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

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the model described here for a hexagonal lattice can be generalized to a surface of arbitrary symmetry.

A more elaborate model will be presented in Section 6.4.3.4.

6.3.1.3 SFFM in Ultrahigh Vacuum

In air, adhesive forces are mainly due to the liquid meniscus which condenses around the tip–sample

contact. Because adsorbed water is always present under ambient conditions, the tip–sample contact is

not a well-deﬁned system. Therefore, although experiments in air are generally much more relevant to

technical problems, experiments performed in ultrahigh vacuum (UHV) are easier to understand and

interpret from a fundamental point of view. Also, most theoretical models on atomic-scale friction assume

a tip–sample contact under UHV conditions, again because this is conceptually the simplest system. This

explains the great efforts being made to set up SFFM in UHV.

The ﬁrst observation of atomic-scale friction in UHV is due to German et al. (1993), who chose

hydrogen-terminated diamond (100) and (111) surfaces as a sample and a diamond tip grown by chemical

vapor deposition (CVD) on the end of a tungsten cantilever. The tip–sample contact was therefore the

hardest possible contact that can be made with known materials. Moreover, the passivated diamond

surface was extremely inert, and, ﬁnally, the surface was a nonlayered material in contrast to many other

samples commonly used in SFFM, such as mica, HOPG, or MoS

. The system chosen by the authors

therefore seems ideal to study wearless friction on an atomic scale.

Figure 6.16 shows two images of the friction force corresponding to the (100) and the (111) surface

taken at an estimated loading force of 15 nN. Both images show stick-slip-like variations of the lateral

force with a periodicity of atomic dimensions. While the variation in the ﬁrst image was reported to be

consistent with a known 2 × 1 reconstruction of the diamond surface (Figure 6.16b), the second image

bears no clear relation to the corresponding lattice (Figure 6.16c). The normal force which was acquired

simultaneously did not show any structure within the resolution limit (0.07 nm peak to peak noise). In

addition to the friction force, the interaction of tip and sample was studied as a function of distance.

The corresponding force vs. distance showed very little hysteresis, an adhesive force of about 8 nN and

a distance dependence in accordance with a pure van der Waals interaction of tip and sample assuming

a tip radius of 30 nm. This was also the radius of curvature which the authors estimated from scanning

FIGURE 6.15 Friction signals for scan lines where the crystal axes are not aligned with respect to the axes of the

cantilever. In this case, the tilting angle was 10

°. The corresponding motion is more complex than in the previous

cases. (From Morita, S. et al. (1996), Surf. Sci. Rep. 23, 1–41. With permission.)

electron microscopy images. In this experiment, the tip–sample contact was much better deﬁned than

in the previously discussed experiments. Assuming that the Hertz theory is still valid at this small scale,

a contact radius of about 1 nm can be estimated, indicating that most probably the contact was not

through a single atom, but was at least of near atomic dimensions.

Another important observation in these experiments is that the friction did not increase linearly with

load. Instead, it ﬁrst increased rather sharply and then remained approximately constant so that the

“differential friction coefﬁcient” was essentially zero. For the range of forces measured, and given the low

precision of the experimental data, we believe that this result is consistent with recent experiments which

show that friction is essentially proportional to the contact area (see Section 6.3.3).

A series of experiments performed explicitly to study the resolution of SFM and SFFM have been made

by Howald et al. (1994a,b, 1995). In their ﬁrst work, the (001) surface of NaF was imaged at room

temperature under UHV conditions. The crystal was cleaved in UHV and examined by low-energy

electron diffraction to ensure its correct orientation and a structurally good cleavage face. The measured

diffraction patterns were found to agree with the cubic cell mesh of the unreconstructed (001) surface.

Figures 6.17a and b show large-scale images of the surface as seen by SFFM. Different cleavage steps are

visible, most clearly in the topographic image. Their height as measured by SFFM were 0.25 and 0.5 nm,

which was in good agreement with the expected value of 0.23 nm for a monatomic step. The lateral force

image showed an increase when the tip moved up a step. Similar behavior has also been found by other

groups, and under different conditions, as, for example, in an electrochemical cell (Weilandt et al., 1997),

and is still not understood in detail. Processes at steps are complex, since a variety of parameters such

as contact area and the normal force may vary. Moreover, atoms at steps have a different coordination

number than on terraces, which in turn might lead to different chemical and physical behavior. Step

edges such as those seen in Figure 6.17 are, however, an ideal structure to test resolution on an atomic

scale. On the one hand, a step edge is an extended object which is easily resolved by SFFM, in contrast

to a single point defect. On the other hand, due to the discrete structure of the lattice, it represents a

well-deﬁned structure of known atomic dimensions. Usually, it is assumed that the tip images the surface.

FIGURE 6.16 (a) Schematic view of the diamond tip, seen as if looking through the tip along the surface normal.

This view is aligned correctly with respect to the two lateral force images shown below. (b) Lateral force image of a

hydrogen-terminated diamond (100) surface. (c) Lateral force image of a hydrogen-terminated diamond (111)

surface. For both images, the scan size is 5.8

× 1.25 nm. The gray scale of the lateral force images corresponds to a

total variation of 11 nN, and the loading force is about 15 nN. (From Germann, G. J. et al. (1993), J. Appl. Phys. 73,

163–167. With permission).

This, however, is not always correct. Quite generally, in SFM and SFFM the sharper object essentially

images the blunter one. The tip only images the surface if the radius of curvature of the tip is much

smaller than the radius of curvature of the sample features. At an atomic step on the sample, however,

the step is usually sharper than the tip; therefore, the surface is imaging the tip. From a simple geometric

analysis, the relation

between the radius R, measured step width S, and known step height H is obtained.

Figure 6.18 shows high-resolution lateral force images. The left image was taken on a ﬂat terrace and

the right image at a monoatomic step. The loading force was about 5 nN. The periodicity of both images

was measured to be 0.45 nm, which corresponds well with the length of the unit cell. This implies that

only one species of the ions within the unit cell were imaged. Similar results have been also observed

with SFM in UHV for ionic crystals, such as NaCl (Meyer and Amer, 1990a), LiF (Meyer, 1991b), and

AgBr (Haefke et al., 1992), while in the case of KBr both kinds of ions have been resolved (Giessibl and

Binnig, 1992). As in the experiments with diamond on diamond described above, simultaneously with

the lateral force an image of the normal force was acquired, but showed no resolution within the noise

level of the instrument. The reason for this is not well understood.

FIGURE 6.17 Large-scale images of the NaF(001) surface taken under UHV

conditions with an SFFM in contact mode. Image (a) shows the topography of

the surface and image (b) the corresponding lateral force. (From Howald, L. et al.

(1994), Phys. Rev. B 49, 5651–5656. With permission.)

FIGURE 6.18 High-resolution lateral force images of the NaF(001) surface. The left image was taken on a ﬂat

terrace; the total scan size is about 3 nm. The right image was taken at a monatomic step with an approximate loading

force of 5 nN and the total scan size is about 5.6 nm. The white and black lines in the right image serve as guidelines

to show that the lattices in the left and right part of this image are shifted by half a lattice constant. This shift, as well

as the vertical stripes in this image is caused by a monatomic step which is not atomically resolved due to the extension

of the contact area. The lattice periodicity is not resolved in the middle of the image. The corresponding diffuse

region of about 1 nm width is a measure of the contact radius. The periodicity of both images is measured to be

0.45 nm. (From Howald, L. et al. (1994), Phys. Rev. B 49, 5651–5656. With permission.)

In the right image in Figure 6.18, at ﬁrst sight no clear evidence for a step is seen. The most evident

features are vertical stripes, which look like noise. However, these stripes are aligned parallel to the step

edges and were not seen on ﬂat terraces (see the left image in Figure 6.18). Analyzing this image in more

detail it can be observed that the center of the image shows a diffuse region without clear periodicity.

Moreover, the periodicity of the lattice corresponding to the upper and lower terrace is shifted by half a

lattice constant. This is exactly what one expects when, as described above, the tip images only one species

of ions. In a cubic lattice of the NaCl type, two atomic layers corresponds to one lattice spacing. Therefore,

the positions of ions which are alike are shifted by half a lattice constant in the layer below and are again

in the same position two layers below. On a monatomic step, the layer below is seen as the lower terrace;

therefore, if only one sort of ions is resolved, a shift of the atomic periodicity has to be observed, as in

fact is the case. From the image discussed the important consequence is drawn that in this case, which

we think is representative for all SFFM images taken up to the present date, the resolution is lower than

the periodicity seen. Taking the width of the diffuse region corresponding to the step as an estimate for

resolution, one ﬁnds a value of about 1 nm, which is consistent with the contact radius that one would

expect for a tip of 10 nm radius (see below) on a ionic crystal at the reported loading force of 5 nN.

From the topographic image at this monatomic step (not shown) a width of about 2 nm is measured,

and the corresponding radius of curvature is calculated to be 8 nm. However, higher steps give values

for the tip radius which are considerably larger: on a biatomic step the width was 6 nm and R = 40 nm.

This implies that on a larger scale, the tip is considerably larger, which in turn seems very reasonable.

Summarizing, this study proves that the resolution of an SFFM tip in contact with the sample is lower

than the periodicity seen and of the order of 1 nm or more, even under UHV conditions. Again, it is

interesting to observe that while an atomic periodicity is seen in the lateral force image, the periodicity

in the normal force is not resolved. This is rather surprising, since a simple hard sphere model predicts

signals of similar structure as well as magnitude for the lateral force and the normal force.

Another important study dealing with friction on an atomic scale is again due to Howald et al. (1994b,

1995). In this study the Si(111) 7 × 7 surface was investigated by SFFM. This surface is well known from

scanning tunneling microscopy (STM) experiments and has a very characteristic structure. Moreover,

height differences are much more pronounced than on other surfaces, due to the complex surface

reconstruction. In the noncontact mode (see discussion below) the authors achieved large-scale images

resolving individual steps; atomic resolution, however, was not obtained (Figure 6.19a). In the contact

regime, on the other hand, the surface was severely damaged. This is reasonable taking into account the

high reactivity of the surface due to the dangling bonds. Under UHV conditions, where contamination

FIGURE 6.19 (a) Large-scale topographic image taken in noncontact

mode of the Si(111) 7

× 7 surface. Images (b) and (c): high-resolution lateral

force images taken in contact mode which show the periodicity and some

internal structure of the Si(111) 7

× 7 lattice. (From Howald, L. et al. (1994),

Phys. Rev. B 49, 5651–5656. With permission.)

layers which passivate the surfaces are absent, one might expect a silicon tip on a silicon surface to simply

weld together to form a nanocontact. Tip and surface atoms will merge and lose memory of where they

came from. This simple view is in fact supported by molecular dynamics simulation of a silicon tip on

the Si(111) 7 × 7 surface (Landman et al., 1989a,b). These simulations also predict nanoneck formation

for other tip–sample systems, in particular for metal–metal contacts (Landmann et al., 1990). If nanoneck

formation occurs, atomic-scale friction is not only limited to the tip–sample interface, which is not well

deﬁned any more, but to atomic rearrangement which can happen within the whole nanoneck. These

processes are discussed in detail in Chapter 11 by Harrison et al.

To avoid welding of tip and sample Howald et al. (1995) covered the tip with PTFE (Teﬂon). This

covering was obtained by imaging a PTFE surface prior to the experiments on silicon. It is known that

this procedure results in the transfer of PTFE onto the tip, to which it adheres as a thin ﬁlm (Wittmann

and Smith, 1991). Other evaporated coverings such as Pt, Au, Ag, Cr, and Pt/C were reported to offer

no improvement as compared with untreated tips. With the PTFE-covered tips, adhesion as well as

friction were reduced signiﬁcantly. The maximum adhesive forces were of the order of 10 nN. Under

best conditions, the atomic periodicity of the Si(111) 7 × 7 surface could be resolved and the typical

stick-slip behavior of the lateral force was observed. The images shown in Figure 6.19b and c were taken

at an approximate loading force of 10 nN, and the total lateral force is 50 nN, whereas its variation due

to the stick-slip motion is about 10 nN.

This study shows the importance of the chemical nature of the tip and of the tip–sample contact and

that in reactive systems a thin passivating ﬁlm is needed to avoid welding of tip and sample.

6.3.1.4 Atomic Resolution in SFM and SFFM

It is important to note that while “true” atomic resolution is quite difﬁcult in SFM and SFFM, it is

standard in the case of STM in vacuum. In the case of SFM, “true” atomic resolution is much more

difﬁcult, but has been achieved in UHV by several groups using STM detection (Giessibl and Binnig,

1992), high-amplitude modulation techniques (Sugawara et al., 1995; Giessibl, 1995), as well as with low-

amplitude modulation and careful tuning of the tip–sample interaction. True atomic resolution has also

been observed in liquids, again with careful adjustment of the tip–sample interaction (Ohnesorge and

Binnig, 1993). The main reason for this difﬁculty in SFM as compared to STM is twofold. On the one

hand, the tunneling current decreases much faster than typical surface forces. Since the lateral resolution

in any scanning probe microscope depends not only on the tip radius, but also on the decay length of

the interaction used for imaging, this implies a higher resolution for an STM as compared with SFM or

SFFM. On the other hand, an STM tip is usually a very stiff system and can therefore be positioned at

(almost) any tip–sample distance. An SFM, however, needs a soft cantilever to convert forces into

displacements which can then be measured. In consequence, instabilities occur and the tip can usually

not be positioned easily very close to the sample, which is the region needed for high-resolution imaging.

These two factors essentially explain the difﬁculty in obtaining true atomic resolution in SFM and SFFM.

One approach to achieve true atomic resolution in SFM and SFFM, therefore, seems to be to use stiff

cantilevers and to start from STM techniques. In a certain respect, this approach is contrary to that

described in this chapter up to this point. The experiments described above were performed in the contact

regime, and the goal was to decrease the normal force and thus interaction as much as possible. The

approach to be described now starts from the tunneling regime with essentially no interaction and tries

to increase interaction to measure normal forces and possibly lateral forces. As we will see, imaging of

normal force with true atomic resolution has been achieved, but not the corresponding imaging of lateral

forces.

Mostly, in the “almost contact regime” the force is not measured directly, but through the force gradient.

The force gradient is measured by detecting a small shift in resonance frequency of the tip–sample system.

The measurement of the force gradient is much more convenient for a variety of reasons. First, resonant

techniques can be applied which result in an increased resolution. Second, since the snapping of the

cantilever has to be avoided, stiff cantilevers have to be used. Therefore, the resolution in direct force

measurements is low (since ∆F

noise

= C·∆z

noise

/c, where c is the force constant of the cantilever), while the

resolution measuring the force gradient is less strongly affected. And ﬁnally, the force gradient has a

stronger variation near the surface than the force itself: if F(z) ∝ 1/z

, then F' (z) ∝ 1/z

n+1

. Moreover,

long-range force components such as van der Waals forces or electrostatic forces are in a sense low-pass

ﬁltered if the force gradient is measured, so that essentially only the short-range interaction is detected.

The ﬁrst measurement of forces in scanning probe microscopy is due to Dürig et al. (1986), who measured

how the spectrum of thermal noise changes as an STM tip approaches a conducting surface. Dürig et al.

(1988, 1990) also measured how the tunneling current I and the force gradient F

vary with the tip–sample

distance. A simple relation between tunneling current and force was proposed by Chen (1991):

(6.9)

This relation essentially holds because, within perturbation theory, the tunneling current is proportional

to the matrix element between the electronic wave functions |

T 〉 and |s/> of the tip and sample,

respectively: I (z) ∝/< · 

T (z)| H

int

|s (z)〉, where H

int

is the interaction Hamiltonian (Tersoff, 1990).

Since this matrix element can be interpreted in terms of an interaction energy between tip and sample,

one ﬁnds Equation 6.9 by differentiation. This equation establishes a relation between STM and SFM

experiments and shows that essentially the same physical quantity is measured with these different

instruments. Note, however, that Equation 6.9 is only correct within perturbation theory when tip and

sample are far away (for STM standards) and therefore only in weak interaction. For strong interaction,

that is, in the “near contact” regime, substantial electronic rearrangement and a lowering of the work

function occurs and correspondingly perturbation theory fails. This is the interesting regime for com-

bined STM and SFM experiments: since the tunneling current and the forces are not easily related, they

can be assumed to be complementary magnitudes.

A detailed analysis of the physics of combined tunneling and force gradient measurements is due to

Dürig et al. (1992). Essentially the proposed technique is to monitor the tunneling current while a very

small oscillation is applied to the tip. It is important to keep this oscillation smaller than the typical length

scale on which the surface forces vary; otherwise, the interaction is averaged over the distance which the

tip moves during oscillation. This oscillation appears in the tunneling current and can be analyzed by

appropriate frequency modulation (FM) techniques (Albrecht et al., 1991, Dürig et al., 1992). With this

measurement technique, two quantities are measured simultaneously, the tunneling current which can be

compared to other STM experiments and the force gradient as an additional source of information.

This method has been applied successfully to obtain true atomic resolution of the variation of the

normal force on the Si(111) 7 × 7 surface (Lüthi, 1996). This is seen in Figure 6.20, and it is evident from

the resolved step and the defect that the resolution is “true” in the sense discussed above. The image shown

corresponds to a variation of the resonance frequency of +2 Hz over the adatom sites and of –6 Hz over

FIGURE 6.20 True atomic resolution image of the Si(111) 7 × 7

surface taken with dynamic force microscopy. The upper image

corresponds to the frequency shift of the tip–sample system as the

average tunneling current was kept constant at 25 pA. Note the

defect in the upper part of the image at the position marked with

the V which demonstrates that the atomic resolution is indeed true.

The lower graph shows line proﬁles of the measured frequency shift.

The upper proﬁle (a) in this graph corresponds to a horizontal line

at the position a in the image and was recorded (presumably) with

a one-atom tip, while proﬁle (b) results from a multiatom tip.

Proﬁle (c) corresponds to the frequency along the step (marked

with the lower arrow and the positions c, 1, 2 in the image). (From

Lüthi, R. et al. (1996), Z. Phys. B 100, 165–167. With permission.)

()

∝

()

the corner holes. The mean tunneling current was 25 pA which caused a total frequency shift of approx-

imately –70 Hz. This kind of image is only possible after careful tuning of the interaction parameters. This

is illustrated in Figure 6.21 which shows the simultaneous recording of the average tip current as well as

the frequency shift vs. the tip–sample distance. The inset corresponds to an expansion of the critical region

which shows approximately the last three nanometers before contact. Three regions can be distinguished

as the tip approaches the sample. First, a long-range attractive region due to van der Waals and electrostatic

interaction. This regime is suitable for noncontact measurements, but atomic resolution is not obtained

since the tip is too far to detect the atomic corrugation. The second regime starts with the appearance of

tunneling current. This is the regime of typical STM operation. Within this regime, the slope of the

frequency shift changes, which has to be taken into account if feedback is performed on this signal. In this

region, stable atomic resolution force (gradient) microscopy is possible. As the tip approaches further, the

frequency shift becomes zero and even positive, due to repulsive interaction. This is the third region. The

point of zero frequency shift corresponds to the maximum adhesive force, and therefore to a point of

strong short-range interaction. As the tip approaches even further, a point of vanishing force is reached

with positive force gradient. At this point the tip–sample system can be interpreted as being chemically

bound at its equilibrium position. Finally, when not only the force gradient, but also the force itself is

positive, a true mechanical contact has been made between tip and sample. In this region, only lattice

periodicity is resolved, but no true atomic resolution is possible because of the extended radius of the

tip–sample contact. As discussed above, in the case of reactive tip–sample conﬁgurations, tip and sample

will weld together and very strong mechanical interaction will occur.

Up to now, lateral forces have only been measured in this true contact regime. For a detailed under-

standing of the atomic processes governing friction it would be of great importance to operate the SFFM

if possible also in the second regime corresponding to strong tip–sample interaction but not to real

mechanical contact. Hopefully, the experimental problems can be solved and this will be achieved in the

near future.

6.3.2 Thin Films and Boundary Lubrication

The previous sections have dealt mainly with atomic-scale resolution in the direction parallel to the

surface. However, SFM and SFFM also have an extreme resolution in the direction perpendicular to the

surface. SFFM can therefore in principle also image what is “on top” of the surface and investigate how

the properties of the surface are modiﬁed by adsorbents and thin ﬁlms. The term thin ﬁlms applies in

FIGURE 6.21 Simultaneously recorded traces of the time-averaged tunneling current I

(a) and of the frequency

shift δν (b) taken as the tip approaches the Si(111) 7

× 7 surface. The onset of the tunneling current is shifted slightly

to the left of the maximum negative frequency shift δν. Inset: the frequency shift on an expanded scale corresponding

to the last few nanometers. (From Lüthi, R. et al. (1996), Z. Phys. B 100, 165–167. With permission.)

the present section usually to coverings merely one or two monolayers thick and therefore to “really thin

ﬁlms.” In the context of tribology, the question of how these very thin ﬁlms can modify the tribological

properties of surfaces leads to the important and vast topic of boundary lubrication, a ﬁeld of great

interest due to its evident technological applications. Accordingly, a lot of research has been made in this

ﬁeld, recently also with SFFM techniques. A detailed analysis of this ﬁeld is beyond the scope of this

section. For details see, for example, reviews by Bhushan et al. (1995), Fujihira (1997), and Carpick and

Salmeron (1997). We will only attempt to show how SFFM can contribute to this ﬁeld.

6.3.2.1 Adsorbed Liquid Films

The most widely used lubricant is probably water in the form of a thin liquid ﬁlm which adsorbs on

most surfaces. This ﬁlm chemically passivates surfaces and lowers long-range adhesion forces since the

van der Waals interaction is weaker through water than through air or vacuum (Israelachvili, 1992). The

superb imaging performance of SFM and SFFM in the contact mode under ambient conditions is

probably mainly due to the lubricating properties of this adsorbed ﬁlm. It prevents tip and sample from

welding together into a strong contact. As discussed above, imaging in UHV is generally much more

difﬁcult. On the other hand, the meniscus force seems to increase the adhesion force and, therefore, the

total force exerted on the surface by the tip. Consequently, the contact area and the friction of the

tip–sample system also increase. Similar effects are known from micromechanics (Matthewson and

Marmin, 1988; Legtenberg et al., 1994; Tas et al., 1997) and magnetic tape disk sliders (Mate, 1992; Mate

and Homola, 1997), where stiction due to adhesion caused by meniscus forces is often an important

problem. In ambient conditions the effect of relative humidity in an SFM and SFFM setup is twofold.

On the one hand, a ﬁlm of thickness (see, for example, Israelachvili, 1992)

(6.10)

with A the Hamaker constant of the tip–sample system, n the number density of the liquid (molecules/m

kT the thermal energy, and x the relative humidity, condenses on the tip as well as on the sample. On

the other hand, a liquid meniscus of radius (Israelachvili, 1992)

(6.11)

the so-called Kelvin radius, where γ is the surface energy of the liquid (γ

 72 mJ/m

), can form

around the tip–sample contact. For water in air at room temperature those equations give d  0.1 nm/log

(x)

1/3

and κ  0.5 nm/ln (x). The water meniscus results in an adhesive force whose magnitude is

approximately (Israelachvili, 1992)

(6.12)

where R is the tip radius and ϑ the contact angle of the meniscus with tip and sample. According to this

equation, the adhesion force should not depend on the relative humidity. However, in typical SFM

experiments the adhesion force does seem to depend on the relative humidity (see below). A more-

detailed analysis of tip–sample capillary interaction can be found in Mamur (1993).

In spite of its importance, we think that rather little research has been done on the effect of this liquid

ﬁlm in SFM and SFFM. Binggeli and Mate (1994) used an SFFM system similar to the one built by

German et al. (1993) to measure adhesion and friction at different humidities. With two ﬁbers normal

nkT

()













()

nkT

men

=π

()

4 γ cos ϑ

and lateral forces could be measured simultaneously. Cantilevers were made by bending tungsten wires

and etching their free end to form a sharp tip of approximately 100-nm radius. Three representative

surfaces were used as samples: SiO

(high hydrophilicity, contact angle of approximately 2°), an amor-

phous carbon ﬁlm (medium hydrophilicity, contact angle of approximately 45°), and a perﬂuoropolyether

lubricant (Fomblin Z-Dol, low hydrophilicity, contact angle of approximately 90°), which is typically

used as a magnetic disk lubricant. The largest effect of humidity on friction and adhesion was found on

SiO

, as might be expected. Essentially, the adhesion force is reduced by approximately a factor of two

on SiO

as well as on the carbon surface if the humidity is increased from 75 to 90%. This implies that

Equation 6.12 has to be used with caution in SFM experiments. The friction, on the other hand, is reduced

by the same amount only on the SiO

surface, but stays constant on the amorphous carbon ﬁlm.

Similar results have been obtained for an Si

tip on mica (Hu et al., 1995). In this system, the friction

coefﬁcient decreased by about a factor of two in the range between 7 and 95% relative humidity. The

friction force itself decreased by almost one order of magnitude in this range. Therefore, the lubricant

effect of water in the Si

–mica system seems to be twofold: on the one hand, the absolute friction force

is reduced and, on the other hand, the friction coefﬁcient is lowered.

Experiments to measure the role of humidity on friction and adhesion were also performed by Fuhihira

et al. (1996). In the range between 10 and 60% they found that neither the friction nor the adhesion

depended signiﬁcantly on the humidity on a hydrophobic surface. On a hydrophilic SiO

surface, however,

both friction and adhesion increased by about a factor of two. We note that this result is not in contra-

diction with the experiment of Binggeli and Mate discussed above (they ﬁnd a decrease of adhesion and

friction at higher humidity), since they cover different humidity ranges. The increase of friction at higher

humidity is explained as a result of a higher adhesion force due to a larger liquid meniscus around tip

and sample. A higher adhesion force implies a large contact area and ultimately a higher friction force

(see Sections 6.3.3 and 6.4.2). Interestingly, the authors propose to use this dependence of friction on

humidity in the case of hydrophilic surfaces to implement a “scanning hydrophilicity microscope”

(Fujihira et al., 1996).

6.3.2.2 Boundary Lubrication

Although adsorbed water on surfaces acts as a lubricant, it is not what is usually understood as a boundary

lubricant. This term is generally used for organic molecules such as Langmuir–Blodgett (LB) ﬁlms or

self-assembling monolayers which are deliberately deposited on surfaces to improve their tribological

properties, that is, to provide better sliding of the surfaces and reduce wear. Boundary lubricants are

essentially organic molecules with carbon chains and some head group. Typically, boundary lubricants

are amphiphilic molecules. The hydrophobic part consists of a hydrocarbon chain with approximately

10 to 30 methylene groups. Alternatively, ﬂuorinated carbon chains are used. The hydrophilic part consists

of a polar end group, such as a carboxylic acid head group. The end group can form strong ionic bonds

with metal ions. Dissolved in water, in the form of fatty acids or as metallic soaps, the molecules form

aggregates with the hydrophilic part exposed to water. With the LB technique, the molecules can be

assembled as two-dimensional aggregates and molecular layers are transferred to a substrate. Alternatively,

self-assembly techniques can be used where the ﬁlm is directly grown at the liquid–solid interface.

Due to this structure, boundary lubricants can be synthesized in an almost inﬁnite variety: the chain

length and its bond character can be varied as well as the head group. Each compound may have distinct

physical and chemical properties. Accordingly, one of the aims of boundary lubrication research is to

characterize the physical and chemical properties that improve lubrication and wear resistance in order

to design and optimize technically relevant boundary lubricants. Typical self-assembling monolayers are

thiols (–SH end group), which bind chemically to gold, and silanes (–SiR

end groups). Very common

LB ﬁlms are Cd–arachidate ﬁlms, which are a well-established standard for boundary lubrication.

The ﬁrst SFFM experiment on boundary lubrication was performed on these ﬁlms (Meyer et al.,

1992a). Figure 6.22 shows a Cd–arachidate ﬁlm of both 1- and 2-bilayer height on an Si wafer substrate,

which is visible on the lowest level. With an applied normal force of 4 nN, the frictional force on the

silicon substrate was found to be 3 nN and about 0.2 nN on areas that were covered with the organic

ﬁlm. No difference in friction was measured between the ﬁrst and second bilayer within an accuracy of

10%. The friction was thus reduced by about a factor of ten on ﬁlm-covered surfaces, which is in

agreement with the magnitude of reduction observed on the macroscopic scale (Bailey and Courtney-

Pratt, 1954). This observation shows that the LB ﬁlm acts as a lubricant on a nanoscopic scale.

At loads between 1 and 10 nN, only small changes in the frictional force on the LB ﬁlms were measured

and are taken in a ﬁrst approximation to the constant (see Figure 6.22d). Wear processes started at forces

above 10 nN. Above this critical value small islands were moved in their entirety, which were then absent

in the topography image. Figure 6.23a and b shows an area on a bilayer ﬁlm, imaged with an nonde-

structive load of 4 nN, while Figure 6.23c and d was taken on the same area imaged with an increased

force of 16 nN. The island indicated by an arrow was sheared to the upper margin of the scanned area.

In a subsequent wide-area topographic scan, the sheared particle was found again. It still had bilayer

FIGURE 6.22 SFFM study of a double bilayer of

Cd–arachidate. Scan size is 2

× 2 µm

. Image (a) shows

the topography of these ﬁlms and image (b) the measured

friction force. The total vertical scale in the topographic

image is 24 nm and in the friction image 14 nN. In the

topographic image the lowest level corresponds to the

silicon substrate, the next level to the ﬁrst bilayer, and the

highest level to the second bilayer of the LB ﬁlm. The

friction force image shows a higher friction on the sub-

strate and the same friction on the single- and double-

bilayer surfaces. Figure (c) is a schematic diagram of the

Cd–arachidate molecules on the substrate. The graph (d)

shows how the lateral force varies with normal load on

the silicon substrate () on the ﬁrst and second bilayer

of the LB ﬁlm () as well as on the step edges (). (From

Meyer, E. et al. (1992), Phys. Rev. Lett. 69(12), 1777–1780.