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Article

Wetting of Composite Surfaces: When and Whythe Area Far from The Triple Line is Important?"

Edward Bormashenko, and Yelena BormashenkoJ. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp407171v • Publication Date (Web): 26 Aug 2013

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1

Wetting of Composite Surfaces:

When and Why the Area Far from The Triple Line is Important?

Edward Bormashenko*, Yelena Bormashenko

Ariel University, Physics Faculty, P.O.B. 3, 40700, Ariel, Israel

Corresponding author: Ed. Bormashenko

E-mail: edward@ariel.ac.il

Postal address: Ariel University, P.O.B. 3, 40700, Ariel, Israel

Tel.: +972-3-9066134

Fax: +972-3-9066621

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Abstract

Apparent contact angles are totally governed by the area of solid surface

adjacent to the triple (three-phase) line. However, apparent contact angles do not

describe the wetting situation exhaustively. The wetting regime is characterized by

both apparent contact angle and the energy of adhesion. The energy of adhesion in

turn depends on the physical and chemical properties of the entire area underneath

the droplet. We demonstrate this experimentally by preparing rough surfaces

exhibiting high apparent contact angles accompanied with the high energy of

adhesion leading to the high contact angle hysteresis. A droplet deposited

axisymmetrically on the superhydrophobic surface comprising non-

superhydrophobic spot holds “sticky” wetting attended with high apparent contact

angles.

Keywords: apparent contact angle; energy of adhesion; Cassie wetting; Wenzel

wetting; contact angle hysteresis; rose petal effect.

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Introduction

The wetting of composite solid surfaces has been subjected to intensive and

hot scientific discussion, started recently by Gao and McCarthy in their paper, entitled

"How Wenzel and Cassie Were Wrong?" The discussion was concentrated on the

question: is the wetting of a composite surface a 1D or 2D affair?1–12

In other words:

is the wetting of a composite surface influenced by a total surface underneath the

droplet, or only the area adjacent to the triple (three-phase) line is important? The use

of the notions of “1D” and “2D” wetting scenarios needs care. The triple line is a

physical object, hence it has certain thickness and width; the last was estimated

experimentally recently as 2-5 µm.13-14

However, the use of these notions is justified

for distinguishing of situations, when the wetting regime is governed by an area of

substrate close to the triple line from those when it is dictated by an entire area

underneath the droplet.

An accurate variational treatment of the problem demonstrates explicitly that

equilibrium apparent contact angles are influenced by the three-phase adjacent area of

solid only.11

This prediction coincides with the experimental findings reported by Gao

and McCarthy.1 The fact that apparent contact angles are governed by physical and

chemical peculiarities of the solid surface close to the triple line may lead to the

misleading conclusion that wetting of composite or rough surface is exhaustively

characterized by considering the solid area in the nearest vicinity of the triple line.

This paper shows that not only apparent contact angle but also energy of adhesion are

important for the correct characterization of the wetting situation. The energy of

adhesion in turn is dictated by the total area of solid surface wetted by a droplet.

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Experimental

Composite surfaces were manufactured as follows. At the first stage

superhydrophobic surfaces were prepared by the hot embossing of low density

polyethylene (LDPE) films. LDPE films were fabricated by extrusion with a single

screw extruder (RCP-0750). The thickness of the extruded films was of about 1 mm.

The obtained films were exerted to hot embossing with the manually operated heated

hydraulic Press P/N 15011/25011 under the pressure of about 10 MPa. The

temperature of embossing was 105 °C. The hot embossing process is illustrated in

Figure 1. Hot embossing was carried out with micro-scaled stainless steel wire gauzes

used as stamps. Gauzes were supplied by A. D. Sinun (Israel). The SEM image of the

gauze is presented in Figure 2.

The gauzes have been glued to 10 cm×10 cm steel plates with the use of the

heat-proof epoxy adhesive. The SEM images of reliefs produced by hot embossing

are depicted in Figure 3A–B. SEM imaging was carried out with high resolution SEM

(JSM-6510 LV). The “hairy” surfaces depicted in Figure 3A-B demonstrated

pronounced superhydrophobicity; apparent contact angles as high as 150±3° and

sliding angles as low as 10° for 10 µl water droplets were registered on these surfaces.

The 4 µl water droplet deposited on the “hairy” superhydrophobic surface is depicted

in Figure 4.

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Figure 1. Scheme of the preparing of superhydrophobic surfaces by hot embossing

process.

Figure 2. SEM image of the stainless steel wire gauzes used for hot embossing of

polymer (LDPE) films. The scale bar is 200 µm.

The non-superhydrophobic spots were produced on the “hairy” surfaces

shown in Figure 3A-B. The surfaces were carefully pressed with a metallic needle at

ambient conditions, thus “hairy” structures shown in Figure 3A-B were destroyed and

heated dies

of the press

moving

die with

gauze

сетка

LDPE film

embossed film

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rough surface reliefs such as depicted in Figure 5A-B were produced. Spots with a

characteristic size of 500 µm comprising destroyed “hairy” reliefs, shown in Figure

5A-B structures were produced.

Large-area rough non-superhydrophobic surfaces with a relief, shown in

Figure 5A-B were manufactured for the purpose of characterization of their wetting

regime.

A

B

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Figure 3. SEM images of hairy superhydrophobic LDPE reliefs produced with the hot

embossing process utilizing metallic gauzes shown in Figure 2 as templates. A. Scale

bar is 100 µm, B. Scale bar is 50 µm.

2-4 µl water droplets were carefully deposited with use of micro-syringe

mounted on precise XYZ stage axisymmetrically on the superhydrophobic surfaces

including non-superhydrophobic rough spots, as shown in Figure 6.

Figure 4. 4 µl water droplet deposited on hairy superhydrophobic surface depicted in

Figure 3.

A

B

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Figure 5. Rough surfaces obtained when a metallic needle was introduced into

“hairy” reliefs depicted in Figure 3A-B. A. Scale bar is 100 µm. B. Scale bar is 50

µm.

Figure 6. Scheme showing axisymmetric deposition of a droplet on a composite

superhydrophobic surface comprising non-superhydrophobic spot.

Apparent contact angles were measured by Ramé-Hart Advanced Goniometer

Model 500-F1. Advancing, receding and sliding angles were measured using a lab-

made supplement to the goniometer, allowing gradual tilting of the surface with a step

of one degree.

Results and Discussion

Hairy LDPE structures, manufactured as described in the Experimental

Section and depicted in Figure 3A-B, demonstrated pronounced superhydrophobicity

i.e. high apparent contact angles °± 3150 (shown in Figure 4) and low contact angle

hysteresis, accompanied by low sliding angles (~10° for 10 µl droplets). The observed

liquid superhydrophobic

relief

non-superhydrophobic

spot

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superhydrophobicity of “hairy” LDPE surfaces is due to the pronounced Cassie-

Baxter air trapping wetting regime resulting in the so-called “lotus effect”.15–24

Large area non-superhydrophobic rough surfaces depicted in Figure 5

demonstrated moderate hydrophobicity. i.e. apparent contact angles of °± 5120 and

high contact angle hysteresis, illustrated with Figure 7. The 4 µl droplet remained

attached to these surfaces, when they were tilted at arbitrary angle, and even when

they were turned upside down, as also shown in Figure 7. The advancing contact

angle established on these surfaces was °± 5122 , and the receding contact angle was

.5102 °±

Figure 7. 4 µl droplet deposited on the large area rough non-superhydrophobic

surface. The droplet is attached to the surface even when the surface is turned upside

down.

The most interesting wetting behavior was observed when a droplet was

deposited axisymmetrically on the superhydrophobic surface comprising non-

superhydrophobic central spot. In this case high apparent contact angles of °± 3150

were accompanied by the high contact angle hysteresis, as shown in Figuer 8. The 2

µl droplet remained adhered to the surfaces even when they turned upside down as

depicted in Figure 8. Thus, we conclude that the composite surface containing non-

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superhydrophobic blemishes demonstrated manifestation of the so-called “rose petal

effect”, reported first by Jiang et al. (Ref. 25) and exposed to intensive experimental

and theoretical research recently.25–29

The heavier 10 µl droplet deposited on these

surfaces (demonstrating high contact angle hysteresis) slides at the sliding angle of

20°. The advancing contact angle established on these surfaces was °± 3165 , and the

receding contact angle was .2129 °±

Figure 8. 2 µl droplet deposited on the superhydrophobic surface comprising non-

superhydrophobic central blemish (see Scheme, presented in Figure 6).

High adhesion of droplets accompanied with high apparent contact angles

could be explained easily in our case. Apparent contact angles are dictated by the

superhydrophobic “hairy” area of the solid surface adjacent to the triple line, shown in

Figure 3 (see Ref. 11). At the same time the energy of adhesion of a droplet is

influenced by the entire area of the wetted solid. Consider for sake of simplicity a

droplet with the radius of the contact area r deposited axysimmetrically on the flat

composite surface, comprising a spot with the radius a, depicted in Figures 9–10A. It

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is supposed that the difference r–a is much larger than the “width” of the triple line,

i.e. µm5>>− ar takes place (see Ref. 13–14).

Let the specific surface energies (interfacial tensions) of the solid/air and

solid/liquid interfaces of the central spot be 11, SLSA γγ and the specific surface energies

of the solid/air and solid/liquid interfaces of the external circle be 22 , SLSA γγ (see

Figures 9-10). The energy of adhesion which is necessary for disconnection of the

droplet could be calculated according to:

SLLSAad GGGW −+= , (1)

where SAG is the free surface energy of the “dry” solid/air interface, LG is the free

surface energy of the liquid/air interface of the basal plane of the disconnected droplet

(shown in Figure 10B), and SLG is the free surface energy of the solid/liquid interface

in the situation, depicted in Figure 10A. Thus, the energy of adhesion of a droplet is

given by:

)()( 22

2

2

1

222

2

2

1 arararaW SLSLSASAad −−−+−+= πγπγγππγπγ . (2)

Involving the Young equations (the composite surface is supposed to be flat),

i.e.: 222111 cos;cos θγγγθγγγ =−=− SLSASLSA (where 21,θθ are the Young contact

angles of central spot/liquid and surrounding circle/liquid pairs respectively) yields a

more compact expression for the adhesion energy:

)cos)(cos( 2

22

1

22 θθγπ ararWad −++= . (3)

For the specific energy of adhesion related to the unit area of solid W~

we have:

)cos)1(cos1(~

22

2

12

2

2θθγπ

π r

a

r

a

r

WW ad −++== . (4)

It is recognized from Eqs. (3)–(4) that the adhesion energy of a droplet

deposited on the flat chemically heterogeneous surface depends on the wetting

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properties of an entire area, wetted by a droplet. Physical and geometrical parameters

characterizing both a central blemish and a surrounding circle appear explicitly in

Eqs. (3)–(4).

Figure 9. Flat chemically heterogeneous surface characterized by the specific surface

energy 2SAγ comprising round blemish, possessing specific surface energy 1SAγ (top

view).

If a droplet is deposited on the rough composite surface (the central spot and

surrounding circle possess roughness f1 and f2 respectively as depicted in Figure 11),

Eqs. (3)–(4) could be easily generalized for the Wenzel wetting regime [30, 31]:

)cos)(cos(*

2

22*

1

22 θθγπ ararWad −++= , (5)

)cos)1(cos1(~ *

22

2*

12

2

2θθγπ

π r

a

r

a

r

WW ad −++== , (6)

where *

2

*

1 ,θθ are the Wenzel apparent contact angles supplied by: 11

*

1 coscos θθ f= ;

22

*

2 coscos θθ f= (recall that the roughness f is defined as the ratio of the real surface

in contact with liquid to its projection onto the horizontal plane). It is distinctly seen

from Eqs. (5)–(6) that the energy of adhesion of droplet is influenced by a surface

energy and roughness of both wetted central spot and a surrounding circle.

����

����

a

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The presented analysis supplies one of the possible qualitative explanations to

the “rose petal effect”; indeed, high apparent contact angles do not necessarily

provide an easy sliding of droplets. There exist various experimental situations, when

“sticky” wetting is attended with high apparent contact angles.25–29, 32, 33

We report

one of such possibilities, when a superhydrophobic surface contains non-

superhydrophobic blemish.

AA

Figure 10. A. Droplet with the radius of the contact area r deposited axisymmetrically

on a flat composite surface, comprising a spot with the radius a (side view).

Interfacial tensions 1SAγ , 2SAγ , 1SLγ , 2SLγ are depicted. B. Droplet disconnected from a

composite surface.

droplet

2a

f1 f2

2r

f2

2r

2r

2a

2a

γSA2 γSL1 γSA1 γSA2

γSL2 γSL2

A B

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Figure 11. Scheme of a drop deposited axisymmetrically on a rough surface

possessing roughness f2 and comprising the round spot of radius a possessing

roughness f1.

The experimental situation discussed in Ref. 32, when high apparent contact

angles were accompanied by high adhesion of a droplet is noteworthy. Liu et al.

reported the reverse Wenzel-to-Cassie transitions observed for heated droplets

deposited on superhydrophobic surfaces.32

In this case, the droplet demonstrated a

high apparent contact angle, governed by the Cassie (vapor trapping) wetting in the

vicinity of the triple line, and has been simultaneously sticky due to Wenzel water

“bridges” connecting the droplet with the central area of the substrate underneath the

droplet.33

Our derivation of the energy of adhesion is based on the traditional Young-

Dupre approach when the energy of droplet wetting the surface is compared to the

energy of the liquid cap (see Figure 10). It is latently supposed that the shape of a

droplet is not changed when it is disconnected from the surface. Shrader suggested

that the droplet detached from the substrate obtains its natural spherical shape and

supplied the corrected equation for the net energy of the droplet adhesion.34

When the

“spherical drop” is taken as the reference state, the energy of adhesion for the

situation, depicted in Figures 9, 10A will be given by:

psessiledroropsphericaldad GGW −= , (7)

where ropsphericaldG is the free energy of formation of the spherical drop from its

saturated vapor, and psessiledroG is the free energy of formation of the sessile drop on a

surface.34

The calculations according to Eq. (7) lead to somewhat cumbersome

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expressions, however psessiledroG obviously depends on the physical and chemical

composition of the solid surface, hence the general conclusion remains the same: the

energy of adhesion depends on the entire surface wetted by a droplet, as it was already

suggested by Tadmor et al.35-36

It is noteworthy that the process of hot embossing of polyethylene films with

micro-scaled stainless steel gauzes reported in our paper allows manufacturing of not

only superhydrophobic but also superoleophobic surfaces. Superoleophobicity is

achieved, when hot embossing is followed by tetrafluoromethane plasma treatment.37

Conclusions

Contact angles are important and easily measured macroscopic physical values

describing the wetting of flat and rough, chemically homogeneous and heterogeneous

solid surfaces. However, the complete macroscopic description of a wetting regime is

achieved when not only the apparent contact angles but also the energy of adhesion

are known. Apparent and Young contact angles are dictated by the area of a solid

surface adjacent to the triple (three-phase) line, whereas the energy of adhesion

depends on the surface energy and roughness of the entire area wetted by liquid. The

paper discusses wetting of the superhydrophobic surface comprising a non-

superhydrophobic blemish. A water droplet with the radius larger than this of a

blemish, deposited on a blemish axisymmetrically, demonstrates the high apparent

contact angle and remains in a “sticky” (high adhesion) wetting state. This

observation can be explained easily with the use of the Dupre equation applied to the

composite surface, showing explicitly that the energy of adhesion of a droplet is

influenced by a surface energy and roughness of both the wetted central spot and the

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surrounding circle. The composite surface reported in the manuscript demonstrates a

manifestation of the “rose petal effect”.

Acknowledgements

The authors are grateful to Dr. G. Whyman for extremely fruitful discussions.

The authors are thankful to Dr. R. Grynyov for his inestimable help in preparing

superhydrophobic surfaces and SEM imaging. The authors are indebted to Mrs.

Natalya Litvak for her help in SEM imaging.

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(35) Tadmor, R.; Bahadur, Pr.; Leh, A.; N’guessan, H. E.; Jaini, R.; Dang, L.

Measurement of Lateral Adhesion Forces at the Interface between a Liquid

Drop and a Substrate. Phys. Rev. Lett. 2009, 103, 266101.

(36) Tadmor, R. Approaches in Wetting Phenomena. Soft Matter 2011, 7, 1577–

1580.

(37) Bormashenko, E.; Grynyov, R.; Chaniel, G.; Taitelbaum, H.; Bormashenko, Y.

Robust Technique Allowing Manufacturing Superoleophobic Surfaces.

Applied Surface Sci. 2013, 270, 98–103.

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