**UFRJ**

# Super-Water-Repellent Fractal Surfaces

Letters

Super-Water-Repellent Fractal Surfaces

T. Onda,*,† S. Shibuichi,† N. Satoh,‡ and K. Tsujii†

Kao Institute for Fundamental Research, Kao Corporation, 2606, Akabane, Ichikai-machi,

Haga-gun, Tochigi, 321-34, Japan, and Tokyo Research Laboratories, Kao Corporation, 2-1-3, Bunka, Sumida-ku, Tokyo, 131, Japan

Received May 30, 1995. In Final Form: November 14, 1995X

Wettability of fractal surfaces has been studied both theoretically and experimentally. The contact angle of a liquid droplet placed on a fractal surface is expressed as a function of the fractal dimension, therangeoffractalbehavior,andthecontactingratioofthesurface. Theresultshowsthatfractalsurfaces canbesuperwaterrepellent(superwettable)whenthesurfacesarecomposedofhydrophobic(hydrophilic) materials. We also demonstrate a super-water-repellent fractal surface made of alkylketene dimer; a water droplet on this surface has a contact angle as large as 174°.

Ultrahydrophobic solid surfaces, which perfectly repel water, would bring great convenience on our daily life. Conventionally, the wettability of solid surfaces has been controlledbychemicalmodificationsofthesurfaces,such as fluorination.1 The present Letter highlights the other factor determining the wettability, i.e., the geometrical structureofsolidsurfaces.2-4 Thereexists,asMandelbrot hasemphasizedinhistextbook,5afascinatinggeometrical structure called fractal, which is characterized by selfsimilarity and a noninteger dimension. Then a question arsies: What is the wettability of the solid surface with a fractal structure? This Letter shows both theoretically and experimentally that fractal surfaces can be either superrepellentorsuperwettabletoaliquid. Furthermore, we demonstrate a super-water-repellent fractal surface madeofalkylketenedimer;awaterdropletonthissurface has a contact angle as large as 174°.

The contact angle ı of a liquid placed on a flat solid surface is given by Young’s equation2 where R12, R13, and R23 denote the interfacial tensions of the solid-liquid, the solid-gas, and the liquid-gas interface, respectively. When a solid surface is rough, Young’s equation is modified into2 where r is a coefficient giving the ratio of the actual area of a rough surface to the projected area.

A fractal surface is a kind of rough surface, so that the wettability of the fractal surface is basically described by eq 2.3 The coefficient r of the fractal surface, however, is very large and can even be infinite for a mathematically ideal fractal surface. Therefore, the modification of the wettability due to surface roughness can be greatly enhancedinthefractalsurface;3thatis,thefractalsurface will be superrepellent (superwettable) to a liquid when ı is greater (less) than 90°.

Strictly speaking, applicability of eq 2 is limited. In fact,eq2cannotgiveanycontactanglewhentheabsolute value of its right-hand side exceeds unity. A correct expression for the contact angle can be derived conveniently by introducing the effective interfacial tension of

† Kao Institute for Fundamental Research, Kao Corporation. ‡ Tokyo Research Laboratories, Kao Corporation.

X AbstractpublishedinAdvanceACSAbstracts,March15,1996.

(1) Watanabe, N.; Tei, Y. Kagaku 1991, 46, 477 [in Japanese]. (2) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; John

Wiley & Sons: New York, 1990; Chapter X, Section 4. (3) Hazlett, R. D. J. Colloid Interface Sci. 1990, 137, 527. (4) Good, R. J.; Mikhail, R. S. Powder Technol. 1981, 29, 53. (5) Mandelbrot, B. B. The Fractal Geometry of Nature; Freeman: San Francisco, CA, 1982.

© Copyright 1996 American Chemical Society

S0743-7463(95)0418-5 C: $12.0 © 1996 American Chemical Society

the solid-liquid fractal interface, Rf12, and that of the solid-gas fractal interface, Rf13. Then the contact angle ıf is given by

SinceRf1j(j)2,3)maybeconsideredthetotalinterfacial energy of the fractal surface per unit projected area, Rf1j can be estimated, as a first approximation, by Rf1j ) (L/l)D-2 R1j. Here, D (2 e D < 3) is the fractal dimension of the surface; L and l are respectively the upper and the lower limit lengths of fractal behavior. Substitution of

To be more precise in estimating Rf1j, we must take account of the adsorption of a gas on the solid-liquid fractal interface and that of a liquid on the solid-gas fractal interface. Then Rf1j can be expressed by where x (0 e x e 1) is the fraction of the area of the fractal surfacecoveredwiththeadsorbedgas,y(0eye1)isthat covered with the adsorbed liquid, and S23 is the area of the gas-liquid interface per unit projected area. The symbol “min” expresses the operation of minimizing the succeedingquantitieswithrespecttoxory;thisoperation corresponds to the fact that adsorption so occurs as to minimize the total interfacial energy. Typically, S23(z)( z ) x, y) can be approximated by a cubic function of z, given

Figure1. Schematicillustrationforcosıfvscosıtheoretically predicted.

Figure2. SEMimagesofthefractalAKDsurface: (a,top)top view, (b, bottom) cross section.

cos ıf ) Rf13 -R f12 R23

Figure 3. Water droplet on AKD surfaces: (a, top) fractal

AKD surface (ıf ) 174°); (b, bottom) flat AKD surface (ı ) 109°). The diameter of the droplets is about 2 m.

2126 Langmuir, Vol. 12, No. 9, 1996 Letters whereŒdenotesthecontactingratioofthefractalsurface (the ratio of the area touching a flat plate placed on the fractal surface). Behavior of ıf determined by eqs 3-6i s shownschematicallyinFigure1,inwhichcosıfisplotted as a function of cos ı ()(R13 -R 12)/R23). The obtained curve coincides with the line of cos ıf ) (L/l)D-2 cos ı in the vicinity of ı ) 90°, but deviates from it owing to the adsorption when ı approaches 0° or 180°.

To verify the theoretical prediction, we have experimentally examined the wettability of various kinds of fractal surfaces. In this Letter, we report the results of the fractal surface made of alkylketene dimer (AKD), which is a kind of wax and one of the sizing agents for papers.

Alkylketenedimermostlyusedinourexperimentswas synthesized from stearoyl chloride with the use of triethylamine as a catalyst and purified up to 98% with a silica gel column. The purity was checked by gel permeation chromatography and capillary gas chromatography;themajorimpuritywasdialkylketone,whichwas producedbythehydrolysisofAKD. AKDsolidfilmswith a thickness of about 100 ím were grown on glass plates; a glass plate was dipped into melted AKD heated at 90 °C and was then cooled at room temperature in the ambience of dry N2 gas. AKD undergoes fractal growth when it solidifies, although the mechanism has not been clarified yet. SEM images of the AKD solid surface are shown in Figure 2.

To find the fractal dimension of the AKD surface, we applied the box counting method to the cross section of one of the AKD films. The AKD film peeled off from the glass plate was cleaved with the aid of a razor blade, and SEM images of its cross section (Figure 2b) were taken at several magnifications. Then the fractal dimension of the cross section, Dcross, has been measured by the box countingmethodandfoundtobe1.29intherangebetween l)0.2ímandL)34ím(seetheinsetofFigure4);below and above the range, Dcross is found to be unity. Thus, the fractal dimension of the AKD surface has been evaluated

Figure 3a shows a water droplet placed on the fractal

AKD surface. This surface, as expected, repels water completely and a contact angle as large as 174° has been obtained. For comparison, we have also examined the wettabilityofamechanicallyflattenedAKDsurface,which was prepared by cutting a fractal AKD surface with a razor blade. The flat AKD surface, however, does not repelwaterverymuch,showingacontactanglenotlarger than 109° (Figure 3b). Comparison of parts a and b of Figure 3 highlights the importance of the fractal effect on the wettability.

The relationship between the contact angle for the fractalAKDsurface,ıf,andthatfortheflatAKDsurface, ı, has also been studied with the use of liquids of various surfacetensions. Astheliquids,weusedaqueoussolutions of1,4-dioxaneatvariousconcentrations;ıbecomessmaller as the concentration of 1,4-dioxane increases. The result isshowninFigure4,inwhichcosıfisplottedasafunction of cos ı. The measurement of the contact angle has been performed several times at each concentration and the dispersion of the data is expressed by error bars. The fractal AKD surface showed advancing and receding contact angles, whose difference was not negligible particularly when ıf was close to 90°, so that we have measured an average contact angle after bringing the water droplet into an equilibrium state by vibrating it. In

Acknowledgment. WethankDr.J.Mino(KaoCorp.) and Professor T. Tanaka (MIT) for their valuable comments. We also thank Mr. Sodebayashi (Kao Corp.) for taking photos of the liquid droplets.

LA950418O

Figure 4. cos ıf vs cos ı determined experimentally for the

AKD surface. The line of cos ıf ) (L/l)D-2 cos ı deduced from the box counting measurement of the fractal AKD surface is also drawn. In the inset, the result of the box counting measurement applied to the cross section of the AKD surface is shown.

Letters Langmuir, Vol. 12, No. 9, 1996 2127