COLLomsANDSURFACES A

ELSEVIERColloids and Surfaces

A: Physicochemical and Engineering Aspects 93 (1994) 1-13

Jaroslaw Drelich a, Jan D. Miller a,*, Amit Kumar b,George M. Whitesides ba Department of Metallurgical Engineering. University of Utah, Salt Lake City, UT 84112, USA

b Department of Chemistry, Harvard University, Cambridge, MA 02138, USA

Received 9 November 1993; accepted 30 April 1994

Abstract

We!l-defined heterogeneous surfaces consisting of hydrophobic and hydrophilic regions were prepared on gold (a2000 A gold film supported on an Si/SiO2/Ti substrate) by patterning self-assembled monolayers (SAMs), using anelastomer stamp. One surface was composed of alternating and parallel hydrophobic (2.5 ~) and hydrophilic (3 ~)strips, and the second surface consisted of alternating hydrophilic squares (3 ~ x 3 ~) separated by hydrophobicstrips (2.5 ~). The wetting characteristics of these well-defined heterogeneous solid surfaces were examined by contactangle measurements. The contact angles for water drops, which varied in pH from 5.8 to 10.0, were measured withthe strips both tangential to and normal to the three-phase contact line. The experimental contact angles are in goodagreement with theory as calculated from the Cassie equation when the three-phase contact line is non-contorted (i.e.the three-phase contact line is situated along the hydrophobic strip). On the other hand, when the strips are normalto the drop edge, corrugation of the three-phase contact line affects the contact angle significantly. Contact angles,measured with the strips normal to the drop edge, were lower by 7-160 than those calculated from the Cassieequation. Analysis of these measurements, together with contact angle/drop size measurements for fully hydrophobicand hydrophilic surfaces, demonstrate the validity of a modified Cassie equation that includes a term describing theline tension contribution.

Keywords: Contact angle; Gold; Line tension; Thio!; Wettability

1. Introduction

Measurements of contact angles are among themost rapid and convenient methods of characteriz-ing surfaces, and are among the most popularmethods used in scientific and industriallaborato-ries for this purpose. These solid surfaces, whetherpolymers, minerals or metals, are not always homo-geneous and clean. Some are composed of two ormore components that differ in surface/interfacialproperties, and thus exhibit heterogeneous charac-teristics. Such surface heterogeneity may also result

from material anisotropy, or non-uniform dissoci-ation of functional groups located at the surface.Many intrinsically homogeneous surfaces areactually heterogeneous because of the adsorptionof contaminants and/or the deposition of dustparticles.

Composite smooth solid surfaces with varyingdegrees of heterogeneity were analyzed by Cassieand Baxter [1,2] and Cassie [3]. Cassie derivedan equation describing contact-angle changes fortwo-component surfaces as follows [3]:

cos ec =11 COS (}1 +12 COS (}2 (1)* Corresponding author. where f 1 is the fractional area of the surface with

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2 J. Drelich et al.jColloids Surfaces A: Physicochem. Eng. Aspects 93 ( 1994) 1-13

The Cassie equation can be derived fromthermodynamic considerations of the free energychange at the three interfaces, solid/vapor, solidiliquid and liquid/vapor (or liquid/liquid). Gibbspostulated [9] that an additional free energy com-ponent for such a three-phase system should beincluded to provide a more complete descriptionof the system. This additional free energy compo-nent, the line tension, results from an excess freeenergy for molecules located at or close to thethree-phase contact line. The excess energy associ-ated with the triple junction was not considered inthe derivation of the Cassie equation. Young [10]also did not consider this excess energy in hisexamination of the three-phase system. Boruvkaand Neumann [11] took into account the linetension and re-examined the equilibrium contactangle for liquid drops at homogeneous, rigid, iso-tropic and smooth solid surfaces; they modifiedYoung's equation as follows [11]:

contact angle (}l, and 12 is the fractional area ofthe surface with contact angle (}2 (the superscriptC indicates Cassie contact angle). Eq. (1), knownas the Cassie equation, reduces to the Cassie-Baxter equation (Eq. (2)) for a porous surface,such as a mesh or screen surface [1,2]:

COSIJC=/1COS(}1-12 (2)

In this case, 12 is the fraction of air spaces (openarea).

Cassie and Baxter [1] experimentally verifiedEq. (2) for water drops on copper screens coatedwith paraffin. Agreement of theory with experimentwas less satisfactory when the water drops wereplaced on wool yarn [2]. Crawford et al. [4]found that the advancing and receding contactangles for water drops on methylated quartz platesvaried with area fraction of trimethylsilyl groupsin a manner similar to that predicted by the Cassieequation (Eq. (1)). Bain et al. [5] studied self-assembled monolayers (SAMs) of alkanethiols(HS(CH2)"X) with different functional groups (X:-OH, -Br, -CN, -COOH) adsorbed onto gold.They found that the Cassie equation holds strictlyonly for systems where interrnolecular forcesbetween surface functionality and probe liquid aredispersive. When water was used as a probe liquid,on surfaces where specific hydrogen bonding effectswere strong, the contact angle varied non-linearlywith surface composition. This non-linearity sug-gests a limitation of the Cassie equation for somesurfaces with molecular-scale heterogeneities.Therrnodynamic analysis of the Cassie equationfor three-phase systems shows that this equationshould be applicable for surfaces composedof macroscopically heterogeneous regions [6]although the situation is less clear for molecular-scale heterogeneities. In this regard, Israelachvilliand Gee proposed another theoretical equation forthe description of surfaces with heterogeneities ofmolecular or atomic size [7]. Further, it wasrecently postulated that the Cassie equationrequires modification to account for the contribu-tion of the free energy associated with the three-phase contact line [8]. This modification (pre-sented later on) seems to be important, especiallyfor heterogeneities of small dimensions (severalmicrometers and less) [8].

(3)Ysv -YSL = YLV COS () + YSLVKgs

where Ysv, YSL and YLV are the interfacial tensionsfor solid/vapor, solidjliquid and liquid/vapor inter-faces respectively; (J is the contact angle; YSLV is theline tension (note that the tension term is used inthe literature to describe the force YSLV) definedthermodynamically as the free energy change forthe three-phase system (I5F) caused by the changein the three-phase contact line length I5L at con-stant temperature T, volume V and interfacial areaA. Thus YSLV = (I5F/I5L)T,V,A. It should be notedthat Kgs = cos (X/pis the geodesic curvature of thethree-phase contact line which is equal to thereciprocal of the drop base radius (Kg. = l/r) for aspherical drop sitting on a flat, horizontal andhomogeneous surface, (X is the angle between thesolid surface and the plane containing the wettingperimeter, and p is the radius of curvature of thethree:'phase contact line.

The force balance, in terms of the interfacial freeenergies, at a solid surface involving a three-phasesystem, in which the equilibrium contact angle isestablished, is shown in Fig. 1.

Although some controversy exists about themagnitude of the line tension, there is a generalconsensus that it is of small magnitude

J. Dre/ich et a/.lCo//oid\' Surfaces A: Physicochem. Eng. Aspects 93 ( 1994) 1-13

lic Crevice

~ -k =")!.v cos8+ ~COSqFor a smooth and horizontal surface composed oftwo components uniformly distributed with circu-lar curvatures of the three-phase contact line(Fig. 2), Eq. (4) is simplified as follows:

Horizontal Plate

COg ~c =11 COg (}1 +12 COg (}2 (5)

\fu,

x(~ -~.'1

On the basis of a theoretical analysis of Eq. (5) itis expected that a corrugation of the three-phasecontact line with radii of local deformation on theorder of hundreds of micrometers should not con-tribute significantly to the equilibrium contactangle, and for such systems the contact anglecalculated from the Cassie equation (Eq. (1» is agood approximation to the observed contact angle[8,27]. The line-tension term should be of impor-tance, however, for systems where the radii ofdeformation of the three-phase contact line are lessthan several micrometers [8,27]. An upper limitfor the size of heterogeneous patches that affectscontact angles through the line-tension term wasdiscussed in our previous contributions [8,27].The lower size limit for the heterogeneity dimen-sion is more difficult to predict. Neumann [28]estimated that there is no contact angle differencebetween the contorted and the smooth three-phasecontact line for surfaces with heterogeneous stripdimensions of approximately 0.1 Jim or less. In thismodel, Neumann did not consider the contributionof the excess energy associated with the triplejunction. In another contribution, Boruvka andNeumann [21] predicted that a corrugation of thethree-phase contact line can be expected for hetero-geneous patches as small as 10 A. Again, they didnot consider a contribution of the line tension tothe free energy of the three-phase system, and theysuggested that this patch size limit would be largerif the line tension was included.

~-')!IL =")!.vcos8+ ~r

Fig. 1. Thermodynamic equilibrium for a spherical liquid dropon a rigid and homogeneous solid surface.

(10-9-10-12 J m-1) [12-17]. Poor accuracy andprecision of experimental techniques and difficul-ties in preparation of atomically smooth andmolecularly homogeneous samples make the deter-mination of the line tension difficult. Also, thetheoretical bases for the calculation of line tensionare very uncertain owing to our limited knowledgeon the contribution of short-range forces to theline free energy (theoretical models for the calcula-tion of the excess energy at the triple junction havebeen recently proposed; see for example Refs.[ 18-20]).

Small values of the line tension(10-9-10-12 J m -1) indicate that the line-tensionterm contributes significantly to the modifiedYoung's equation (Eq. (3» only for small drops orbubbles (radii of the drop (bubble) base smallerthan several micrometers). When the liquid is incontact with a heterogeneous surface composed ofchemically distinct patches, the three-phase contactline is corrugated, as illustrated in Fig. 2 [8,21-25].Local deformations of the three-phase contact linemay have diameters smaller than several microns.In such systems the excess energy at the triplejunction may contribute significantly to the equilib-

4 J. Drelich et al.jCol/oids Surfaces A: Physicochem Eng. Aspects 93 (1994) 1-13

Parallel Strips To determine the validity of the modified Cassieequations (Eqs. (4) and (5)), examination of solidsurfaces with well-defined heterogeneity is required.Preparation of well-defined heterogeneous surfaces,especially with heterogeneities of several microme-ters or less in size, has been technically difficult.Recent work has shown that adsorption of thiolsfrom solution onto a gold surface leads to thepreparation of SAMs that are model organic sur-faces [31-35]. Patterning of the SAM on gold bycontact printing using an elastomer stamp [35] isan especially convenient technique for the prepara-tion of well-defined heterogeneous surfaces. Mosaicpatterns with micron dimensions can be preparedusing this technique and the organic functionalityexposed at the surface can be controlled easily.

Model organic surfaces with well-defined hetero-geneity were prepared by patterning SAMs on agold surface to examine the validity of the Cassieand modified Cassie equations, as part of a cooper-ative research program between University of Utahand Harvard University. Two heterogeneous sur-faces were prepared. Alternating and parallelhydrophobic and hydrophilic strips, and hydro-philic squares separated by hydrophobic strips,were examined by contact angle measurements.Experimental contact angle data for water dropsplaced on these surfaces support the contentionthat a corrugation of the three-phase contact lineis of particular significance in contact angle meas-urements at heterogeneous surfaces. The experi-mental results also provide evidence for the validityof the Cassie equation (systems with a non-contorted three-phase contact line) and for thevalidity of the modified Cassie equation (systemswith a corrugated three-phase contact line).

s.>e,

Uniform Circles

"YsLV2r-

ContactLine

"YSLVI-r-e.>e.

Cross-Sectional View of Sessile Dropon Heterogeneous Solid Surface

77T

cos~c= fl coset + fzcosez -.J- (~ -~ )'LV rl rz

From theoretical considerations, it appears thatthe lower limit for the heterogeneous patch sizethat affects a corrugation of the three-phase contactline may be somewhere between 10 and 1000 A.No experimental effort has, however, examined theeffect of heterogeneity, both size and distribution,on the contact angle. Theoretical considerationsmay also be flawed when the radius of curvatureapproaches molecular size, since the macroscopicand microscopic thermodynamic properties of thesystem may be different. For example, the linetension may change as a result of the curvature ofthe three-phase contact line (note that the effect ofcurvature on surface tension has already beendiscussed [29,30]).

2. Experimental procedure

2.1. Preparation of surfaces

Stamps were fabricated from polydimethylsilox-ane (PDMS); Fig. 3 describes the process. A tem-plate consisting of the desired features was madeusing conventional photolithography. The tem-plate was placed in a plastic petri dish. A 10: 1(v: v) mixture of PDMS-Sylgard Silicone

Fig. 2. Nature of the three-phase contact line for hetero.geneous surfaces.

J. Drelich et al.fColloids Surfaces A: Physicochem. Eng. Aspects 93 ( 1994) 1-13 5

ia) 1-2 pm T '4 Photoresist pattern

!

PDMS peeled away from the

master

PDMS

r-.~r-b)

---

I Exposure ofPDMSto thiol solution

PDMS

~ r'L,t-"\-"'r'

~ Hydrophobic AlkanethiolStamping onto goldsubstrate

c)

" The thickness or thealkanethiolate layer is 12 A.

d)

e)

Fig. 3. Schematic for the fabrication of model heterogeneous surfaces.

Elastomer 184 and Sylgard Curing Agent 184(Dow Corning Corp., Midland, MI) was pouredinto the petri dish. It was not necessary to put themixture of PDMS-elastomer and curing agentunder vacuum to remove dissolved oxygen. ThePDMS cured at room temperature in the labora-tory ambient for 30-60 min. This cure was followedby additional curing at 650 C for approximately1 h or until the polymer was rigid. Mter coolingto room temperature, the PDMS stamp was care-fully peeled from the template.

A piece of lint-free paper was moistened with asolution of hexadecanethiol (HS(CH2h6CH3,1-10 mM in ethanol). Inking was accomplishedby simply touching the active surface of the stampto the moistened paper. Alternatively, the ink was

poured directly onto the stamp, and the stamp wasallowed to dry. The stamp was then placed on thesubstrate with the inked side in contact withthe bare gold surface (gold film was prepared byelectron beam evaporation of high purity goldonto a silicon wafer that had been precoated withtitanium to improve adhesion). Mter removal ofthe stamp, the gold surface was washed for 1-5 swith a 1 mM solution of diundecane disulfidecarboxylic acid (S[(CH2hlCOOHL) in ethanol.The surface was first washed in a stream of ethanolfor a few seconds and then dried in a stream ofnitrogen. Fig. 4 presents scanning electron micro-graphs of the model heterogeneous surfacesexamined.

Slides with freshly deposited gold film were

Gold (50-200 nm) supportedon 10 nm Ti adhesion layer.

6 J. Drelich et al.fColloids Surfaces A: Physicochem. Eng. Aspects 93 ( 1994) 1-13

immersed for about 5 s into the 1 mM {solution of hexadecanethiol or the 1 mM (solution of diundecane disulfide carboxylicorder to prepare homogeneous surfaces ofphobic and hydrophilic nature respectivel)removal from the adsorbate solution, slidtwashed with ethanol and then dried in a strnitrogen.

2.2. Contact angle measurements

The sessile-drop technique for contactmeasurements was used as described in theture [36] using an NRL goniometer (Ram-Inc., USA). The surfaces were washed with {and distilled/deionized water before eachment and placed in a controlled-atmosphereHart chamber. A water drop was introducethe solid surface through a micro syringe aneedle remained in contact with the drothree-phase contact line of the water drcmade to advance or retreat by adding or witing a small volume of water and the ad,and receding contact angles, respectivel)measured after 30-45 s at both sides of th(The drop base diameter was controlled4-5 mm for all systems examined. The langles were measured for 8-12 drops OJsides, for each system, and the average (angle values are reported. All measuremen'made in water-saturated air. Distilled andized water (pH 5.8::1: 0.1) and commercialof pH 7.0 and 10.0 were used in all experimstereoscopic microscope coupled with a '(Carl Zeiss, Jena, Germany) was used tothe three-phase contact line for the water d

The dynamic captive-bubble technique wfor the examination of the bubble size effectcontact angle (discussion of this techniquesented in Refs. [37,38]). The air bubbles of'size were generated in water with a syring,the solid surface. Released bubbles were c"at the solid surface as a result of bouyant tr.and attachment. A Zeiss stereo microscope cwith a camera was used to examine the s1the bubbles at the solid surface. The contacwas measured from photographs with an al

Fig. 4. Scanning electron micrographs of model surfaces. Upperphotograph: 3 IUD hydrophilic strips (Au-S[(CHVllCOOHh)and 2.5 IUD hydrophobic strips (Au-S(CH2h6CH3). Lowerphotograph: 3 IUD x 3 ~m hydrophilic squares in hydrophobicfield.

J. Drelich et al.jCol/oids Surfaces A: Physicochem Eng. Aspects 93 ( 1994) 1-13

[39]. Poorer agreement between experimental andliterature contact angle values was observed forthe hydrophilic surface. For example, the advanc-ing contact angle for the distilled water drop wasfound to be 61 ° whereas that reported in a previous

contribution was about 50° [39]. Also, the contactangle hysteresis for the hydrophilic surface wasfound to be 20-25° compared to 40-50° reportedby Troughton et al. [39].

The advancing contact angles measured forheterogeneous surfaces differed significantly,depending on the position of the water drop edgeat which the contact angle was measured (see.Table

1). For the heterogeneous surface composedof alternating and parallel strips, the advancingcontact angles measured with the drop edge normalto the strips were found to be much lower (8-16°)than those measured with the drop edge tangentialto the strips (Fig. 5 illustrates the drop sides atwhich contact angles were measured). When thewater drop was placed onto a heterogeneous sur-face composed of hydrophilic squares surroundedby hydrophobic strips, two distinct advancing con-tact angles were also observed. When the three-phase contact line crossed the hydrophilic squaresadvancing contact angles were found to be 7-12 olower than those measured at the drop edgeattached to the hydrophobic strip (Fig. 5 illustratesthe edge positions of the water drop at which

of :i: 2 ° for large bubbles and :i: 3 ° for small

bubbles.A ring technique was applied for surface tension

measurements of water using a Digital-TensiometerK10T (Kruss, GmbH, Germany) with an accuracyof 0.2 mN m -1. The results obtained with theinstrument were corrected in relation to the liquiddensity and the height of the lamella in maximumtension using factors of Harkins and Jordan asspecified in the instrument manual.

All experiments were performed at a temperatureof 22:i: loC.

3. Results and discussion

3.1.

Advancing and receding contact angle data

The advancing and receding contact angles forwater drops were measured for hydrophilic, hydro-phobic and heterogeneous surfaces. The experi-mental data are presented in Table 1. Theadvancing contact angle values (107-108°) mea-sured for the hydrophobic surface were in closeagreement with those (110-112°) reported in aprevious contribution [39]. The contact anglehysteresis (i.e. the difference between the advancingand receding contact angle) of 14--16° was closeto the hysteresis of 10° reported in the literature

Table IContact angle values (deg) for water drops (4-5 mm drop base diameter)

pH Hydrophobicsurface

Au-S(CH2)16CH362

Heterogeneous surfacesHydrophilicsurface

Au-S[(CH2)11COOHb1J1

3 ~ hydrophilic/2.5 ~hydrophobic parallel strips

3 ~ x 3 ~ hydrophilicsquares in hydrophobic field

Measuredtangentiallyto the strips,IJC

Measurednormallyto the strips,/)MC

Measuredat the boundaryof the pattern,fJC

Measuredacrossthe patternIJMC

5.8 AdvRecAdvRecAdvRec

61.1 :t 1.838.4 :t 3.750.1 :t 1.030.6:t 3.431.7:t 1.810.3:t 2.6

108.4 :t 2.892.6:t 3.3

107.8:t 2.491.6 :t 2.7

106.9 :t 3.192.7:t 2.9

85.8 :t 3.5 69.454.268.350.958.539.3

93.0:f: 2.0 81.1 :.t 1.7

7.0 76.5 :t 3.0 88.3 :!: 2.3 81.2.i: 2.1

10.0 70.5::!: 2.1 83.8 ::!: 3.2 74.2 :t 2.0

Adv, advancing contact angie; Rec, receding contact angie.

t3.4t 4.4

t 1.5t4.6t3.7t5.1

8 J. Drelich et al.fColloid!' Surfaces A: Physicochem. Eng. Aspects 93 ( 1994) 1-13

and measured with the drop edge normal to thestrips. For a heterogeneous surface composed ofsquares it was difficult to specify the position ofthe retreating three-phase contact line with respectto the hydrophilic squares or hydrophobic strips.Mostly, there was non-uniform movement of theretreating drop edge across the strips and also thethree-phase contact line was observed to jumpfrom one surface site to another. In view of theabove, the only reproducible receding contactangles for heterogeneous surfaces were obtainedwhen measured with the drop edge normal to thestrips. Measurements of the receding contact anglesfor model heterogeneous surfaces will receive moreattention in our future experiments.

3.2. Line/pseudo-line tension data for"homogeneous" surfaces

Hydrophilic Squares in Hydrophobic Field

\"t '.JtD

e"Coorru..tedoontect lin.

:: :::::::. ::::.:::::e" ::::::: ::::::::: :::::::

on-corrucontect I

1'-.-

The effect of bubble size on contact angle wasexamined for hydrophilic and hydrophobic sur-faces in order to determine the line tension values(note that receding contact angle or intermediatecontact angle, contact angle between receding andadvancing, are measured with the dynamic captive-bubble technique [38]). The experimental data areshown in Figs. 6 and 7 for hydrophilic and hydro-phobic surfaces respectively. Non-linear correla-tions between cos e and 1/r were obtained for bothhydrophilic and hydrophobic surfaces (Figs. 6 and7). Such non-linearity has also been observed

~~~

CASSIE EQUATION:

cosif =f, coset + f,cos8,

MODIFIED CASSIE EQUATION:

cos9'"'=f,cos8.+f.cose.- iJ~ +~)

Fig. 5. Contact angle measurements for a water drop on twowell-defined heterogeneous surfaces. The contact angle fJMc isobserved for a corrugated three-phase contact line and ec fora non-corrugated three-phase contact line.

contact angles were measured). The data presentedin Table 1 support the statement that corrugationof the three-phase contact line has a significantimpact on contact angle.

Some of the receding contact angle measure-ments for model heterogeneous surfaces were alsoperformed. At this time, the only acceptable experi-mental data for the receding contact angle arepresented in Table 1 and they were obtained at theheterogeneous surface composed of parallel strips

J: Drelich etal./Colloids Surfaces A: Physicochem. Eng. Aspects 93 (1994) 1-139

Fig. 7. The effect of bubble size on contact angle for thehydrophobic surface (Au-S(CH2)16CH3).

nificant dissociation of carboxylic groups occursunder alkaline conditions. The contact angle meas-urements were made with water drops in whichthe pH was changed from 5.8 to 10. For suchsystems, the hydrophilic surface is naturally hetero-geneous at the molecular scale owing to the pres-ence of dissociated, -COO -, and undissociated,

-COOH, carboxylic groups (note the scatter in thecontact angle data and deviation from the linearcos 8 vs. l/r relationship decrease with increasingpH for the experimental data presented in Fig. 6).

Owing to the non-linearity between cos 8 andl/r, the modified Young equation (Eq. (3)) couldnot be used to calculate a true line tension value,but a pseudo-line tension value could be deter-mined [26,27,37J. The concept of the pseudo-linetension was suggested by Good and Koo [22J forinterpretation of the observed changes in contactangle with drop (bubble) size for systems withsurface heterogeneity. The pseudo-line tensionY:L v can be calculated from the linear range of aplot of cos 8 vs. l/r for hydrophilic and hydro-phobic surfaces, Y:LV = [L1(cos 8)/L1(I/r)JYLv, but ofcourse this is an approximation; it changes for theentire range of bubble sizes (Figs. 6 and 7). Tworanges of bubble size were selected from Figs. 6and 7; those with r> 100 IJ.m and those withr < 55 JJ.ID for the hydrophilic surface, and thosewith r> 125 JJ.ID and r< 110 JJ.ID for the hydro-phobic surface. These ranges were selected becausein each range the cos 8 vs. l/r relationship can beapproximated as a linear relationship and theresults for systems with varying pH can be

compared.On the basis of contact angle data for different

bubble sizes, the pseudo-line tension values (Y:LV)were calculated and are presented in Table 2. Asrecognized by Gershfeld and Good [40 J thereexists the two-dimensional analog of the Laplacepressure, Y:LV/r, across such a curved three-phasecontact line. The pseudo-line tensions were foundto be negative for all systems when the contactangle was measured through the aqueous phase.The negative value indicates that the vector of thetwo-dimensional Laplace pressure is directed awayfrom the aqueous phase. The pseudo-line tension,as calculated for the hydrophilic surface, wasfound to be in the range, -5.0 x 10-7 to

for other systems in our previous studies[25-27,37,38]. Several factors were examined toaccount for the non-linearity in previous systemsand these included surface heterogeneity, surfaceroughness, the effect of gravity, and solid strain inthe vicinity of the three-phase contact line. It hasbeen found that surface heterogeneity is responsiblefor the non-linearity [25-27,37,38], but the natureof the heterogeneity for such "homogeneous" sur-faces has not been identified. In this study, contactangle hysteresis of 20-250 and 14-160 wasobserved for hydrophilic and hydrophobic surfacesrespectively. Oxidation of thiols and/or contamina-tion of the surface during transportation of thesamples from Harvard University to the Universityof Utah could have occurred. Also owing to theextremely short time of contact of the gold filmwith the ethanol-thiol solution (1-5 s) duringorganic monolayer preparation microdefects inself-assembled monolayers could occur and con-tribute to the surface heterogeneity. Further, itshould be noted that the hydrophilic surface iscomposed of thiols adsorbed onto gold with car-boxylic groups exposed to the environment. Thesecarboxylic groups dissociate on contact with wateras follows:

-S(CH2)11COOH =-S(CH2)11COO- + H+

The extent of dissociation of the carboxylic groupsdepends on the pH of the aqueous phase, and fromprevious results [39] it can be expected that sig-

10 J. Dre/ich et a/.ICo//olds Surfaces A: Physicochem Eng. Aspects 93 ( 1994) 1-13

Table 2Pseudo-line tension values

-9.3 X 10-7 J m-1 for large bubbles (bubblebase radius r> 100 ~), and -2.4 x 10-8 to-5.0 X 10-8 J m-l for small bubbles (bubble baseradius r < 55 ~). In the case of the hydrophobicsurface, the corresponding pseudo-line tensionswere found to be about one order of magnitudesmaller.

presented in Table 1. On the basis of these data,the contact angles for the model heterogeneoussurfaces were calculated from the Cassie equationand results are presented in Table 3 for conditionswhere the three-phase contact line is not contorted,i.e. the drop edge does not cross the pattern. Goodagreement between contact angle values measuredat a position where the three-phase contact linewas not affected by heterogeneous strips or squares(no contortion of the triple junction by hydrophilicor hydrophobic regions of the model pattern), andthose calculated from the Cassie equation wasobtained. The difference between experimental con-tact angle values and those calculated from theCassie equation did not exceed 30 as is evidentfrom the data presented in Table 3.

3.3. Experimental verification of Cassie equationforwell-defined heterogeneous surfaces

3.4. Experimental verification of modified Cassieequation for well-defined heterogeneous surfaces

When the drop edge crossed the pattern, forboth heterogeneous surfaces, corrugation of thethree-phase contact line was observed and didsignificantly affect the contact angle (Table 1).Contact angles, measured at such positions, werefound to be significantly lower than those calcu-lated from the Cassie equation (compare experi-mental data from Table 1 with those calculatedfrom the Cassie equation and presented in Table 3).Only the modified Cassie equation for a binarysystem (Eq. (5)), incorporating the pseudo-linetension term, can reasonably describe such contactangles (Eq. (7); note that the complexity of thisequation follows from the non-linear cos (J vs. l/rrelationships for the "homogeneous" hydrophilic

The experimental contact angle data werecompared with those calculated from the Cassieequation and the modified Cassie equation forheterogeneous surfaces. When the contact anglewas measured for a model heterogeneous surfacecomposed of parallel strips and with the three-phase contact line tangential to the strips (seeFig. 5) or composed of squares and with a dropbase edge located at the hydrophobic strip (seeFig. 5) (no corrugation of the three-phase contactline), the Cassie equation (Eq. (1)) was found tobe applicable:

cOS(}C=!lCOS(}1+!2COS(}2 (6)

where subscripts 1 and 2 describe the hydrophilicand hydrophobic regions respectively. The hydro-philic and hydrophobic area fractions of the modelsurfaces were calculated from the dimensions ofstrips and squares, and found to be! 1 = 0.5455 and! 2 = 0.4545 for the model surface with parallelstrips, and!l =0.2975 and!2=0.7025 for the surfacewith squares. The advancing contact angles forwater drops on fully hydrophilic or hydrophobicsurfaces were determined experimentally and are

J. Drelich et al./Colloids Surfaces A: Physicochem. Eng. Aspects 93 ( 1994) 1-1311

(7)

three-phase contact line was close to the assumedshape (see Fig. 8). Limited magnification and reso-lution capabilities of the optical equipment did notpermit a more detailed analysis of the corrugation.

The contact angle values for heterogeneous sur-faces when the drop edge crossed the pattern werecalculated using the modified Cassie equation (Eq.(7)) together with both contact angle data (Table 1)and pseudo-line tension values (Table 2), as deter-mined for fully hydrophilic and hydrophobic sur-faces, and they are presented in Table 4. Thecalculated contact angle values differ by 1-9° fromthose determined exp~rimentally (Table 4 ).Thedifference may be attributed to the uncertainty inthe determination of the pseudo-line tensions andthe uncertainty in the local deformation of thethree-phase contact line.

An additional comment is required to explainwhy the line tension effect was not observed inprevious investigations of the effect of surfaceheterogeneity on contact angle. In experiments ofCassie and Baxter [1,2], heterogeneous surfaceswere composed of hydrophobic wires (70 and130 ~ in diameter) or fabrics (18 Jlm in diameter)with contact angles larger than 100°. The hetero-geneous surfaces were composed of much largerpatches than examined in our systems, and of

where Y:LV is the pseudo-line tension, YLV is thesurface tension of aqueous phase, r1 and r2 are thehalf-widths of hydrophilic and hydrophobic stripsor squares respectively, rc is the characteristic valueof the bubble base radius as determined from thedata presented in Figs. 6 and 7 (see Table 2).

For simplification it has been assumed that thecorrugations of the three-phase contact line in thehydrophilic and hydrophobic regions are symmet-rical and the local deformations affected by theseregions are circular with a diameter equal to thewidth of the strips or squares. This assumptionallows for the calculation of the contact angle forthe water drop with a corrugated three-phasecontact line but should be considered as a roughapproximation. Although the shape of the dropedge might have been more complex [27], micro-scopic observation indicated that the shape of the

Table 3Contact angle values (OC) as calculated from the Cassie equation(Eq. (6)) using contact angle data for hydrophilic and hydro-phobic surfaces, and as determined experimentally for modelheterogeneous surfaces (the three-phase contact line is notcontorted)

Advancing contact angle, OC (deg)pH

Parallel strips Squares

Fig. 8. Corrugation of the three-phase contact line as observedby optical microscopy for a water drop located at themodel heterogeneous surface composed of 3 11m hydro-philic (Au-S[(CHzhlCOOHb) and 2.51lIn hydrophobic(Au-S(CHzh6CH3) parallel strips. The liquid drop edge isobserved from the top.

Calculated Experimental Calculated Experimental

5.87.0

10.0

83:t 278:t 271 :t 2

86:t 477:t 371 :t 2

95:t 291 :t 287:t 2

93:t 289:t 284:t3

12 J. Drelich et al.jCo//oidr Surfaces A: Physicochem. Eng. Aspects 93 ( 1994) 1-13

Table 4Contact angle values ((JMC) as calculated from the modified Cassie equation (Eq. (7) using contact angle data and the pseudo-linetensions calculated from the contact angle/drop size relationships for fully hydrophilic and hydrophobic surfaces, and as determinedexperimentally for model heterogeneous surfaces (the three-phase contact line is contorted)

pH Contact angle, OMC (deg)

Adv, advancing contact angie; Rec, receding contact angie.

course, the corrugation of the three-phase contactangle becomes less significant for such heterogenei-ties as examined by Cassie and Baxter. Also, aspresented in this contribution, there is only a smalleffect of the line tension on contact angle forhydrophobic surfaces. Even smaller changes incontact angle with bubble size were observed fora carefully prepared polyethylene film [27]. In thisregard, the effect of three-phase contact line corru-gation on contact angle may have been too smallto have been observed by Cassie and Baxter.

Additional experimental support for the Cassieequation was provided by Crawford et al. [4] formethylated quartz plates. However, a careful analy-sis of the experimental data presented by Crawfordet al. [4] indicates that in most cases the contactangles are not predicted by the Cassie equation.The scatter in contact angles may be attributed tothe experimental uncertainty of the measurementsbut also may be the effect of corrugation of thethree-phase contact line. There are also additionaleffects that make the interpretation of contactangle data on methylated quartz surfaces difficult,such as non-uniform methylation and formationof multilayer films or molecular clusters [25,41,42].

surfaces consisting of alternating and parallelhydrophobic and hydrophilic strips (sample 1called "parallel strips") and hydrophilic squaresseparated by hydrophobic strips (sample 2 called"squares") were prepared on an evaporated goldfilm supported on a silicon wafer. The wettingcharacteristics of these model heterogeneous solidsurfaces consisting of mosaics of self-assembledmonolayer films were examined by contact anglemeasurements. The contact angles for water dropsin the pH range 5.8-10.0 were measured. Theexperimental contact angles were in agreementwith those calculated from the Cassie equation,when the three-phase contact line was non-contorted (the strips were tangential to the dropedge for the "parallel strips" sample or the waterdrop edge was in the hydrophobic field for the"square" sample).

When the drop crossed the "square" patternsurface or when the strips were normal to the dropedge for the "parallel strips" surface, corrugationof the three-phase contact line influenced the con-tact angle significantly. Contact angles, measuredin these cases, were much lower than those calcu-lated from the Cassie equation. Analysis of thesemeasurements, together with those for fully hydro-phobic and hydrophilic surfaces, demonstrates thenecessity for a modified Cassie equation thatincludes a term describing the line tension contri-bution to the three-phase system.

4. Conclusions

By patterning a self-assembled monolayer usingan elastomer stamp, well-defined heterogeneous

J. Drelich et al.fColloids Surfaces A: Physicochem. Eng. Aspects 93 ( 1994) 1-13 13

Acknowledgment

The support of the U.S. Department of Energy,contract number DE-FC21-89MC26268, is grate-fully recognized.

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