Wetting 101

Wetting 101

(Parte 1 de 3)

DOI: 10.1021/la902206c 14105Langmuir 2009, 25(24), 14105–14115 Published on Web 07/23/2009 pubs.acs.org/Langmuir ©2009 American Chemical Society

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 reviewour 2006-2009publications onwetting andsuperhydrophobicityin amanner designedto serveas auseful 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 generationsofstudentsandscientists toamisunderstanding ofthe wettingofsolidsbyliquids.Wereviewouranalysesof 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.


Our objective in writing this feature article is compound, and wementionthreeaspectsofits substance.First,wewanttoreview our recent (2006-2009) work on wetting, formatting it in a coherentconceptualframeworkthatwouldbedifficultforreaders to construct from our rather pointillistic publications that did not appear in any logical sequence. Second, we want to place the reviewedresearchintohistoricalcontext,bothtoacknowledgethe 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.7Thereisadiscreteandmeasurablecontactanglebetween the sphere and the surface at the circular solid/liquid/vapor threephase contact line. This angle defines a cone (or a cylinder if the contactangleis90 )withanapexonthewatersideofthesurfaceif the contact angle is <90 or with an apex on the solid 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

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:

Butitisnecessarytopremiseoneobservation,whichappearsto 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’sachievementsindicategenius(severaltimesover),9but he simply did not have time (he died at 5 years old) between his medical practice and research, developing a wave theory of light, describingastigmatism,proposing than theretinacandetectthree 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 examplesofsurfacesthathave“anappropriateangle”(nocontact angle hysteresis;some of this research is described below), and they did not succeed in over 9.9% of the attempts. It is very unlikelythatYoungcouldhavefoundevenonesuchmaterialthat 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, andhowlongafterapplicationthemeasurementismade;onmost 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.

†Part of the “Langmuir 25th Year: Wetting and superhydrophobicity” special issue.

*Corresponding author. E-mail: tmccarthy@polysci.umass.edu. (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, 2, 339. (5) Zhang, X.; Shi, F.; Niu, J.; Wang, Z. J. Mater. Chem. 2008, 18, 621. (6) Qu er e, 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 digitized and is available at w.google.com/books .

(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.

14106 DOI: 10.1021/la902206c Langmuir 2009, 25(24), 14105–14115

Invited Feature Article Gao and McCarthy

It recedes with a constant contact angle, θR, characteristico ft he surface chemistry and topography (Figure 1a). If the surface is cooledtobelowthedewpointandwatercondensesonthedropor ifwateriscarefullyaddedtothedropwithasyringe,thenthedrop volume and contact angle increase and again the same contact areais maintained untilthe dropbegins toadvance (Figure 1b). It does so at a constant advancing contact angle, θA, which is also characteristic of the surface chemistry and topography. A meta- stable 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.1,12

I Contact angle hysteresis explained.13 I Lotus effect explained.14,15

Webegan thisresearchinMarch 2005 ata timewhen one ofus

(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 surfacesinthe1980sand1990s.21-24Wemeasuredadvancingand 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 behaviorto distinguish chemicalandphysicaldifferences 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,2 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 anglewasreportedtobe“aslargeas174 .”Wetookthiscomment 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

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 reachedat2andθRremainsconstantduringsubsequentevaporation.(b)Adropofwateradvancingonasurfaceasaresultofcondensation; 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.

(1) 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, 2, 6234. (14) Gao, L.; McCarthy, T. J. Langmuir 2006, 2, 2966. (15) Gao, L.; McCarthy, T. J. Langmuir 2006, 2, 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 1 is a plot of citations versus year that shows the growth of superhydrophobicity.

(21) Lee, K.-W.; McCarthy, T. J. Macromolecules 1988, 21, 3353. (2) 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. (3) 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.

Gao and McCarthy Invited Feature Article 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(GaoandMcCarthy)thatisreviewedbelowandoutlined above focuses, further defines, and applies concepts that were already introduced in our earlier three papers.

HowandWhyWenzelandCassieWereWrongandWhy 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 designedwith theobjective ofmethodicallydisprovingthe theories of Wenzel and Cassie,1 and (3) to describe simple experiments (demonstrations)withresultsthatareobviousbutcontrarytowhat would be predicted using the Wenzel and Cassie theories.12 We review these here and add a mental exercise involving morphing poststhatwe believe helpsto formulateanintuitiveunderstanding.

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 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,covalentbonds,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 forceswith energiesandcouldnot have.Hedidnot know of surface free energy or of thermodynamics. Gibbs and Helmholtz were not yet born (nor was Dupr e), and Carnot was 8 years old. Young did not write an equation but states clearly, using the wordforcemultipletimes,whatcanbeexpressedinequationform as eq 1, where FSV, FLV,a nd FSL are the forces

FSV ¼ FLV cos θ þ FSL ð1Þ that Young ascribes to the “cohesion of superficial particles” at the surfacesofthe solidand liquidand the commonsurface ofthe 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,a nd 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 confusingsubstitutionofthedirectionalforcesatalineenvisioned by Young with nondirectional interface properties (energy per unit area - erg/cm2) cannotb ea ttributedt oY oung but to Wenzel. Equation 1 (Young’s statement) is no more valid

(35) Youngblood, J. P.; McCarthy, T. J. Macromolecules 1999, 32, 6800. (36) Oner, D.; McCarthy, T. J. Langmuir 2000, 16, 7. (37) Kusumaatmaja, H.; Vrancken, R. J.; Bastiaansen, C. W. M.; Yeomans, J.

Phys. 2005, 122, 104902. (43) McHale, G. Langmuir 2007, 23, 8200. (4) 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 1 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) .

(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.

14108 DOI: 10.1021/la902206c Langmuir 2009, 25(24), 14105–14115

Invited Feature Article Gao and McCarthy because eq 2 can be derived using thermodynamic arguments. Equation 3, the Wenzel equation, is the equation cos θ ¼ RðγSV -γSLÞ γLV ð3Þ incorrectlyattributed to Young(eq 2) with γSV and γSL multiplied byWenzel’sroughnesscoefficientR, whichisdefined as theratioof the contour surfacearea to the projectedsurface area. We quote directly from Gray’s neglected paper48 regarding Wenzel: “he confused surface tensionand surface free energy to such an extent astouseanarearoughnesscoefficient.”Graygoesontostate,“This confusionhas been perpetuated by subsequent workers.”Cassie wasoneofthem.Equation4,theCassieorCassie-Baxterequation, is again the misrepresentedstatement of Young (eq 2) for a solid containingtwo componentswith differentsurface free energies. f1 and f2 are definedas the area fractions of the two components.

cos θ ¼ f 1ð1γSV -1γSLÞ γLV þ f 2ð2γSV -2γSLÞ γLV

Gray’s paper, whichaddresses the issue ofconfusing force with energy, may bemoreconvincing to somethanthe argumentsthat we make here. We feel that Gray, however, did not give Wenzel and Cassie sufficientcredit. Their papersare 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 thatinterfacialareasaffectwetting.Therearenumerousexamples 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,asfarasit is able,somoldtheliquidwithinitthatitshall beas 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 energyper 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 Qu er e on page 1 of their 2004 text53 state, “A liquid surface 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 backdownsuddenlythemomenttheliquidmembraneispierced.” These two statements by Qu er e 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.

Figure2eshowsthecommondepictionofvectorsthatareusedto representforcesinYoung’sstatement.Thatthreeelasticmembranes, working to minimizetheirareasin the configurationof Figure2d, shouldforman equilibriumcontactangleisintuitiveto most people and the way that they view (and have learned)Young’s equation. AbsentfromthisimagearetheparticlesthatYoungenvisioned8with short-range attractive forces. Absent also from this image is the perspectiveofSchwartz52whostates,concerningforces,“Physically, theyoperatein each phase withina fewmoleculardiametersof the othertwo phases.Neitherthe statenor the geometryof the phase interfaces in the regions remote from the line boundaryhas any directeffectonthecontactangle.”Absentaswellfromtheimagein Figure2d is the perspective that we had hopedto bringin ref 1.

Figure 2. Liquid-vapor (a), liquid-solid (b), and solid-vapor (c)“elasticmembranes”inmechanicalequilibriumatacontactline (d). The vectors generally used (e) to represent the forces in Young’s statement.

(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 w.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.; Qu er e, D. Capillarity and Wetting Phenomena; Springer: New York, 2004.

Gao and McCarthy Invited Feature Article

It is not difficult to envision why people without these perspectiveswouldusetheWenzelandCassie theories(particularlyif 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 underasessiledrop(Figure3a,b) wouldchangethecontactangle. Using this faulty logic, the contact angle should also change if either of the other interfaces is adulterated (Figure 3c,d).

(Parte 1 de 3)