This document summarizes an experiment that used atomic force spectroscopy to measure adhesion forces between an atomic force microscope tip and mica or quartz surfaces in both air and water environments. The key findings were: 1) Adhesion forces were significantly higher in air than in water due to capillary forces present in air. 2) Adhesion forces varied more on rougher quartz surfaces compared to smoother mica surfaces. 3) Variability in adhesion force measurements at the same point on a surface was attributed to small differences in tip-sample contact location each time.

1. J. Adhesion Sci. Technol., Vol. 17, No. 16, pp. 2141–2156 (2003)
Ó VSP 2003.
Also available online - www.vsppub.com
Mapping of adhesion forces on soil minerals in air
and water by atomic force spectroscopy (AFS)
F. L. LEITE1;2
, A. RIUL, JR. 3
and P. S. P. HERRMANN1;¤
1 EMBRAPA Agricultural Instrumentation,Rua XV de Novembro 1452, CEP 13560-970, São Carlos,
São Paulo, Brazil
2 Instituto de Física de São Carlos, Universidade de São Paulo (USP), CEP 13560-970, São Carlos,
São Paulo, Brazil
3 Departamento de Física, Biologia e Química, FCT - Universidade Estadual Paulista (UNESP),
CEP 19060-900, Presidente Prudente, São Paulo, Brazil
Received in nal form 23 September 2003
Abstract—The adhesion force between an atomic force microscope (AFM) tip and sample surfaces,
mica and quartz substrates, was measured in air and water. The force curves show that the adhesion
has a strong dependence on both the surface roughness and the environmental conditions surrounding
the sample. The variability of the adhesion force was examined in a series of measurements taken at
the same point, as well as at different places on the sample surface. The adhesion maps obtained from
the distributionof the measured forces indicatedregions contaminatedby either organiccompounds or
adsorbed water. Using simple mathematical expressions we could quantitativelypredict the adhesion
force behavior in both air and water. The experimental results are in good agreement with theoretical
calculations,where the adhesion forces in air and water were mostly associated with capillaryand van
der Waals forces, respectively. A small long-range repulsive force is also observed in water due to the
overlapping electrical double-layersformed on both the tip and sample surfaces.
Keywords: Atomic force spectroscopy;atomic force microscopy; adhesion forces; soil minerals.
1. INTRODUCTION
Atomic force microscopy [1] (AFM) is a powerful tool for the investigation of the
surface morphology of polymers [2], biological materials [3], as well as in the
study of magnetic [4], frictional [5] and adhesion forces [6–9] and surface charges
[10] of solid materials. More recently, Atomic Force Spectroscopy (AFS) has
been shown to be useful to measure the interaction force (e.g. adhesion force) and
chemical properties of sample surfaces [11, 12]. Measurements of surface–surface
¤
To whom correspondence should be addressed at EMBRAPA. Phone: (55-16) 274-2477. Fax:
(55-16) 272-5958. E-mail: herrmann@cnpdia.embrapa.br

2. 2142 F. L. Leite et al.
interactions at the nano-scale [13–15] are important because many materials have
changed properties in this range [16–20]. Generally, in air the tip–sample surface
interaction is a result of the superimposition of the van der Waals, electrostatic and
capillary forces [11, 21]. On the other hand, two surfaces can interact in water
through an electric double-layer, van der Waals and hydration forces [22].
Adsorbed water plays an important role in adhesion measurements, since it is
responsible for the capillary force between the AFM tip and sample surface. In
particular, with muscovite mica the adsorbed water is so strongly bound to the
mica surface that it is impossible to remove it by simply ‘outgassing’ under UHV
conditions or through a gentle heating of the sample [23]. Muscovite mica is ideal
for studying a variety of surface phenomena since it is an aluminosilicate that can be
easily cleaved yielding an atomically planar surface. It is well known that organic
ions and simple compounds are picked up by clays (similarly to inorganic ions), and
surface spectroscopy studies indicate the presence of carbon on the surface of air-
cleaved mica [24]. The carbon is undoubtedly from organic origin, although there
are evidences from surface reactivity with carbon dioxide [25]. Quartz, on the other
hand, has a much rougher surface than mica, which is readily re ected in the force
spectroscopy results.
The formation of a water lm on the surface of materials, mainly on soil
minerals, is an important feature because it is related to many physical, chemical
and biological processes occurring in soils [26–28]. The investigation of capillary
phenomenon by AFM represents a new way of characterizing the dynamics of
aggregates. The tip/sample interaction in such different materials can be graphically
represented by AFS [29, 30], which is used here to show how the adhesion (pull-
off force) between the AFM tip and solid surfaces varies with both substrate
morphology and the environment. Adhesion maps were used to illustrate sample
regions that had been contaminated with organic compounds. This paper focuses on
the importance of both the local curvature and contamination of the sample surface
on adhesion measurements. In addition, we note that the force spectroscopy is a
useful tool to observe the in uence of repulsive forces acting in liquid media.
2. EXPERIMENTAL
Muscovite mica and quartz plates were used as samples. Mica can be easily cleaved
in laboratory air to yield an atomically planar surface, as shown in Fig. 1 (surface
roughness ¼ 0.1 nm). The mica used here was kindly donated by Dr. Jane
Frommer from IBM Almaden Research Center (San Jose, CA, USA). This material
is important for biological studies [30] and to investigate the fundamental principles
of adhesion [31, 32], friction [33], vapor adsorption [34], contact angles [35], and
surface forces involving gas, vapor and liquid systems [36, 37]. Quartz substrates
were cleaned with a piranha solution as the surface cleaning agent, according to the
experimental procedures described in Ref. [38].

3. Mapping of adhesion forces on soil minerals AFS 2143
Figure 1. Topographic view, at the atomic level, of the mica muscovite surface showing the
periodicity of the K atoms.
All measurements were carried out on a Topometrix TMX 2010 Discoverer
Atomic Force Microscope, operating in contact mode. The cantilevers have a
spring constant, k D 0:13 § 0:01 N/m and tip curvature radius, R D 23 § 5 nm.
The values of length (L), width (W) and thickness (t) of the cantilever and the
tip radius (Fig. 2), were measured with a Philips model XL30-FEG Scanning
Electron Microscope (SEM). The cantilever elastic constant was calculated using
the following equation [39]:
k D EWt3
=4L3
; (1)
where E (approx. 7:3£1010
N/m2
) is the Young modulus of the cantilever material.
The piezoscanner is normally liable to display a behavior that departs from
linearity between the force and the piezoscanner displacement. In order to check
the accuracy of the measurements, subsidiary experiments were performed with a
Topometrix standard grade silicon (Si) coated with quartz (average height: 24.0 nm
and pitch: 15.0 ¹m). The errors in length measurements were lower than those
expected for the standard grade [40], being 2.5% and 0.1% for average height and
pitch, respectively. The scanner used in the experiments has maximum scan ranges
of 7 ¹m in both x and y direction.
The force curves (cantilever de ection versus sample displacement) were ob-
tained by measuring the vertical displacement of the sample — driven by the
piezoscanner — and the de ection of the cantilever with respect to its position at
rest. The curves were acquired in ambient conditions with 47 § 3% relative humid-
ity and 25 § 1±
C temperature. Adhesion forces were measured in Milli-Q®
water
with a special cell developed by Topometrix consisting of a glass support with two
ori ces for the inlet and outlet of liquids and an O-ring for sealing it. Force curves
were digitally acquired at 100 points equally spaced from each other over the sam-
ple surface scanned area. Each force curve was comprised of a row of a maximum

4. 2144 F. L. Leite et al.
(a)
(b)
Figure 2. SEM micrographs of the silicon tip (a) and silicon cantilever (b) used.
250 data points acquired during the vertical movements of approach and retraction
of the cantilever. Statistical software (StatSoft, 1999 version) was used to create the
adhesion maps.

5. Mapping of adhesion forces on soil minerals AFS 2145
The adhesion forces on mica were examined by measuring the pull-off forces
between the tip and the sample surface in the equipment calibration mode. All
measurements were performed in both gas (air) and liquid (water) environments.
The pull-off force detected at ambient conditions is comprised of both van der Waals
and capillary forces. Since the effect from the capillary component is eliminated in
water, the measured force in a liquid system is mainly attributed to the van der
Waals interaction. Unfortunately, van der Waals forces are not the only forces
in water. In the approach curve, just before the attractive van der Waals region,
there is a repulsive force that raises the force curve over the zero line, which is the
electric double-layer force, arising from charging of both sample and tip surfaces in
liquids [41].
3. RESULTS AND DISCUSSION
Figure 3a shows typical force curves for mica in air. As the piezoscanner extends
upward approaching the tip from 1 to 2, the tip is pulled down by the attractive force
and jumps to contact with the surface at 2. As the piezoscanner continues to extend,
the cantilever bends upward as the tip presses onto the surface. In this case, from 2
to 3, the slope of the force–distance curve provides information on the elasticity of
the sample. When the tip reaches position 3, the piezoscanner retracts from the tip
and the cantilever relaxes. As the sample continues to retract, the cantilever begins
to bend downward, points 3 and 4, due to the adhesion force, until reaching the
break point 4 at which the cantilever rebounds sharply upward to 5.
The adhesion force measured between points 4 and 5 can be expressed as:
Fadhes D k±max; (2)
where Fadhes is the adhesion force (nN), k and ±max are the elastic constant and the
maximum de ection of the cantilever, respectively.
For mica (Fig. 3b), the force curves in water are similar to those in air, except that
the noise in this case is much higher due to uctuations in density and/or viscosity
of the liquid and the piezoscanner approach speed [41]. This is indeed the reason
why force curves cannot be obtained in some liquids. Besides, the adhesion force is
much lower in a liquid, responsible for the behavior between points 4 and 5, as will
be explained further.
Because the adhesion force is an important parameter for the surface properties of
materials, we have investigated the accuracy of the measurements. Using equation
(1) we estimated the adhesion forces from 30 measurements in air and water to
be, respectively, 30 § 3 nN and 12 § 1 nN, showing that the environment has
practically no effect on the data scatter. The 10% variation in the data obtained at
the same point might be related to the fact that in 30 measurements the tip touches
the sample surface at different points, within what we referred to as the critical
variability radius, av. The de nition of this critical variability radius is given in
Fig. 4, where the dark circle below the tip corresponds to the tip–sample contact

6. 2146 F. L. Leite et al.
(a)
(b)
Figure 3. Typical force curves for mica in air (a) and in water (b).
area. The white circle corresponds to the maximum area of interaction between the
tip and the sample surface (Av D ¼a2
v ) as the piezoscanner retracts and approaches
in pull-off force measurements. This critical variability radius depends on the
previous history of the piezoscanner (creep, non-linearity, hysteresis, age, etc.) and

7. Mapping of adhesion forces on soil minerals AFS 2147
Figure 4. Critical variability radius, av, associated with the maximum variation of positioningof the
piezoscanner in the measured force curves.
Table 1.
Average values of adhesionforce to freshly cleavedmica in air and water and the variabilityassociated
with them
Points Average value of the Variability
adhesion force 1F (%)
F (nN)
Air Water Air Water
1 29 § 3 16 § 2 10.3 12.5
2 32 § 3 17 § 2 9.4 11.8
3 28 § 4 15 § 2 14.3 13.3
4 28 § 3 14 § 2 10.7 14.2
5 31 § 3 15 § 2 9.7 13.3
Average value over 100 25 § 4 12 § 2 16.0 16.6
measurements
on the mechanical and electronic factors of the equipment such as vibration, thermal
stability, feed-forward control and noise level (data not shown).
Figure 5a shows the topography of the muscovite mica freshly cleaved in
air onto which force curve measurements were taken in ve different regions.
Figure 5b and 5c illustrates the corresponding adhesion map plots, in air and water,
respectively. Each point represents 10 force curve measurements. In Fig. 5b and 5c
the z-axis depicts the adhesion force magnitude while the xy plane corresponds to
the sample surface. The variation in adhesion force, Fad, is given in Table 1, ranging
from 9% to 14% depending on the region scanned during measurements in air or
water. This con rms the statement in the previous paragraph that the environment
has no signi cant effect on the adhesion variability. There is a 52% decrease in
adhesion due to the meniscus removal, which is responsible for the capillary effect
in the force curves in air. The adhesion shown in Fig. 5c is attributed mostly to van
der Waals forces, while the capillary component dominates the adhesion forces in
air (Fig. 5b).

8. 2148 F. L. Leite et al.
(a)
(b)
(c)
Figure 5. (a) Topographical image of the mica surface with a roughness of 0.1 nm. Adhesion map
plots illustrating the variability of the adhesion forces onto mica in air (b) and water (c). The average
adhesion forces were F D .25 § 4/ nN in air and F D .12 § 1/ nN in water. The black regions
correspond to values up to 30% above the average adhesion.

9. Mapping of adhesion forces on soil minerals AFS 2149
(a)
(b)
Figure 6. (a) Histogram illustrating how the adhesion to quartz varies. (b) Schematic diagram
showing the interaction between the AFM tip and the sample surface, and its in uence on the
magnitude of the measured adhesion force (adapted from Ref. [50]).
In order to con rm the importance of surface roughness, adhesion forces were
measured on quartz samples, which had a higher surface roughness (>1 nm) for
a scanned area of 1 ¹m2
. Such high value compared with that on mica leads to a
larger variation in the adhesion force as the area is scanned, as shown in Fig. 6a.
The adhesion force varied within 16% on smoother regions and 29% on rougher
areas. The increased adhesion in smoother areas is consistent with the literature
[42–45] as the surface properties at the nano-scale level, such as adhesion, are
strongly in uenced by the topography of the sample surface. Moreover, even a
small surface roughness decreases signi cantly the adhesion force [46].

10. 2150 F. L. Leite et al.
A commonly used representation of the tip/sample surface system is to consider
the tip as a sphere of radius R and the sample surface as a plane [47, 48], as it
was considered here. Figure 6b shows how the sample topography in uences the
adhesion force. The maximum adhesion force is reached when the tip is in region
3 where there is a larger contact area than those in regions 1 and 4, since a large
part of the tip is in contact with the sample surface. The minimum adhesion force is
measured in region 2 where the contact area is reduced and the effective bending is
minimum. Therefore, adhesion maps are able to reveal differences in the topography
of the samples. Willing et al. [49] studied adhesion based on the use of a colloidal
probe in conjunction with the force-volume technique, where the spatial variation
of the adhesion was visualized by analyzing the force-volume data with a software
to create adhesion area maps.
Figure 7 shows three adhesion maps acquired in different regions of mica after
2 h of air exposure with constant humidity. The adhesion map in region A
(Fig. 7a) indicates a decrease of approximately 33% in the adhesion force. The
difference in roughness between regions A, B (Fig. 7b) and C (Fig. 7c) is small and,
therefore, the maximum deviation in the adhesion force due to roughness should
be smaller than 17% (regional variability, Table 1) for a mica sample. Thus, the
33% decrease in region A is assumed to arise from organic contamination, since the
mica becomes hydrophobic after air exposure [50, 51]. The observed differences
in force-curve measurements have been attributed to the adsorbed layer formed on
mica surfaces cleaved in laboratory air. This adsorbed layer has often been referred
to as ‘organic’, because of the presence of organic carbon detected by surface
spectroscopic techniques such as SSIMS [52] and XPS [53]. The thickness and
composition of this adsorbed layer on mica will vary depending on the laboratory
atmosphere and the experimental procedures used.
The adhesion force is in uenced by the sample conditions. Considering that part
of this force is caused by adsorbed water, it is important to clarify the contamination
effect in the pull-off force measurements. The presence of an organic contaminant
layer onto a solid surface changes the contact angle, thus in uencing the adsorption
of a water layer over the sample surface. Consequently, changes in adhesion will be
observed. The adhesion maps will show how the spatial variations of the sample–tip
interactions depend on the surface conditions.
The regions B and C illustrated in Fig. 7, have a thin water layer, as will be shown
later. The capillary force is given by [54]:
Fair
cap D 2¼R°lv.cos µ1 C cos µ2/; (3)
where °LV is the liquid–vapor interfacial free energy, R is the radius of the AFM
tip and µ1 and µ2 are the contact angles of water for the mica surface and the tip,
respectively. For freshly cleaved mica, the water contact angle is ¼0±
and for
oxidized silicon tip (exposed to air) the contact angle is ¼79±
(data not shown).
Contact angle measurements were made with an optical microscope with a digital
camera by measuring the angle between the surface and the tangent drawn on the

11. Mapping of adhesion forces on soil minerals AFS 2151
(a)
(b)
(c)
Figure 7. Adhesion maps onto mica: (a) region A (R D 1:3 Å; F D .16 § 3/ nN), (b) region B
(R D 1:1 Å; F D .23 § 3/ nN); and (c) region C (R D 1:1 Å; F D .24 § 4/ nN). Each adhesion map
corresponds to a scanning area of 1 ¹m2. The black regions correspond to values up to 30% above
the average adhesion.

12. 2152 F. L. Leite et al.
water droplet image ( ve measurements were made on each surface of mica). The
surface free energy of the adsorbed water layer is °lv D 72:0 mJ/m2
.
The resultant capillary adhesion force due to the presence of adsorbed water is
15 § 3 nN, from equation (3), with an estimated scatter of 20% due to errors in the
measurements of contact angle and radius of curvature of the tip. This theoretical
value is lower than that in Fig. 7 for regions B and C, because the contribution from
van der Waals forces (FvdW) to adhesion was not taken into account in the theoretical
calculation. The equation that relates the van der Waals forces (contact adhesion in
the condensate, FvdW) and capillary forces is given by [32]:
Fair
adhes D 2¼R°lv.cos µ1 C cos µ2/ C FvdW; (4)
where the second term on the right-hand side of equation (4) is the contact adhesion
from the van der Waals forces [55]. One may eliminate capillary forces by
measuring adhesion with both sample and AFM tip in the water, allowing one to
estimate the contribution from the van der Waals forces only.
The force measured on the AFM cantilever in a liquid environment can be
estimated using the Derjaguin–Muller–Toporov (DMT) [56] theory as:
Fwater
vdW D 2¼R$132; (5)
where R is the AFM tip radius and $132 is the work of adhesion per unit area
between the AFM Si tip (subscript 2) and the sample surface (subscript 1) in a liquid
environment (subscript 3). The DMT equation applies to rigid systems with low
adhesion and small radii of curvature, but it can underestimate the true contact area.
Equation (5) is correct for a spherical tip in contact with a planar surface, valid for
long-ranged attraction around the periphery of the contact area, with the tip–sample
geometry being constrained to remain Hertzian [57]. In other words, the DMT
theory is the Hertzian theory with an offset due to surface forces, and no hysteresis
between loading and unloading. However, Beach et al. [58] showed that the pull-off
forces were not very sensitive to the maximum applied load suggesting that the use
of continuum elastic contact mechanics in the analysis of measured force curves was
not as straightforward as usually assumed in the literature. In our case, the work of
adhesion (Si tip–water–mica) is $132 D 0:11 J/m2
, resulting in an adhesion force
of 16 § 2 nN in water. From equation (4) it is possible to obtain the theoretical
value of the adhesion force in air on freshly cleaved mica, which is 31 § 5 nN.
The adhesion force results in air presented in Fig. 7b and 7c, Fadhes D 23 § 3
and Fadhes D 24 § 4 nN, respectively, demonstrate that the experimental data are
consistent with the calculated values.
In order to separate the adhesion force fractions from each other, the pull-off
forces were measured under two conditions in the same experimental assembly.
Figure 8 shows a comparative plot between theoretical and experimental results in
air and water. Histogram A shows a good agreement between the experimental pull-
off forces in air and the theoretical results using equation (4), with the differences
within the expected variation. This histogram represents the sum of the capillary

13. Mapping of adhesion forces on soil minerals AFS 2153
Figure 8. Histogram illustrating the theoretical and experimental variations of the adhesion force
components in air and water.
and van der Waals interaction forces, i.e. Fair
adhes D Fcap C FvdW. Histogram B shows
the experimental and theoretical (equation (5)) results in water. It can be seem that
the error bars do not overlap, indicating that the differences are no more than the
22% estimated error, con rming the existence of the repulsive force due to double
layer. This histogram represents the adhesion effect caused mainly by the van der
Waals interaction between the tip and the sample, i.e. Fwater
adhes D FvdW. Histogram C
shows the capillary force component obtained from equation (3) and the difference
between the experimental pull-off forces in air and water, i.e. Fair
adhes ¡Fwater
adhes D Fcap.
The difference between the theoretical (16 § 2 nN) and experimental (12 § 1 nN)
values for water, presented in Histogram B, comes from the repulsive forces
between the tip and the mica surface. When immersed in a polar liquid medium
like water, surface charges are induced on both the tip and the sample surface
due to ionization, dissociation or spontaneous adsorption of charged species. To
keep the electrical neutrality, opposite ionic species are held together closer to the
tip/sample surface forming an electric double-layer. When mica is placed in water,
the mechanism of the double-layer formation is attributed to the KC
dissolution, as
well as ionic exchange between KC
and H3OC
(or HC
) [59]. The existence of the
electrical double-layer is con rmed by the force curves, as shown in Fig. 9, where
an upward trend appears before the attractive van der Waals interaction. Toikka
et al. [60] showed that the double layer decreases the adhesion force, and that the
apparent adhesion force depends on the pH of the solution. The authors con rmed

14. 2154 F. L. Leite et al.
Figure 9. Typical force curve for mica under water. The upward trend pointed in the gure is
indicativeof the double-layereffect. The zero line represents that part the force curve in which the tip
exerts no force on the sample, i.e. when the tip and sample are far apart, and the tip does not de ect.
the existence of this phenomenon by measuring adhesion forces in different pH
solutions between an iron sample and silica colloidal probe.
The interaction between electric double-layers from different surfaces may be ei-
ther attractive or repulsive, having different magnitudes, depending on the surface-
charge properties of the tip and sample materials, concentration of ionic con-
stituents, ionic strength, pH, and temperature. The effects of the electric double-
layer forces on adhesion force measurements are only now beginning to be explored
[60], and the results presented here might provide a better understanding on soil
mineral interactions.
Adhesion maps obtained from force spectroscopy have shown clearly how surface
contamination, roughness and the environmental conditions in uence the adhesion
forces. Little attention, however, is paid to the use of AFS for application in
agricultural and colloidal science.
4. CONCLUSIONS
The force curves obtained on some soil mineral particles (mica and quartz) show
clearly that the adhesion force is sensitive to both the surface roughness and the
environmental conditions.
The magnitude of adhesion depends on the roughness and local curvature of the
sample surface, with a slight increase in the adhesion force in smoother regions. We
have shown that adhesion forces estimated from several measurements taken at the

15. Mapping of adhesion forces on soil minerals AFS 2155
same place on the sample surface vary within 13% on mica and 29% on the much
rougher quartz substrate.
The scatter in the measured curvature radius and elastic constant of the tip
provides an error source to the adhesion force of typically 20% and 8%, respectively.
The adhesion maps made from hundreds of measurements at different points allow
one to obtain information on heterogeneities in sample topography and on organic
contamination. For example, carbon contamination on mica, possibly from human
contact or carbon dioxide from air, affects the force curves. This was corroborated
by the good agreement between the theoretical and experimental adhesion values
obtained in both air and water. With the adhesion maps for samples in air and in
water, a distinction can be made between capillary and van der Waals components
of the adhesion force.
Acknowledgements
The authors are grateful to CNPq, the nanobiotechnology network (CNPq/MCT)
for the nancial support and to Prof. Osvaldo N. Oliveira, Jr. for useful discussions
and revision of this manuscript.
REFERENCES
1. G. Binnig, C. F. Quate and Ch. Gerber, Phys. Rev. Lett. 56, 930–933 (1986).
2. R. F. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria and O. N. Oliveira, Jr., Nanotech-
nology 14, 101–108 (2003).
3. I. Penegar, C. Toque, S. D. A. Connell, J. R. Smith and S. A. Campbell, in: Proceedings of the
10th International Congress on Marine Biofouling, Melbourne, Australia (1999).
4. Y. Martin and H. K. Wickramasinghe,Appl. Phys. Lett. 50, 1455–1457 (1987).
5. R. Erlandsson, G. Hadziioannou, C. M. Mate, G. M. McClelland and S. Chiang, J. Chem. Phys.
89, 5190–5193 (1988).
6. C. Jacquot and J. Takadoum, J. Adhesion Sci. Technol. 15, 681–687 (2001).
7. H. K. Christenson and P. M. Claesson, Adv. Colloid Interface 91, 391–436 (2001).
8. L. H. G. Segeren, B. Siebum, F. G. Karssenberg, J. W. A. van den Berg and G. J. Vancso,
J. Adhesion Sci. Technol. 16, 793–828 (2002).
9. A. Ata, Y. Rabinovich and R. K. Singh, J. Adhesion Sci. Technol. 16, 337–346 (2002).
10. C. Schonenberger and S. F. Alvarado, Phys. Rev. Lett. 65, 3162–3164 (1990).
11. L. Sirghi, N. Nakagiri,K. Sugisaki,H. Sugimura and O. Takai, Langmuir 16, 7796–7800 (2000).
12. A. Mendez-Vilas, M. L. Gonzalez-Martin, L. Labajos-Broncano and M. J. Nuevo, J. Adhesion
Sci. Technol. 16, 1737–1747 (2002).
13. S. Fujisawa, E. Kishi, Y. Sugawara and S. Morita, Phys. Rev. B 51, 7849–7857 (1995).
14. D. M. Taylor, Thin Solid Films 331, 1–7 (1998).
15. A. Torii, M. Sasaki, K. Hane and S. Okuma, Sensors Actuators A Phys. 40, 71–76 (1994).
16. R. García and R. Pérez, Surf. Sci. Rep. 47, 197–301 (2002).
17. M. Binggeli and C. M. Mate, J. Vac. Sci. Technol. B 13, 1312–1315 (1995).
18. M. Scherge, X. Li and J. A. Schaefer, Tribol. Lett. 6, 215–220 (1999).
19. Q. Ouyang, K. Ishida and K. Okada, Appl. Surf. Sci. 169, 644–648 (2001).
20. H. A. Mizes, K.-G. Loh, R. J. D. Miller, S. K. Ahuja and E. F. Grabowski, Appl. Phys. Lett. 59,
2901–2903 (1991).

16. 2156 F. L. Leite et al.
21. F. Mugele, T. Becker, R. Nikopoulos,M. Kohonen and S. Herminghaus,J. AdhesionSci. Technol.
16, 951–954 (2002).
22. L. Sirghi, N. Nakagiri, H. Sugimura and O. Takai, Jpn. J. Appl. Phys. 40, 1420–1424 (2001).
23. H. K. Christenson, J. Phys. Chem. 97, 12034–12041 (1993).
24. K. G. Bhattacharyya,J. Electron Spectrosc. Relat. Phenom. 63, 289–306 (1993).
25. K. G. Bhattacharyya,Langmuir 5, 1155–1162 (1989).
26. G. E. Brown, Jr., A. L. Foster and J. D. Ostergren, Proc. Natl. Acad. Sci. USA 96, 3388–3395
(1999).
27. D. R. Nielsen, J. W. Hopmans and K. Reichardt, Scale Dependence and Scale Invariance in
Hydrology. Cambridge University Press, Cambridge (1988).
28. R. Wiesendanger, Scanning Probe Microscopy and Spectroscopy — Methods and Applications.
Cambridge University Press, Cambridge (1994).
29. G. A. Willing and R. D. Neuman, Langmuir 18, 8370–8374 (2002).
30. H. H. P. Fang, K.-Y. Chan and L.-C. Xu, J. Microbiol. Methods 40, 89–97 (2000).
31. R. G. Horn, J. N. Israelachviliand F. J. Pribac, J. Colloid Interface Sci. 115, 480–492 (1987).
32. H. K. Christenson, J. Colloid Interface Sci. 121, 170–178 (1988).
33. A. M. Homola, J. N. Israelachvili, M. L. Gee and P. M. McGuiggan, Trans. ASME J. Tribology
111, 675–682 (1989).
34. D. Beaglehole and H. K. Christenson, J. Phys. Chem. 96, 3395–3403 (1992).
35. J. Schultz, K. Tsutsumi and J.-B. Donnet, J. Colloid Interface Sci. 59, 272–276 (1977).
36. J. N. Israelachvili,Intermolecularand Surface Forces, 2nd edn. Academic Press, New York, NY
(1991).
37. H. K. Christenson, J. Dispersion Sci. Technol. 9, 171–206 (1988).
38. C. E. Borato, P. S. P. Herrmann, L. A. Colnago, O. N. Oliveira and L. H. C. Mattoso, Braz. J.
Chem. Eng. 14, 367–373 (1997).
39. D. Tabor, Gases, Liquids and Solids and Other States of Matter, 3rd edn. Cambridge University
Press, Cambridge (1991).
40. AFM Standard-B,P/N 10-10299, Topometrix.Maximum Deviation: averageheightD 8%; pitch
D 2.5% (standard grade).
41. B. Cappella, P. Baschieri, C. Frediani, P. Miccoli and C. Ascoli, IEEE Eng. Med. Biol. 16, 58–65
(1997).
42. T. Stifter, E. Weilandt, O. Marti and S. Hild, Appl. Phys. A 66, S597–S605 (1998).
43. K. L. Johnson, Tribology Int. 31, 413–418 (1998).
44. R. Jones, H. M. Pollock, J. A. S. Cleaver and C. S. Hodges, Langmuir 18, 8045–8055 (2002).
45. E. R. Beach, G. W. Tormoen, J. Drelich and R. Han, J. Colloid InterfaceSci. 247, 84–89 (2002).
46. K. N. G. Fuller and D. Tabor, Proc. R. Soc. London A 345, 327–342 (1975).
47. J. N. Israelachvili,Surf. Sci. Rep. 14, 109–159 (1992).
48. T. Stifter, O. Marti and B. Bhushan, Phys. Rev. B 62, 13667–13673 (2000).
49. G. A. Willing, T. H. Ibrahim, F. M. Etzler and R. D. Neuman, J. Colloid Interface Sci. 226,
185–188 (2000).
50. B. Cappella and G. Dietler, Surf. Sci. Rep. 34, 1–104 (1999).
51. J. Hu, X.-D. Xiao, D. F. Ogletree and M. Salmeron, Surf. Sci. 344, 221–236 (1995).
52. M. G. Dowsett, R. M. King and E. H. C. Parker, J. Vac. Sci. Technol. 14, 711–717 (1977).
53. L. Xu and M. Salmeron, Langmuir 14, 5841–5844 (1998).
54. Y. Ando, Wear 238, 12–19 (2000).
55. T. Eastman and D. M. Zhu, Lagmuir 12, 2859–2862 (1996).
56. B. V. Derjaguin, V. M. Muller and Yu. P. Toporov, J. Colloid Interf. Sci. 53, 314–326 (1975).
57. J. Hertz, Reine Angew. Math. 92, 156–171 (1881).
58. E. R. Beach, G. W. Tormoen and J. Drelich, J. Adhesion Sci. Technol. 16, 845–868 (2002).
59. E. F. Souza, G. Ceotto and O. Teschke, J. Mol. Catal. A 167, 235–243 (2001).
60. G. Toikka, R. A. Hayes and J. Ralston, Langmuir 12, 3783–3788 (1996).