Bhushan B. Nanotribology and Nanomechanics: An Introduction

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990 Bharat Bhushan and Huiwen Liu

15. B. Bhushan, J.N. Israelachvili, U. Landman: Nanotribology: Friction, wear and lubrica-

tion at the atomic scale, Nature 374, 607–616 (1995)

16. B. Bhushan: Handbook of Micro/Nanotribology, 2nd edn. (CRC, Boca Raton 1999)

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and wear. In: Modern Tribology Handbook Vol.2: Materials, Coatings, and Industrial

Applications, ed. by B. Bhushan (CRC, Boca Raton 2001) pp.909–929

18. J. Ruhe, G. Blackman, V.J. Novotny, T. Clarke, G.B. Street, S. Kuan: Thermal attach-

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J. Tribol. 118, 663–668 (1996)

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faces using atomic force/friction force microscopy, J. Vac. Sci. Technol. A 14, 2378–

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21. H. Liu, B. Bhushan: Nanotribological characterization of molecularly-thick lubricant

ﬁlms for applications to MEMS/NEMS by AFM, Ultramicroscopy 97, 321–340 (2003)

22. G.S. Blackman, C.M. Mate, M.R. Philpott: Interaction forces of a sharp tungsten tip

with molecular ﬁlms on silicon surface, Phys. Rev. Lett. 65, 2270–2273 (1990)

23. G.S. Blackman, C.M. Mate, M.R. Philpott: Atomic force microscope studies of lubri-

cant ﬁlms on solid surfaces, Vacuum 41, 1283–1286 (1990)

24. X. Ma, J. Gui, K.J. Grannen, L.A. Smoliar, B. Marchon, M.S. Jhon, C.L. Bauer: Spread-

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25. C.A. Kim, H.J. Choi, R.N. Kono, M.S. Jhon: Rheological characterization of perﬂuo-

ropolyether lubricant, Polym. Prepr. 40, 647–649 (1999)

26. M. Ruths, S. Granick: Rate-dependent adhesion between opposed perﬂuo-

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bricants for magnetic thin-ﬁlm rigid disks, J. Appl. Phys. 81, 5384–5386 (1997)

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disks studied by friction force microscopy, Surf. Coat. Technol. 62, 373–379 (1993)

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layer lubrication, Appl. Phys. Lett. 61, 2240–2242 (1992)

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at solid–liquid interface, Chem. Phys. Lett. 223, 336–340 (1994)

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tip and thin-ﬁlm magnetic rigid disks by friction force microscopy, Adv. Info. Storage

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

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cromachined electrostatic micromotors using an atomic force/friction force microscope,

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croscopy: Part II – application to magnetic media, ASME J. Tribol. 116, 389–396 (1994)

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

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of long-term static friction, J. Appl. Phys. 15, 4649–4656 (1999)

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Part IV

Biomimetics

Lotus Eﬀect: Roughness-Induced Superhydrophobic

Surfaces

Bharat Bhushan, Michael Nosonovsky, and Yong Chae Jung

Superhydrophobic surfaces have considerable technological potential for various

applications due to their extreme water-repellent properties. These surfaces with

high contact angle and low contact angle hysteresis also exhibit a self-cleaning

eﬀect and low drag for ﬂuid ﬂow. These surfaces are of interest in various ap-

plications, including self-cleaning windows, exterior paints for buildings, naviga-

tion ships, textiles, and applications requiring a reduction in ﬂuid ﬂow, e.g., in

micro/nanochannels. Superhydrophobic surfaces prevent formation of menisci at

a contacting interfaces and can be used to minimize high adhesion and stiction.

Certain plant leaves, notably lotus leaves, are known to be superhydrophobic due

to their roughness and the presence of a thin wax ﬁlm on the leaf surface, and the

phenomenon is known as the “Lotus eﬀect.” Extremely water-repellent superhy-

drophobic surfaces can be produced by using roughness combined with hydropho-

bic coatings. In this chapter, the theory of roughness-induced superhydrophobicity

is presented followed by the characterization data of natural leaf surfaces and artiﬁ-

cial superhydrophobicsurfaces. Wetting is studied as a multiscale process involving

the macroscale (water droplet size), microscale (surface texture size), and nano-

scale (molecular size). This includes fundamental physical mechanisms of wetting,

responsible for the transition between various wetting regimes, contact angle and

contact angle hysteresis. Practical aspects of design of superhydrophobic surfaces

are also discussed.

19.1 Introduction

The primary parameter that characterizes wetting is the static contact angle, which

is deﬁned as themeasurable anglethat a liquid makeswith a solid.The contact angle

dependson severalfactors,such asroughnessand the mannerof surfacepreparation,

and its cleanliness [2,61]. If the liquid wets the surface (referred to as wetting liquid

or hydrophilic surface), the value of the static contact angle is 0 ≤ θ ≤ 90

◦

, whereas

if the liquid does not wet the surface (referred to as non-wetting liquid or hydropho-

bic surface), the value of the contact angle is 90

◦

<θ≤ 180

◦

. The term hydropho-

996 B. Bhushan et al.

bic/philic, which was originally applied only to water (“hydro-” means “water” in

Greek), is often used to describe the contact of a solid surface with any liquid. The

term “oleophobic/philic” is used sometimes with regard to the wetting by oil. Sur-

faces with high energy, formed by polar molecules, tend to be hydrophilic, whereas

those with low energy and built of non-polar molecules tend to be hydrophobic.

Surfaces with the contact angle between 150° and 180° are called superhy-

drophobic. For ﬂuid ﬂow applications, in addition to the high contact angle, su-

perhydrophobic surfaces should also have very low water contact angle hysteresis.

In the case of these surfaces, water droplets roll oﬀ (with some slip) the surface

and take contaminant with them providing self-cleaning ability, known as the Lotus

eﬀect. The contact angle hysteresis is the diﬀerence between the advancing and re-

ceding contact angles, which are two stable values. It occurs due to roughness and

surface heterogeneity. Contact angle hysteresis reﬂects a fundamental asymmetry

of wetting and dewetting and the irreversibility of the wetting/dewetting cycle. It is

a measure of energy dissipation during the ﬂow of a droplet along a solid surface.

For a droplet moving along the solid surface (for example, if the surface is tilted),

the contact angle at the front of the droplet (advancing contact angle) is greater than

that at the back of the droplet (receding contact angle), due to roughness, resulting

in the contact angle hysteresis (Fig. 19.1a). Surfaces with low contact angle hystere-

sis have a very low water roll-oﬀ angle, which denotes the angle to which a surface

must be tilted for roll oﬀ of water drops (i.e., very low water contact angle hystere-

sis) [18,19,46,69,73]. It is understood that during roll-oﬀ of water droplets, some

slip is associated. Superhydrophobic surfaces have low drag for ﬂuid ﬂow and low

tilt angle. The self-cleaning surfaces are of interest in various applications, includ-

ing self-cleaning windows,windshields, exterior paintsfor buildings and navigation

ships, utensils, roof tiles, textiles, and applications requiring a reduction of drag in

ﬂuid ﬂow, e.g., in micro/nanochannels.

Wetting may lead to formation of menisci at the interface between solid bodies

during sliding contact, which increases adhesion and friction. As a result of this,

the wet friction force is greater than the dry friction force, which is usually undesir-

able [10,13–15].On the other hand, high adhesionis desirable in some applications,

such as adhesive tapes and adhesion of cells to biomaterial surfaces; therefore, en-

hancedwetting roughnesswouldbe desirable inthese applications.Numerousappli-

cations,such asmagnetic storagedevices andmicro/nanoelectromechanicalsystems

(MEMS/NEMS), requiresurfaces with low adhesion and stiction [10–12,16,20].As

the size of these devices decreases, the surface forces tend to dominate over the vol-

ume forces, and adhesion and stiction constitute a challenging problem for proper

operation of these devices. This makes the development of non-adhesive surfaces

crucial for many of these emerging applications.

In the last decade, materials scientists paid attention to natural surfaces, which

are extremely hydrophobic. Among them are leaves of water-repellent plants such

as Nelumbo nucifera (lotus) and Colocasia esculenta, which have high contact an-

gles with water [8,17,32,92,131].First, the surface of the leaves is usually covered

with a range of diﬀerent waxes made from a mixture of hydrocarbon compounds

19 Lotus Eﬀect: Roughness-Induced Superhydrophobic Surfaces 997

Fig. 19.1. (a) Schematics of a droplet on a tilted

substrate showing advancing (θ

adv

) and reced-

ing (θ

rec

) contact angles. The diﬀerence between

these angles constitutes the contact angle hystere-

sis. Conﬁgurations described by the (b) Wenzel

equation for the homogeneous interface (19.6), (c)

Cassie–Baxter equation for the composite interface

with air pockets (19.9), and (d)the Cassie equation

for the homogeneous interface (19.10)

that have a strong phobia of being wet. Second, the surface is very rough due to

so-called papillose epidermal cells, which form asperities or papillae. In addition to

the microscale roughness of the leaf dueto the papillae, the surface of the papillae is

also rough with sub-micron sized asperities composed of the wax [131]. Thus, they

have hierarchical micro- and nano-sized structures, which were studied extensively

by Bhushan and Jung [17]. The water droplets on these surfaces readily sit on the

apex of nanostructures because air bubbles ﬁll in the valleys of the structure under

the droplet. Therefore, these leaves exhibit considerable superhydrophobicity. The

water droplets on the leaves remove any contaminant particles from their surfaces

when they roll oﬀ, leading to self cleaning ability referred to as the Lotus-eﬀect [92].

Other examples of biological surfaces include duck feathers and butterﬂy wings.

Their corrugated surfaces provide air pockets that prevent water from completely

touching the surface. Study and simulation of biological objects with desired prop-

998 B. Bhushan et al.

erties is referred to as “biomimetics”. Biomimetics involves taking engineering so-

lutions from nature, mimicking them and implementing them in an application. The

word biomimetics is derived from a Greek word “biomimesis” meaning to mimic

life. Severalother names are used as well, such as bionics and biognosis.Mimicking

the lotus eﬀect falls in the ﬁeld of biomimetics.

One of the ways to increase the hydrophobic or hydrophilic properties of the

surface is to increase surface roughness; so roughness-induced hydrophobicity has

become a subject of extensive investigation. Extremely water-repellent (superhy-

drophobic) surfaces have been produced by applying a patterned roughness com-

bined with hydrophobic coatings which may satisfy the need for the non-adhesive

surfaces [16,18,19,31,67–69]. Wenzel [133] found that the contact angle of a liquid

with a rough surface is diﬀerent from that with a smooth surface. Cassie and Bax-

ter [34] showed that gaseous phase including water vapor, commonly referred to as

“air” in the literature, may be trapped in the cavities of a rough surface, resulting in

a composite solid-liquid-air interface, as opposed to the homogeneous solid-liquid

interface. The two models describe two possible wetting regimes or states: the ho-

mogeneous (Wenzel) and the composite (Cassie–Baxter or just Cassie) regimes.

Shuttleworth and Bailey [124] studied spreading of a liquid over a rough solid sur-

face and foundthat the contact angle at theabsolute minimumof surface energycor-

respondsto the values predictedby Wenzel [133] or Cassie and Baxter [34].Johnson

and Dettre [66] showed that the homogeneous and composite interfaces correspond

to the two metastable equilibrium states of a droplet. Many authors have investi-

gated recently the metastability of artiﬁcial superhydrophobicsurfaces and showed

that whether the interface is homogeneous or composite may depend on the history

of the system, in particular whether the liquid was applied from the top or from the

bottom [24,56,79,86,87,108,109]. Extrand [46] pointed out that whether the in-

terface is homogeneous or composite depends on droplet size, due to the gravity. It

was suggested also that the so-called two-tiered (or double) roughness, composed

by superposition of two roughness patterns at diﬀerent length-scale [57,110,127],

and fractal roughness [120] may lead to superhydrophobicity.

Herminghaus[57] showed that certain self-aﬃne proﬁles may result in superhy-

drophobic surfaces even for wetting liquids, in the case the local equilibrium con-

dition for the triple line (line of contact between solid, liquid and air) is satisﬁed.

Nosonovsky and Bhushan [97, 98] pointed out that such conﬁgurations, although

formally possible, are likely to be unstable. Nosonovsky and Bhushan [98,99] pro-

posed a probabilistic model for wetting of rough surfaces with a certain probabil-

ity associated with every equilibrium state. According to their model, the overall

contact angle with a two-dimensional rough proﬁle is calculated by assuming that

the overall conﬁguration of a droplet occurs as a result of superposition of numer-

ous metastable states. The probability-based concept is consistent with the exper-

imental data [16, 18, 19, 68, 79], [69], which suggests that transition between the

composite and homogeneous interfaces is gradual, rather than instant. Nosonovsky

and Bhushan [100,101,103–106] have identiﬁed mechanisms, which lead to desta-

bilization of the composite interface, namely, the capillary waves, condensation

19 Lotus Eﬀect: Roughness-Induced Superhydrophobic Surfaces 999

and accumulation of nanodroplets, and surface inhomogeneity. These mechanisms

are scale-dependent with diﬀerent characteristic scale lengths. To eﬀectively re-

sist these scale-dependent mechanisms, a multiscale (hierarchical) roughness is re-

quired. High asperities resist the capillary waves, while nanobumps prevent nano-

droplets from ﬁlling the valleys between asperities and pin the tripe line in case of

a hydrophilic spot.

Variouscriteriahavebeen formulated to predictthe transitions from a metastable

compositestate to a wetted state [16,48,68,69,101–104,106,109].Extrand [48] for-

mulated the transition criterion referred to as the contact line density criterion which

was obtained by balancing the droplet weight and the surface forces along the con-

tact line. Patankar [109] proposed a transition criterion based on energy balance.

There is an energy barrier in going from a higher energy Cassie–Baxter droplet to

a lower energyWenzel droplet. Themost probablemechanism is that thedecrease in

the gravitational potential energy during the transition helps in overcoming the en-

ergy barrier. This energy barrier was estimated by considering an intermediate state

in which the waterﬁlls the groovesbelowthecontact areaof a Cassie–Baxter droplet

but the liquid-solid contact is yet to be formed at the bottom of the valleys. These

criteria were tested on selected experiments from the literature [23, 56,107,137].

Bhushanet al. [16] and Nosonovskyand Bhushan [101,102]found that the transition

occurs at a critical value of the spacing factor, a non-dimensional parameter which

is deﬁned as the diameter of the pillars divided by the pitch distance between them

for patterned surfaces, and its ratio to the droplet size. Bhushan and Jung [18,19]

and Jung and Bhushan [68,69] proposed the transition criterion based on the pitch

distance between the pillars and the curvature of droplet governed by the Laplace

equation, which relates pressure inside the droplet to its curvature. In addition, the

transition can occur by applying external pressure on the droplet, or by the impact

of droplet on the patterned surfaces [9,33,79,115].

It hasbeen demonstratedexperimentallythat roughnesschangescontact anglein

accordance with the Wenzel model. Yost el al. [138] found that roughness enhances

wetting of a copper surface with Sn-Pb eutectic solder, which has a contact angle

of 15–20° for smooth surface. Shibuichi et al. [120] measured the contact angle of

various liquids (mixtures of water and 1,4-dioxane) on alkylketen dimmer (AKD)

substrate (contact angle not larger than 109° for smooth surface). They found that

for wetting liquids, the contact angle decreases with increasing roughness, whereas

for non-wetting liquids it increases. Semal et al. [117] investigated the eﬀect of sur-

face roughness on contact angle hysteresis by studying a sessile droplet of squalane

spreading dynamically on multilayer substrates (behenic acid on glass) and found

an increase in microroughness slows the rate of droplet spreading. Erbil et al. [44]

measured the contact angle of polypropylene(contact angle of 104° for smooth sur-

face) and found that the contact angle increases with increasing roughness. Burton

and Bhushan [31] measured contact angle with roughness of patterned surfaces and

found that in the case of hydrophilic surfaces, it decreases with increasing rough-

ness, and for hydrophobicsurfaces, it increases with increasingroughness. Bhushan

1000 B. Bhushan et al.

and Jung [17–19] and Jung and Bhushan [67–69] studied wetting properties of hy-

drophobic and hydrophilic leaves and patterned surfaces and found similar trends.

To study superhydrophobicity, patterned surfaces are created and contact angle

is measured to understand how roughness structure aﬀects contact angle. Whether

the Cassie–Baxter regime is present or not depends on the roughness structure and

droplet radius. Evaporation studies are useful in characterizing wetting behavior

because droplet with various sizes can be created to evaluate the transition criterion

on a patterned surface. Many researchers have considered the evaporation of small

droplets of liquid on solid surfaces [29,43,68,69,102–106,116]. It has been shown

that the wetting state changes from the Cassie–Baxter to Wenzel state as the droplet

becomes smaller than a critical value on patterned surfaces during evaporation [68,

69,89,102–106].

An environmental scanning electron microscope (ESEM) can be used to con-

dense or evaporate water droplets on surfaces by adjusting the pressure of the water

vapor in the specimen chamber and the temperature of the cooling stage. Transfer

of the water droplet has been achieved by a specially designed micro-injector de-

vice on wool ﬁbers and then imaged at room temperature in ESEM [39]. Images of

water droplets show strong topographic contrast in ESEM such that reliable contact

angle measurements can be made on the surfaces [125]. Water condensation and

evaporation studies on synthetic patterned surfaces were carried out by Jung and

Bhushan [69] and Nosonovsky and Bhushan [102–106] where the change of contact

angle was related with the surface roughness.

In this chapter, numerical models, which provide relationships between rough-

ness and contact angle, and contact angle hysteresis as well as the Cassie–Wenzel

regime transition, are discussed. The role of microbumps and nanobumps is ex-

amined by analyzing surface characterization on the micro- and nanoscale of hy-

drophobic and hydrophilic leaves. Along with measuring and characterizing surface

roughness, the contact angle and adhesion and friction propertiesof these leaves are

also considered. The knowledge gained by examining these properties of the leaves

and by quantitatively analyzing the surface structure, will be helpful in designing

superhydrophobic surfaces. Micro- and nanopatterned polymers (hydrophobic and

hydrophilic) are fabricated to validate models and to provide design guidelines for

superhydrophobic surfaces. These surfaces are examined by measuring their con-

tact angle. To further examine the eﬀect of meniscus force and real area of contact,

scale dependence is considered with the use of AFM tips of various radii. Also in

this chapter, criteria for the transition from the Cassie–Baxter to Wenzel regime are

discussed. To investigate how the droplet size inﬂuences the transition, a study of

droplet evaporation is conducted on silicon surfaces patterned with pillars of two

diﬀerent diameters and heights and with varying pitch values and deposited with

a hydrophobic coating. An environmental scanning electron microscope (ESEM)

study on the wetting behavior for a microdropletwith about 20µm radius on the pat-

terned Si surfaces is presented. The importance of hierarchical roughness structure

on destabilization of air pockets is discussed. Finally, the techniques of producing

superhydrophobicsurfaces are described.

19 Lotus Eﬀect: Roughness-Induced Superhydrophobic Surfaces 1001

19.2 Modeling of Contact Angle for a Liquid in Contact

with a Rough Surface

19.2.1 Contact Angle Deﬁnition

In this section, the dependence of the contact angle on the surface tension is consid-

ered for a liquid in contact with a solid surface, forming a homogeneous interface.

The surface atomsor moleculesof liquids orsolids haveenergyabovethat of similar

atoms and molecules in the interior, which results in surface tension or free surface

energy being an important surface property. This property is characterized quantita-

tively by the surface tension or free surface energy γ, which is equal to work, that

is required to create a unit area of the surface at constant pressure and temperature.

The units of γ are J/m

or N/m and it can be interpreted either as energyper unit sur-

face area or as tension force per unit length of a line at the surface. When a solid is

in contact with liquid, the molecular attraction will reduce the energy of the system

below that for the two separated surfaces. This is expressed by the Dupré equation

= γ

+ γ

−γ

, (19.1)

where W

is the work of cohesion per unit area between two surfaces, γ

and γ

are the surface energies (surface tensions) of the solid against air and liquid, and

is the surface energy (surface tension) of liquid against air [61].

If a droplet of liquid is placed on a solid surface, the liquid and solid surfaces

come together under equilibrium at a characteristic angle called the static contact

angle θ

. This contact angle can be determined from the condition of the net sur-

face free energy of the system being minimized [2, 61]. The total energy E

tot

given by

tot

= γ

+ A

)−W

, (19.2)

where A

and A

are the contact areas of the liquid with the solid and air, re-

spectively. It is assumed that the droplet is small enough so that the gravitational

potential energy can be neglected. It is also assumed that the volume and pressure

are constant, so that the volumetric energy does not change. At the equilibrium dE

tot

= 0, which yields

(dA

+ dA

)−W

= 0 . (19.3)

For a droplet of constant volume, it is easy to show using geometrical considera-

tions, that

/ dA

= cosθ

. (19.4)

Combining(19.1), (19.3)and (19.4),the well-knownYoung equationfor the contact

angle is obtained

cosθ

−γ

. (19.5)