article5.pdf

J. Adhesion Sci. Technol., Vol. 20, No. 6, pp. 563–587 (2006) VSP 2006.Also available online - www.vsppub.com

The effects of nanostructure and composition on thehydrophobic properties of solid surfaces

P. F. RIOS 1, H. DODIUK 1, S. KENIG 1,∗, S. MCCARTHY 2 and A. DOTAN 1

1 Department of Plastics Engineering, Shenkar College of Engineering and Design,12 Anna Frank St, Ramat-Gan 52526, Israel

2 Department of Plastics Engineering, MA University of Massachusetts at Lowell, 883 BroadwayStreet, Lowell, MA 01854-5130, USA

Received in final form 19 March 2006

Abstract—The effects of nanoroughness and chemical composition on the contact and sliding angleson hydrophobic surfaces were studied theoretically and experimentally. A theoretical model basedon forces developed at the contact area between a liquid drop and hydrophobic smooth or nano-roughened surface was developed and compared with the existing models, which are based onforces developed at the periphery between the drop and the solid surface. The contact area basedmodel gives rise to an interfacial adhesion strength parameter that better describes the drop-slidingphenomenon. Consequently, relationships were derived describing the dependence between theinterfacial adhesion strength of the liquid drop to the surface of a given composition, the mass ofthe drop, the measured contact angles and the sliding angle. For a given surface chemistry, the slidingangle on a nanometric roughened surface can be predicted based on measurements of contact anglesand the sliding angle on the respective smooth surface. Various hydrophobic coatings having differentsurface nanoroughnesses were prepared and, subsequently, contact angles and sliding angles on themas a function of drop volume were measured. The validity of the proposed model was investigatedand compared with the existing models and the proposed model demonstrated good agreement withexperimental results.

Keywords: Nanoroughness; nanometric; contact angle; sliding angle; hydrophobic surfaces; interfacialadhesion strength; coatings.

1. INTRODUCTION

The energetics of solid surfaces and its effect on the interaction with liquidsplays an important role in a variety of applications, such as adhesive bonding,polymer coating, printing, etc., where a high degree of wetting is desired. In

∗To whom correspondence should be addressed. Tel.: (972-3) 613-0111. Fax: (972-3) 613-0019.E-mail: [email protected]

564 P. F. Rios et al.

other applications like water and ice repellency, anti-stick, easy-cleaning and self-cleaning surfaces, wetting is undesirable.

The thermodynamics between a solid and a liquid were first described by Youngin 1805 [1]. The Young’s equation correlates the surface tensions of the liquid, thesolid and the gas surrounding them to the contact angle formed between the liquidand the solid substrate. The contact angle is related to the generally used term‘wetting’. Adamson [2] has defined wetting as a phenomenon where the contactangle between the liquid drop and the solid surface approaches zero; while non-wetting means that the contact angle is greater than 90◦. Generally, when thecontact angle is less than 90◦ the surface is called hydrophilic; when the contactangle is greater than 90◦ the surface is hydrophobic. A surface having a watercontact angle greater than 150◦ is usually classified as ultra-hydrophobic, i.e., awater repellent surface. Young considered smooth surfaces when he expressed hisideas. Wenzel [3, 4] recognized the importance of surface roughness and proposeda modification to the Young’s equation, which included a roughness factor definedas the ratio between the actual rough surface area and the geometric projectedarea. Young and Wenzel considered chemically homogeneous surfaces. Cassieand Baxter [5, 6] extended Wenzel’s work to non-homogeneous surfaces. Cassie’sEquation (1) relates the contact angle θ ′ for a chemically heterogeneous surfacecomposed of a fraction f1 of chemical type 1 and of fraction f2 of chemical type2, where θ1 and θ2 are the contact angles measured on type 1 and type 2 surfaces,respectively.

cos θ ′ = f1 cos θ1 + f2 cos θ2, (1)

f1 + f2 = 1. (2)

Cassie and Baxter extended their model to porous surfaces. In this case f1 isthe solid–liquid interface fraction and f2 the air–liquid interface fraction. For theair–liquid interface θ2 = 180◦; then, by substituting θ2 for 180◦ in equation (1),equation (3) is obtained for porous surfaces, where θ ′ is the contact angle for theporous surface, f is the solid fraction of the porous surface and θ is the contactangle for the smooth solid surface.

cos θ ′ = f cos θ + f − 1. (3)

Although Cassie and Baxter developed their model for porous surfaces, it couldalso be used for rough hydrophobic surfaces. On a hydrophobic rough surface,the liquid repellency impedes the liquid from fully penetrating into the depressionsof the roughness morphology. Penetration of pores will occur spontaneously onlyfor θ < 90◦ [7]. According to Youngblood and McCarthy [8] a pressure greaterthan 3 m water is needed to force the liquid into pores of micrometers in size.Accordingly, the critical parameters that affect the contact angle are the crests widthand the distance between them and not the depth of the depressions on the roughsurface.

Effects of nanostructure and composition on the hydrophobic properties of solid surfaces 565

Figure 1. Comparison between the contact fraction fC (Cassie) and fR (proposed model) for anoriginal smooth surface with θ = 120◦.

Using equation (3), equation (4) can be derived, where θ ′ is the contact angle forthe rough surface, fC is the contact area fraction between the liquid and the roughhydrophobic surface (according to Cassie) and θ is the contact angle for the smoothsolid surface [9].

f = fC = cos θ ′ + 1

cos θ + 1. (4)

While Cassie’s equation applies to a surface composed of well-separated anddistinct domains, further work by Israelachvili and Gee [10] dealt with chemicalheterogeneities of atomic or molecular scale. Based on intermolecular and surfaceforces theories they derived the following equation:

(1 + cos θ ′)2 = f1(1 + cos θ1)2 + f2(1 + cos θ2)

2. (5)

Nano-structured surfaces characterized by nano-scale roughness require specialattention. Starting from Israelachvili’s equation (5) and following the same line ofreasoning used to obtain equation (4), a novel relationship is proposed, as definedin equation (6), where θ ′ is the contact angle for the nano-rough surface, fR is thecontact fraction between the liquid and the nano-rough hydrophobic surface and θ

is the contact angle for the original smooth solid surface.

f = fR =(

cos θ ′ + 1

cos θ + 1

)2

. (6)

A comparison between fC and fR is presented in Fig. 1 for a smooth surfacewith θ = 120◦. It can be concluded from Fig. 1 that for a hydrophobic surface ahigh degree of roughness is needed to achieve ultra-hydrophobicity. For instance,to increase the contact angle from 120◦ to 150◦, fC = 0.27, while fR = 0.07, i.e.,the liquid drop makes contact with only 7% of the solid surface.

Nishino et al. [11] demonstrated that the highest water contact angle could beobtained for a regularly aligned and closely-packed surface composed of CF3


groups. Accordingly, the highest theoretical water contact angle on a flat andsmooth solid surface is 120◦. Further increase of the contact angle can be obtainedonly by varying the surface roughness. It is commonly accepted that ultra-hydrophobicity can be obtained by a proper combination of surface chemistry andsurface roughness.

From a practical point of view, the contact angle is not the only significant para-meter for defining hydrophobicity. For ultra-hydrophobic surfaces, self-cleaning isof importance. In this application, a low level of water-drop adhesion is of signifi-cance. The adhesion of a water drop to a surface can be characterized by the criticaltilting angle on the surface at which a liquid drop, with a certain weight, begins toslide down the tilted plane. Murase and co-workers [12, 13] have shown that a highcontact angle surface does not necessarily show a low sliding angle. They showedthat a fluoro-polymer with a contact angle of 117◦ possessed a higher sliding an-gle than poly(dimethylsiloxane) with a contact angle of 96◦. From a self-cleaningpoint of view, it does not matter how high the contact angle is, provided that thewater drop rolls off the surface. Consequently, a more comprehensive definition ofan ultra-hydrophobic surface should specify the highest possible contact angle (asclose to 180◦ as possible) and the lowest possible sliding angle (as close to 0◦ aspossible).

2. SURFACE MODELING

Different models have been proposed to correlate contact angles, sliding angles andinteraction energies between a liquid and a smooth or rough surface. The existingmodels and the newly proposed one are discussed and compared in light of welldesigned experimental results.

2.1. Smooth surfaces

The radius R of a liquid drop on a smooth surface can be calculated from its densityρ, mass m and the contact angle of the liquid with the solid θ (Fig. 2). Assuming

Figure 2. Schematic representation of a water drop on a smooth solid surface.


Figure 3. Schematic representation of a water drop on a tilted solid surface.

that the drop is a perfect sphere the radius of the drop can be calculated accordingto equation (7):

R =(

3m

ρπ(2 − 3 cos θ + cos3 θ)

) 13

. (7)

The radius r of the contact area between the drop and the solid is given byequation (8):

r = R sin θ. (8)

When the horizontal smooth plane is tilted, the contact area is assumed to remaincircular with radius r , even if the drop is deformed by tiling. These results arebased on the assumptions that there are no moments and rotational forces acting onthe drop, as depicted in Fig. 3. The pull force acting on the drop is the gravitationalforce (mg sin α) and the adhesion force opposing this movement is FA. At the onsetof drop motion, the forces acting on the drop will be at equilibrium according toequation (9):

FA = mg sin α. (9)

2.1.1. Model A. If the adhesion of the liquid drop to the solid is assumed to bethe result of the forces acting at the contact periphery between the drop and the solid(as in the Young’s equation), then:

FA = KA2πr, (10)

where KA is a constant with units of surface tension (N/m) or energy (J/m2) and is ameasure of the adhesion energy between the two phases. Combining equations (9)and (10), the Von Buzágh and Wolfram equation [14] is obtained:

sin α = KA2πr

mg. (11)


Many authors have used this equation as a starting point for their models[12, 13, 15, 16]. Substituting r in equation (11) from equations (7) and (8) thefollowing expression is obtained:

sin α = KA2π

g

(3


) 13

sin θm− 23 . (12)

According to equation (12), for a given liquid and solid surface (ρ and θ constant)the sine of the sliding angle α depends on the mass of the drop to the −2/3 power.KA represents the interaction energy (constant for a given surface chemistry) andis given by equation (13), which was obtained in a very similar form by Miwa andco-workers [16]:

KA =(

ρ(2 − 3 cos θ + cos3 θ)

3

) 13 g

2

(m

π

) 23 sin α

sin θ. (13)

2.1.2. Model B. This model is based on similar assumptions as the previousmodel, i.e., the interaction energy is a consequence of peripherial forces and surfacetensions. The thermodynamic work of adhesion WA required to separate a liquidfrom a solid phase is given by the Young–Dupre equation (14) [17] in terms of γLV,the liquid surface tension, and the contact angle θ .

WA − πe = γLV(1 + cos θ), (14)

where πe is the spreading pressure. πe is small when θ is finite and becomessignificant when θ approaches zero. Thus, for hydrophobic surfaces πe can beneglected. Thus, the Young–Dupre equation becomes:

WA = γLV(1 + cos θ). (15)

Furmidge [18] derived equation (16) based on equation (15), where θa and θr arethe advancing and receding contact angles, respectively, and w is the width of thecontact area of the drop perpendicular to the direction of movement.

mg sin α = wγLV(cos θr − cos θa). (16)

Furmidge’s equation (16) is very popular and a number of previous authors usesimilar models for the calculation of interaction energies of liquid drops on tiltedsolid surfaces [19–24]. These are hysteresis based models with some modificationsbut basically are similar to that of Furmidge.

Using the assumption that the shape of the contact angle remains almost circular,then w = 2r and equation (16) becomes equation (17):

sin α = 2r

mgγLV(cos θr − cos θa). (17)


As with the previous model, substituting r in equation (17) using equations (7)and (8) gives a new equation (18):

sin α = 2γLV(cos θr − cos θa)

g

[3


] 13

sin θm− 23 . (18)

Also in this case, for a given liquid and solid surface (i.e., γLV, θ , θa and θr

constant), sin α depends on the mass of the drop to the −2/3 power. The maindifference between this model and the previous one is that sin α can be calculateddirectly from the measured parameters γLV, θ , θa and θr, without the use of theenergy constant KA, used in the previous model.

2.1.3. Model C. Models A and B are based on the assumption that the adhesionof the liquid drop to the solid surface is the result of the forces developed at theperiphery of the contact area between the liquid drop and the solid. However,when evaluating the sliding angle a different approach should be taken. Thisapproach should include the adhesion phenomenon of the liquid drop to the solid,resulting from the intermolecular forces developed in the interfacial contact area.The interfacial forces attract the liquid molecules to the solid molecules also inthe contact area of the drop with the solid and not only along the periphery.Consequently, the proposed model hypothesizes that the force of adhesion isproportional to the contact area between the drop and the solid as:

FA = KCπr2, (19)

where KC is a constant with units of force/area (N/m2 = Pa) and is a measure of theadhesion strength between the liquid and the solid. Combining equations (9) and(19), equation (20) is obtained:

sin α = KCπr2

mg. (20)

Substituting r in equation (20) from equations (7) and (8) the following expressionis obtained:

sin α = KCπ

g

(3


) 23

sin2 θm− 13 . (21)

Hence, for a given liquid and solid surface (i.e., ρ and θ constant) sin α dependson the mass of the drop to the −1/3 power. KC is the interfacial adhesion strength(constant for a given surface chemistry) and is given by:

KC =(

ρ(2 − 3 cos θ + cos3 θ)

3

) 23

g(m

π

) 13 sin α

sin2 θ. (22)


Figure 4. Schematic representation of a water drop on a horizontal rough solid surface.

2.2. Models for rough surfaces

On a hydrophobic rough surface the liquid is prevented from penetrating theroughness depressions. Assuming an idealized rough surface, (Fig. 4), the contactangle changes from θ for a smooth surface to θ ′ for a rough surface. As a result r

and R also change to r ′ and R′, respectively. Both equations (7) and (8) hold andbecome for a rough surface:

R′ =(

3m

ρπ(2 − 3 cos θ ′ + cos3 θ ′)

) 13

, (23)

r ′ = R′ sin θ ′. (24)

Furthermore, provided that f is the interface contact fraction between the liquidand the solid, the effective interface contact perimeter will be 2πr ′f and theeffective interface contact area will be πr ′2f . Based on these principles thefollowing models are suggested.

2.2.1. Model A. The interaction energy constant KA depends on the chemistry ofthe solid surface. However, the introduction of roughness may change the surfacechemistry by changing the molecular configuration at the surface. Therefore, weassume that KA for a smooth surface becomes K ′

A for a rough surface. Thus, FA

becomes F ′A:

F ′A = K ′

A2πr ′f, (25)

and

sin α′ = K ′A2πr ′fmg

. (26)

Substituting r ′ in equation (26) from equations (23) and (24):

sin α′ = K ′A2πf

g

(3

ρπ(2 − 3 cos θ ′ + cos3 θ ′)

) 13

sin θ ′m− 23 . (27)


In addition:

K ′A =

(ρ(2 − 3 cos θ ′ + cos3 θ ′)

3

) 13 g

2f

(m

π

) 23 sin α′

sin θ ′ . (28)

Substituting f in equation (28) by fC as in equation (4), K ′AC, the interaction

energy constant, using the Cassie contact fraction is derived as:

K ′AC =

(ρ(2 − 3 cos θ ′ + cos3 θ ′)

3

) 13 g

2

(cos θ + 1

cos θ ′ + 1

)(m

π

) 23 sin α′

sin θ ′ . (29)

Similarly substituting f in equation (28) by fR as in equation (6), K ′AR, the

interaction energy constant, using the modified Israelachvili contact fraction, isobtained as:

K ′AR =

(ρ(2 − 3 cos θ ′ + cos3 θ ′)

3

) 13 g

2

(cos θ + 1

cos θ ′ + 1

)2 (m

π

) 23 sin α′

sin θ ′ . (30)

2.2.2. Model B. For a rough surface:

F ′A = wf γLV(cos θ ′

r − cos θ ′a). (31)

Thus:

sin α′ = 2r ′fmg

γLV(cos θ ′r − cos θ ′

a). (32)

Substituting r ′ in equation (32) from equations (23) and (24):

sin α′ = 2f γLV

g

(3

ρπ(2 − 3 cos θ ′ + cos3 θ ′)

) 13

(cos θ ′r − cos θ ′

a) sin θ ′m− 23 . (33)

Also in this case, f in equation (33) can be substituted by fC as in equation (4) orby fR as in equation (6), depending on the scale of surface roughness.

2.2.3. Model C. For a rough surface:

F ′A = K ′

Cπr ′2f. (34)

Thus:

sin α′ = K ′Cf πr ′2

mg. (35)

Substituting r’ in equation (35) from equations (23) and (24):

sin α′ = K ′Cπf

g

(3

ρπ(2 − 3 cos θ ′ + cos3 θ ′)

) 23

sin2 θ ′m− 13 . (36)


In addition:

K ′C =

(ρ(2 − 3 cos θ ′ + cos3 θ ′)

3

) 23 g

f

(m

π

) 13 sin α′

sin2 θ ′ . (37)

Substituting f in equation (37) by fC as in equation (4), K ′CC, the interaction

adhesion strength constant, using the Cassie contact fraction, is obtained as:

K ′CC =

(ρ(2 − 3 cos θ ′ + cos3 θ ′)

3

) 23

g

(cos θ + 1

cos θ ′ + 1

)(m

π

) 13 sin α′

sin2 θ ′ . (38)

Similarly substituting f by fR as in equation (6), K ′CR, the interaction adhesion

strength constant, using the Israelachvili modified contact fraction, is obtained as:

K ′CR =

(ρ(2 − 3 cos θ ′ + cos3 θ ′)

3

) 23

g

(cos θ + 1

cos θ ′ + 1

)2 (m

π

) 13 sin α′

sin2 θ ′ . (39)

2.2.4. Sliding angles on rough surfaces. When calculating the interaction ener-gies and adhesion strengths for rough surfaces it was assumed that the introductionof roughness might alter the surface molecular configuration; therefore, K for asmooth surface was modified to K ′ for a rough surface. In this way, the changesin interaction energies and adhesion strengths can be taken into consideration topredict the corresponding changes of the sliding angles. However, it is more likelythat when roughness is introduced the surface chemistry does not change. SinceK depends on surface chemistry, it should not change significantly when a surfaceis roughened. When this assumption is made, the sliding angle on a rough surfacecan be calculated from measurements of the contact angle and sliding angle for thesmooth surface and the contact angle for the rough surface. Hence, the followingmethodology is proposed:

(a) Measure the average ‘smooth’ contact angle θ , and the smooth sliding angle α,as a function of drop volume, for a given hydrophobic surface.

(b) Calculate the average ‘smooth’ surface energy and/or adhesion strength: KA

and KC.

(c) Measure the average ‘rough’ contact angle θ ′, for a given rough hydrophobicsurface.

(d) Calculate the contact interface fraction between the liquid and the solid usingfC or fR, depending on the roughness scale.

(e) Calculate the predicted ‘rough’ sliding angles as a function of drop volumeusing equations (40)–(45), for the different models:

sin α′AC = KA2π

g

(cos θ ′ + 1

cos θ + 1

)(3

ρπ(2 − 3 cos θ ′ + cos3 θ ′)

) 13

× sin θ ′m− 23 , (40)


sin α′AR = KA2π

g

(cos θ ′ + 1

cos θ + 1

)2 (3

ρπ(2 − 3 cos θ ′ + cos3 θ ′)

) 13

× sin θ ′m− 23 , (41)

sin α′BC = 2γLV

g

(cos θ ′ + 1

cos θ + 1

)(cos θ ′

r − cos θ ′a)

×(

3

ρπ(2 − 3 cos θ ′ + cos3 θ ′)

) 13

sin θ ′m− 23 , (42)

sin α′BR = 2γLV

g

(cos θ ′ + 1

cos θ + 1

)2

(cos θ ′r − cos θ ′

a)

×(

3

ρπ(2 − 3 cos θ ′ + cos3 θ ′)

) 13

sin θ ′m− 23 , (43)

sin α′CC = KCπ

g

(cos θ ′ + 1

cos θ + 1

)(3

ρπ(2 − 3 cos θ ′ + cos3 θ ′)

) 23

× sin2 θ ′m− 13 , (44)

sin α′CR = KCπ

g

(cos θ ′ + 1

cos θ + 1

)2 (3

ρπ(2 − 3 cos θ ′ + cos3 θ ′)

) 23

× sin2 θ ′m− 13 . (45)

It should be emphasized that for all models sin α is proportional to the solidsurface fraction f . Consequently, if f → 0 then α → 0. Hence, it can be concludedthat the rougher the surface becomes, the lower is the sliding angle. Furthermore, inthe case of hydrophobic surfaces, where the liquid does not penetrate the roughnessdepressions, small scale roughness should lead to a reduction in the actual contactarea between the drop and the solid surface (like a ‘Fakir’ bed) and to a reductionof the adhesion strength. In addition, the sliding angle, which depends stronglyon the contact angle, falls sharply as the contact angle increases. Figure 5 depictsthe sliding angle for a 5-µl water drop on a rough surface as a function of thecontact angle for models A and C. It is assumed that the ‘smooth’ contact angle is120◦ and the 5-µl drop will start rolling off a totally vertical surface (α = 90◦).A can be seen, for a ‘rough’ contact angle of more than 155◦ the predicted slidingangles are less than 5◦. Thus, when the contact angle reaches 155◦ the surfacewill become increasingly self-cleaning. At contact angle of 165◦ the sliding anglesapproach zero. Among the calculated angles, α′

CR is the fastest decreasing slidingangle, reaching less than 5◦ at a contact angle slightly over 140◦. According to theproposed model, the lowest sliding angle will be reached when nanoscale roughnessis achieved.


Figure 5. Sliding angle on a rough surface as a function of contact angle for a 5-µl water drop(smooth contact angle is 120◦).

An alternative representation to equations (40)–(45) can be derived. For ModelA, combining equations (13), (27) and (4) results in equation (46):

sin α′AC =

((2 − 3 cos θ + cos3 θ)

(2 − 3 cos θ ′ + cos3 θ ′)

) 13 sin θ ′

sin θ

(cos θ ′ + 1

cos θ + 1

)sin α. (46)

Combining equations (13), (27) and (6), equation (47) is obtained:

sin α′AR =

((2 − 3 cos θ + cos3 θ)

(2 − 3 cos θ ′ + cos3 θ ′)

) 13 sin θ ′

sin θ

(cos θ ′ + 1

cos θ + 1

)2

sin α. (47)

For Model B, combining equations (18), (33) and (4), equation (48) is derived:

sin α′BC =

((2 − 3 cos θ + cos3 θ)

(2 − 3 cos θ ′ + cos3 θ ′)

) 13(

cos θ ′r − cos θ ′

a

cos θr − cos θa

)sin θ ′

sin θ

×(

cos θ ′ + 1

cos θ + 1

)sin α. (48)

Combining equations (18), (33) and (6) results in equation (49):

sin α′BR =

((2 − 3 cos θ + cos3 θ)

(2 − 3 cos θ ′ + cos3 θ ′)

) 13(

cos θ ′r − cos θ ′

a

cos θr − cos θa

)sin θ ′

sin θ

×(

cos θ ′ + 1

cos θ + 1

)2

sin α. (49)


For Model C, combining equations (22), (36) and (4), equation (50) is obtained:

sin α′CC =

((2 − 3 cos θ + cos3 θ)

(2 − 3 cos θ ′ + cos3 θ ′)

) 23 sin2 θ ′

sin2 θ

(cos θ ′ + 1

cos θ + 1

)sin α, (50)

and finally, combining equations (22), (36) and (6), equation (51) is derived:

sin α′CR =

((2 − 3 cos θ + cos3 θ)

(2 − 3 cos θ ′ + cos3 θ ′)

) 23 sin2 θ ′

sin2 θ

(cos θ ′ + 1

cos θ + 1

)2

sin α, (51)

where θ , θa, θr and α are the contact and sliding angles for a smooth surface andθ ′, θ ′

a, θ ′r and α′ are the contact and sliding angles for a rough surface. Equations

(46)–(51) indicate that the predicted sliding angle on a rough surface is proportionalto the sliding angle on the smooth surface. Equations (46)–(51) render the samevalues as equations (40)–(45); however, for drop volumes that do not roll off thesmooth surface even when it is vertical these equations are not applicable, becausesin α cannot be determined. Furthermore, equations (40)–(45) include averagesurface energy or adhesion strength, K , that are independent of drop volume andsin α. Thus, the values of sliding angles on rough surfaces can be calculated evenfor drop volumes that do not roll off a smooth surface but could roll off a roughsurface. Consequently, equations (40)–(45) will be used preferably in the followingcalculations for rough sliding angles.

3. EXPERIMENTAL

To verify the validity of the various derived models, an experimental program wasdesigned.

In the first part of the experimental program, three chemically different, uncoatedand unroughened surfaces were evaluated: poly(tetrafluoroethylene) (PTFE) sheet(Virgin PTFE, Lanza Nuova, Italy); commercial polycarbonate (PC) resin (FDAgrade, Makrolon 3108, Bayer, Germany) and poly(methyl methacrylate) (PMMA)resin (FDA grade, Diakon CLH 952T, Lucite International, USA). The PC andPMMA resins were injection molded using a highly polished mould, rendering highoptical quality transparent rectangular specimens (light transmission >90%), 3 mmthick. The FDA grade, with minimum additives, was chosen in order to minimizethe effect of migrating additives on the results.

In the second part of the experimental program the PC smooth specimens werecoated with a commercial fluoroalkylsilane solution: tridecafluorooctyltriethoxysi-lane dissolved in i-propanol (Dynasylan F8263, Degussa, Germany, hereafter re-ferred as FAS/P). The PC samples were dipped in the silane solution for 3 min,removed and then heated at 110◦C for 120 min. Other authors [25–28] have foundthat the length and flexibility of the fluoroalkyl molecule have an effect on the sur-face energy decrease (and therefore contact angle increase) due to enhanced segre-gation of the CF3 chain-end on the surface. Finally, to reduce the sliding angle and


increase the contact angle on the PC samples, functionalized polyhedral oligomericsilsesquioxane (POSS) compounds [29] were used to create nanotexture. POSS ischaracterized by a cage-like structure having a diameter of 1.5 nm. Unlike silicaand modified nanoclays, each POSS molecule may contain covalently bonded func-tionalities. The POSS compound selected was based on trifluoro (3) cyclo-pentylPOSS (C50H93F39O12Si10, FL0590 Hybridplastics, Hattiesburg, MS, USA, hereafterreferred as FPOSS). This compound contains long fluoroalkyl side groups similarto those present in the selected fluoroalkylsilane. It is expected that whether the PCsubstrates are coated with the FAS/P or with the FPOSS compounds or a mixture ofthe two, the fluorine-based surface chemistry remains the same. On the one hand,the addition of FPOSS is not expected to change significantly the basic fluorine sur-face chemistry; on the other hand, the nanometric cage-like structure is expectedto create a nanoscaled surface texture, which according to the proposed models isexpected to reduce the sliding angle. Hence, FPOSS was mixed in different concen-trations with FAS/P. Mixing was carried out for 5 min using a high-speed homoge-nizer. The resulting solution was used to coat the PC substrates by dipping for 3 minand then dried at 110◦C for 120 min. FPOSS was also dissolved in different concen-trations in α, α, α-, trifluorotoluene (TFT). Mixing was performed for 2 h using amagnetic stirrer. The PC samples were submerged in the formulation for a period of10 s and dried. After coating, all samples were conditioned in controlled laboratoryconditions (25◦C, 60% RH) for 24 h before any measurements were performed.

The static contact angle was measured according to the sessile drop method usinga commercial video based, software controlled, contact angle analyzer (OCA 20,Dataphysics Instruments, Germany). Deionized and ultra-filtered water (0.2 µm fil-ter) was used for the measurements. In a preliminary step, it was found that therewere no significant changes in the contact angle as a function of drop volume in therange of drop volumes used in this work (1–30 µl). The contact angle obtained bythis method is one of the many thermodynamically allowed metastable states, exper-imentally indistinguishable from the actual equilibrium contact angle. However, thecontact angle measured by this method is the one used as the experimental contactangle for the purpose of the discussed models [16]. The sliding angle was measuredusing a tilting unit (TBU90E, Dataphysics Instruments, Germany) incorporated intothe contact angle analyzer. A drop was first deposited on the horizontal substrateand after equilibrium the substrate plane was tilted at a rate of 100◦/min until the on-set of drop motion. The sliding angle was found to vary with drop volume and wasmeasured as a function of water drop volume in the range of 1–30 µl. The advanc-ing and receding angles were measured using the tilt method with the same tiltingunit and methodology as for the sliding angle. In the tilt method, the plane of thesolid and the sessile drop are tilted at a low constant velocity. Because of the tilting,the angles of the drop with the solid change, increasing on one side and decreasingon the other. At a certain plane slope, the drop starts to slide on the solid surface.The dynamic contact angles were recorded at the onset of drop motion. The higherone in the direction of the motion is the advancing contact angle and the lower one


opposite to the direction of the motion is the receding contact angle. The contactangles and sliding angles were measured using video-based software (SCA 20, Dat-aphysics Instruments, Germany). To evaluate coatings quality, light transmission(LT) and haze were measured using a Hazemeter (BYK Gardner, Germany). Themorphology was investigated by an atomic force microscope (AFM, Veeco, USA)in the non-contact mode. Surfaces region analysis was performed and the sam-ples were characterized quantitatively by measuring the root mean square roughnessRrms. Qualitatively characterization was performed with AFM topography images.

4. RESULTS

4.1. Uncoated smooth surfaces

4.1.1. Contact angles. Figure 6 contains photographs from the OCA20 videocontact angle analyzer for 5-µl water sessile drops used for measuring the static

Figure 6. Sessile drops for static contact angle measurements: (a) PMMA, (b) PC, (c) PTFE.


Figure 7. Tilted drops for advancing and receding angle measurements: (a) PMMA, (b) PC, (c) PTFE.

Table 1.Static and dynamic contact angles on smooth solids

Parameter PMMA PC PTFE

θ (deg) 72.5 ± 3.3 81.3 ± 0.7 111.9 ± 3.0θa (deg) 76.0 ± 3.0 82.2 ± 1.3 115.7 ± 2.3θr (deg) 57.9 ± 2.7 73.8 ± 1.1 93.6 ± 4.8

contact angle on PMMA, PC and PTFE. The increase in the contact angle fromPMMA to PTFE is evident.

Figure 7 shows the same drops after the sample plane had been tilted. Theseshapes were used for the measurement of the advancing (right) and receding (left)contact angles.

Table 1 summarizes the results of the static and dynamic contact angles for thedifferent materials. Measurements were made in five different sample locations


Figure 8. Sliding angles for different materials.

and for different drop volumes. Contact angles and hysteresis do not depend ondrop volume. The results expressed in Table 1 represent the average and standarddeviation for all measurements and volumes.

4.1.2. Sliding angles. Figure 8 depicts the average sliding angles as a function ofvolume for the three materials studied. For all three solids, small drops did not slideeven for vertical (90◦) solid position. As the drop volume increased the drops startedto slide. The sliding angle decreased with drop volume. This general behavior is inagreement with previous studies [12, 13, 16].

4.2. Coated surfaces

4.2.1. Coating quality. Coating quality was evaluated visually and with the useof a Hazemeter. FAS/P spread and adhered well to the surface of the PC substrate.For the uncoated PC sample, light transmission (LT) was 92.6% and haze was0.45%. After coating with FAS/P, LT stayed at 92.6%, but the haze increasedslightly to 0.53%. A special effort was directed towards creating a nanostructuredsurface. To maintain a surface transparent, its roughness should be lower than thevisible wavelength (400–750 nm), i.e., on the order of 100 nm [30]. The haze levelwas the indicating factor for the level of agglomeration. High haze factors indicatedhigh levels of agglomeration, while low haze values signify nano-dispersion. Thebest results were obtained for FPOSS dissolved in TFT. For 3 wt% FPOSS solutionthe LT was 95.1% and the haze was 5.9%. In this case, the coated sample maintainedits transparency and uniformity and agglomerates could not be seen by the nakedeye.

4.2.2. Contact angles. The contact angles for three different coatings are sum-marized in Table 2. An increase of the contact angle θ is observed for the FPOSScoated surfaces. The highest value is obtained with FPOSS in TFT. The lower stan-dard deviation of the results for the last case compared to the other ones indicatesthat good uniformity and good dispersion were obtained.


Figure 9. Sliding angles for various coatings on PC substrates.

Table 2.Contact angles for different coatings on PC substrates

Parameter FAS/P 3 wt% FPOSS

In FAS/P In TFT

θ (deg) 89.3 ± 2.6 107.8 ± 6.8 110.0 ± 2.7θa (deg) 95.9 ± 2.4 110.9 ± 1.4 112.5 ± 0.9θr (deg) 79.1 ± 2.9 99.5 ± 1.1 106.7 ± 1.9

Table 3.Surface roughness for uncoated and coated PC substrates

Parameter Uncoated PC FAS/P 3 wt% FPOSS(in TFT)

Rrms (nm) 1.5 3.1 14.5

4.2.3. Sliding angles. The sliding angles for the studied coatings are depictedin Fig. 9. While the FAS/P coating demonstrated increased contact angle it alsoincreased the sliding angle, comparable to the uncoated PTFE sample (Fig. 8). Theaddition of FPOSS texturing agent reduced the sliding angle. The lowest slidingangles were obtained for the sample coated with FPOSS in TFT.

4.2.4. Morphology. The root mean square roughness Rrms for the uncoated PCsample, the FAS/P coated sample and the FPOSS (in TFT)-coated samples arepresented in Table 3. AFM topography images of the same samples are shown inFig. 10. The uncoated PC sample presents a very low value of the Rrms and can beconsidered smooth. The FAS/P coating increases somewhat the roughness, but the


(a)

(b)

(c)

Figure 10. AFM topography images: (a) uncoated PC, (b) FAS/P, (c) 3 wt% FPOSS (in TFT).


Rrms still remains very low; thus, this sample also can be considered smooth. Thusit can be seen that the FAS/P coating, while changing the surface chemistry hasnot significantly changed the surface roughness. The effect of FPOSS as a surfaceroughener can be seen by the significant increase in the Rrms for this sample. Theroughness increase can also be qualitatively visualized in the topographic images inFig. 10.

5. DISCUSSION

5.1. Uncoated smooth surfaces

The results depicted in Table 1 and Fig. 8 show that PC has a higher contact anglethan PMMA and at the same time a lower sliding angle. Hence, PC is morehydrophobic than PMMA. PTFE demonstrates a different relationship between thecontact angle and sliding angle. As Table 1 indicates, PTFE shows the highestcontact angle and at the same time the highest sliding angle. If hydrophobicityis characterized by a combination of high contact angle and low sliding anglethen PTFE does exhibit a real hydrophobic advantage over PC or PMMA. Table 4

Figure 11. Experimental and calculated sliding angles (sin α) from Models A, B and C, for theuncoated PC sample.

Table 4.Interaction energy KA, according to Model A, and interaction adhesion strength KC, according to theproposed model

Parameter PMMA PC PTFE

θ (deg) 72.5 ± 3.3 81.3 ± 0.7 111.9 ± 3.0KA (mJ/m2) 8.2 ± 0.3 4.0 ± 0.6 17.7 ± 0.5KC (Pa) 6.6 ± 0.6 4.0 ± 1.5 19.3 ± 0.3


summarizes the calculated values of the interaction energy according to Model A(KA) and the interaction adhesion strength according to the proposed Model C (KC).

Average KA and KC were calculated using equations (13) and (22), respectively,and the measured values of θ and α for different drop sizes. PMMA has the lowestcontact angle but an intermediate sliding angle between PC and PTFE, therefore itsinteraction energy KA or interaction adhesion strength KC is intermediate betweenPC and PTFE. PC has an intermediate contact angle but its sliding angle is thelowest of all three materials; therefore, its interaction energy or strength is thelowest. Finally, PTFE has the highest contact and sliding angles; therefore, itsinteraction energy or interaction adhesion strength is significantly higher than thoseof the two other materials. Both models render interaction values compatible withthe experimental findings. Figure 11 shows a comparison between the experimentalvalues of sin α and the calculated values of sin α according to Model B using themeasured values of θ , θa and θr (equation (18)), for PC specimens. The respectiveModels A and C (equations (12) and (21)), using the average values of KA andKC, were added for comparison. Good agreement can be seen between the generalbehavior of the experimental values and the three models.

5.2. Coated surfaces

The PC sample coated with FAS/P has only fluoroalkyl surface chemistry and ac-cording to the AFM measurements it can be assumed to represent a ‘smooth’ ref-erence sample for comparison with the FPOSS-modified ‘rough’ samples. Accord-ingly, the ‘smooth’ interaction energy according to Model A, KA and the ‘smooth’interaction adhesion strength according to Model C, KC were calculated usingequations (12) and (22), respectively, rendering KA = 11.8 ± 0.3 mJ/m2 andKC = 10.7 ± 1.3 Pa. The interaction energies and strengths for the ‘rough’ FPOSS-modified samples were calculated for Model A and Model C using the Cassie con-tact fraction fC (equation (4)) and the Israelachvili-modified contact fraction fR

(equation (6)). Furthermore, the interaction energies K ′AC (equation (29)), K ′

AR(equation (30)), K ′

CC (equation (38)) and K ′CR (equation (39)) were calculated and

are summarized in Table 5. Surface roughness in the nanorange reduces the contactarea for a hydrophobic surface due to inability of the water drops to penetrate theroughness depressions. Thus, the effective contact area between the liquid and thesolid is reduced. In addition, the increase in the contact angle contributes furtherto the reduction of the contact area. Consequently, the combined effects reduce thecontact area and, consequently, reduce the overall bonding force attaching the waterdrop to the solid and thus the resultant sliding angle. Thus, if the interaction en-ergy or adhesion strength is equal for smooth and rough surfaces, the sliding anglereduction is a consequence of the contact area reduction. The change in K meansthat the surface composition has changed, i.e., the density or the arrangement of thehydrophobic moieties at the surface has changed. Two cases can be envisioned. Inthe first case, the measured sliding angle is higher than the expected one. In thiscase, the reduction of the sliding angle is not enough to account for the reduction


Table 5.Surface contact fractions, interaction energies and interaction adhesion strengths according to differentmodels for coated samples

Parameter FAS/P 3 wt% FPOSS

In FAS/P In TFT

θ (deg) 89.3 ± 2.6 107.8 ± 6.8 110.0 ± 2.7α (deg) (30-µl drop) 38 15 8fC 1 0.69 ± 0.11 0.65 ± 0.04K ′

AC (mJ/m2) 11.8 ± 0.3 9.7 ± 1.3 5.7 ± 1.2K ′

CC (Pa) 10.7 ± 1.3 12.3 ± 3.9 7.6 ± 3.4fR 1 0.48 ± 0.14 0.42 ± 0.06K ′

AR (mJ/m2) 11.8 ± 0.3 14.1 ± 1.9 8.8 ± 1.9K ′

CR (Pa) 10.7 ± 1.3 18.0 ± 5.7 11.7 ± 5.3

FAS/P sample is assumed smooth, so: fC = fR = 1, K ′AC = K ′

AR = KA and K ′CC = K ′

CR = KC.

of the contact area. Hence, K has to assume a higher value to account for this highsliding angle. In the second case, the measured sliding angle is lower than the ex-pected one. In this case, K has to assume a lower level. It can be seen in Table 5 thatfor FPOSS (in TFT) most models render lower interaction parameters. In this case,the interaction adhesion strengths calculated according to Model C are closer to the‘smooth’ values than for Model A predictions. Specifically when the Israelachvili-modified contact fraction (K ′

CR) is used, the value is 11.7 Pa, very close to 10.7 Pa,for the ‘smooth’ value (KC).

5.3. Sliding angles on rough surfaces

In the previous section, it was assumed that the incorporation of the texturingagents, even when inert, might change the surface chemistry by changing the surfaceconfiguration of the molecules. Alternatively, it can be hypothesized that when aninert texturing agent is added, the surface chemistry is maintained and so are therespective K values.

When this assumption is made, the sliding angle on the rough surface can becalculated and predicted based on measurements of the contact angle and slidingangle for the smooth surface and the contact angle for the rough surface.

As already stated the FAS/P sample has a similar fluoroalkyl surface chemistry asthat of the FPOSS additive but without the nanotexturing effect of the FPOSS. Thus,the ‘smooth’ surface parameter needed to predict the rough surface contact anglesaccording to equations (40)–(45) (KA, KC, θ smooth, θa smooth, θr smooth) can beextracted from the smooth sample. Namely KA smooth = 11.8 mJ/m2, KC smooth= 10.7 Pa, θ smooth = 89.3◦, θa smooth = 95.9◦ and θr smooth = 79.1◦ (Tables 2and 5). Figure 12 shows the measured sliding angles for samples containing 3 wt%FPOSS (in TFT), compared to the predicted sliding angles calculated accordingto equations (40)–(45). For this sample the best FPOSS dispersion and opticalquality was achieved. It can be seen in Fig. 12 that Model A using the Israelachvili-


Figure 12. Experimental versus predicted sliding angles for 3 wt% FPOSS (in TFT).

modified contact fraction fits best for low-volume water drops (<15 µl). ModelC, using the same contact fraction concept, fits best the experimental results forlarger-volume drops (>15 µl). Model A assumes that the drop adhesion to the solidsurface is a consequence of the contact perimeter, while Model C assumes that it isa consequence of the contact area. The ratio of the contact perimeter to the contactarea is:

Drop contact perimeter

Drop contact area= 2πr

πr2= 2

r. (52)

For small drops the contact perimeter is dominant over the contact area; therefore,it fits better the Model A. For larger drops the contact area is dominant overthe contact perimeter: therefore, it fits better the Model C. Model B predictslower values in both cases than the experimentally observed ones. The fact thatthe Israelachvili-modified contact fraction fits better the experimental results thanthe Cassie contact fraction, in addition to the good optical quality and low haze,suggests that for this sample good nanodispersion was achieved.

6. CONCLUSIONS

It is widely accepted that high hydrophobicity can be obtained only by a propercombination of surface chemistry and surface roughness. Moreover, it has beenrecognized that both the contact angle and the sliding angle are of significance fora complete description of surface energetics. In the current work, three theoreticalmodels for the calculation of interaction energy or adhesion strength between aliquid drop and a solid surface have been used. Calculations were carried outfor both smooth and rough surfaces. The first two models used are based onequations developed by Von Buzágh, Wolfram and Furmidge. In these models, itis assumed that adhesion forces that are developed between the liquid and the solidare dependent on the contact perimeter. In this study, a third model is proposed.


The model assumes that the interfacial adhesion between the drop and the soliddepends on the contact area and not on the perimeter length. This is a more suitableapproach, since the drop sliding phenomenon depends on the balance between thedrop weight (size) and the total adhesion force between the drop and the surface.Moreover, in this work, the Israelachvili equation for describing contact angles onnon-homogeneous surfaces was further developed for hydrophobic surfaces withroughness on the nanometer scale. The interaction energies and adhesion strengthswere first evaluated for three chemically different, smooth polymer surfaces. Itwas found that the models predicted interaction adhesion strengths compatible withthe experimental results. Hydrophobic smooth surfaces were prepared by coatingpolycarbonate surfaces with fluoroalkylsilane solution. Roughness was introducedby means of FPOSS coating. The cage-like nano-structure roughness, if FPOSSis properly nanodispersed, creates a nanoscaled surface texture. This nanoscaleroughness is likely to increase the contact angle and reduce the sliding angle. Thevalidity of the new proposed model was investigated and compared with the othermodels. When a nanodispersion of the nanoroughening FPOSS agent was formed,good agreement between the model and the experimental results was obtained. Forsmall drops, when the contact perimeter is dominant over the contact area, a betterfit was found for the models that assume drop adhesion as a consequence of thecontact perimeter. For larger drops, when the contact area is dominant over thecontact perimeter, a better fit was found with the new model that assumes that dropadhesion is the result of the contact area.

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