pubs.acs.org/Langmuir © 2009 American Chemical Society
Wetting 101°† Lichao Gao and Thomas J. McCarthy* Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003 Received June 18, 2009. Revised Manuscript Received July 8, 2009 We review our 2006-2009 publications on wetting and superhydrophobicity in a manner designed to serve as a useful primer for those who would like to use the concepts of this field. We demonstrate that the 1D (three-phase, solid/liquid/ vapor) contact line perspective is simpler, more intuitive, more useful, and more consistent with facts than the disproved but widely held-to-be-correct 2D view. We give an explanation of what we believe to be the reason that the existing theoretical understanding is wrong and argue that the teaching of surface science over the last century has led generations of students and scientists to a misunderstanding of the wetting of solids by liquids. We review our analyses of the phenomena of contact angle hysteresis, the lotus effect, and perfect hydrophobicity and suggest that needlessly complex theoretical understandings, incorrect models, and ill-defined terminology are not useful and can be destructive.
Background Our objective in writing this feature article is compound, and we mention three aspects of its substance. First, we want to review our recent (2006-2009) work on wetting, formatting it in a coherent conceptual framework that would be difficult for readers to construct from our rather pointillistic publications that did not appear in any logical sequence. Second, we want to place the reviewed research into historical context, both to acknowledge the contributions of former group members that led to our recent experiments and to acknowledge the literature on wetting and superhydrophobicity. Our comments on and references to the literature are not meant to serve as any sort of review1-6 other than one that recounts publications that had an impact on our directions and that were used to interpret our data. Third, but in fact foremost and the reasoning behind our choice of title, we want this article to be a useful tool for students and educators of wetting. When a drop of water is placed or falls onto a solid surface, a sessile drop forms in the shape of a sphere sectioned by the surface.7 There is a discrete and measurable contact angle between the sphere and the surface at the circular solid/liquid/vapor threephase contact line. This angle defines a cone (or a cylinder if the contact angle is 90°) with an apex on the water side of the surface if the contact angle is 90°. That there is an “appropriate angle of contact” (his words) for every solid/liquid pair was suggested in 1804 by Thomas Young8 in “An Essay on the † Part of the “Langmuir 25th Year: Wetting and superhydrophobicity” special issue. *Corresponding author. E-mail:
[email protected].
(1) References 2-6 are reviews of superhydophobicity. (2) Feng, X.; Jiang, L. Adv. Mater. 2006, 18, 3063. (3) Roach, P.; Shirtcliffe, N. J.; Newton, M. I. Soft Matter 2008, 4, 224. (4) Genzer, J.; Efimenko, K. Biofouling 2006, 22, 339. (5) Zhang, X.; Shi, F.; Niu, J.; Wang, Z. J. Mater. Chem. 2008, 18, 621. (6) Quere, D. Ann. Rev. Mater. Res. 2008, 38, 71. (7) A sessile drop is a sphere section in shape as long as its height (perpendicular to the surface) is less than twice the capillary length of the liquid, which depends on surface tension, density, and the gravitational constant. Larger sessile liquid objects are puddles. See ref 53. The possibilities other than sessile drop formation are spreading of the drop (θA/θR = 0°/0°) and rejection of the drop by the surface (θA/θR = 180°/180°). See ref 16. (8) Young, T. Phil. Trans. R. Soc. London 1805, 95, 65. This essay has been digitized and is available at www.google.com/books .
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Cohesion of Fluids.” We quote a sentence from the second paragraph of this essay that has led to thousands of person-years of research, many people’s careers, much confusion, and needless complication of the field of wetting: But it is necessary to premise one observation, which appears to be new, and which is equally consistent with theory and with experiment; that is, for each combination of a solid and a fluid, there is an appropriate angle of contact between the surfaces of the fluid, exposed to the air, and to the solid. Young’s achievements indicate genius (several times over),9 but he simply did not have time (he died at 55 years old) between his medical practice and research, developing a wave theory of light, describing astigmatism, proposing than the retina can detect three colors, deciphering the rosetta stone, proposing a universal phoenetic alphabet, inventing a method to tune musical instruments, describing the elastic modulus, and multiple other pastimes to check that this “necessary premise” is indeed consistent with experiment.10 Three researchers in our group worked for a total of ∼4 person-years doing experiments directed at preparing examples of surfaces that have “an appropriate angle” (no contact angle hysteresis;some of this research is described below), and they did not succeed in over 99.99% of the attempts. It is very unlikely that Young could have found even one such material that exhibited this behavior on a small fraction of its surface. After making this premise in his essay, he goes on to demonstrate his faith in it at length and in detail. It is a faulty premise. Instead of forming “an appropriate angle of contact”, water drops make many angles that are not reproducible. The reproducibility depends on the surface, the method of drop application, and how long after application the measurement is made; on most surfaces the contact angle will vary by 20° or more. If a drop on a surface is allowed to evaporate in a low-humidity environment or if water is carefully withdrawn from the drop with a syringe, then the drop decreases in volume and contact angle, maintaining the same contact area with the surface until it begins to recede. (9) Robinson, A. The Last Man Who Knew Everything; Pi Press: New York, 2006. (10) Young does not actually say that his premise is consistent with both theory and experiment but “equally with both.” His essay certainly suggests his belief in this premise and that the wording is not meant as a qualification; however, this man’s intelligence is daunting and can convince the reader to “read in between the lines” and even suppose divine powers.
Published on Web 07/23/2009
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Figure 1. (a) A drop of water receding on a surface as a result of evaporation; the drop is pinned at the three-phase contact line until θR is reached at 2 and θR remains constant during subsequent evaporation. (b) A drop of water advancing on a surface as a result of condensation; the drops is pinned at the three-phase contact line until θA levels off at 6. (c) A drop of water sliding on an inclined surface.
It recedes with a constant contact angle, θR, characteristic of the surface chemistry and topography (Figure 1a). If the surface is cooled to below the dew point and water condenses on the drop or if water is carefully added to the drop with a syringe, then the drop volume and contact angle increase and again the same contact area is maintained until the drop begins to advance (Figure 1b). It does so at a constant advancing contact angle, θA, which is also characteristic of the surface chemistry and topography. A metastable drop can be formed (and a photograph taken) with any angle between the advancing and receding contact angles. This is one reason that it is important that both advancing and receding contact angles be reported to characterize a surface; one static, metastable angle is less meaningful and designates an angle somewhere between θR and θA. For a drop to move on a tilted surface (Figure 1c), the drop must both advance (on the downhill side) and recede (on the uphill side); it must also distort from a section of a sphere to a complex shape with different contact angles around the entire perimeter of the drop. The relationship between these angles, θR and θA, is not simple. The next sections of this article are based on eight Langmuir publications and one J. Am. Chem. Soc. publication and are arranged according to the following outline: I How Wenzel and Cassie were wrong and why most people believe they were right.11,12 II Contact angle hysteresis explained.13 III Lotus effect explained.14,15 IV Perfect hydrophobicity (θA/θR =180°/180°).16-18 V Wetting terminology.19 We began this research in March 2005 at a time when one of us (L.G.) had never done research on wetting and the other (T.J.M.) had not worked in this field since the previous decade (and millennium). The field of superhydrophobicity was just gaining traction at this time.20 Our group had used contact angle to study polymer surface modification and chemistry at polymer (11) Gao, L.; McCarthy, T. J. Langmuir 2007, 23, 3762. (12) Gao, L.; McCarthy, T. J. Langmuir 2009, 25, 7249. (13) Gao, L.; McCarthy, T. J. Langmuir 2006, 22, 6234. (14) Gao, L.; McCarthy, T. J. Langmuir 2006, 22, 2966. (15) Gao, L.; McCarthy, T. J. Langmuir 2006, 22, 5998. (16) Gao, L.; McCarthy, T. J. J. Am. Chem. Soc. 2006, 128, 9052. (17) Gao, L.; McCarthy, T. J. Langmuir 2007, 23, 9125. (18) Gao, L.; McCarthy, T. J. Langmuir 2008, 24, 362. (19) Gao, L.; McCarthy, T. J. Langmuir 2008, 24, 9183. (20) Figure 1 of ref 11 is a plot of citations versus year that shows the growth of superhydrophobicity.
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surfaces in the 1980s and 1990s.21-24 We measured advancing and receding water contact angles of many thousands of surfacemodified polymer samples. Our interests also included polymer adsorption, and to follow this process, we again made thousands of contact angle measurements.25-28 When our interests expanded to include covalently attached monolayers, yet again we measured thousands of contact angles.29-32 We used contact angle as an analytical technique to follow chemical changes, determine extents of reaction or adsorption, and characterize surface structure. We did not study wetting but used wetting behavior to distinguish chemical and physical differences between surfaces. We learned what we knew about wetting by wrestling with data and trying to interpret it. In particular, we did not develop an understanding of wetting through theory. Often reactions that were carried out to modify polymer surfaces were corrosive,22 leading to rough surfaces that exhibited anomalous contact angle data. We quickly abandoned these approaches in favor of those that gave smooth surfaces from which we could interpret contact angle data. In 1996, Langmuir published a paper33 by Onda et al. and featured a photograph of a surface supporting a nearly 180° sessile water drop on the cover of the issue. This paper certainly caught the attention of our group, and our reaction was complex: very impressed, unimpressed, jealous, and critical. The contact angle was reported to be “as large as 174°.” We took this comment and the photograph to imply that the advancing angle was 174° and that the receding angle was significantly lower (or the drop would not have been stationary, see below). Our written reaction was a 1999 Langmuir paper34 with multiple coauthors (an anomaly for our group) that criticized the earlier Langmuir paper for not adequately reporting contact angle data and neglecting to (21) Lee, K.-W.; McCarthy, T. J. Macromolecules 1988, 21, 3353. (22) Dias, A. J.; McCarthy, T. J. Macromolecules 1984, 17, 2529. (23) Lee, K.-W.; McCarthy, T. J. Macromolecules 1988, 21, 309. (24) Cross, E. M.; McCarthy, T. J. Macromolecules 1990, 23, 3916. (25) Phuvanartnuruks, V.; McCarthy, T. J. Macromolecules 1998, 31, 1906. (26) Rajagopalan, P.; McCarthy, T. J. Macromolecules 1998, 31, 4791. (27) Lev€asalmi, J. M.; McCarthy, T. J. Macromolecules 1997, 30, 1752. (28) Chen, W.; McCarthy, T. J. Macromolecules 1997, 30, 78. (29) Fadeev, A. Y.; McCarthy, T. J. Langmuir 1999, 15, 3759. (30) Fadeev, A. Y.; McCarthy, T. J. Langmuir 2000, 16, 7268. (31) Fadeev, A. Y.; McCarthy, T. J. Langmuir 1999, 15, 7238. (32) Cao, C.; Fadeev, A. Y.; McCarthy, T. J. Langmuir 2001, 17, 757. (33) Onda, T.; Shibuichi, S.; Satoh, N.; Tsujii, K. Langmuir 1996, 12, 2125. (34) Chen, W.; Fadeev, A. Y.; Hsieh, M. C.; Oner, D.; Youngblood, J.; McCarthy, T. J. Langmuir 1999, 15, 3395.
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cite numerous related earlier publications. In this paper and two others35,36 published in 1999 and 2000, we summarized our understanding of wetting and superhydrophobicity and believed that we had completed our research in this area. Our recent research (Gao and McCarthy) that is reviewed below and outlined above focuses, further defines, and applies concepts that were already introduced in our earlier three papers.
How and Why Wenzel and Cassie Were Wrong and Why Most People Believe They Were Right11,12 In our papers on which this section is based, we tried to accomplish several things. Three of these were (1) to give our best explanation of the origin and basis of the faulty understanding of the contact angle that is held by the majority of researchers using and/or studying wetting and is perpetuated by the Wenzel and Cassie theories,12 (2) to report the results of experiments that were designed with the objective of methodically disproving the theories of Wenzel and Cassie,11 and (3) to describe simple experiments (demonstrations) with results that are obvious but contrary to what would be predicted using the Wenzel and Cassie theories.12 We review these here and add a mental exercise involving morphing posts that we believe helps to formulate an intuitive understanding. Many students of and researchers involved in wetting have learned from the literature and/or textbooks that the Wenzel and Cassie theories and equations are useful for interpreting the wetting of surfaces with regard to their roughness and chemical composition. They often are, but they are fundamentally flawed. If used carelessly without an understanding of their flaws, they can lead to incorrect predictions, wrong interpretations, and much wasted time and effort. For reasons that we discuss below, there is a consensus among researchers in the field, abundantly demonstrated by their publications and their citations of Wenzel and Cassie, that the Wenzel and Cassie equations are right. In fact, they are considered by some to be laws. References 37-39 and40-42 are six recent examples of where Wenzel’s theory and Cassie’s theory, respectively, have been referred to as Wenzel’s Law and Cassie’s Law.37-42 A comment that we made in the Conclusion and Comments section of our controversial43-47 paper11 concerning the Wenzel and Cassie theories is, “They support the incorrect concepts that contact area is important and interfacial free energies dictate wettability.” We believe that the principal origin of this widespread misunderstanding is twofold: first, from the analysis of a statement in Young’s “Essay”8 using the perspective of thermodynamics and second, from the way in which surface tension has been taught (and learned) for the last century using soap bubbles, soap films, and stretched elastic membranes as models. Surface tension and surface free energy are discrete and different quantities.48 Surface tension is a tensor that acts (35) Youngblood, J. P.; McCarthy, T. J. Macromolecules 1999, 32, 6800. (36) Oner, D.; McCarthy, T. J. Langmuir 2000, 16, 7777. (37) Kusumaatmaja, H.; Vrancken, R. J.; Bastiaansen, C. W. M.; Yeomans, J. M. Langmuir 2008, 24, 7299. (38) Patrı´ cio, P.; Pham, C.-T.; Romero-Enrique, J. M. Eur. Phys. J. 2008, E26, 97. (39) Kuo, C. S.; Tseng, Y. H.; Li, Y. Y. Chem. Lett. 2006, 35, 356. (40) Iwamatsu, M. J. Colloid Interface Sci. 2006, 297, 772. (41) Martic, G.; Blake, T. D.; De Coninck, J. Langmuir 2005, 21, 11201. (42) Mykhaylyk, T. A.; Evans, S. D.; Hamley, I. W.; Henderson, J. R. J. Chem. Phys. 2005, 122, 104902. (43) McHale, G. Langmuir 2007, 23, 8200. (44) Nosonovsky, M. Langmuir 2007, 23, 9919. (45) Panchagnula, M. V.; Vendantam, S. Langmuir 2007, 23, 13242. (46) Gao, L.; McCarthy, T. J. Langmuir 2007, 23, 13243. (47) Marmur, A.; Bittoun, E. Langmuir 2009, 25, 1277. (48) Gray, V. R. Chem. Ind. 1965, 23, 969. We cited this paper in ref 12. We should have cited it in ref 11 and a number of our other publications, but we were unaware of it. Prior to our citation, this forgotten work was previously cited in 1997 (once) and before that in 1986 (once) .
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perpendicularly to a line on a surface and is a force per unit length (dyn/cm). Surface tension can be understood from the perspective of the force required to start peeling a certain width of adhesive tape from a surface or the force that the contractile surface of a sessile drop makes at a contact line; the units of dyn/cm are intuitive. The surface free energy is a scalar nondirectional property of an area of a surface and is energy per unit area (erg/cm2). It can be understood as the work required to make more surface area (bring molecules from the bulk to the surface);49 the units of erg/cm2 are intuitive. Because these quantities are mathematically equivalent at equilibrium, mathematically minded people have regarded them as interchangeable.50 People whose thoughts center around thermodynamics have used this equivalence both to attempt to determine useful thermodynamic quantities from contact angle data and to derive equations that may be useful in predicting or interpreting contact angle data. How surface free energy directly relates to the contact angle or to the forces at a three-phase contact line is not intuitive. Young’s 1804 statement8 concerns the balance of forces between what he understood as particles. Young did not know of molecular structure, covalent bonds, metallic bonding, dipoles, or hydrogen bonding. He viewed liquids and solids as collections of particles that attract one another and “produce the effect of a uniform tension of the surface.” He “assumed as consonant both to theory and observation, that the contractile force of the common surface of two substances, is proportional, other things being equal, to the difference of their densities.” Young did not confuse forces with energies and could not have. He did not know of surface free energy or of thermodynamics. Gibbs and Helmholtz were not yet born (nor was Dupre), and Carnot was 8 years old. Young did not write an equation but states clearly, using the word force multiple times, what can be expressed in equation form as eq 1, where FSV, FLV, and FSL are the forces F SV ¼ F LV cos θ þ F SL
ð1Þ
that Young ascribes to the “cohesion of superficial particles” at the surfaces of the solid and liquid and the common surface of the solid and liquid. This equation is not derived or proven, nor does it need to be; it is the simple balance of forces in a plane operating on a line. This equation is valid when the solid surface is smooth, rough, clean, dirty, homogeneous, or heterogeneous. Today we think of these forces, compare them, and balance them using dyn/cm units. Equation 2, which is most commonly called and accepted as (has become) cos θ ¼
γSV -γSL γLV
ð2Þ
Young’s equation, where γSV, γSL, and γLV are the surface free energies, is Young’s statement from the perspective of the contact angle; however, forces have been substituted by energies. This confusing substitution of the directional forces at a line envisioned by Young with nondirectional interface properties (energy per unit area - erg/cm2) cannot be attributed to Young but to Wenzel. Equation 1 (Young’s statement) is no more valid (49) Squeezing a spherical drop between perfectly hydrophobic (θ = 180°)16,17 surfaces is an intuitively obvious way to picture surface free energy. The drop changes shape from a section of a sphere, increasing its surface area. Bulk molecules must move from the bulk to the surface, and work is required to do this. Figure 3 in ref 17 and Figure 3 in ref 18 show photographs of the compression of water drops using surfaces with 180° contact angles. (50) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces; Wiley Interscience: New York, 1997.
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because eq 2 can be derived using thermodynamic arguments. Equation 3, the Wenzel equation, is the equation RðγSV -γSL Þ ð3Þ cos θ ¼ γLV incorrectly attributed to Young (eq 2) with γSV and γSL multiplied by Wenzel’s roughness coefficient R, which is defined as the ratio of the contour surface area to the projected surface area. We quote directly from Gray’s neglected paper48 regarding Wenzel: “he confused surface tension and surface free energy to such an extent as to use an area roughness coefficient.” Gray goes on to state, “This confusion has been perpetuated by subsequent workers.” Cassie was one of them. Equation 4, the Cassie or Cassie-Baxter equation, is again the misrepresented statement of Young (eq 2) for a solid containing two components with different surface free energies. f1 and f2 are defined as the area fractions of the two components. cos θ ¼
f 1 ð1 γSV -1 γSL Þ f 2 ð2 γSV -2 γSL Þ þ γLV γLV
ð4Þ
Gray’s paper, which addresses the issue of confusing force with energy, may be more convincing to some than the arguments that we make here. We feel that Gray, however, did not give Wenzel and Cassie sufficient credit. Their papers are insightful, profound, and demonstrably abundantly useful. We cannot provide more useful theories or more precise equations. It is, however, a fact that they have contributed to faulty intuition. We see the second aspect of the origin of faulty intuition to be the practice of teaching and learning surface science using soap bubbles, soap films, and elastic membranes as models. These are no doubt useful teaching and learning tools, but care needs to be taken in their use because they can lead and have led to the belief that interfacial areas affect wetting. There are numerous examples of this teaching in the literature, and we cite four. We chose these not to be critical but because we highly recommend them as a result of the insight of their authors. C. V. Boys, in his classic “Soap Bubbles and the Forces Which Mold Them,”51 which is based on lectures given in 1889-1890, refers repeatedly to the “elastic skin” of water: “it acts as if it were an elastic skin made of something like very thin india-rubber, only that it is perfectly and absolutely elastic.” The last paragraph of his first lecture begins, “The chief result that I have endeavored to make clear today is this. The outside of a liquid acts as if it were an elastic skin, which will, as far as it is able, so mold the liquid within it that it shall be as small as possible.” This invokes the image of a water balloon to most students. In a 1969 review52 of capillarity, Schwartz states “A liquid-fluid surface behaves like a stretched elastic membrane in that it tends to contract.” Adamson and Gast in the latest edition of the text50 that has trained surface scientists since 1960 uses the example of a soap film stretched across a wire frame with one movable side to explain how “Although referred to as a free energy per unit area, surface tension may equally be thought of as force per unit length.” These authors favor using surface free energy over surface tension “because of its connection to thermodynamic language” and state that “the two terms are used interchangeably in this book.” de Gennes, Brochard-Wyart, and Quere on page 1 of their 2004 text53 state, “A liquid surface (51) Boys, C. V. Soap Bubbles and the Forces That Mould Them; Society for Promoting Christian Knowledge: London, 1896. There are a number of editions of this book, and the style, wording, and figures differ. The text quoted is from the 1896 version that has been digitized and is available online at www.google.com/books. (52) Schwartz, A. M. Ind. Eng. Chem. 1969, 61, 10. We were unaware of this neglected paper until recently. It has not been cited in papers concerned with wetting. . (53) deGennes, P.-G.; Brochard-Wyart, F.; Quere, D. Capillarity and Wetting Phenomena; Springer: New York, 2004.
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Figure 2. Liquid-vapor (a), liquid-solid (b), and solid-vapor (c) “elastic membranes” in mechanical equilibrium at a contact line (d). The vectors generally used (e) to represent the forces in Young’s statement.
can be thought of as a stretched membrane characterized by a surface tension that opposes its distortion.” These authors also use the soap film model with one movable side (glass rods instead of wires) and on page 4 state, “If the frame is tilted, it is even possible for the mobile rod to climb up the incline, only to fall back down suddenly the moment the liquid membrane is pierced.” These two statements by Quere et al., taken together, clearly support the faulty intuition that events at interfaces, away from the contact line, will affect the contact angle. Figure 2 shows an image of the mechanical balance of “contracting skins,” “stretched membranes”, or “elastic membranes” described by these authors and envisioned by most students. Liquid/vapor (a), solid/liquid (b), and solid/vapor (c) tensions balance one another (d) to generate an equilibrium contact angle. Figure 2e shows the common depiction of vectors that are used to represent forces in Young’s statement. That three elastic membranes, working to minimize their areas in the configuration of Figure 2d, should form an equilibrium contact angle is intuitive to most people and the way that they view (and have learned) Young’s equation. Absent from this image are the particles that Young envisioned8 with short-range attractive forces. Absent also from this image is the perspective of Schwartz52 who states, concerning forces, “Physically, they operate in each phase within a few molecular diameters of the other two phases. Neither the state nor the geometry of the phase interfaces in the regions remote from the line boundary has any direct effect on the contact angle.” Absent as well from the image in Figure 2d is the perspective that we had hoped to bring in ref 11. Langmuir 2009, 25(24), 14105–14115
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Figure 3. The Wenzel and Cassie theories suggest that the contact angle defined by three interfacial energies (a) would change upon adulterating the (b) liquid-solid, (c) liquid-vapor, or (d) solidvapor interface.
It is not difficult to envision why people without these perspectives would use the Wenzel and Cassie theories (particularly if they learned them as laws) believing that the area roughness and relative area fractions affect the contact angle. Nor is it difficult to envision these people believing that they can determine surface roughness or area fractions from contact angle data. Without these perspectives, one might believe that piercing, perforating, roughening, or chemically changing the solid-liquid interface under a sessile drop (Figure 3a,b) would change the contact angle. Using this faulty logic, the contact angle should also change if either of the other interfaces is adulterated (Figure 3c,d). Equations 3 and 4 are consistent with the observed data for many surfaces that have been studied over the past 60+ years, but many examples of where they are inconsistent have also been reported.54 We and others believed that the predictions of these theories and the extent to which data are consistent with them are fortuitous but not right. This contention was made weakly several times in the past but was ignored by most in favor of the Wenzel and Cassie theories. Pease55 did not, in 1945, directly question these theories but clearly suggested the ideas behind the questioning. (54) See Extrand, C. W. Langmuir 2003, 19, 3793 and references cited therein. (55) Pease, D. C. J. Phys. Chem. 1945, 49, 107.
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Bartell directly questioned56 Wenzel’s theory in 1953 and showed that the contact angles of drops on surfaces containing roughness within the contact line were identical to those of smooth surfaces. Extrand54 showed that the three-phase structure at the contact line, not the liquid-solid interface beneath the drop, controls the contact angle. He prepared surfaces with chemically heterogeneous islands that exhibited contact angles identical to surfaces without islands when the islands were in the interior of the contact line. We stressed34-36 that the contact angle and hysteresis are a function of the contact line structure and that the kinetics of drop movement, rather than thermodynamics, dictates wettability. For several years before we submitted the paper11 labeling Wenzel and Cassie as “wrong”, we wrestled with the issues (benefits and detriments) of pointing out that useful equations are wrong. After these years of “tip-toeing around” Wenzel and Cassie, thinking that they have done more good than harm, the field of superhydrophobicity was born and the number of people affected by these equations increased exponentially. We were trying to be both responsible and useful and believe that the provocative tone of this paper’s title will contribute to this usefulness. We do not review most of our data here but refer the reader to our publication11 to gain an appreciation for the excess consistent data that was reported. Results from multiple experiments on multiple samples at multiple length scales were reported. Much of the data were superfluous and redundant, all of the data were predictable (if you ignored Wenzel’s and Cassie’s theories and used a simple contact line perspective), and all of it made the same point over and over again;that the Wenzel/Cassie perspective is not consistent with the facts. We made the statement1 that our results, as well as others’ that we refer to, “indicate that contact angle behavior (advancing, receding and hysteresis) is determined by interactions between the liquid and the solid at the three phase contact line alone and that the interfacial area within the contact perimeter is irrelevant”. (The Wenzel and Cassie theories are based on the region that we refer to as irrelevant.) We measured advancing and receding water contact angles with different sizes of water drops on surfaces containing spots of different sizes within the contact lines of the sessile drops (Figure 4). We also reported contact angles inside the spots. The spots were smoother, rougher, or chemically different from the field of the surfaces that surrounded them. The length scales of the spots and drops spanned the dimensions (were both smaller and larger than those) of normal contact angle analysis. The length scale of the topography used for roughness was chosen to be in the range that dramatically affects the contact angle.36 The chemistries of the two components were chosen to maximize differential wetting.31 Table 1 shows water contact angle data recorded using sessile drops of varying contact diameter (D in Figure 4 and Table 1) of surfaces containing rough spots of different diameter (d in Figure 4 and Table 1) in smooth fields. These samples were prepared on silicon (wafer) substrates using photolithography, plasma cleaning, and chemical modification (vapor phase with PFA(Me)2SiCl).
This monofunctional reagent can react only30 to form a covalently attached monolayer; no oligolayers form. Also shown (56) Bartell, F. E.; Shepard, J. W. J. Phys. Chem. 1953, 57, 455.
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in Table 1 are the area fractions of liquid-solid contact (f1 and f2 are the area fractions inside and outside the spot, respectively) and the contact angles calculated using eq 4. The contact angles used to calculate the values are θA/θR =117°/82° for the smooth area (outside the spot) and θA/θR =168°/132° for the rough areas
Figure 4. Depictions of (a) a hydrophilic spot in a hydrophobic field, (b) a rough spot in a smooth field, and (c) a smooth spot in a rough field. (d) SEM indicating the topography of the rough regions in b and c. d in a-c indicates the spot diameter; D indicates the drop diameter. The scale bar in d is 10 μm. Table 1. Contact Angles for Surfaces with a Rough Spot on a Smooth Field (Surfaces b) d (mm) 1 1 1 1 1.5 1.5 1.5 1.5 2 2 2 2
D (mm)
f1
f2
0.5 1.1 1.2 1.3 0.7 1.6 1.7 1.8 0.7 2.1 2.2 2.3
1.00 0.83 0.69 0.59 1.00 0.88 0.78 0.69 1.00 0.91 0.83 0.76
0.00 0.17 0.31 0.41 0.00 0.12 0.22 0.31 0.00 0.09 0.17 0.24
θA/θR (calcd) 152°/122° 145°/115° 140°/108° 156°/125° 150°/119° 145°/115° 158°/126° 153°/122° 148°/118°
θA/θR (obsd) 168°/132° 117°/81° 117°/82° 117°/81° 166°/134° 117°/82° 117°/81° 117°/82° 165°/133° 117°/82° 117°/81° 118°/82°
(inside the spot). The data show apparently smooth surfaces (θA/θR =117°/82°) for all values of d, D, f1, or f2 when a rough spot was within the contact line. The values calculated using Cassie’s equation (eq 4) are meaningless. Figure 5 shows selected frames from a videotape of water drops being advanced on a surface containing a rough spot. In Figure 5a-d, the drop advances outward on the rough spot with a high advancing contact angle, similar to that measured with a goniometer (θA ≈ 168°). When it reaches the perimeter of the spot, it spreads onto the smooth surface (gravity is a driving force) and exhibits a lower contact angle (Figure 5e), similar to that measured with a goniometer (θA ≈ 117°). Note that the video camera had to zoom out (the needle is apparently thinner) to view the drop. This angle is maintained as the drop is further advanced (Figure 5f). Data such as these and Bartell’s56 and Extrand’s54 disprove Wenzel’s and Cassie’s theories and suggest that considering the contact angle and interpreting the contact angle data from the perspective of the contact line and not the contact area are more meaningful. In our paper, we made the comment, “Wenzel’s and Cassie’s equations are valid only to the extent that the structure of the contact area reflects the ground-state energies of contact lines and the transition states between them.” Perhaps we should not have included the word “only” because clearly there are many situations where the contact area reflects the contact line structure and the Wenzel and Cassie equations will be fortuitously consistent. To make our point, we deliberately prepared samples where this was not the case. We stated, “We do not advocate never using Wenzel’s and Cassie’s equations.” The double negative was deliberate. We have used and will use these equations, advocate doing so, and do not believe that new theories that address contact line tortuousness, contact line continuity, or chemical composition fluctuations at contact lines are necessary or would be useful; we think the Wenzel and Cassie theories are just fine in this regard. Despite the experimental disproof of the Wenzel and Cassie theories and the direct title of our 2006 paper, blind use of the equations has continued. To help address this, we described12 four experiments, more accurately called demonstrations, that more graphically remake the point that contact lines are important and that contact areas are not. The results of these demonstrations should be obvious, predictable, and intuitive. Two of these demonstrations are repeated here, and a thought experiment is described. Demonstration 1. Figure 6a shows a photograph of six 1.2-cm-wide, 0.6-cm-deep troughs that were milled in a 30 30 1.3 cm3 block of high-density polyethylene. Hydrophilic stripes (monolayers of poly(vinyl alcohol)) on the base of the troughs were prepared by the adsorption of poly(vinyl alcohol) from
Figure 5. Selected frames of a videotape of a droplet advancing from a rough spot onto a smooth field. 14110 DOI: 10.1021/la902206c
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Figure 6. (a) Parallel troughs milled in a block of polyethylene. (b) Hydrophilic stripes of poly(vinyl alcohol) monolayers imaged by wetting with water containing rhodamine B. (c) Water puddles (containing rhodamine B) of equal volume that span the hydrophilic stripes shown in b. (d) The puddles move in concert when the polyethylene block is tilted. (e) Is there a magical force that can operate from point x, y, or z that can affect events at o?
aqueous solution.34 Polyethylene exhibits contact angles of θA/θR =90°/78°, and the poly(vinyl alcohol) monolayers exhibit contact angles of θA/θR =60°/12°. The stripes are shown wetted with water containing rhodamine B in Figure 6b. Puddles of equal volume were applied to the troughs so that they more than spanned the hydrophilic stripes (Figure 6c). The puddles were lined up in the troughs by removing and adding liquid to one edge or the other of the puddle. When the polyethylene block was tilted, the puddles moved (advanced on the downhill side and receded on the uphill side) in concert. This indicates that advancing and receding events are independent of any structure under the puddles. This should be obvious and intuitive. There is no force or mechanism by which the advancing front and receding back edge of these puddles (Figure 6d,e) can sense structures centimeters removed from them. Demonstration 2. This demonstration is based on “The Housewife Problem” on page 37 of Quere et al.53 “The Housewife Problem: A bucket containing 6 L of water is emptied onto the ground. Calculate the wet surface area A for θ = 180° and for θ = 1°. (Answers: 1 m2; 120 m2.)”53 We have carried out many derivatives of this experiment on a small scale to study 2D fluidics57 If 6 L of water was gradually poured onto a circular spot of area less than 1 m2 with θ = 1° in a field with θ=180°, then the answer would still be 1 m2. The spot would “fill up” until a contact angle of 180° was reached, and then the puddle would advance onto the perfectly hydrophobic field.58 The thickness of the puddle would be the same everywhere: twice the capillary length of water.53 A border of perfectly hydrophobic tile at the perimeter of a kitchen would contain very large spills. Thought Experiment. Imagine an array of micrometric circular hydrophobic posts that are separated at a distance such (57) Wier, K. A.; Gao, L.; McCarthy, T. J. Langmuir 2006, 22, 4914. (58) In practice on much smaller spots prepared by UV/ozone treatment of a perfectly hydrophobic surface,16 the puddle bursts through one place on the line and stays attached to the hydrophilic spot. If the surface is moved in a circular motion (swirled), then the puddle precesses around the completely wet spot with little friction.
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Figure 7. (a) Hydrophobic circular posts randomly arranged at a fixed distance. (b) Depiction of a contact line of a water drop on this surface. How would the contact line behave if the posts were changed to have elliptical cross sections pointing randomly north/ south and east/west? (c) How would the contact line behave if the ellipticity changed further and the ellipse direction was random? (d) How would the contact line behave if the ellipses were rotating (e) or had two levels of topography (f)?
that liquid water does not intrude between them at atmospheric pressure. They are close to equidistant from one another and have no directional order. Figure 7a shows posts that are arranged in a Penrose tile pattern (there is no orientation in the plane). The post tops occupy about 20% of the area (f1 =0.2 in eq 4) and 80% is composed of air (f2=0.8). Figure 7b shows a likely stable contact line of a drop of water on this surface. Now imagine that the posts change shape (without changing area) from circular to elliptical (Figure 7c) and are randomly arranged either north/south or east/ west. You will imagine that the contact line of the drop distorts with wavelength and amplitude that scale with the ellipse shape and separation. You might also imagine that it is easier for a drop or puddle to slide northeast than either north or east: its advancing and receding edges might get more impeded by northpointing ellipses when trying to move east or by east-pointing ellipses when trying to move north. Next imagine (Figure 7d) that the ellipticity changes further (again with no area change) and that the ellipse orientation becomes random. You might now imagine that the contact line will be further distorted and that it may move from one metastable state to another with less of a barrier. We now ask you to think in three different paths: (a) What if the ellipses were rotating (Figure 7e)? (b) What if the ellipse had a second level of topography (Figure 7f)? (c) What if the ellipse tops were beveled with respect to the plane of the post tops (not shown)? Now imagine that all three (a-c) have occurred. The contact line is now tortuous in three dimensions, and the surface is moving (advancing and receding) it on all points of the contact DOI: 10.1021/la902206c
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line. If you have followed this fantasy, then you will consider the next three sections of this article on hysteresis, the lotus effect, and perfect hydrophobicity to be trivial extensions, in fact, only applications, of your understanding.
Contact Angle Hysteresis Explained13 When a drop moves on a surface, it has to both advance on the downhill side and recede on the uphill side (Figure 1c). The difference between advancing and receding contact angles is termed hysteresis; this has been the subject of a significant body of literature over the past few decades and has re-emerged as a popular topic because of recent interest in superhydrophobicity. As discussed above, because most researchers in the field of wettability incorrectly regarded wettability from the perspectives of contact areas and thermodynamics, hysteresis was impossible to explain. Explanations of hysteresis were in general not explanations but short lists of things that can affect the contact angle: roughness, chemical heterogeneity, and interactions between the probe fluid and the surface. Theoreticians have stated47 with regard to advancing and receding contact angles, “we do not yet have any theory for interpreting them.” Hysteresis is trivial to explain from the perspective of the contact line, and we do not believe that any theory will be very useful. Consider a drop on a horizontal surface that moves from one equivalent contact area to another. This could be caused by the movement of the surface, a vibration, or by a gust of 100% humidity wind. Figure 8 is a 2D representation of this event. The drop advances from 6 to 7 and recedes from 2 to 3. The shaded circles in the Figure between 3 and 6 represent interfacial water molecules that do not move as the drop does. Consistent with the no-slip boundary condition of fluid mechanics, the only interfacial water molecules that move during this event (open circles in Figure 8) are those that wet a new surface and dewet a previously wet surface. The drop moves like a “tank tread”;a vast majority of tread tines in contact with the ground are stationary during any time span. In the limiting case of a very small movement, say 0.5 nm, the only interfacial water molecules that move are those on the three-phase contact line (of 0.5 nm width). The structure and stability of the three-phase contact line is thus central to the movement process. Drops can move by sliding (near-surface water molecules are exchanged with interfacial ones in a tank-tread fashion and the bulk of the drop remains stationary with respect to itself as a frame of reference), rolling (water molecules at the liquid-vapor interface exchange with interfacial ones and all water molecules in the drop rotate with movement), or some combination of or mechanism in between these two extremes. The drop may move by sliding at some points of the contact line and rolling at other points or may advance by rolling and recede by sliding. The drop needs to either advance or recede along the entire three-phase contact line in order to move. Unless the hysteresis is zero, a
Figure 8. Two-dimensional representation of a water droplet moving from one position to an equivalent one. The shaded circles represent interfacial water molecules that do not move during this process. 14112 DOI: 10.1021/la902206c
Figure 9. A droplet must change shape from a section of a sphere with increasing liquid-vapor interfacial area (and energy) in order to move.
change in the shape of the drop from a section of a sphere is required before it can move. A 2D representation of this is shown in Figure 9. This necessary shape change can be regarded as an activation barrier to motion that can be quantified by the increase in liquid/vapor interface area, Ea = γLVΔALV. This equation assumes that the solid-liquid contact area remains constant. If this is not the case, then the activation energy would be Ea = γLVΔALV + γSLΔASL + γSVΔASV. ΔASL and ΔASV could be positive or negative and must sum to zero. It is not necessary that advancing and receding events be concerted, and the extent to which they might be synchronous could vary. Advancing and receding events can be very different processes (not the reverse of one another) with very different activation energies. Advancing events might induce receding events or vise versa. This implies that there could be multiple different activation energies for synchronous or sequential events that occur around the perimeter of the contact line by various mechanisms. This suggests that the activation energy for drop movement and hysteresis is more complex than is described in Figure 9. The shape of a moving drop and its liquid-solid contact shape will depend upon the relative rates of advancing and receding events on the perimeter. The shape of moving drops has been studied59-63 and does not have simple geometry. We emphasize here that it is intuitive to understand hysteresis quantitatively using the scalar quantity surface free energy because it takes work to distort the drop (bring bulk molecules to the surface and increase the surface area). The force required to begin the motion of the drop is a function of the hysteresis, and eq 5 is operative. This was proposed64 by Furmidge in 1962, who references earlier mg sin
R ¼ γLV ðcos θR - cos θA Þ w
ð5Þ
reports of related expressions. The equation predicts the minimum angle of tilt (R) at which a sessile drop (with surface tension γLV) will spontaneously move, where θA and θR are the advancing and receding contact angles, g is the force due to gravity, and m and w are the mass and width (horizontal to the direction of drop movement) of the sessile drop.
Lotus Effect Explained14,15 The ability of the lotus leaf and other natural materials to promote water repellency and self-cleaning by inducing water drops to roll on them inspired numerous research groups to prepare synthetic analogues.2-6 Work in the early part of the current decade was prompted in large part by Barthlott and Neinhuis’ report65 on the lotus effect. Roughness at two or more (59) (60) (61) (62) (63) L163. (64) (65)
ElSherbini, A. I.; Jacobi, A. M. J. Colloid Interface Sci. 2004, 273, 556. ElSherbini, A. I.; Jacobi, A. M. J. Colloid Interface Sci. 2004, 273, 566. Extrand, C. W.; Kumagai, Y. J. Colloid Interface Sci. 1995, 170, 515. Kim, H. Y.; Lee, J. L.; Kang, B. H. J. Colloid Interface Sci. 2002, 247, 372. Suzuki, S.; Nakajima, A.; Kameshima, Y.; Okada, K. Surf. Sci. 2004, 557, Furmidge, C. G. L. J. Colloid Sci. 1962, 17, 309–324. Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1.
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Figure 10. (a) Scanning electron microscopy image of the surface containing 4 8 40 mm3 staggered rhombus posts. (b) SEM image of the surface shown in panel a after being treated with methyltrichlorosilane. (c) Contact line events upon advancing. (d) Contact line events upon receding.
length scales had been implicated as the cause of this effect,33,66-68 but no speculation as to why multiple length scales is important had been offered. We published two papers14,15 in 2006 concerning the lotus effect with three objectives: (1) to explain it, showing two reasons why two length scales of topography are important in the lotus leaf, (2) to point out that this effect was well known in the 1940s, and (3) to describe a simple method, based on a commercially available material, by which acres of an artificial lotus leaf could be made using 1940s technology; we review only the first objective here. A smooth silicon surface and one containing staggered rhombus posts36 (Figure 10a) were hydrophobized using a reaction30 with dimethyldichlorosilane that introduces no topographical changes. The smooth surface exhibits advancing and receding contact angles of θA/θR=104°/103°, and the rhombus-patterned surface exhibits θA/θR =176°/156°. Water drops come to rest on this post-containing surface and move (roll) only when the surface is tilted a few degrees from the horizontal. When a drop rolls on the tops of posts, the barriers for advancing and receding differ significantly. Figure 10c shows a schematic representation of the advancing events that occur during drop movement (rolling). There is no kinetic barrier to advancing. The contact line does not move, but instead sections of the liquid-vapor interface (at 176° from the surface) descend onto and spontaneously spread over the next post tops (θA = 104°) to be wet. Receding events are very different (Figure 10d). The drop is at θR=156°, and the post tops exhibit θR=103° so the contact line cannot recede across the post tops and must disjoin from entire post tops in concerted events in order to move. This receding contact line pinning gives rise to the 20° hysteresis observed. This hysteresis, due to receding contact line pinning, was eliminated by introducing nanoscopic topography on the tops of the posts (Figure 10b). Water drops do not come to rest and roll effortlessly on this surface containing these two length scales of topography. The receding contact angle of the post tops of this surface is the same as that of the macroscopic drop, and the receding contact line is no longer pinned. Contact angles are θA/θR =>176°/>176° with no apparent hysteresis. (66) Shirtcliffe, N. J.; McHale, G.; Newton, M. I.; Chabrol, G.; Perry, C. C. Adv. Mater. 2004, 16, 1929. (67) Zhang, G.; Wang, D.; Gu, Z.-Z.; M€ohwald, H. Langmuir 2005, 21, 9143. (68) Sun, T.; Feng, L.; Gao, X.; Jiang, L. Acc. Chem. Res. 2008, 38, 644.
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The dual-length-scale topography affects the activation barrier for contact line recession by lowering the transition -state energy barrier between metastable states. This is most easily pictured as increasing the ground-state energy of the metastable states. In addition to this kinetic effect, there is a thermodynamic one as well that involves different physics: the (Laplace) pressure at which water intrudes between the posts.69 For a given geometry (area and contact perimeter of a unit cell), the Laplace pressure is a function of only the contact angle (-cos θ) of the post tops. Increasing the contact angle of the post tops from 104° to >176° increases the Laplace pressure by a factor greater than 4. This would allow spacing the posts at greater distances and taking greater advantage of the “apparent slip” on the air between posts that yields drag reduction. The lotus leaf, with tens-of-micrometers length scale topography, requires a smaller, submicrometer-scale roughness to exhibit the lotus effect. Multiple-lengthscale topography is not, however, a requirement for the lotus effect; the right combination of surface dynamics, contact line topology (connectivity), and tortuousity (see Figure 7 and the thought experiment, above) are sufficient. All three are not required.
Perfect Hydrophobicity (θA/θR =180°/180°)16-18 Early in the 1940s, researchers at the General Electric Company (GE) discovered that mixtures of methylchlorosilanes (MenSiCl4 - n) could be prepared from elemental silicon and chloromethane and that these mixtures could be used to hydrophobize surfaces.70,71 Similar work72 on hydrophobization was carried out at Corning Glass Works in directions that helped spawn Dow Corning. Patnode’s 1942 GE patent7 did not claim mixtures of SiCl4 and methylchlorosilanes to be hydrophobizing agents, and it was likely later when Norton73 (also at GE) recognized that a particular one of these is special and claimed (CH3)3SiCl and SiCl4, which form a minimum-boiling azeotrope that boils (54.5 °C) ∼3 °C below the two pure components. The pure reactive organosilanes (and SiCl4) are now commercially (69) Dettre, R. H.; Johnson, R. E., Jr. S. C. I. Monograph No. 25; Society of Chemical Industry: London, 1967; p 144. (70) Rochow, E. G. J. Am. Chem. Soc. 1945, 67, 963. (71) Patnode, W. I. U.S. Patent 2,306,222, Dec. 22, 1942. (72) Hyde, J. F. U.S. Patent 2,439,689, Apr. 13, 1948. (73) Norton, F. J. U.S. Patent 2,412,470, Dec. 10, 1946.
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available, and their vapor-phase and solution-phase reactions with hydrated silica surfaces under carefully controlled conditions are fairly well understood.29,30,74 We studied reactions of silica surfaces (polished silicon wafers) with controlled-composition mixtures of these silanes under a variety of solution, vapor, catalyzed, uncatalyzed, competitive, and sequential conditions (thousands of experiments), some of which must have closely recreated work that was done in the 1940s but not published. That many different surface topographies should form from these reactive monomers and water as a comonomer is intuitive: SiCl4 and CH3SiCl3 polymerize to form 3D structures, (CH3)2SiCl2 polymerizes to form linear (and liquid) segments, and (CH3)3SiCl is a chain terminator. A number of the mixtures under certain conditions create surfaces with extremely high advancing and receding contact angles. In particular, the measured receding contact angles are higher than the measured advancing ones. We had observed this behavior previously with only one material17,34 and were aware of only one report of “negative” hysteresis.75 We published two papers based on two of the reactions that we studied: methyltrichlorosilane in toluene solution and the SiCl4/(CH3)3SiCl azeotrope in the vapor phase. The CH3SiCl3 reaction was reproduced hundreds of times, and conditions were fine tuned so that “perfectly hydrophobic” (θA/θR =180°/180°) surfaces could be obtained for an average of 7 out of 10 samples in a single reactor. We believe that the surfaces that failed contained silanol defects because they could generally be made perfectly hydrophobic by treatment with trimethylsilyliodide. We did not expend the same amount of effort in perfecting the conditions of the azeotrope reaction. We reported our experiments as attempts to reproduce the conditions of the GE patent and described the water-contact-angle behavior of the surfaces prepared from this azeotrope vapor as θA/θR =g176°/g176°. There are three issues that we addressed while carrying out this research that warrant comment here, and we mention them in closing this section. First, it is intuitively obvious that many perfectly hydrophobic surfaces could be made: When a drop contacts a surface and changes shape from a sphere to a sessile drop, the total water surface area increases (counting the liquid-solid surface) if the volume stays constant. If the surface has a chemistry and topography such that that there is essentially no contact and no stable “toe hold” for a contact line to be pinned, then the drop will not change shape from a sphere. Our 2000 paper on length scales of topography suggests that surfaces containing posts of the same height that promote contact line tortuousness in only two dimensions are not sufficient to relieve contact line pinning and achieve perfect hydrophobicity. The strategies in the thought experiment above and Figure 7, however, are sufficient. Figure 11 shows SEM images of modified silicon wafers that were exposed to the (CH3)3SiCl/SiCl4 azeotrope vapor for different lengths of times. Contorted filaments with diameters of ∼30 nm grow in an apparent 1D chain-growth fashion from nucleation sites that are visible after 30 s of exposure to the azeotrope vapor. The filaments observed after 10 min of exposure/reaction appear very similar in structure to the methyltrichlorosilane-derived surfaces. Water droplets are completely rejected from these surfaces and do not form contact lines; the surface topography is too tortuous. Second, how can we distinguish between perfect hydrophobicity and 179°? Our first thought was that we needed to go to space: (74) Jia, X.; McCarthy, T. J. Langmuir 2003, 19, 2449. (75) Clark, J. C.; Debe, M. K.; Johnson, H. E.; Ross, D. L.; Schultz, R. K. U.S. Patent 5,674,592, Oct. 7, 1977.
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Figure 11. SEM images of silicon exposed to the (CH3)3SiCl/SiCl4 azeotrope for 30 s (a), 1 min (b), 2 min (c), 4 min (d), 6 min (e), and 10 min (f).
Figure 12. Selected frames of a video of a (CH3)3SiCl/SiCl4 azeotrope-derived surface (top) contacting, compressing, and being released from a sessile water droplet. The reflection of the sessile droplet defines the surface of the silicon wafer.
a surface with
