Nanogeometry Matters: Unexpected Decrease of Capillary Adhesion Forces with Increasing Relative Humidity

Nanocapillary forces

Nanogeometry Matters: Unexpected Decrease of Capillary Adhesion Forces with Increasing Relative Humidity

small 20

DOI: 1

M. KöbIMM-InIsaac N E-mail

E. SahDeparUniver28049E-mail

The sticking effect between hydrophilic surfaces occurring at increasing relative humidity (RH) is an everyday phenomenon with uncountable implications. Here experimental evidence is presented for a counterintuitive monotonous decrease of the capillary adhesion forces between hydrophilic surfaces with increasing RH for the whole humidity range. It is shown that this unexpected result is related to the actual shape of the asperity at the nanometer scale: a model based on macroscopic thermodynamics predicts this decrease in the adhesion force for a sharp object ending in an almost fl at nanometer-sized apex, in full agreement with experiments. This anomalous decrease is due to the fact that a signifi cant growth of the liquid meniscus formed at the contact region with increasing humidity is hindered for this geometry. These results are relevant in the analysis of the dynamical behavior of nanomenisci. They could also have an outstanding value in technological applications, since the undesirable sticking effect between surfaces occurring at increasing RH could be avoided by controlling the shape of the surface asperities at the nanometric scale.

1. Introduction

Moisture alters the cohesion among particles in powders

and the adhesion of particles to surfaces. The principal reason

for this effect is the formation of a liquid meniscus at the con-

tact region between the two objects in question. The attrac-

tive force caused by such a liquid meniscus is called “capillary

force”. For hydrophilic surfaces it predominates over other

surface forces under ambient conditions. [ 1 ]

Understanding the way humidity infl uences adhesion is

of fundamental importance when treating with powders, [ 2 ]

10, 6, No. 23, 2725–2730 © 2010 Wiley-VCH Verlag Gmb

0.1002/smll.201001297

er , Prof. F. Briones , Dr. M. Luna stituto de Microelectrónica de Madrid (CNM-CSIC)ewton 8, PTM, 28760 Tres Cantos, Madrid, Spain

: [email protected]

agún , Dr. P. García-Mochales , Prof. J. J. Sáenz tamento de Física de la Materia Condensadasidad Autónoma de Madrid Madrid, Spain: [email protected]

in friction-related problems, [ 3 ] and in phenomena driven by

hydrophobic interactions and has, thus, implications in impor-

tant industries such as the pharmaceutical, food, and mate-

rials industries. Given the fact that macroscopic tribology

phenomena involve the contact of a multitude of micro- and

nanometric asperities, [ 3–5 ] a profound understanding of the

capillary forces occurring at a single asperity contact is of

fundamental importance. This is particularly relevant in the

rapidly growing fi eld of nano/biotechnology, in which

capillary-induced adhesion and friction become a serious

tribological concern. Nature provides uncountable examples

of adhesion mechanisms involving capillary forces and is

the source of bioinspired strategies in the design of adhesive

systems. An especially inspiring example, which has aroused

great scientifi c interest over the last decade, is the adhesion

and friction of the gecko pad during climbing and traversing

ceilings. [ 6 ] Gecko pads exhibit a fi ne structure of hierarchi-

cally arranged fi bers which, by means of van der Waals and

capillary forces, enable the geckos to adhere to surfaces with

great effi ciency. [ 6–11 ] A current technological effort is focused

on the biomimetic design of surfaces with controlled adhe-

sive and lubricant properties. [ 10 ] Some applications, however,

2725H & Co. KGaA, Weinheim wileyonlinelibrary.com

M. Köber et al.

2726

full papers

Figure 1 . Decreasing adhesion force. a) Adhesion force measured between a sharp Si tip and a fl at mica sample as a function of the RH, for three different tips. Nominal tip radii are < 7 nm for (i) and (iii) and about 2 nm for (ii). The experiments were performed with a maximum applied load of 10 nN. b) SEM images showing the three tips after they had been used to measure the adhesion force (scale bars: 60 nm). Within the resolution the nominal tip radius was preserved after all three experiments.

??????

k=0.082 N/m k=1.24 N/m

a b

k=2.1 N/m

c

k=0.082 N/m k=1.24 N/m

a b

k=2.1 N/m

c

b

a

(ii) (iii)(i)

0 20 40 60 80 1001

2

3

4

Adh

esio

n F

orce

(nN

)

Relative Humidity (%)

(i) (ii) (iii)

require low adhesion forces. Nanodevices, for example, may

lose reliability because of capillary-induced adhesion and

friction, which can even prevent them from working. [ 12 ] In

any case, tailoring the adhesion at the nanoscale presents a

technological challenge.

On account of this, an extensive study of the capillary

forces acting at micro- and nanoasperity contacts has been

performed over the last few years. [ 1 , 5 , 12–24 ] Despite all these

efforts, the underlying principles of capillary adhesion are

not fully understood even for a single nanoscale contact. The

reason lies in the large number of parameters involved in

the process. Nanoasperity shape, contact radius, length, con-

tact angles, relative humidity (RH), etc. are known to play

a crucial role in determining the adhesion properties. It is

extremely diffi cult to control all the relevant parameters at

the nanoscale level and, in practice, quantitative results are

not fully reproducible.

In spite of the diversity of the experimentally obtained

adhesion force versus RH curves, all the reported curves

have one feature in common: starting from low RH values

the adhesion force increases with humidity. In fact, the curves

show either a monotonous increase [ 1 , 18 ] or a maximum at

a certain humidity value [ 16 , 17 , 20 , 25 ] (see Reference [1] for a

recent review of experimental and theoretical studies on

the humidity dependence of the adhesion force). This trend

refl ects the expected natural behavior we are familiar with,

for example, when playing with sand: with dry sand we cannot

build a sandcastle; a certain amount of water, though, makes

the particles stick to each other.

Herein, we report on the inverse effect: even in dry

environments (at low humidity values) the adhesion force

decreases with increasing RH. Starting from 0% RH we

observe a monotonous decrease of the adhesion force for

the entire RH range between two hydrophilic materials.

These experimental results were obtained with the atomic

force microscope (AFM) by both using sharp monocrystal-

line silicon tips of very small tip apex ( < 10 nm) and applying

very low normal loads ( < 10 nN). In addition, a theoretical

model that explains these experimental fi ndings has been

developed using continuum theory and the formation of

minimum-energy water necks. We conclude that the decrease

in the adhesion force between hydrophilic surfaces is related

to the object’s geometry: only a sharp object fi nished in an

almost fl at (truncated) nanometer-sized apex gives rise to

this behavior.

2. Results

2.1. Experimental Results

Experiments were carried out with a commercial AFM

(Nanotec Electronica, Cervantes FullMode AFM System,

http://www.nanotec.es/) enclosed in a humidity-controlled

chamber. Adhesion force versus RH curves were obtained

by measuring force versus distance curves (from which adhe-

sion forces were extracted) [ 26 ] while increasing the RH slowly

from 0 to 100% (see the Experimental Section for details on

www.small-journal.com © 2010 Wiley-VCH Verlag G

the measurement procedure). Adhesion forces were meas-

ured between a fl at muscovite mica substrate cleaved prior to

the experiment and monocrystalline silicon as well as silicon

nitride tips (for a detailed description of the tips employed,

see the Experimental Section). These materials are predomi-

nantly hydrophilic (the contact angles for mica, Si 3 N 4 , and

Si0 2 are 0, 3, and 20 ° , respectively [ 27 , 28 ] ).

Curve progressions of adhesion force versus RH curves

obtained with different AFM tips may differ considerably

from one another, but we can clearly distinguish two trends

when employing monocrystalline silicon tips: decreasing

curves and curves displaying a maximum. From the results

of a series of experiments we can conclude that this dif-

ferent adhesion force behavior is clearly related to the tip

dimensions. When the tip radius exceeds 15 nm we fi nd the

common behavior reported in the literature [ 1 , 16 , 19 , 29 ] with a

maximum at a certain humidity value. However, whenever

tip apex dimensions are maintained suffi ciently small (radius

< 10 nm), the adhesion force either decreases in the whole

humidity range or decreases until it reaches a constant value!

Examples of this monotonous decrease are shown in Figure 1 a.

The scanning electron microscopy (SEM) images of the tips

taken after each experiment show (Figure 1 b) that—within

the resolution—in all three cases the nominal tip radius is

preserved (see also the Supporting Information). This pres-

ervation is achieved by means of controlling the maximum

applied normal load after the tip–sample contact, thus

ensuring that the tip would hardly impress on the surface.

For the data shown in Figure 1 , the maximum normal force

exerted on the cantilever was less than 10 nN.

mbH & Co. KGaA, Weinheim small 2010, 6, No. 23, 2725–2730

Decrease of Capillary Adhesion Forces with Increasing Relative Humidity

Figure 2 . Common maximum behavior. a) Adhesion force versus RH curves for three different tips on a fl at mica surface. (i): Initially sharp Si tip (nominal radius < 7 nm), normal force limited to 50 nN; (ii): Si 3 N 4 tip of nominal tip radius 15 nm, no normal load limitations; (iii): special case with initially sharp tip and normal force limited to 18 nN; at about RH 65% the tip crashed against the sample (the load remained 18 nN). b) SEM images showing the three tips after they had been used to measure the adhesion force. Scale bars: 60 nm. The SEM images of the tips taken after the experiments show larger tip radii than the nominal values.

b

k=0.11 N/mk=2.0 N/m

a (iii)(ii)

k=2.4N/mk=0.11N/m

(i)

k=2.0N/mb

a

0 20 40 60 80 1000

10

20

30

40

(i) (ii) (iii)

Relative Humidity (%)

Adh

esio

n F

orce

(nN

)

If, on the contrary, we let the maximum normal load reach

tens of nanonewtons during the measurement of the force

versus distance curves, the tip dimensions are not preserved

and the force versus RH curves show a maximum at a certain

humidity value. Figure 2 a (experiment (i)) shows an example

in which an initially sharp monocrystalline Si tip was used to

measure the adhesion force on mica allowing high applied

loads (50 nN). The SEM image (Figure 2 b, (i)) taken after the

experiment had been performed shows a truncated tip with a

radius of 20 nm. In previous works where tips were used for

scanning at a load of 30 nN, the tips show the same truncated

shapes. [ 24 ] In addition to the SEM evidence, larger values of

the adhesion force indicate larger tip radii. [ 30 ]

When silicon nitride tips with a larger initial radius

(15 nm nominal) were employed, the maximum behavior was

always observed. Experiment (ii) in Figure 2 a is an example

(the normal force was not limited). The general trend—the

occurrence of a maximum—is the same as that for curve (i),

although both the position and width of that maximum differ

for the different tips. After the experiment the tip radius is

25 nm (Figure 2b, (ii)).

A special experiment is presented in Figure 2 a (iii), which

further exemplifi es the key role of the tip apex dimensions in

the capillary adhesion force. In this particular case, an occa-

sional accident happened in the middle of the experiment

which caused a signifi cant increase of the monocrystalline

Si tip radius and therewith a dramatic change in the curve

© 2010 Wiley-VCH Verlag Gmbsmall 2010, 6, No. 23, 2725–2730

progression. At the beginning of the experiment (starting

from low RH), the monocrystalline Si tip radius was small

(nominal tip radius < 7 nm) and the normal load applied

was limited to 18 nN. At some point during the experiment

(RH ≈ 65%) a power outage led to the crashing of the tip

against the sample, which resulted in cleavage of the tip

apex. SEM inspection after the completion of the experiment

revealed a tip radius of 18 nm. Hence, in this experiment

there is a small tip radius for the humidity range between

0 and 65% and a larger tip apex size from 65% on. Both the

behavior and magnitude of the adhesive force correspond to

these different tip dimensions: at low humidities the trend is

similar to that for a tip of small radius and for RH > 65% the

curve shows the decline of a broad maximum, the behavior

that is typical for large tip radii.

Throughout a series of 17 experiments we observed that

the tip size and shape at the nanoscale have a dramatic effect

on the humidity dependence of the capillary force. Although

the tip shape was known to infl uence the capillary forces [ 18 ]

(increasing with humidity for conical tips or having a broad

maximum for quasi-spherical apexes), to our knowledge

the monotonous decrease observed in our experiments has

not been reported. To understand the origin of the different

adhesion force behaviors, we developed a theoretical model

that determines the capillary adhesion forces between a fl at

hydrophilic surface and a sharp hydrophilic object of dif-

ferent apex shapes and sizes.

2.2. Theoretical Results

We consider a simplifi ed model based on equilibrium

thermodynamics, similar to the one used to describe the hys-

teresis associated with the formation and rupture of liquid

bridges. [ 22 ] As in previous theoretical work, [ 1 , 5 , 15 , 18 , 22 , 24 ] our

approach is based on macroscopic continuum theory. [ 5 ] This

approach is valid even when dimensions fall below a few

nanometers, which is the range where the discrete molec-

ular nature of the liquid could be relevant. [ 32 ] Molecular

dynamics [ 33 , 34 ] and Monte Carlo [ 31 , 35 ] simulation studies have

also been carried out, which confi rmed the validity of the

continuum theory.

After condensation, the liquid meniscus is assumed

to have a constant radius of curvature R c . For a given

tip shape and tip–sample distance D , the pendular ring

geometry is fi xed by R c and the tip and sample contact

angles. The equilibrium properties of the water meniscus

depend on the “excess” grand potential [ 36 , 37 ] given by the

sum of surface, � S = ( (SLV − SLT − SLS)� , and volume,

� V = (V(

RT(Lm

ln (1/H))

≡ (V 1r K� , contributions, where S

represents the surface area of the liquid–vapor (LV), liquid

sample (LS) and liquid–tip (LT), and ( ≡ (LV is the liquid–

vapor surface energy. Tips and samples used in the experi-

ments are predominantly hydrophilic. To simplify matters, in

the model we consider zero contact angles (for hydrophilic

surfaces, an increase in the contact angle leads to a decrease

in the adhesion force magnitude but does not change the

adhesion force versus humidity curve behavior [ 24 ] ). Quali-

tative changes in the dependence of adhesion on RH are

2727H & Co. KGaA, Weinheim www.small-journal.com

M. Köber et al.

2728

full papers

Figure 3 . Capillary forces versus geometry. a) Sketch of the modeled tip geometry and water meniscus. b–f) Calculated adhesion force versus humidity for different values of the tip apex form factor b / a ( = 25, 1, 0.2, 0.04, and 0.01, respectively) and the ellipsoid transverse semi axis a . In (b) the results for a quasi-conical tip ( b / a = 25, a = 5 nm) are shown for different aperture angles. In (c–f) the solid lines are results for tips with ν = 10 ° and different a values. In (f) the dashed line corresponds to a quasi-truncated tip with a = 5 nm and ν = 30 ° .

expected at much larger contact angles or for hydrophobic

surfaces. [ 9 ] Lm is the molar volume, R = 8.31 J mol − 1 K − 1 , and

H is the RH. At a given temperature, the condensation energy

is proportional to the meniscus volume V and inversely pro-

portional to (the absolute value of) the Kelvin radius r K . For

D smaller than a critical distance, the grand potential as a

function of R c presents a local minimum � 0 D, Req (D))

� ,

which corresponds to a meniscus of radius R c = R eq in equi-

librium. Assuming that the meniscus evolves in thermody-

namic equilibrium, the pulling-off force is simply given by

F = − ∂��0/∂ D .

To study a large family of tip shapes, the tip was mod-

eled as a cone with an ellipsoidal cap end, the cone side

being tangential to the ellipsoid (see Figure 3 a). The tip

shape is then characterized by three parameters: the cone

angle ( ν ), the transverse (horizontal) semi axis of the apex

( a ), and the apex form factor b / a , where b is the conjugate

(vertical) semi axis. By varying b / a it is possible to study the

force versus RH curves for a continuum family of tip apex

shapes: prolate ( b / a > 1), conventional spherical apex ( b / a = 1),

oblate ( b / a < 1), and quasi-truncated blunt ( b / a < < 1) tips.

By changing the cone angle ν , the effect of the tip sharp-

ness on the capillary force can be analyzed. Naturally, the

capillary force also depends on the initial tip–sample

distance D . [ 18 , 25 ]

Calculated capillary adhesion force versus RH curves

are depicted in Figure 3 for different tip shapes and sizes

at a fi xed tip–sample distance D = 0.2 nm (mimicking the

www.small-journal.com © 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinhe

presence of an adsorbed water layer

on the sample). Figure 3 b and c repro-

duce the expected results for conical

and spherical tips. For a relatively small

aspect ratio ( b / a = 0.2, Figure 3 d) the

results resemble those obtained with the

paraboloidal model discussed in Refer-

ence [18]. The adhesion curve still shows

a maximum but its behavior has changed

in comparison with the spherical model:

the general shape of the curve changes

with the tip size and the maximum posi-

tion decreases with decreasing size. In

contrast, sharp oblate and blunt tips with

a > > b (Figure 3 e and f) show a com-

pletely different behavior. If the tip

is relatively large ( a ≈ 8 nm) and not

too fl at ( b / a ≈ 0.04), the force curve still

presents a maximum at very low humidity.

In the limit of an almost truncated tip

( b / a ≤ 0.01, a ≤ 5 nm), the force decreases for

the whole RH range. Very close to satura-

tion, the force may increase again with RH,

and show a minimum for large cone opening

angles ( ν ≥ 25 ° ), as shown in Figure 3 f.

3. Discussion

To understand the different behaviors,

we note that the equilibrium force is

approximately given by the Laplace pressure acting on the

cross-sectional area defi ned by the radius r 2 of the contact

line at the top of the meniscus,

F ≈ PLaplaceBr 22

≈ ((

RT

(Lmln (1/H)

)Br 2

2 =(rKBr 2

2 .

Except for some limiting cases, our results are well

described by this simple expression. In this formula the

behavior of the force versus RH can be seen as a result of

two competing effects. As RH increases, the Laplace pres-

sure decreases (independently of the objects’ geometry)

while the meniscus cross section increases (this increase

does depend on geometry). As a simple example, we

can consider a conical tip shape where r 2 increases linearly

with r K . The capillary force on the cone then grows line-

arly with r K (diverges as the inverse of ln(1/ H )), in agree-

ment with Figure 3 b. Since the curvature of the meniscus is

approximately given by the Kelvin radius, the cross section

and, subsequently, the behavior of the adhesion with RH

mainly depend on the shape of the tip at the scale deter-

mined by the Kelvin radius. This is illustrated in Figure 4 , in

which both r 2 and F versus RH are plotted for a relatively

blunt tip (with b / a = 1/25 and a = 5 nm). At low RH, that is,

small r K , the Kelvin radius fi ts beneath the fl at end of the tip

apex and r 2 grows very rapidly with r K (with RH). Near the

edge of the fl at area apex, where the tip surface curvature

im small 2010, 6, No. 23, 2725–2730

Decrease of Capillary Adhesion Forces with Increasing Relative Humidity

Figure 4 . Meniscus blockade. Calculated radius r 2 of the contact line at the top of the meniscus and capillary adhesion force F cap versus RH for a relatively blunt tip ( b / a = 1/25, a = 5 nm).

is high, an increase in the meniscus curvature radius (i.e.,

r K ) does not lead to an appreciable increase in r 2 (keeping

a zero contact angle with the tip surface). Hence the adhe-

sion force decreases. We could then say that the meniscus

growth is blocked (pinned) by the high-curvature regions of

the tip apex. Since r K is in the nanometer range, the adhe-

sion curves depend on the details of the tip shape at the

nanoscale.

The presented model does not mimic exactly any real

tip–sample system since real tips, in general, exhibit a more

complex structure than the one modeled here. We did not

consider the possible effects of the RH dependence on the

adsorption isotherm of the water fi lm [ 25 ] or the possibility of

an “ icelike” structure of the adsorbed water. [ 19 ] Nonetheless,

the model shows that the different behaviors observed in

the experiment can be understood by simply taking into

account the tip shape at the nanoscale. Note the quanti-

tative agreement between theory and experiment when

assuming a transverse radius of a ≈ 1 nm and a form factor of

b / a ≈ 0.01 ( a can be > 1 nm if the contact angle is > 0), which

would imply an ultrasharp tip with an almost atomically fl at

apex!

This result is consistent with the fact that the sharp tips

(with radii below 10 nm) used in the experiments were made

of monocrystalline Si, which presents a nearly perfectly fl at

fracture surface at the tip apex [ 38 ] (see the Experimental Sec-

tion and the Supporting Information). Considering both the

theoretical discussion and the experimental adhesion curves,

tips with “large” apex (radius > 15 nm) should present some

residual curvature (very small b ) in the form of atomic ter-

races or dislocations causing a deviation from the almost per-

fectly fl at surface (notice that for a radius of 15 nm and b / a ≈

1/15, b is of the order of 1 nm). These differences in the apex

geometry, which lead to very different behaviors of the adhe-

sion force, cannot be easily determined from standard SEM

images.

© 2010 Wiley-VCH Verlag Gmbsmall 2010, 6, No. 23, 2725–2730

4. Conclusion

We have obtained experimental evidence for a counter-

intuitive decrease of the capillary force between hydrophilic

surfaces with increasing RH. In concordance with the

experimental results, in the theoretical simulation we iden-

tifi ed the tip apex shape as the origin of different adhe-

sion force versus RH behaviors. The monotonous decrease

of the adhesion force is only found for a sharp truncated

object with a narrow contact region. The large variety of

meniscus force behaviors found for different tip shapes

emphasizes the importance of geometry in the capillary

phenomena at the nanometer scale. The results imply that

for a correct interpretation of AFM adhesion maps, the tip

size and shape have to be taken into account—hydrophilic

samples do not necessarily yield a capillary force increase

with increasing moisture. Our results are also relevant in

the analysis of the dynamical behavior of nanomenisci. [ 39 ]

Furthermore, our fi ndings could be of relevance in tech-

nological applications, since the undesirable sticking effect

between surfaces occurring at increasing RH could be

avoided by controlling the shape of the surface asperities at

the nanometric scale.

5. Experimental Section

Experimental Procedure : The RH was increased by intro-ducing humid air (by flowing dry nitrogen (N 2 ) through ultrapure Milli-Q water (Millipore)) at a controlled flow rate into the chamber. The AFM cantilever’s vertical velocity was as low as 10 nm s − 1 during all the force curves, thus ensuring that the meniscus would be in equilibrium with the surrounding atmos-phere and, furthermore, minimizing tip damage due to the impact. The cantilever’s force constant k was determined by Sader’s method. [ 40 ] Both tip and sample surface were electri-cally grounded during all experiments to minimize the effect of electrostatic forces.

AFM Tips : The tips employed in the experiments shown here were: “Nanosensors PointProbe Plus” for experiments (i) and (iii) of Figure 1 and (i) and (iii) of Figure 2 (monocrystalline Si, tip radius < 7 nm, cone angle at tip apex ≈ 10 ° ; http://www.nanosensors.com/PointProbe_Plus.pdf); “Nanosensors Super-SharpSilicon” for experiment (ii) of Figure 1 (monocrystalline Si, radius ≈ 2 nm, cone angle < 7 ° for the last 150 nm; http://www.nanosensors.com/SuperSharpSilicon.pdf); and Olympus OMCL-RC800PSA-W type (Si 3 N 4 , nominal tip radius 15 nm; http://probe.olympus-global.com/en/en/specnitrideE.html) for experiment (ii) of Figure 2 . The single-crystal Si cantilevers are aligned parallel to the < 110 > direction (Nanosensors FAQ: http://www.nanosensors.com/faq.html), this direction therefore being perpendicular to the axis of height of the tetrahedron-shaped tip. Taking into account that the < 110 > direction is the direction along which cracks are easily propagated [ 41 ] and that the preserved tips present a small tip apex (≤5 nm tip radius, see transmission electron microscopy images in the Supporting Information), a perfectly fl at fracture surface free of crystalline imperfections is most likely being obtained throughout this rela-tively small extension.

2729H & Co. KGaA, Weinheim www.small-journal.com

M. Köber et al.

2730

full papers

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements

This work was supported by the Spanish MICINN through the projects FIS2009–13430-C02–02, CTQ2005–07993-C0202/BQU, NAN2004–09125-C07–02, PET2007_0315, TRA2009_0206 and by the “Comunidad de Madrid Microseres Program” S2009/TIC-1476. M.K. acknowledges fi nancial support from the CSIC through an I3P scholarship.

[ 1 ] H. J. Butt , M. Kappl , Adv. Colloid Interface Sci. 2009 , 146 , 48 – 60 .

[ 2 ] L. Bocquet , E. Charlaix , S. Ciliberto , J. Crassous , Nature 1998 , 396 , 735 – 737 .

[ 3 ] I. L. Singer , H. M. Pollock in Fundamentals of Friction: Macroscopic and Microscopic Processes , Kluwer , Dordrecht 1991 .

[ 4 ] C. M. Mate in Tribology on the Small Scale: A Bottom Up Approach to Friction, Lubrication, and Wear , Oxford University Press , Oxford 2008 .

[ 5 ] J. Israelachvili in Intermolecular and Surface Forces , Academic , San Diego , 1991 .

[ 6 ] K. Autumn , Y. A. Liang , S. T. Hsieh , W. Zesch , W. P. Chan , T. W. Kenny , R. Fearing , R. J. Full , Nature 2000 , 405 , 681 – 685 .

[ 7 ] K. Autumn , M. Sitti , Y. C. A. Liang , A. M. Peattie , W. R. Hansen , S. Sponberg , T. W. Kenny , R. Fearing , J. N. Israelachvili , R. J. Full , Proc. Natl. Acad. Sci. USA 2002 , 99 , 12252 – 12256 .

[ 8 ] G. Huber , H. Mantz , R. Spolenak , K. Mecke , K. Jacobs , S. N. Gorb , E. Arzt , Proc. Natl. Acad. Sci. USA 2005 , 102 , 16293 – 16296 .

[ 9 ] T. W. Kim , B. Bhushan , J. R. Soc. Interface 2008 , 5 , 319 – 327 . [ 10 ] L. F. Boesel , C. Greiner , E. Arzt , A. del Campo , Adv. Mater. 2010 ,

22 , 2125 – 2137 . [ 11 ] J. S. Kwaki , T. W. Kim , Int. J. Precis. Eng. Manuf. 2010 , 11 ,

171 – 186 . [ 12 ] B. Bhushan , Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci. 2008 ,

366 , 1499 – 1537 . [ 13 ] T. Thundat , X. Y. Zheng , G. Y. Chen , S. L. Sharp , R. J. Warmack ,

L. J. Schowalter , Appl. Phys. Lett. 1993 , 63 , 2150 – 2152 . [ 14 ] M. Binggeli , C. M. Mate , Appl. Phys. Lett. 1994 , 65 , 415 – 417 .

www.small-journal.com © 2010 Wiley-VCH Verlag Gm

[ 15 ] C. Gao , Appl. Phys. Lett. 1997 , 71 , 1801 – 1803 . [ 16 ] X. D. Xiao , L. M. Qian , Langmuir 2000 , 16 , 8153 – 8158 . [ 17 ] M. Y. He , A. S. Blum , D. E. Aston , C. Buenviaje , R. M. Overney ,

R. Luginbuhl , J. Chem. Phys. 2001 , 114 , 1355 – 1360 . [ 18 ] O. H. Pakarinen , A. S. Foster , M. Paajanen , T. Kalinainen ,

J. Katainen , I. Makkonen , J. Lahtinen , R. M. Nieminen , Model. Simul. Mater. Sci. Eng. 2005 , 13 , 1175 – 1186 .

[ 19 ] D. B. Asay , S. H. Kim , J. Chem. Phys. 2006 , 124 , 174712 . [ 20 ] A. Fukunishi , Y. Mori , Adv. Powder Technol. 2006 , 17 , 567 – 580 . [ 21 ] M. Paajanen , J. Katainen , O. H. Pakarinen , A. S. Foster , J. Lahtinen ,

J. Colloid Interface Sci. 2006 , 304 , 518 – 523 . [ 22 ] E. Sahagun , P. Garcia-Mochales , G. M. Sacha , J. J. Saenz , Phys.

Rev. Lett. 2007 , 98 , 176106 . [ 23 ] A. A. Feiler , J. Stiernstedt , K. Theander , P. Jenkins , M. W. Rutland ,

Langmuir 2007 , 23 , 517 – 522 . [ 24 ] M. Farshchi-Tabrizi , M. Kappl , H. J. Butt , J. Adhes. Sci. Technol.

2008 , 22 , 181 – 203 . [ 25 ] D. B. Asay , S. H. Kim , Langmuir 2007 , 23 , 12174 – 12178 . [ 26 ] A. L. Weisenhorn , P. K. Hansma , T. R. Albrecht , C. F. Quate , Appl.

Phys. Lett. 1989 , 54 , 2651 – 2653 . [ 27 ] H. Klauk , M. Halik , U. Zschieschang , G. Schmid , W. Radlik ,

W. Weber , J. Appl. Phys. 2002 , 92 , 5259 – 5263 . [ 28 ] J. Bauer , G. Drescher , M. Illig , J. Vac. Sci. Technol. B 1996 , 14 ,

2485 – 2492 . [ 29 ] L. Xu , A. Lio , J. Hu , D. F. Ogletree , M. Salmeron , J. Phys. Chem. B

1998 , 102 , 540 – 548 . [ 30 ] E. S. Yoon , S. H. Yang , H. G. Han , H. Kong , Wear 2003 , 254 ,

974 – 980 . [ 31 ] J. Jang , M. Yang , G. Schatz , J. Chem. Phys. 2007 , 126 , 174705 . [ 32 ] A. O. Parry , C. Rascon , N. B. Wilding , R. Evans , Phys. Rev. Lett.

2007 , 98 , 226101 . [ 33 ] E. J. W. Wensink , A. C. Hoffmann , M. E. F. Apol , H. J. C. Berendsen ,

Langmuir 2000 , 16 , 7392 – 7400 . [ 34 ] D. Seveno , J. De Coninck , Langmuir 2004 , 20 , 737 – 742 . [ 35 ] J. K. Jang , G. C. Schatz , M. A. Ratner , J. Chem. Phys. 2004 , 120 ,

1157 – 1160 . [ 36 ] F. Restagno , L. Bocquet , T. Biben , Phys. Rev. Lett. 2000 , 84 ,

2433 – 2436 . [ 37 ] R. Evans in Liquids and Interfaces , Elsevier , New York 1989 . [ 38 ] K. H. Chung , Y. H. Lee , D. E. Kim , Ultramicroscopy 2005 , 102 ,

161 – 171 . [ 39 ] C. Jai , J. P. Aime , D. Mariolle , R. Boisgard , F. Bertin , Nano Lett.

2006 , 6 , 2554 – 2560 . [ 40 ] J. E. Sader , J. W. M. Chon , P. Mulvaney , Rev. Sci. Instrum. 1999 ,

70 , 3967 – 3969 . [ 41 ] R. Perez , P. Gumbsch , Phys. Rev. Lett. 2000 , 84 , 5347 – 5350 .

Received: July 27, 2010 Revised: August 23, 2010Published online: November 11, 2010

bH & Co. KGaA, Weinheim small 2010, 6, No. 23, 2725–2730