APPARENT SURFACE FREE ENERGY OF SUPERHYDROPHOBIC SURFACES

Emil Chibowski

Department of Physical Chemistry, Faculty of Chemistry, Maria Curie-Sklodowska University, Lublin, Poland

Abstract. Superhydrophobicity results from nano- and/or micro- protrusions present on a hydrophobic surface. Such surfaces are commonly characterized by advancing water contact angle, which amounts at least 150o. Contact angle hysteresis also appears on such surfaces. Generally, two types of wetting are usually considered for rough surfaces, i.e. the drop suspended on the protrusions (Cassie-Baxter case), or the collapsed drop (Wenzel case). In the case of arranged posts present on a superhydrophobic surface some experiments show that the advancing contact angle does not change while the receding one depends on the post size and spacing. In this paper is shown that more light can be shed on wetting properties of superhydrophobic surfaces if their apparent surface free energy is calculated from an equation relating the probe liquid surface tension and the advancing and receding contact angles, that is, the contact angle hysteresis. With the help of this equation mentioned above the two cases of wetting can be distinguished. Some simulated and experimental results are presented.

INTRODUCTION

Real solid surfaces practically always possess chemical and/or texture inhomogeneities. They cause contact angle hysteresis, considered as resulting from pinning of the liquid contact line. However, even on molecularly smooth surface some amount of hysteresis is found too. During past three decades numerous papers have been published in which different theoretical models are described to explain nature of the contact angle hysteresis. Among them, differently patterned model surfaces were considered. Lately investigations dealing with the hysteresis, including superhydrophobic surfaces, are of great interest (1-8). It is now well known that superhydrophobicity appears on hydrophobic surfaces on which micro- and/or nano- protrusions are present. The superhydrophobic surfaces are commonly characterized by water contact angle, which has to be at least 150o or larger. Now also the receding contact angles are more often reported in some papers and two types of wetting /dewetting processes are considered. Namely, the drop can be suspended on the posts (i.e. the Cassie-Baxter case) or it fills the interstices between them, which is Wenzel case (9-11). Some experiments were performed that showed on arranged posts the advancing contact angle did not change, while the receding one depended on the post size and spacing (6). Generally, it is considered that in case of suspended drop the hysteresis can be smaller in comparison to the collapsed drop. However, in 2007 Gao and McCarthy (12) published a provocatively titled paper: “How Wenzel and Casie were wrong”, in which, basing on their experimental results, they concluded “that contact angle behavior (advancing, receding, and hysteresis) is determined by interactions of the liquid and the solid at the three-phase contact line alone and that the interfacial area within the contact perimeter is irrelevant”. In consequence several comments and replies have been published (13-15). For example Nosonovsky (13) proposed generalized forms of Wenzel and Cassie equations derived by him and

5-18 claimed that they can be applied “when the size of the solid surface roughness/heterogeneity details are small compared to the size of the liquid-vapor.” Then Panchagnuala and Vedantman (14) in their comments maintain that Cassie equation can be used if appropriate surface area fraction is considered, i.e. the fraction that contact line experience during its advancing should be used in Cassie equation. In reply, Gao and McCarthy (16) stated that those issues they had published were actually “restatement of issues that have already been published” and that Wenzel and Cassie equations “should be used with knowledge of their faults”. They also remained their papers in which they considered contact line, and not the area fractions, that helped understanding of hysteresis, the lotus effect and perfectly hydrophobic surfaces (18,19). However, after that McHale (15) has published a paper entitled “Cassie and Wenzel: were they really wrong?” in which he discusses the conditions under which on “more randomly structured surfaces” Cassie-Baxter and Wenzel equations can be applied. This is possible if the surface fraction from Cassie-Baxter and roughness parameter from Wenzel equations are taken as global parameters of the surface and are not defined to the contact area of the droplet. He also argues that local form of these equations “allow patterning of the surface free energy”. In case of superhydrophobic surface the local form of Cassie-Baxter equation can be applied for the suspended on the posts droplet, then the apparent contact angle should result from minimizing surface free energy by small displacements of the contacting line. If a penetration of the liquid to the interstices between the posts takes place, then Wenzel state occurs. Whyman et al. (3) present “rigorous derivation of Young, Casie-Baxter and Wenzel equations”, in which they presume the free displacement of the triple line. They have derived an equation relating the potential barrier energy of the line displacement and the advancing and receding contact angles. The energy is determined by the liquid adhesion and the solid roughness. Some interesting features of the system resulted. Namely, the larger hysteresis the larger the energy is (the Wenzel and Cassie states, respectively). The equation predicts low CAH values for low contact angles. CAH does not depend on the equilibrium contact angle in a broad range of the contact angles (50o – 140o), but in case of superhydrophobic surface the dependence is important. The CAH value is not much dependent on the drop volume, but in case of small it is, where CAH may overcome the value of equilibrium contact angle. Finally, in case of a liquid having lower surface tension its CAH should be larger in comparison to that of higher surface tension. The cited above papers show that contact angle hysteresis is again a ‘hot issue’, which now also involves superhydrophobic surfaces. However, the purpose of this paper is not debate about mechanisms and theoretical description of the contact angle hysteresis, but it deals with an approach proposed to characterize solid surfaces via their apparent surface free energy as determined from the apparent contact angle hysteresis and the liquid surface tension, including superhydrophobic surfaces too. It is believed that such parameter may deliver more information than the advancing and receding contact angles alone.

SOLID SURFACE FREE ENERGY

The problems of experimental determination and theoretical description of solid surface free energy are well known. At present most often used approach is that proposed by van Oss (20), in which the energy is considered as the sum of apolar LW AB Lifshitz-van der Waals s (mostly London dispersion) and Lewis acid-base s AB - interactions, and the s is expressed by geometric mean of electron-donor s and

5-19 + electron acceptor s contributions. To determine the components one has to measure contact angle of three probe liquids, two of which have to be polar. Usually for this purpose diiodomethane (as an apolar liquid), water and formamide are used, for which arbitrary components of their surface tension are determined assuming for water at + - room temperature equality of its acidic and basic interactions, i.e. s = s = 25.5 mJ/m2. However, using different sets of three probe liquids than those mentioned above the determined for the same solid surface components of the same kind differ more or less. Among other reasons, it seems important is the ‘hidden assumption’ that the interactions coming from the solid surface are of the same strength irrespective for the liquid used. This seems to be debatable, because the acid-base interactions are mostly due to hydrogen bonding, whose strength varies depending on the origin of H and O, N or F atoms. They can range from 1-2 kJ/mol to 155 kJ/mol. For example O– H:O (21 kJ/mol) and N–H:O (8 kJ/mol). Therefore the values obtained from van Oss’ method are averaged interactions of the solid surface, which are also relative because of the above assumption for water hydrogen bonding interactions. Actually, so far we do not have any direct and thermodynamically well supported method for solid surface free energy determination, and specially its components. This problem was discussed in details by Lyklema (21). Nevertheless, even these imperfect methods of the energy determination are useful to track its changes for a surface being in question. Recently a new approach to determination of the apparent solid surface free tot energy s has been proposed (22-25). It allows evaluation of the energy form the advancing a and receding r contact angles of one liquid only, whose surface tension is l. The equation reads:  (1 cos  ) 2  tot  l a s (1) (2  cos  r  cos a ) The detailed discussion about its validity has been published elsewhere [23-25]. It should be mentioned here that the surface energy evaluated with the help of Eq.(1) depends to some extent on the kind of probe liquid used and the kind of solid surface. The reasons for this were discussed above. Originally it was considered that when the three-phase contact line had receded a film of the liquid is left behind the drop, which reflects in the receding contact angle. The presence of such a film is shown now by Bormashenko et al. (26). In this paper Eq.(1) is applied for testing apparent surface free energy changes in aspect of superhydrophobic surfaces. Some simulated results as well as experimental ones based on the literature contact angles are presented.

SIMULATED CALCULATIONS OF APPARENT FREE ENERGY CHANGES FOR HYDROPHOBIC AND SUPERHYDROPHOBIC SURFACES

Figure 1 shows changes in the apparent surface free energy of a superhydrophobic solid surface calculated from Eq.1 as a function of the advancing contact angle of water at different values of the contact angle hysteresis. The range of advancing contact angles used is from 120o to 170o, and two sets of the contact angle hysteresis are examined, i.e. a low 5o and 10o, and a large one 50o and 60o. Although the apparent o surface free energy at these contact angles is generally small, especially for adv > 150 (superhydrophobic surfaces) its changes are distinguishably different for these two sets of CAH. At the same advancing contact angle and higher hysteresis (50-60o) visibly lower than at low CAH = 5-10o. Thus, the Cassie-Baxter and Wenzel cases of the superhydrophobic surfaces are clearly depicted.

5-20 Next, Fig.2 presents changes in the apparent surface free energy as a function of the hysteresis for several values of the advancing contact angles, again starting with the angle of 120o. For such a solid if no hysteresis appears, the apparent free energy of its surface interacting with water is about 18 mJ/m2, which is characteristic for Teflon surface. If the hysteresis is as large as 70o, the energy drops to about 10 mJ/m2. If the advancing contact angle is 150o, for zero-hysteresis case the energy amounts only 5 mJ/m2 and decreases to ca. 1.5 mJ/m2 at 70o CAH.

20 18 Hysteresis,  -  5 A R t o t

4.5 s , 4  18 y g r

4.0 Hysteresis e o n

16 e

5 3 o 3.5 o e e

10 r f 16 5 o

e 2 50 3.0 c 2 m 0 a / f

60 r J o

14 2 u

m 150 s

2.5 , t t o n t s m 2

e 1

 14 r /

2.0 o t a 160 p n J

o e p m o r

A 170 / 12 a 1.5 0 10 p m p J

A 0 10 20 30 40 50 60 70 80 90 100 1.0 , 12

t Hysteresis, degrees m o

0.5 t

, o

10 s t o  o 50 t 0.0 10

t  = 120 s

A  150 155 160 165 170 n

t 8 Advancing contact angle, degrees e

r

n 8 a e p

r o

p o a 6 60

A 6 130 p p

A 4 4 140o 2 2 150o o 160 o 0 0 170 120 130 140 150 160 170 0 10 20 30 40 50 60 70 80 90 100 Advancing contact angle, degrees Hysteresis, degrees

Fig. 1. Apparent surface free energy of a Fig. 2. Apparent surface free energy of a solid surface versus water advancing solid surface versus water contact angle contact angle and different the contact hysteresis and different advancing angle hysteresis. contact angles. The general feature of apparent energy vs. hysteresis relationship is the energy decrease with increasing CAH. However, the relative decrease of the energy depends strongly on the advancing contact angle value. This is depicted in Fig. 3. As can be seen, with increasing advancing contact angle the apparent surface free energy o o drastically decreases at the same CAH. For example, for A = 120 and CAH = 10 the

energy decreases by 13.6 % only relative its value at zero hysteresis. However, if A amounts 170o, at the same hysteresis the energy decrease reaches nearly 60 %. Obviously the decrease in absolute values is large in the former case, i.e. from 18.2 to 15.7 mJ/m2, and from 0.55 to 0.22 15.7 mJ/m2, respectively. This figure also well illustrates differences between the two cases of wetting, that is suspended or collapsed drops, for hydrophobic and superhydrophobic surfaces.

0 10 %

, t 20 o t s  30 n i

e o s 40

a  = 120 A e

r 50

c o

e 130 d

60 o e 140 v i

t 70 o a

l 150 e 80 o R 160 90 o 170 100 0 10 20 30 40 50 60 70 80 Contact angle hysteresis, degrees Fig. 3. Relative decrease in the apparent surface free energy of a solid versus water contact angle hysteresis and different values of the advancing contact angles.

5-21 APPARENT SURFACE FREE ENERGY CHANGES OF REAL SUPERHYDROPHOBIC SOLIDS For these calculations of apparent surface free energy changes the literature contact angle data from Öner and McCarthy paper (2) were used. The contact angles were measured on silane-modified silicon wafer surfaces on which square post of different sizes and 40 m height were produced by photolithography. The posts were hexagonally arrayed at the distances equal to their size. Then three different silanes were used; dimethyldichlorosilane (DMDCS), n-octyl-dimethylchlorosilane (ODMCS), and heptadecafluoro-1,1,2,2-tetrahydrodecyl-dimethylchlorosilane (FDDSC). The contact angles taken from the paper, together with the contact angle hystereses are listed in Table 1, where there are also listed contact angles and the hysteresis measured on smooth surfaces covered with the silanes. Table 1. Advancing and receding contact angles of water and their hystereses measured on silanized silicon surface possessing different size square posts. silicon DMDCS ODMCS FDDCS surface A/R, deg hysteresis A/R, deg hysteresis A/R, deg hysteresis with posts deg deg deg smooth 107/102 5 102/94 8 119/110 9 2 m 176/141 35 174/141 33 170/146 24 8 m 173/134 39 173/139 34 170/140 30 16 m 171/144 27 174/134 40 168/145 23 32 m 168/142 26 170/132 38 170/146 24 64 m 139/81 58 114/64 50 149/100 49 128 m 116/80 36 95/58 37 131/93 38

As can be seen, the contact angles and hystereses sharply increase for the surfaces possessing the posts in comparison to the smooth surfaces. For the posts between 2 m and 32 m both the contact angles and hystereses values are similar. The greatest values of the hysteresis appear if 64 m posts are present. However, from the contact angles and the hystereses it is difficult to distinguish any differences between these three surfaces. But, much clearer picture is obtained if the apparent surface free energies are calculated from Eq. (1). Thus calculated energies are presented in Fig.4.

2 m /

J 30 1 m

, 25 y g

r 20 e n

e 15 2 e

e 10 r

f 3

e 5 c a f r

u s

0.4 t n e

r 0.3 a 1- ODMCS p 0.2 p 2- DMDCS A 0.1 3- FDDCS 0.0 0 20 40 60 80 100 120 Size of square post, m

Fig. 4. Changes of apparent surface free energy of silane-modified silicon surface possessing different size square posts 40 m high. Three different silanes were used for the surface modification (see text).

5-22 In the figure there are also shown the energy values calculated for smooth surfaces. Depending on the kind of the silane used the free energy of smooth surface ranges from 16.5 to 26.5 mJ/m2. The greatest apparent free energy possesses the smooth surface covered by n-octyldimethylchlorosilane –Si(CH3)2{(CH2)7CH3}, while the lowest one the smooth fluorinated surface covered with Si(CH2)2{(CF2)7CF3}. In fact 2 the energy of the surface covered by =Si(CH2)2 (DMDCS) is very close (24.3 mJ/m ) to that covered by ODMCS. However, if the posts have been produced on the surface, whose cross-sections are between 2 and 32 m, the apparent surface free energy drops to extremely low values, almost to 0 - 0.15 mJ/m2. If the post sizes are 64 -128 m the energy increases, but still it is lower than that of smooth surface, respectively. Fig.4 also shows that in the case of 40 m high posts their cross sections up to 32 m are not important for the superhydrophobic effect. Moreover, from practical point of view also the kind of silane is not important for the resulting apparent surface free energy. But, this is not the case if a larger size posts are present on the surface, and the energy increase is the largest in the case of n-octyldimethylsilane, where for the posts 128 m it approaches the value of the smooth surface. This must be due to the presence of relatively long n-octyl chains, because the energy of the surface with only dimethyl groups is much lower, if 128 m posts are present (DMDCS, Fig.4).

0.18 ODMCS surface 1- 16x16 m 0.16 2- 32x32 m 2 m / 0.14 J m

, 0.12 y g r

e 0.10 n

e 0.08 e e

r 2 f

0.06 e c a

f 0.04 r u

S 0.02 1 0.00 20 40 60 80 100 120 140 Post height, m Fig. 5. Apparent surface free energy changes of silicon/ODCMS covered surface possessing square 16  16 m or 32  32 m posts of different heights.

Effect of the post height on the apparent surface free energy can be also interesting. Using the contact angles published by the same authors (2) , which were measured on square posts 16  16 m or 32  32 m but of different height, on the surface covered by ODCMS silane, the calculated apparent surface free energy is presented in Fig. 5. As could be expected from the contact angle values the energy values are extremely low, but they are a bit large for the large-surface posts. With increasing height of the posts the energy changes are not monotonic. The fluctuations could be ascribed to the experimental error of contact angle measurements. On the other hand, the changes of the energy on these two surfaces run in a very similar way, but shifted each another. Therefore one can consider them as real ones being due to tiny changes in the wetting mechanism. To show usefulness of Eq.(1) for investigation of the apparent surface free energy changes caused by a solid surface treatment, below some other results are presented. Fig. 6 shows changes of the energy of a silicon surface grafted with different silanes (27). As can be seen, in the case of dimethylchlorosilane in the range of 1 to 18 carbon atoms the energy is practically independent on the R chain length. However, it strongly depends in the case of dichloro- and trichloro- silane. But, if the R chain consists of 6 and more carbon atoms the apparent surface free energy is in fact very

5-23 similar for all three silanes used (Fig.6). Next, in Fig. 7 are plotted the energy changes of gold and glass covered from the gaseous phase with poly(-methylstyrene) possessing average molecular weight 685 or 1300 (28). Again, the curves show that if the film thickness is 100 nm and more the kind of substrate on which the film is deposited has no meaning for the film surface energy. The energy is about that characteristic for a solid paraffin wax. It is worth to pay attention that the apparent surface free energies for the silicon grafted with the silanes (Fig. 6) and sufficiently thick poly(-methylstyrene) films (Fig. 7) are comparable.

40 m Silicon grafted with the silanes 2 / m

2 38 / J M =1300, on gold J n

38 m

m , 36 M =1300, on glass , n - R(CH ) SiCl y

y 3 2

36 g g r M =685, on glass r 34 n

- R CH SiCl e 3 2 e

34 n n

- RSiCl e e 3 32

e

e 32 e e r r f 30 f

30 e

e c c

a 28 a f f

28 r r u u

s 26 s

26 t t n n e

e 24 r

r 24 a a p p 22 22 p p A A 20 20 0 2 4 6 8 10 12 14 16 18 20 0 50 100 150 200 250 300 Number of carbon atoms in R chain PMS film thickness, nm

Fig. 6. Apparent surface free energy of Fig. 7. Apparent surface free energy of silane grafted silicon surfaces as a gold and glass surfaces covered with function of the number of methylene poly(-methylstyrene) film depending on groups in the R chain. its thickness.

It may be also interesting to learn about apparent surface free energy of the same surface, but determined from the contact angles of different liquids, for example highly polar water, nonpolar n-hexadecane, and almost nonpolar diiodomethane. Such results are presented in Fig.8 for silicon surface grafted with 12 different monochlorosilanes (1). They possessed various aliphatic hydrocarbon chains (for details see ref. 24). If hexadecane was used as the probe liquid, the apparent free energy is the same for the all surfaces, about 25 mJ/m2, which results from London dispersion interactions. If diiodomethane was the probe liquid, the apparent surface free energy is bigger and slightly depends on the alkane chains structure, and it ranges from 33 to 40 mJ/m2. While the surface tension of n-hexadecane is 26.4 mN/m, so that of diidomethane amounts 50.8 mN/m. This liquid may also slightly interact as the electron-acceptor, if in contact with an electron-donor site on bare silicon surface patches. However, the apparent energy calculated from water contact angles strongly depends on the silane structure bonded to the silicon surface. Except for two silanes (Fig.8), the energy values are grouped into two groups, 21-26 mJ/m2 and 38-42 mJ/m2. The structure of the silanes within each of these two groups have some similarities (see the table at Fig.8). The higher values of the energy indicate that the film structure is not very compact and some water can penetrate to bare silicon surface, and the lower values of the energy suggest a tight structure of the films. The lowest value of the energy, 15 mJ/m2, is obtained for the surface possessing exposed three methyl groups, ‘stretching’ from the surface at a distance of three –C–. The groups interact with water by the dispersion forces only, and probably they well screen the silicon surface from water molecules. It is worth to note that the dispersion

5-24 interactions of water (21.8 mJ/m2) are weakest ones among these three probe liquids. It is also interesting that the silanes possessing long aliphatic chains, –C8H17, and – C18H37 show the highest apparent surface free energy.

m

/ 45 2 J Water ///-Si

m ///-Si CH2I2 , 40

y ///-Si

g ///-Si r ///-Si e 35 n-C H n 16 34 ///-Si

e ///-Si

e 30 ///-Si

e ///-Si C H

r 8 17 f

///-Si C18H37

e 25 ///-Si c a ///-Si f

r 20 u S 15

20 25 30 35 40 45 50 55 2 Liquid dispersion surface free energy, mJ/m Fig. 8. Apparent surface free energy of silicon surface grafted with different chlorosilanes, whose structures are shown. The values are calculated from advancing and receding contact angles of water, n-hexadecane and diidodomethane.

Finally, it may be interesting to depict the relationship between total apparent surface free energy (calculated from the contact angle hysteresis) and the dispersion d part of the energy s , calculated from Fowkes equation and the advancing contact angle a. d d 1/2 WA = l (1+cosa) = 2(s l ) (2)

d Where WA is the work of adhesion, and l is the dispersion component of probe liquid d surface tension. In case of an apolar liquid its total surface free energy l equals l . tot d The discussed above s and s values for the same silanes are plotted in Fig.9, where the contact angles of n-hexadecane and diiodomethane were applied. It is obvious that d tot s component cannot be larger than the apparent total surface free energy s . In the case of apolar probe liquid the relationship between total apparent surface free energy of the solid and its dispersion component reads (24, 25): tot d γs γs  2  cos θa  cos θr  (3) 4

o d tot o From Eq.3 results that if a = r = 90 , s should amount ½ s , while if a = r = 0 , d tot s would be equal to s . As is seen in Fig.9 the dispersion component determined from both hexadecane and diiodomethane advancing contact angles is smaller than the apparent surface free energy determined from the appropriate contact angle hysteresis. If the energies were tot d determined from hexadecane contact angles the differences between s and s are smaller (0–1.5 mJ/m2) than corresponding differences if the energies were calculated from diiodomethane contact angles (5-8 mJ/m2). This must result from the different strength of the interactions of these two apolar liquids, whose surface tensions are 26.4 mN/m (hexadecane) and 50.8 mN/m (diiodomethane).

5-25

27.0 1 ///-Si From n-C H contact angles 26.5 16 34 2 26.0 ///-Si

25.5 3 ///-Si 25.0

d 2

m  4 / 24.5 s ///-Si J tot m

, 24.0  y s 5

g ///-Si r

e 23.5 n e 6 ///-Si e 23.0 e r

f 0 1 2 3 4 5 6 7 8 9 10 11 12 13

e

c 7 ///-Si a f

r 40 u

S From CH I contact angles 38 2 2 8 ///-Si 36 34 9 ///-Si 32 30 d 10 ///-Si 28  s 26 tot  24 s 11 ///-Si C18H37 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Type of silane 12 ///-Si C8H17 Fig. 9. Apparent total surface free energies and their dispersion components of the silanes bonded to silicon surface determined from n-hexadecane and diiodomethane contact angles. CONCLUSIONS Although hydrophobic and superhydrophobic surfaces can be characterized by the value of water advancing contact angle, their wetting properties are better depicted if the apparent surface free energy is calculated, where also the receding contact angle is applied. This also allows to distinguish between Cassie and Wenzel cases of the surface wetting, as well the time-dependent changes in the energy can be evaluated. REFERENCESS 1. Fadeev Y, A, McCarthy T, J: ‘Trialkylsilane Monolayers Covalently Attached to Silicon Surfaces: Wettability Studies Indicating that Molecular Topography Contributes to Contact Angle Hysteresis, Langmuir, 1999, 15, 3759-66. 2. Öner D, McCarthy T, J: ‘Ultrahydrophobic Surfaces. Effects of Topography Length Scales on Wettability’, Langmuir, 2000, 16, 7777-82. 3. Whyman G, Bormashenko E, Stein T: ‘The rigorous derivation of Young, Cassie- Baxter and Wenzel equations and the analysis of the contact angle hysteresis’, Chem. Phys. Lett. 2008, 450, 355-359. 4. Gao L, McCarthy J: ‘”Artificial Lotus Leaf” Prepared Using a 1945 Patent and a Commercial Textile’, Langmuir, 2006, 22, 5998-00. 5. Li W, Amirfazli: ‘A thermodynamic approach for determining the contact angle hysteresis for superhydrophobic surfaces’, J. Colloid Interface Sci. 2005, 292, 195-01. 6. Dorrer Ch, Rühe, ‘Advancing and Receding Motion on Ultrahydrophobic Post Surfaces’, Langmuir, 2006, 22, 7652-57. 7. Long J, Hyder M,N, Huang R,Y,M, Chen P, ‘Thermodynamic modeling of contact angles on rough, heterogeneous surfaces’, Adv. Colloid Interface Sci. 2005, 118, 173-190. 8. Krasovitski B, Marmur A, ‘Drops Down the Hill: Theoretical Study of Limiting Contact Angles and the Hysteresis on a Tilted Plate’, Langmuir, 2005, 21, 3881-85. 9. Bormashenko E, Pogreb R, Whyman G, Erlich M, ‚Cassie-Wenzel Wetting

5-26 Transition in Vibrating Drops Deposited on Rough Surfaces: Is the Dynamic Cassie-Wenzel Wetting Transition a 2D or 1D Affair’, Langmuir, 2007, 23, 6501-03. 10. Kusumaatmaja H, Yeomans J,M, ‘Modeling Contact Angle Hysteresis on Chem- ically patterned and Superhydrophobic Surfaces’, Langmuir 2007, 23, 6019-32. 11. Quéré D, Lafuma A, Bico J, ‘Slippy and sticky microtextured solids’, Nanotechnology, 2003, 14, 1109-12. 12. Gao L, McCarthy T,J, ‘How Wenzel and Cassie Were Wrong’, Langmuir, 23, 3762-65. 13. Nosonovsky M, ‘On the Range of Applicability of the Wenzel and Casie Equations’, Langmuir, 2007, 23, 9919-9920. 14. Panchagnula M,V, Vedeantam S, ‘Comment on How Wenzel and Cassie Were Wrong by Gao and McCarthy’, Langmuir, 2007, 23, 13242. 15. McHale G, ‘Cassie and Wenzel: Were They Really So Wrong?’, Langmuir, 2007, 23, 8200-05. 16. Gao L, McCarthy T,J, ‘Reply to “Comment on How Wenzel and Cassie Were Wrong by Gao and McCarthy”’, Langmuir, 2007, 23, 13243. 17. Gao L, McCarthy T,J, ‘Contact Angle Hysteresis Explained’, Langmuir, 2006, 22, 6234-37. 18. Gao L, McCarthy T,J, Langmuir, ‘The “Lotus Effect” Explained: Two Reasons Why Two Length Scales of Topography Are Important’, Langmuir, 2006, 22, 2966-67. 19. Gao L, McCarthy T,J, ‘A Commercially Available Perfectly Hydrophobic o Material (A/R = 180 )’, Langmuir, 2007, 23, 9125-27. 20. Van Oss C J, ‘Acid-base interfacial interactions in aqueous media’, Colloids Surface A, 1993, 78, 1-49. 21. Lyklema J, ‘The surface tension of pure liquids.Thermodynamic components and corresponding states, Colloids Surf. A, 1999, 145, 413-21. 22. Chibowski E: ‘Contact Angle Hysteresi due to a film present behin the drop’, in ‘Contact Angle, Wettability and Adhesion’, Vol.2, ed K.L. Mittal, VSP, Utrecht, 2002, pp.265-288. 23. Chibowski E, ‘Surface free energy of a solid from contact angle hysteresis’, Adv. Colloid Interface Sci. 2003, 103, 149-172. 24. Chibowski, E. ‘Surface free energy and wettability of silyl layers on silicon determined from contact angle hysteresis’, Adv. Colloid Interface Sci. 2005, 113, 121-31. 25. Chibowski, E. ‘On some relations between advancing, receding and Young’s contact angles’, Adv. Colloid Interface Sci. 2007, 133, 51-591. 26. Bormashenko E, Bormashenko Y, Whyman G, Pogreb R, Musin, Jager R, Barkay Z, ‘Contact Angle Hysteresis on Polymer Substrates Established with Various Experimental Techniques, Its Interpretation, and Quantitative Characterization’, Langmuir, 2008, 24, 4020-25. 27. Fadev A,Y, McCarthy T,J, ‘Self-Assembly Is Not the Only Reaction Possible between Alkyltrichlorosilanes and Surfaces: Monomolecular and Oligomeric Covalently Attached Layers of Dichloro- and Trichloroalkylsilanes on Silicon’, Langmuir, 2000, 16, 7268-74. 28. Lee Y-L, Chen C-H, Yang Y-M, ‘Surface Morphology and Wetting Behavior of Poly(α-methylstyrene) Thin Films Prepared by Vacuum Deposition’, Langmuir 1998, 14, 6980-86.

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