efforts to explicitly characterize
Phil. Trans. R. Soc. A (2008)
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1414
N. S. Tambe and B. Bhushan
coefficient of friction
0.15
polysilicon
0.10
Si(100)
DLC
0.05
PDMS
A1
SiO2
Si(111)
PMMA
diamond
Au (111)
SiC
0
10 –4
10 –3
HOPG
10 –2
10 –1
1
10
1/E (GPa–1)
Figure 5. Coefficient of friction dependence on Young’s modulus. Measurements were conducted
using a Si3N4 tip at 208C and 50% RH ( Tambe & Bhushan 2005f ).
the nanoscale friction and adhesion of various materials on the basis of their
mechanical properties remain limited though. Recently, Tambe & Bhushan
(2005f ) have established a link between Young’s modulus of materials and their
coefficient of friction and adhesive force over a range of sliding velocities.
Table 2 lists the materials used in this study along with their Young’s modulus
(E ) and the corresponding coefficient of friction values. Also listed are the
materials studied by previous researchers under identical experimental and
environmental conditions. In the case of the materials for which a range of values
has been reported for the coefficient of friction, the average values are listed. A
clear trend was observed for the coefficient of friction dependence on E (figure 5).
Low-E materials show higher coefficient of friction when compared with the highE materials. (It has to be noted that the sliding interface will only undergo elastic
deformations under the very low normal loads used in the experiments.) This
result can be intuitively inferred from the classical theories of friction (Bowden &
Tabor 1964; Bhushan 1999b; Persson 2000). An approximate relation can be
developed between the coefficient of friction and Young’s modulus by assuming a
single-asperity elastic contact and using Hertzian contact analysis. For most
sliding interfaces though, the contact is often a multi-asperity contact and no
closed-form analytical solutions exist. Numerical methods have to be employed
for solving problems dealing with multi-asperity contact (Bhushan 1999b).
Moreover, nanoscale friction and adhesion are largely dependent on the sample
surface roughness and the shear strength of the sliding interface (Bhushan 1999b;
Persson 2000). Table 2 indicates that the roughness values of the samples are not
the same, although they are comparable. In light of this limitation on the
analytical formulations and the inherent complexity involved in relating
the nanoscale friction and adhesion to the material properties, the near
logarithmic dependence of the coefficient of friction on Young’s modulus shown
by a wide variety of materials in the experimental data is extremely interesting.
Only HOPG stands out as an anomaly in this trend and this is owing to its
extremely low shear strength.
Figure 6 shows the velocity dependence of adhesion and the coefficient of
friction over a range of velocities for different materials. The contour maps
(figure 6) give Young’s modulus dependence of these two quantities for the same
Phil. Trans. R. Soc. A (2008)
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1415
Nanoscale friction and wear maps
PDMS
PMMA
102 Si(100)
Al
coefficient of friction
(d )
0.2
PMMA
Si(100)
PDMS
Al
0.1
DLC
0
1
10
103
104
102
–1
velocity (µm s )
160 nN
103
102
20
10
DLC
10
(c)
velocity (µm s–1)
(b) 104
velocity (µm s–1)
adhesive force (nN)
(a) 103
104
0.16
103
102
0.04
10
105
1
10
102
,
Young s modulus (GPa)
Figure 6. Velocity dependence of (a) adhesive force and (c) coefficient of friction for various
materials and (b,d ) contour plots giving the dependence as a function of Young’s modulus
( Tambe & Bhushan 2005f ).
materials. Some very interesting trends are revealed by the contour maps.
Adhesion is high for low-E materials and at low sliding velocities, and it
gradually decreases with an increase in velocity. The velocity dependence of
friction and adhesion in the case of viscoelastic polymers (such as PDMS used in
this study) is well known, and is defined by a definite peak occurring at a specific
sliding velocity (Moore 1972). Similar behaviour was found even in the case of
materials with higher Young’s modulus where the adhesive force increased with
the velocity and reached a peak. Moreover, the peak was attained at higher
velocities for materials with higher E value. The contour map for coefficient of
friction also reveals peculiar trends. At low velocities, the coefficient of friction
decreases with increasing Young’s modulus, and this decrease is found to be
nearly logarithmic in nature (figure 5). However, at high velocities, this trend is
reversed and the coefficient of friction is found to increase with increasing
Young’s modulus. At high velocities, friction is primarily governed by impact
deformations and ploughing effect (Bhushan 1999b; Tambe & Bhushan 2005b).
Thus, while low-E materials are able to absorb most of the impacts during
sliding, for the high-E materials, the impacts during sliding result in high
friction. DLC is the only high-E material that shows a decrease in the coefficient
of friction at very high sliding velocities. The reason for this anomaly is the phase
transformation of the amorphous DLC to a low shear strength graphite-like
phase (Voevodin et al. 1996; Grill 1997; Tambe & Bhushan 2005e).
The contour map reveals a small central zone of very low friction. The
corresponding adhesive force values for this zone are also moderate. This can be
considered as a ‘sweet spot’ and corresponds to an ideal material that a tribologist
would like to choose. HOPG falls in this zone. Various other zones of interest are
Phil. Trans. R. Soc. A (2008)
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1416
>1 mm s–1
m increases with
,
Young s modulus
high
adhesion
<10 µm s–1
increasing sliding velocity
N. S. Tambe and B. Bhushan
high
sweet spot,
adhesion
moderate adhesion
low m
m decreases with
,
Young s modulus
soft
material
low
friction and
adhesion
hard
material
increasing Young,s modulus
Figure 7. Map for identifying tribologically ideal materials with low friction and adhesion. At low
velocities (less than 10 mm sK1), the coefficient of friction (m) decreases logarithmically with
Young’s modulus. At high velocities (more than 1 m sK1), m increases with an increase in Young’s
modulus. The ‘sweet spot’ corresponds to materials with low m and moderate adhesion. The ideal
zone for material selection is however the one where both m and adhesion are either low or
moderate and is the shaded diagonal portion ( Tambe & Bhushan 2005f ).
shown in figure 7. They indicate the dependence of Young’s modulus on the
operating parameters and thus can be used as a guide for material selection for
various nanotechnology applications. We find that, from the tribology point of
view, low-E materials show promise for high sliding velocity applications, while
high-E materials are more suitable for relatively lower sliding velocities.
Material maps created by plotting the coefficient of friction and adhesion as a
function of Young’s modulus reveal various interesting facets of the behaviour of
nanoscale friction. For example, the coefficient of friction decreased with increasing
velocity for materials with low Young’s modulus, but the reverse was true for
materials with high Young’s modulus. The map shows that if the sliding velocities are
high, then a compliant material would perform better than a stiffer material.
4. Nanoscale wear maps and mechanisms
Similar to friction mapping, one way of exploring the broader wear patterns is to
construct wear mechanism maps that summarize data and models for wear,
thereby showing mechanisms for any given set of conditions. Figure 8a shows
the wear maps obtained for Si(100) by varying different operating parameters.
The wear mark is roughly located at the centre of each image. The arrow marks
on the sides of the AFM images indicate the beginning and the end of the wear
marks. A larger area was imaged after the wear mapping tests to enable
comparison of the worn surface with respect to the virgin surface in its vicinity.
The AFM images reveal the dependence of wear on the operating parameters.
Drastic failure was observed for high normal loads. This is evident from the large
amount of debris found for the experiment conducted by keeping the sliding
Phil. Trans. R. Soc. A (2008)
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Nanoscale friction and wear maps
1417
velocity and the number of sliding cycles constant at 2.5 mm sK1 and 500,
respectively, and varying normal load from 0 to 5000 nN. For low loads, no
visible wear debris is found. Wear edges start becoming visible approximately for
loads over 2000 nN and ultimately catastrophic failure is seen at and above
approximately 4000 nN. A similar experiment was conducted by maintaining a
constant sliding velocity and varying the number of sliding cycles and the normal
load, but the number of cycles was increased to 2500 and the normal load was
varied from 0 to 1000 nN. In this case, no catastrophic failure was observed. The
wear mark was visible in the form of piled-up debris at the edges. The pile-up was
higher at higher normal loads. This indicates that for the given set of test
parameters, the effect of normal load is more pronounced. The third AFM image
in figure 8a corresponds to the wear map obtained by keeping the sliding velocity
and the normal load constant at 2.5 mm sK1 and 1000 nN, respectively, and
varying the number of sliding cycles from 0 to 250 across the scan area. In this
case, the amount of debris pile-up was minimal and the wear mark edges were
barely visible.
Figure 8b shows the results obtained for DLC. Wear maps were obtained by
varying the normal load from 0 to 1000 nN and keeping the number of sliding
cycles and the sliding velocity constant. For experiments conducted at
200 mm sK1, the wear mark edges were barely visible. However, considerable
wear was visible for a sliding velocity of 2.5 mm sK1. The wear mark generated
suggests that the effect of sliding velocity is more profound than that of the
normal load. The larger concentration of debris particles, towards the end of
the wear region, indicates that in general higher wear occurs for higher normal
loads as expected. The effect of the number of sliding cycles on wear behaviour
was investigated by keeping the normal load constant at 500 nN and the sliding
velocity constant at 2.5 mm sK1. The wear mark generated from these
experiment shows larger accumulation of wear debris for a larger number of
sliding cycles. The wear marks for DLC appear ‘fuzzy’ as the loose debris easily
moves during imaging. In comparison with Si(100), DLC sample shows larger
amount of wear debris for lower normal loads and number of sliding cycles.
Also, the effect of sliding velocity is found to be more profound on the
generation of wear particles. The mechanisms of wear in both Si(100) and
DLC are completely different. While Si(100) is a brittle material and wear
occurs by two- and three-body abrasion, for DLC wear is the result of phase
transformation as discussed above.
The wear maps in figure 8 indicate that wear debris particles are generated
only for certain combinations of sliding velocities, normal loads and number
of sliding cycles. In these wear maps, only one operating parameter was
varied at a time. To obtain true wear maps that can reveal different wear
mechanisms simultaneously, it is necessary to vary both normal load and
sliding velocity and investigate the resulting wear. Such a nanowear map
obtained for DLC for a normal load range of 0–1000 nN and sliding velocity
range of 0–2.5 mm sK1 is shown in figure 9. Wear debris was seen to form only
for particular sliding velocities and normal loads, i.e. beyond certain threshold
frictional energy dissipation. Hence, the wear area was curved indicating that
for lower velocities and lower normal loads, there is no phase transformation.
For clarity, the wear mark corners are indicated by white dots in the AFM
Phil. Trans. R. Soc. A (2008)
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1418
N. S. Tambe and B. Bhushan
effect of normal load
(b)
5 nm
wear mark
edges
0–5000 nN
0 –1000 nN
(a)
0
2 µm
2 µm
2.5 mm s–1, 500 cycles
200 µm s–1, 25 cycles
0 –1000 nN
wear mark
edges
2 µm
2 µm
2.5 mm s–1, 2500 cycles
2.5 mm s–1, 25 cycles
0 –250 cycles
effect of number of sliding cycles
2 µm
2.5 mm s–1, 1000 nN
2 µm
2.5 mm s–1, 500 nN
Figure 8. (a) Wear maps showing the effect of normal load and sliding velocity, as well as the effect of
the number of sliding cycles for Si(100). (b) Wear maps showing the effect of normal load and sliding
velocity, as well as the effect of the number of sliding cycles for DLC ( Tambe & Bhushan 2005h).
image and the various zones of interest over the entire wear mark are
illustrated in figure 9.
Analogous to nanowear mapping, the nanoscale friction maps can also be
generated by extending the same technique to monitoring of the friction force
during scanning for wear. In §3, we discussed the nanoscale friction mapping
as a function of two operating parameters: sliding velocity and normal load. In
addition, friction force can be plotted as a function of the number of sliding
cycles, thereby giving the time dependence as well. The nanofriction mapping
in conjunction with the nanowear mapping can provide valuable information
regarding the operating parameter dependence of nanoscale friction and wear.
Tambe & Bhushan (2005d ) have demonstrated the effectiveness and utility of
these techniques when used in tandem while studying the phase transformation-related reduction in friction force for DLC.
Phil. Trans. R. Soc. A (2008)
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1419
Nanoscale friction and wear maps
(a)
2 µm
5 nm
wear mark
corners
0
(b)
region of
highest wear
increasing
normal load
0–1000 nN
wear mark
boundary
(dashed line)
phase transformation
boundary
increasing velocity
0 –2.5 mm s–1
Figure 9. (a) AFM image and (b) schematic of nanowear map illustrating the influence of sliding
velocity and normal load on the wear of DLC resulting from phase transformation. Curved area in
(b) shows debris lining and is indicative of the minimum frictional energy needed for phase
transformation ( Tambe & Bhushan 2005h).
5. Friction and wear mechanisms on nanoscale and comparison
with macroscale
Friction and wear are part and parcel of all walks of life, and for interfaces that are in
close or near contact, tribology and mechanics are supremely important. They can
critically influence the efficient functioning of devices and components. Friction and
wear at a sliding interface depend on the operating conditions such as normal load
and sliding velocity; material properties such as Young’s modulus and hardness;
environmental conditions such as humidity and the medium to which the interface
is exposed, such as air, a specific gas or simply water; and interface properties such
as surface roughness and surface energy. Many of the commonly observed friction
and wear mechanisms are shown in figure 10. A review of classical literature
involving the pin-on-disc type of set-up as well as recent investigations with AFMs
(Tambe 2005) would show that the order in which the mechanisms are illustrated in
the figure from left to right follows from an increasing order of dominance with the
increasing sliding velocity and/or normal load, with the ones on the left found to
dominate at low sliding velocities and/or normal loads. It should of course be noted
that this precedence order is an observation found from studying many materials,
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1420
N. S. Tambe and B. Bhushan
individual
atoms
friction
force
Rt
impact wear
debris
meniscus
bridge
scan length
Ry(OH)x
atomic
stick–slip
tribochemical
reactions
meniscus bridges
meniscus bridge formation at near- contacting
asperities is governed by the asperity spacing e
e > emax
AFM
tip
sample
surface
near-contacting
asperity
viscous fluid
film shearing
zone of plastic
deformation
asperity impacts /
plastic deformations
phase transformations
phase transformation at the
tip sample interface
meniscus
bridges
viscous fluid
film shearing
interface layer
contacting asperity
Figure 10. Most commonly observed mechanisms of friction and wear: nanoscale and macroscale.
coatings and lubricants and could be different for some cases. On the macroscale,
most of these mechanisms exist but they may not all have a role to play
simultaneously. On the nanoscale, however, this is not the case. The nanoscale
friction force follows a complex nonlinear dependence on multiple, often
interdependent, interfacial and material properties.
Studies have shown that the fundamental laws of friction, as stated by
Amontons and Coulomb, no longer hold on the nanoscale and tribological
properties such as coefficient of friction and wear rates can be different on the
nanoscale than on the macroscale (Bhushan et al. 1995; Bhushan & Kulkarni
1996; Bhushan 1999a,c, 2007a). Many studies have shown a strong size or scale
dependence for mechanical properties such as indentation hardness (Bhushan &
Koinkar 1994; Bhushan & Kulkarni 1996; Bhushan et al. 1996; Bhushan 1998,
1999a–c, 2007a; Nix & Gao 1998; Hutchinson 2000), tensile strength (Hutchinson
2000) and bending strength (Sundararajan & Bhushan 2002), indicating that the
bulk properties of many materials differ from those on the micro/nanoscale. The
scale invariance of the theory of linear elasticity and the conventional plasticity
theories has lead to the formulation of the strain-gradient plasticity theory
(Fleck et al. 1994; Nix & Gao 1998; Gao et al. 1999; Huang et al. 2000;
Hutchinson 2000). The theory, developed for microscale deformation, predicts a
dependence of mechanical properties on the strain gradient, which is scale
dependent. Recently, the strain-gradient plasticity theory has been used for
modelling the scale effects in friction and wear (Bhushan & Nosonovsky 2003,
2004a,b; Nosonovsky & Bhushan 2005).
These studies indicate that micromechanical devices may behave in ways that
cannot be predicted from their larger counterparts. It is encouraging in this
regard to find that materials’ properties at small scales can be superior.
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Nanoscale friction and wear maps
1421
Nanoscale friction and wear mapping can help identify some sweet spots that
would give ultralow friction and near-zero wear. Mapping nanoscale friction and
wear as a function of operating conditions and interface properties is a valuable
tool and has the potential to impact the very way in which we design and select
materials for nanotechnology applications.
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